Remove Electronic signature Word Later

[full disclosure: I’m VP Digital Transformation at Solutions Notarius Inc., a company that supplies electronic and digital signature solutions]It completely depends on the requirements. I do not believe there is a uniquely better e-signature solution for all scenarios. For example, if the type of documents to be signed require low to medium reliability only, most modern e-signature platforms could be ok, subject to meeting legal requirements in the applicable jurisdiction, but if the document must meet stringent regulatory and statutory requirements that include high reliability of identity of signers, those platforms do not typically meet that threshold.Ideally, you would analyze, define and obtain agreement as to what constitutes the minimal acceptable legal reliability threshold you are willing to accept - or that readers of that document will accept. Next, define the technology requirements that correspond to that threshold. Finally, research e-signature options that meet these requirements and provide the best combination of price, features, scalability, etc..Finally, it should be noted that higher legal reliability e-signature platforms and solutions can always accommodate lower reliability documents while the converse is not true…

"Illusion" is an interesting choice of words. To acquire the kind of understanding I think you're after, let's back up a bit and see if we can excavate the foundation of this question. Let me start with a quote. “The voyage of discovery lies not in seeking new horizons, but in seeing with new eyes.” ~ Marcel Proust An examination of the double-slit experiment will give us a good introduction to the mystery you have singled out. But to make that examination worthwhile, we need to make sure that we are familiar with an important effect known as interference. [i]Interference applies universally to all interacting waves. A water wave, for instance, can be described as a disturbance in the shape of the water’s surface. This disturbance produces regions where the water level is higher and regions where it is lower than the undisturbed value. The highest part of each ripple is called a peak and the lowest part is called a trough. Typically waves involve periodic succession, peak followed by trough followed by peak and so on. In general, we can define a wavelength as the distance between identical parts of adjacent waves. Measurements from peak to peak, or trough to trough, for example, give the same value for wavelength.Figure 1 Peaks and troughs of wavesWhen waves interact in a medium, they interfere. For example, if we drop two rocks into spatially separated parts of a pond, their waves will interfere when they cross. (Figure 2) When a peak of one wave and a peak of another wave come together, the height of the water rises to a height equal to the sum of the two peaks. Similarly, when a trough of one wave and a trough of another wave cross, the depression of the water's surface dips to the sum of the two depressions. And when a peak of one wave crosses with a trough of another, the (at least partially) cancel each other out. The peak of one wave contributes a positive displacement while the trough of the other wave contributes a negative displacement. If the two waves have equal magnitude, then there will be perfect cancelation and the water's surface will be flat, just as it was before any wave existed.Figure 12-2 Constructive and destructive interference Keeping these rules of interference in mind, let’s turn our attention to light. If we take a laser emitting a single wavelength—a single color, and shine it on a screen that has a slit etched into it (Figure 3), what image should we expect to see on the wall behind the screen? [ii] Classically speaking, we would expect to see a stripe of light on the wall. (Classically means according to our four-dimensional intuition, or the rules of Euclidean geometry.) It turns out that this is what we see. In this sense light’s behavior correlates perfectly with our Euclidean intuition.Figure 12-3 Expected single slit projectionWhat image should we expect to see on the wall if we etch a second slit on our screen and cover the first slit with a black piece of tape? Well, our classical intuitions tell us to expect a line of light projected on the wall, just like we did before, except this line of light should be offset from the first. Again, this is exactly what we see when we perform the experiment. So far all of this is straightforward and conceptually trivial. But as it turns out, we are only one step away from a profound mystery. We discover this mystery by removing the piece of tape. To understand the impact of this mystery, ask yourself: What sort of projection do we expect to see on the wall when both slits are open?Classical intuition tells us that we should see two parallel bands of light on the wall (Figure 4).Figure 4 Expected double slit projectionBut this is where our classical training (our Euclidean intuition) lets us down. This is also where classical mechanics breaks down. When we perform this experiment, something completely counterintuitive happens, contradicting our Euclidean intuitions. A distinct interference pattern is projected on the wall (Figure 5).Figure 5 Actual double slit projection The bright and dark bands produced in this double-slit experiment are telltale signs that light propagates as a wave. [iii] Interference patterns are key signatures of waves. The problem is that this wavelike characteristic directly clashes with our observations of light’s particulate behavior. After all, photons are always found in point-like regions rather than spread out like a wave, and individual photons are always found to have very discrete amounts of energy. When measuring a wave, you would expect to find its energy spread out over a region instead of being concentrated in one location. So how are we supposed to make sense of this observation? What is going on?These diametrically opposed properties of light are verified facts. Contradictory as they may seem, they are here to stay. They have forced us to the seemingly paradoxical conclusion that light is both a wave and a particle. But how can this be? How can it be both? Although many scientists have found thewave-particle duality of light to be conceptually vague and schizophrenic, this description has persisted. In fact, after the wave-particle concept was adopted as an accurate description of light, it was extended to describe electrons and, eventually, all of matter. This transition was nothing short of a revolution.Up until 1910, atoms were simplistically viewed as miniature solar systems with the nucleus making up the “central star” and orbiting electrons being “planets”. [iv] The wave-particle duality of light and matter rejected this view and pointed to a signNowly different architecture for atoms. Of course, this conceptual transition did not take hold over night.In 1924, Prince Louis de Broglie found that in addition to their particle like character, [v] electrons also possessed a wavelike character. In 1927, Clinton Davisson and Lester Germer followed this up by firing a beam of electrons at a piece of nickel crystal, which acted as a barrier analogous to the one used in the double-slit experiment. A phosphor screen recorded the resultant pattern of electrons. [vi] When they examined the screen, they observed an interference pattern just like the one produced in the double-slit experiment, showing that even electrons have wavelike properties.These experiments shook the foundation of physics by threatening the structure of classical mechanics and destroying humanity’s intuitive framework of reality. But it didn’t stop there. The next step was to tune the beam of electrons down so that the electron gun fired just a single electron at a time. Similar experiments were later used with lasers wherein individual photons were fired seconds apart from each other. The results were mind-bending.Completely against expectation these experiments also produced interference patterns over time as the collection of electrons (or photons) continued to build (Figure 6).Figure 12-6 Over time individual photons construct an interference patternThese observations only added to the confusion. Waves are supposed to be a collective property—something that has no meaning when applied to separate, particulate ingredients. (A water wave, for example, involves a large number of water molecules.) So how can a single electron, or a single photon, be a wave? Furthermore, wave interference requires a wave from one place to interact with a wave from another place. So how can interference be relevantly applied to a single electron or photon? While we are considering such questions, we should also ask, if a single electron or photon is a wave, then what is it that is “waving”? [vii]To answer these questions, Erwin Schrödinger proposed that the stuff that makes up electrons might be smeared out in space and that this smeared electron essence might be what waves. If this idea was correct then we would expect to find all of the electron’s properties, spread out over a distance, but we never do. Every time we locate an electron, we find all of its mass and all of its charge concentrated in one tiny, point-like region. Max Born came up with a different idea. He suggested that the wave is actually a probability wave. [viii] Einstein tinkered with a similar idea when he hypothesized that these waves were optical observations that refer to time averages rather than instantaneous values. Inserting a probability wave (also called a state vector, or a wave function) as a fundamental aspect of Nature delivers another blow to our common-sense ideas about how things truly operate. It suggests that experiments with identical starting conditions do not necessarily lead to identical results because it claims that you can never predict exactly where an electron will be in a single instant. You can only define a probability that we will find it over here, or over there, at any given moment. Two situations with the same probabilistic starting conditions, say of a single particle, might not produce the same results, because the particle can be anywhere within that probability distribution. From a classical perspective, the discovery that the microscopic universe behaves this way is absolutely baffling. Nevertheless, it is how we have observed Nature to be.This leads us to a rather interesting precipice. It seems that the map we have been using to chart physical reality somehow dissolves when we look closely at it. The rules of four-dimensional geometry simply fail to accurately map Nature when we examine the smallest scales. Nature doesn’t strictly behave as our old Euclidean map dictates. Stumbling upon this discovery forces us to face a vital question. Is Nature ultimately and fundamentally probabilistic in a way that we may never understand, as many modern physicists have chosen to believe; or, is this probabilistic quality a byproduct of our reduced dimensional representation of Nature?After pondering these questions long and hard, some physicists have come to believe that the tapestry of spacetime is analogous to water: that the smooth appearance of space and time is only an approximation that must yield to a more fundamental framework when considering ultramicroscopic scales. As far as I can tell, however, up until now this point has only been entertained abstractly. Geometrically resolving a molecular structure for space might resolve our greatest quantum mechanical mysteries, but as of yet, no one has taken that final step. No one has developed a self-consistent picture from this geometric insight. No one has moved beyond the mathematical suggestion that spacetime is analogous to water, or interpreted the theoretical quanta of space as being physically real. Consequently, a framework that enables conceptualization of what is meant by the “molecules” or “atoms” of spacetime has not been developed.Eight decades of meticulous experiments have confirmed the predictions of quantum mechanics based on this wave function, or probability wave, description with amazing precision. “Yet there is still no agreed-upon way to envision what quantum mechanical probability waves actually are. Whether we should say that an electron’s probability wave is the electron, or that it’s associated with the electron, or that it’s a mathematical device for describing the electron’s motion, or that it’s the embodiment of what we can know about the electron is still debated.” [ix]Although quantum mechanics describes the universe as having an inherently probabilistic character, we don’t experience the effects of this character in our day-to-day lives. Why is this? The answer, according to quantum mechanics, is that we don't see quantum events like a chair being here now and then across the room in the next instant, because the probability of that occurring, although not zero, is absurdly miniscule. But what exactly makes the probability for large things to act, as electrons do, so small? At what scales do such effects become important? And, why should the macroscopic universe be so different from the microscopic universe?As if these newly uncovered characteristics of reality weren’t obscure enough, quantum physicists conceptually fuddle things further by suggesting that without observation things have no reality. They claim that until the position of an electron is actually measured the electron has no definite position. Before it is measured, the position exists only as a probability, and then suddenly, through the act of measuring, the electron miraculously acquires the property of position.Einstein acutely recognized the absurdity of this claim. When approached with this conjecture, he famously quipped, “Do you really believe that the moon is not there unless we are looking at it?” [x] To him everything in the physical world had a reality independent of our observations. Measurements that suggested otherwise were mere reflections of the incompleteness by which we currently map and comprehend physical reality. To many quantum physicists, however, the unobserved Moon’s existence became a matter of probability. To them, a discoverable, complete map of physical reality, with the ability to resolve an underlying determinism, became nothing more than a myth—a romantic dream.The mathematical projection of quantum mechanics can be statistically matched with our four-dimensional observations, but when it comes to a conceptual explanation of those observations, it completely lets us down. Intuitive explanations cannot be gleaned from a framework of physical reality that is assumed to be fundamentally probabilistic. By definition, randomness blurs causality. This vague description of physical reality keeps us from grasping a deeper truth by allowing what should be the most basic of concepts to drip into a realm of nonsense.As an example of the confusion that stems from swallowing the standard quantum mechanical interpretation “guts, feathers, and all,” consider the fact that a probabilistic treatment of quantum mechanics leads us to the conclusion that the double-slit experiment can be explained by assuming that a photon actually takes both paths. We can combine the two probability waves emerging from both slits to statistically determine where a photon will land on a screen. The result mimics an interference pattern.According to this, we can explain interference patterns by assuming that one photon somehow always manages to go through both slits, but is this really what is going on? Does a photon really travel along both paths? Can this count as an explanation if we have no coherent sense of what it means? You might notice that if we were to design our experiment with three slits, then we would have to consider whether or not the photon really travels all three routes. This question can be extended for as many slits as you like, but the fundamental conceptual problem remains the same.In order to solve this mystery, you may suggest that we place detectors in front of the slits to determine if the photons are actually going through both slits, or just one. When we do this, we always find that individual photons pass through one slit or the other—never both. But, when we measure the position of individual photons we no longer get an interference pattern and so the question retains its ambiguity. Some have taken this to mean that the act of observation forces wave properties to collapse into a particle, but how and why this theoretical collapse occurs still lacks explanation.Because probability waves are not directly observable and because photons (and electrons) are always found in one place or another when measured, we might be tempted to think that probability waves might not be real—that they were never really there. If that is true, then how are the interference patterns created? Surely these probability waves exist, but in what sense? What are they referencing? Why is it that whenever we know which path the photon takes, we get a classical image instead of an interference pattern? How does the detection of a photon, or an electron, change its behavior?To date, these questions have yet to be resolved. In fact, more clever experiments designed to solve these questions have only deepened the mystery. For example, let’s perform the double-slit experiment again, but this time let’s place devices in front of the slits, which mark (but do not stop or detect) the photons before they pass through the slits. This marking allows us to examine the photons that strike the screen and subsequently determine which slit they passed through. Thus we only gain knowledge of which path the photon takes after the path has been completed. For some reason, however, when we do this we find that the photons do not build up an interference pattern. They form a classical image (Figure 4).Once again, it seems that “which-path” information inhibits us from probing these ghostly waves. But is it really the fact that we gain the ability to determine which path a photon goes through—independent of when we gain that information—that disrupts the interference pattern? Or does our marking of the photon somehow disrupt its interference potential?To explore this question, we perform what’s known as the quantum eraser experiment. We start with the same set up we just described. Then we place another device between each slit and the screen, which completely removes the mark from the photon. We already know that the marked photons project a classical image. Will an interference pattern reemerge if we remove the effects of this mark—if we lose the ability to extract the which-path information?When we perform this experiment the interference pattern does return (Figure 7). Does this mean that photons somehow choose how to act, based on our knowledge of them? Or does it imply something even stranger—that the photons are always both particles and waves simultaneously? How are we to understand either conclusion?Figure 12-7 An interference pattern Another curiosity of Nature is known as the photoelectric effect. Philipp Lenard first discovered this effect through controlled experiments in 1900. When light shines on a metal surface, it causes electrons to be knocked loose and emitted. Knowing this, Lenard designed an experiment that allowed him to control the frequencyof the incoming light. During the experiment, he increased the frequency of the light—moving from infrared heat and red light to violet and ultraviolet. Greater frequencies caused the emitted electrons to speed away with more kinetic energy. After discovering this, Lenard reconfigured his experiment to allow him to control the intensity of the incoming light. He used a carbon arc light that could be made brighter by a factor of 1,000.Because both experiments involved increasing the amount of incoming light energy he expected to have identical results. In other words, because the brighter, more intense light had more energy, Lenard expected that the electrons emitted would have more energy and speed away faster. But that’s not what happened. Instead, the more intense light produced more electrons, but the energy of each electron remained the same. [xi]In response to these experiments Einstein suggested that light is composed of discrete packets called photons. Under this assumption, light with higher frequency would cause electrons to be emitted with more energy, and light with higher intensity, that is, a higher quantity of photons, would result in emission of more electrons—just as we observe.The problem with this solution (a solution that is now universally accepted among physicists) is that it doesn’t provide us with a clear description for what the light quanta are. Why does light come in quantized packets? Near the end of his life Einstein lamented over this problem in a letter to his dear friend Michele Besso. He wrote, “All these fifty years of pondering have not brought me any closer to answering the question, what are light quanta?” [xii] It’s been another fifty years and we seem as confused as ever over how it is that light is quantized into little discrete packets called photons.In the midst of these enigmas lies the uncertainty principle, which states that knowledge of certain properties inhibits knowledge of other complimentary properties. For example, the more accurately we determine the position of an electron, the less we can determine its momentum, and vise versa.Heisenberg tried to explain the uncertainty principle by appealing to the observer effect; claiming that it was simply an observational effect of the fact that measurements of quantum systems cannot be made without affecting those systems. [xiii] Since then, the uncertainty principle has regularly been confused with the observer effect. [xiv] But the uncertainty principle is not a statement about the observational success of current technology. It has nothing to do with the observer effect. It highlights a fundamental property of quantum systems, a property that turns out to be inherent in all wave-like systems. [xv] Uncertainty is an aspect of quantum mechanics because of the wave nature it ascribes to all quantum objects.If our current description of quantum mechanics is fundamental, if there is nothing beneath the state vector—a claim that defines the heart of the standard interpretation of quantum mechanics—then this uncertainty principle may be a sharp enough dagger to kill our quest for an intuitive understanding of physical reality. The corrosive power of the uncertainty principle, when mixed with our current paradigm, is poignantly illustrated by an old story involving Niels Bohr. According to the story, Bohr was once asked what the complementary quality to truth is. After some thought he answered—“clarity.” [xvi] Unlike classical mechanics, which describes systems by specifying the positions and velocities of its components, quantum mechanics uses a complex mathematical object called a state vector (also called the wave function [xvii]) to map physical systems. Interjecting this state vector into the theory enables us to match its predictions to our observations of the microscopic world, but it also generates a relatively indirect description that is open to many equally valid interpretations. This creates a sticky situation, because to “really understand” quantum mechanics we need to be able to specify the exact status of and to have some sort of justification for that specification. At the present, we only have questions. Does the state vector describe physical reality itself, or only some (partial) knowledge that we have of reality? “Does it describe ensembles of systems only (statistical description), or one single system as well (single events)? Assume that indeed, is affected by an imperfect knowledge of the system, is it then not natural to expect that a better description should exist, at least in principle?” [xviii] If so, what would this deeper and more precise description of reality be?To explore the role of the state vector, consider a physical system made of Nparticles with mass, each propagating in ordinary three-dimensional space. In classical mechanics we would use Npositions and N velocities to describe the state of the system. For convenience we might also group together the positions and velocities of those particles into a single vector V, which belongs to a real vector space with 6N dimensions, called phase space. [xix]The state vector can be thought of as the quantum equivalent of this classical vector V. The primary difference is that, as a complex vector, it belongs to something called complex vector space, also known as space of states, or Hilbert space. In other words, instead of being encoded by regular vectors whose positions and velocities are defined in phase space, the state of a quantum system is encoded by complex vectors whose positions and velocities live in a space of states. [xx]The transition from classical physics to quantum physics is the transition from phase space to space of states to describe the system. In the quantum formalism each physical observable of the system (position, momentum, energy, angular momentum, etc.) has an associated linear operator acting in the space of states. (Vectors belonging to the space of states are called “kets.”) The question is, is it possible to understand space of states in a classical manner? Could the evolution of the state vector be understood classically (under a projection of local realism) if, for example, there were additional variables associated with the system that were ignored completely by our current description/understanding of it?While that question hangs in the air, let’s note that if the state vector is fundamental, if there really isn’t a deeper-level description beneath the state vector, then the probabilities postulated by quantum mechanics must also be fundamental. This would be a strange anomaly in physics. Statistical classical mechanics makes constant use of probabilities, but those probabilistic claims relate to statistical ensembles. They come into play when the system under study is known to be one of many similar systems that share common properties, but differ on a level that has not been probed (for any reason). Without knowing the exact state of the system we can group all the similar systems together into an ensemble and assign that ensemble state to our system. This is done as a matter of convenience. Of course, the blurred average state of the ensemble is not as clear as any of the specific states the system might actually have. Beneath that ensemble there is a more complete description of the system’s state (at least in principle), but we don’t need to distinguish the exact state in order to make predictions. Statistical ensembles allow us to make predictions without probing the exact state of the system. But our ignorance of that exact state forces those predictions to be probabilistic.Can the same be said about quantum mechanics? Does quantum theory describe an ensemble of possible states? Or does the state vector provide the most accurate possible description of a single system? [xxi]How we answer that question impacts how we explain unique outcomes. If we treat the state vector as fundamental, then we should expect reality to always present itself in some sort of smeared out sense. If the state vector were the whole story, then our measurements should always record smeared out properties, instead of unique outcomes. But they don’t. We always measure well-defined properties that correspond to specific states. Sticking with the idea that the state vector is fundamental, von Neumann suggested a solution called state vector reduction (also called wave function collapse). [xxii] The idea was that when we aren’t looking, the state of a system is defined as a superposition of all its possible states (characterized by the state vector) and evolves according to the Schrödinger equation. But as soon as we look (or take a measurement) all but one of those possibilities collapse. How does this happen? What mechanism is responsible for selecting one of those states over the rest? To date there is no answer. Despite this, von Neumann’s idea has been taken seriously because his approach allows for unique outcomes.The problem that von Neumann was trying to address is that the Schrödinger equation itself does not select single outcomes. It cannot explain why unique outcomes are observed. According to it, if a fuzzy mix of properties comes in (coded by the state vector), a fuzzy mix of properties comes out. To fix this, von Neumann conjured up the idea that the state vector jumps discontinuously (and randomly) to a single value. [xxiii] He suggested that unique outcomes occur because the state vector retains only the “component corresponding to the observed outcome while all components of the state vector associated with the other results are put to zero, hence the name reduction.” [xxiv]The fact that this reduction process is discontinuous makes it incompatible with general relativity. It is also irreversible, which makes it stand out as the only equation in all of physics that introduces time-asymmetry into the world. If we think that the problem of explaining uniqueness of outcome eclipses these problems, then we might be willing to take them in stride. But to make this trade worthwhile we need to have a good story for how state vector collapse occurs. We don’t. The absence of this explanation is referred to as the quantum measurement problem.Many people are surprised to discover that the quantum measurement problem still stands. It has become popular to explain state vector reduction (wave function collapse) by appealing to the observer effect, asserting that measurements of quantum systems cannot be made without affecting those systems, and that state vector reduction is somehow initiated by those measurements. [xxv] This may sound plausible, but it doesn’t work. Even if we ignore the fact that this ‘explanation’ doesn’t elucidate howa disturbance could initiate state vector reduction, this isn’t an allowed answer because “state vector reduction can take place even when the interactions play no role in the process.” [xxvi] This is illustrated by negative measurements or interaction free measurements in quantum mechanics.To explore this point, consider a source, S, that emits a particle with a spherical wave function, which means its values are independent of the direction in space. [xxvii] In other words, it emits photons in random directions, each direction having equal probability. Let’s surround the source by two detectors with perfect efficiency. The first detector D1should be set up to capture the particle emitted in almost all directions, except a small solid angle θ, and the second detector D2 should be set up to capture the particle if it goes through this solid angle (Figure 8).Figure 8 An interaction-free measurement When the wave packet describing the wave function of the particle signNowes the first detector, it may or may not be detected. (The probability of detection depends on the ratio of the subtended angles of the detectors.) If the particle is detected by D1 it disappears, which means that its state vector is projected onto a state containing no particle and an excited detector. In this case, the second detector D2will never record a particle. If the particle isn’t detected by D1 then D2 will detect the particle later. Therefore, the fact that the first detector has not recorded the particle implies a reduction of the wave function to its component contained within θ, implying that the second detector will always detect the particle later. In other words, the probability of detection by D2 has been greatly enhanced by a sort of “non-event” at D1. In short, the wave function has been reduced without any interaction between the particle and the first measurement apparatus.Franck Laloë notes that this illustrates that “the essence of quantum measurement is something much more subtle than the often invoked ‘unavoidable perturbations of the measurement apparatus’ (Heisenberg microscope, etc.).” [xxviii] If state vector reduction really takes place, then it takes place even when the interactions play no role in the process, which means that we are completely in the dark about how this reduction is initiated or how it unfolds. Why then is state vector reduction still taken seriously? Why would any thinking physicist uphold the claim that state vector reduction occurs, when there is no plausible story for how or why it occurs, and when the assertion that it does occur creates other monstrous problems that contradict central tenets of physics? The answer may be that generations of tradition have largely erased the fact that there is another way to solve the quantum measurement problem.Returning to the other option at hand, we note that if we assume that the state vector is a statistical ensemble, if we assume that the system does have a more exact state, then the interpretation of this thought experiment becomes straightforward; initially the particle has a well-defined direction of emission, and D2records only the fraction of the particles that were emitted in its direction.Standard quantum mechanics postulates that this well-defined direction of emission does not exist before any measurement. Assuming that there is something beneath the state vector, that a more accurate state exists, is tantamount to introducing additional variables to quantum mechanics. It takes a departure from tradition, but as T. S. Eliot said in The Sacred Wood, “tradition should be positively discouraged.” [xxix] The scientific heart must search for the best possible answer. It cannot flourish if it is constantly held back by tradition, nor can it allow itself to ignore valid options. Intellectual journeys are obliged to forge new paths.So instead of asking whether of not wave-particle duality is an illusion, perhaps we should ask whether wave-particle duality implies that the state vector is the most fundamental description of a quantum mechanical system, or if a deeper level description exists? That's an open question, and at the moment there are many possible answers — interpretations of quantum mechanics that are equally aligned with the empirical evidence. What's your answer?For more on this topic, and to discover how pilot-wave theory is elucidated by the assumption that the vacuum is a superfluid, see Einstein's Intuition, available in black and white softcover, full color softcover, full color hardcover, an iBook, and as an audiobook.[i] The discussion on interference and the double-slit experiment that follows is further developed by Brian Greene, (2004). The Fabric of the Cosmos: Space, Time and the Texture of Reality. New York: Knopf, pp. 84–84. Greene’s discussion was used as a general guide here.[ii] In order to show diffraction (a fuzzy border of light on the projected image) the slit must have a width that does not greatly exceed the wavelength of the color of the light that we have chosen.[iii] Light’s wave nature was first revealed in the mid-seventeenth century through experiments performed by the Italian scientist Francesco Maria Grimaldi, and was later expanded upon by experiments performed in 1803 by the physician and physicist Thomas Young. (1807). Interference of Light; Alan Lightman. A Sense Of The Mysterious. pp. 51–52, 71.[iv] Before the “planetary model” of the atom, physicists pictured the atom being a plum-shaped blob (the nucleus) with tiny protruding springs that each had an electron stuck to its end. When the atom absorbed energy it was thought that these electrons would jiggle (oscillate) on the ends of their springs. Consequently, any atom that was above its ground state of energy was understood to be an “excited atomic oscillator,” This depiction of the atom wasn’t overthrown until 1900. At that point in history the physical existence of atoms was still controversial. It was replaced by the planetary model, which in turn was replaced by the electron cloud model we use today—a model that was initiated in 1910 and was secured by 1930. Gary Zukav. The Dancing Wu Li Masters, pp. 49–50.[v] Electrons can be individually counted and you can individually place them on a drop of oil and measure their electric charge. Richard Feynman. (1988). QED, The Strange Theory of Light and Matter. Princeton University Press, p. 84.[vi] According to de Broglie’s doctoral thesis all matter has corresponding waves. The wavelength of the “matter waves” that “correspond” to matter depends upon the momentum of the particle. Specifically, , which falls into an important group of equations along with Planck’s equation ) and the ever famous . (λ, pronounced “lambda,” stands for wavelength, h is Planck’s constant, and pronounced ‘nu’ represents the frequency of a photon) From this equation we are told to expect that when we send a beam of electrons (something we might traditionally think of as a stream of particles) through tiny openings, like the spacing between atoms in a piece of nickel crystal, the beam will diffract, just like light diffracts. The only requirement here is that the spacing between the atoms of the material must be as small, or smaller, than the electron’s corresponding wavelength—just like the slits in our double-slit experiment. When we perform the experiment, diffraction and therefore interference, occurs exactly as wave mechanics predicts.[vii] Part of the problem here is that in keeping with our four-dimensional intuition we tend to assume a particle aspect in the double-slit experiment without accounting for nonlocality. By doing this we are technically violating Heisenberg’s uncertainty principle and missing the bigger picture.[viii] M. Born. (1926). Quantenmechanik der Stossvorgänge. Zeitschrift für Physik 38, 803–827; (1926). Zur Wellenmechanik der Stossvorgänge. Göttingen Nachrichten 146–160.[ix] Brian Greene. (2004), p. 91.[x] Albert Einstein quoted in Einstein by Walter Isaacson.[xi] Walter Isaacson. Einstein, pp. 96–97.[xii] Ibid.[xiii] Werner Heisenberg. The Physical Principles of the Quantum Theory, p. 20.[xiv] Masano Ozawa. (2003). Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement. Physical Review A 67 (4), arXiv:quant-ph/0207121; Aya Furuta. (2012). One Thing Is Certain: Heisenberg’s Uncertainty Principle Is Not Dead. Scientific American.[xv] L. A. Rozema, A. Darabi, D. H. Mahler, A. Hayat, Y, Soudagar, & A. M. Steinberg. (2012). Violation of Heisenberg’s Measurement—Disturbance Relationship by Weak Measurements. Physical Review Letters 109 (10).[xvi] Steven Weinberg. Dreams Of A Final Theory, p. 74.[xvii] For a system of spinless particles with masses, the state vector is equivalent to a wave function, but for more complicated systems this is not the case. Nevertheless, conceptually they play the same role and are used in the same way in the theory, so that we do not need to make a distinction here. Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 7.[xviii] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. xxi.[xix] There are 6N dimensions in this phase space because there are N particles in the system and each particle comes with 6 data points (3 for its spatial position (x, y, z) and 3 for its velocity, which has x, y, zcomponents also).[xx] The space of states (complex vector space or Hilbert space) is linear, and therefore, conforms to the superposition principle. Any combination of two arbitrary state vectors and within the space of states is also a possible state for the system. Mathematically we write where & are arbitrary complex numbers.[xxi] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 19.[xxii] Chapter VI of J. von Neumann. (1932). Mathematische Grundlagen der Quantenmechanik, Springer, Berlin; (1955). Mathematical Foundations of Quantum Mechanics, Princeton University Press.[xxiii] It might be useful to challenge the logical validity of the claim that something can “cause a random occurrence.” By definition, causal relationships drive results, while “random” implies that there is no causal relationship. Deeper than this, I challenge the coherence of the idea that genuine random occurrences can happen. We cannot coherently claim that there are occurrences that are completely void of any causal relationship. To do so is to wisk away what we mean by “occurrences.” Every occurrence is intimately connected to the whole, and ignorance of what is driving a system is no reason to assume that it is randomly driven. Things cannot be randomly driven. Cause cannot be random.[xxiv] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 11.[xxv] Bohr preferred another point of view where state vector reduction is not used. D. Howard. (2004). Who invented the Copenhagen interpretation? A study in mythology. Philos. Sci. 71, 669–682.[xxvi] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 28.[xxvii] This example was inspired by section 2.4 of Franck Laloë’s book, Do We Really Understand Quantum Mechanics?, p. 27–31.[xxviii] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 28.[xxix] T. S. Eliot. (1921). The Sacred Wood. Tradition and the Individual Talent.

Good question. My guess is either:Satoshi was a truly selfless individual who wanted bitcoin to remain consensus based.Satoshi is dead and is not really committed to anonymity; orSatoshi is actually a group of people. Probably including several of the likely suspects below. Although the original code may have been written by one person the language in chat rooms, message boards and even the white paper itself suggest many unique contributors. Given this vision there were also probabaly non coders/developers who helped distribute the idea and were essentially “the political advocates” who brought the code to the internet at large. These are likely some of the people listed below that I have seen referenced as “potential Satoshi’s” (although none of these leads ever panned out).In a 2011 article in The New Yorker, Joshua Davis claimed to have narrowed down the identity of Nakamoto to a number of possible individuals, including the Finnish economist Dr. Vili Lehdonvirta and Irish student Michael Clear , then a graduate student in cryptography at Trinity College Dublin and now a post-doctoral student at Georgetown University.In October 2011, writing for Fast Company, investigative journalist Adam Penenberg cited circumstantial evidence suggesting Neal King, Vladimir Oksman and Charles Bry could be Nakamoto.They jointly filed a patent application that contained the phrase "computationally impractical to reverse" in 2008, which was also used in the bitcoin white paper.May 2013, Ted Nelson speculated that Nakamoto is really Japanese mathematician Shinichi Mochizuki.Later, an article was published in The Age newspaper that claimed that Mochizuki denied these speculations, but without attributing a source for the denial.A 2013 article in Gawker listed Gavin Andresen, Jed McCaleb, Casey Botticello, or a government agency as possible candidates to be Nakamoto. Dustin D. Trammell, a Texas-based security researcher, was suggested as Nakamoto, but he publicly denied it. Casey Botticello, the head of the Cryptocurrency Alliance has refused to comment.In 2013, two Israeli mathematicians, Dorit Ron and Adi Shamir, published a paper claiming a link between Nakamoto and Ross William Ulbricht. The two based their suspicion on an analysis of the network of bitcoin transactions, but later retracted their claim.Some considered Nakamoto might be a team of people; Dan Kaminsky, a security researcher who read the bitcoin code.

The Government of India enacted its Information Technology Act 2000 with the objectives stating officially as: “to provide legal recognition for transactions carried out by means of electronic data interchange and other means of electronic communication, commonly referred to as "electronic commerce", which involve the use of alternatives to paper-based methods of communication and storage of information, to facilitate electronic filing of documents with the Government agencies and further to amend the Indian Penal Code, the Indian Evidence Act, 1872, the Bankers' Books Evidence Act, 1891 and the Reserve Bank of India Act, 1934 and for matters connected therewith or incidental thereto.The Act essentially deals with the following issues: Legal Recognition of Electronic Documents Legal Recognition of Digital Signatures Offenses and Contraventions Justice Dispensation Systems for cyber crimes.CYBER CRIME- Cyber Crime is not defined officially in IT Act or in any other legislation. In fact, it cannot be too. Offence or crime has been dealt with elaborately listing various acts and the punishments for each, under the Indian Penal Code, 1860 and related legislations. Hence, the concept of cyber crime, is just a "combination of crime and computer". Cybercrime means any illegal behavior directed by means of electronic operations that targets the security of computer systems and the data processed by them. Furthermore any illegal behavior committed by means of, or in relation to, a computer system or network, including such crimes as illegal possession and offering or distributing information by means of a computer system or network. Any contract for the sale or conveyance of immovable property or any interest in such property; Any such class of documents or transactions as may be notified by the Central Here are some of the sections of the IT Act 2000 which are related to cyber crimes: Section 43 - Penalty and Compensation for damage to computer, computer system, If any person without permission of the owner or any other person who is in-charge of a computer, computer system or computer network – (a) accesses or secures access to such computer, computer system or computer network or computer resource (b) downloads, copies or extracts any data, computer data, computer database or information from such computer, computer system or computer network including information or data held or stored in any removable storage medium; (c) introduces or causes to be introduced any computer contaminant or computer virus into any computer, computer system or computer network- (d) damages or causes to be damaged any computer, computer system or computer network, data, computer database, or any other programmes residing in such computer, computer system or computer network-3. (e) disrupts or causes disruption of any computer, computer system, or computer network; (f) denies or causes the denial of access to any person authorised to access any computer, computer system or computer network by any means (h) charges the services availed of by a person to the account of another person by tampering with or manipulating any computer of a computer, computer system or computer network- (g) provides any assistance to any person to facilitate access to a computer, computer system or computer network in contravention of the provisions of this Act, rules or regulations made there under, (h) charges the services availed of by a person to the account of another person by tampering with or manipulating any computer, computer system, or computer network, (i) destroys, deletes or alters any information residing in a computer resource or diminishes its value or utility or affects it injuriously by any means, (j) Steals, conceals, destroys or alters or causes any person to steal, conceal, destroy or alter any computer source code used for a computer resource with an intention to cause damage, he shall be liable to pay damages by way of compensation to the person so affected. Section 43A - Compensation for failure to protect data Where a body corporate, possessing, dealing or handling any sensitive personal data or information in a computer resource which it owns, controls or operates, is negligent in implementing and maintaining reasonable security practices and procedures and thereby causes wrongful loss or wrongful gain to any person, such body corporate shall be liable to pay damages by way of compensation, not exceeding five crore rupees, to the person so affected. Section 65 - Tampering with Computer Source Documents If any person knowingly or intentionally conceals, destroys code or alters or causes another to conceal, destroy code or alter any computer, computer programme, computer system, or computer network, he shall be punishable with imprisonment up to three years, or with fine up to two lakh rupees, or with both. Section 66 - Computer Related Offences If any person, dishonestly, or fraudulently, does any act referred to in section 43, he shall be punishable with imprisonment for a term which may extend to two three years or with fine which may extend to five lakh rupees or with both. Section 66A - Punishment for sending offensive messages through communication service Any person who sends, by means of a computer resource or a communication device, (a) any information that is grossly offensive or has menacing character; (b) any information which he knows to be false, but for the purpose of causing annoyance, inconvenience, danger, obstruction, insult, injury, criminal intimidation, enmity, hatred, or ill will, persistently makes by making use of such computer resource or a communication device, (c) any electronic mail or electronic mail message for the purpose of causing annoyance or inconvenience or to deceive or to mislead the addressee or recipient about the origin of such messages shall be punishable with imprisonment for a term which may extend to three years and with fine. Section 66B - Punishment for dishonestly receiving stolen computer resource or communication device. Whoever dishonestly receives or retains any stolen computer resource or communication device knowing or having reason to believe the same to be stolen computer resource or communication device,4. shall be punished with imprisonment of either description for a term which may extend to three years or with fine which may extend to rupees one lakh or with both. Section 66C - Punishment for identity theft Whoever, fraudulently or dishonestly make use of the electronic signature, password or any other unique identification feature of any other person, shall be punished with imprisonment of either description for a term which may extend to three years and shall also be liable to fine which may extend to rupees one lakh. Section 66D - Punishment for cheating by personation by using computer resource Whoever, by means of any communication device or computer resource cheats by personating; shall be punished with imprisonment of either description for a term which may extend to three years and shall also be liable to fine which may extend to one lakh rupees. Section 66E - Punishment for violation of privacy Whoever, intentionally or knowingly captures, publishes or transmits the image of a private area of any person without his or her consent, under circumstances violating the privacy of that person, Explanation - For the purposes of this section: (a) “transmit” means to electronically send a visual image with the intent that it be viewed by a person or persons; (b) “capture”, with respect to an image, means to videotape, photograph, film or record by any means; (c) “private area” means the naked or undergarment clad genitals, pubic area, buttocks or female breast; (d) “publishes” means reproduction in the printed or electronic form and making it available for public; (e) “under circumstances violating privacy” means circumstances in which a person can have a reasonable expectation that-- (i) he or she could disrobe in privacy, without being concerned that an image of his private area was being captured; or (ii) any part of his or her private area would not be visible to the public, regardless of whether that person is in a public or private place. shall be punished with imprisonment which may extend to three years or with fine not exceeding two lakh rupees, or with both. Section-66F Cyber Terrorism Whoever,- with intent to threaten the unity, integrity, security or sovereignty of India or to strike terror in the people or any section of the people by – (i) denying or cause the denial of access to any person authorized to access computer resource; or (ii) attempting to penetrate or access a computer resource without authorisation or exceeding authorized access; or (iii) introducing or causing to introduce any Computer Contaminant and by means of such conduct causes or is likely to cause death or injuries to persons or damage to or destruction of property or disrupts or knowing that it is likely to cause damage or disruption of supplies or services essential to the life of the community or adversely affect the critical information infrastructure specified under section 70, Whoever commits or conspires to commit cyber terrorism shall be punishable with imprisonment which may extend to imprisonment for life. Section 67 - Punishment for publishing or transmitting obscene material in electronic form Whoever publishes or transmits or causes to be published in the electronic form, any material which is lascivious or appeals to the prurient interest or if its effect is such as to tend to deprave and corrupt persons who are likely, having regard to all relevant circumstances, to read, see or hear the matter contained or embodied in it, shall be punished on first conviction with imprisonment of either description for a term which5. may extend to two three years and with fine which may extend to five lakh rupees and in the event of a second or subsequent conviction with imprisonment of either description for a term which may extend to five years and also with fine which may extend to ten lakh rupees. Section 67A - Punishment for publishing or transmitting of material containing sexually explicit act, etc. in electronic form Whoever publishes or transmits or causes to be published or transmitted in the electronic form any material which contains sexually explicit act or conduct shall be punished on first conviction with imprisonment of either description for a term which may extend to five years and with fine which may extend to ten lakh rupees and in the event of second or subsequent conviction with imprisonment of either description for a term which may extend to seven years and also with fine which may extend to ten lakh rupees. Section 67B - Punishment for publishing or transmitting of material depicting children in sexually explicit act, etc. in electronic form Whoever:- (a) publishes or transmits or causes to be published or transmitted material in any electronic form which depicts children engaged in sexually explicit act or conduct or (b) creates text or digital images, collects, seeks, browses, downloads, advertises, promotes, exchanges or distributes material in any electronic form depicting children in obscene or indecent or sexually explicit manner or (c) cultivates, entices or induces children to online relationship with one or more children for and on sexually explicit act or in a manner that may offend a reasonable adult on the computer resource or (d) facilitates abusing children online or (e) records in any electronic form own abuse or that of others pertaining to sexually explicit act with children, shall be punished on first conviction with imprisonment of either description for a term which may extend to five years and with a fine which may extend to ten lakh rupees and in the event of second or subsequent conviction with imprisonment of either description for a term which may extend to seven years and also with fine which may extend to ten lakh rupees: Section 69 - Powers to issue directions for interception or monitoring or decryption of any information through any computer resource.- (1) Where the central Government or a State Government or any of its officer specially authorized by the Central Government or the State Government, as the case may be, in this behalf may, if is satisfied that it is necessary or expedient to do in the interest of the sovereignty or integrity of India, defence of India, security of the State, friendly relations with foreign States or public order or for preventing incitement to the commission of any cognizable offence relating to above or for investigation of any offence, it may, subject to the provisions of sub-section (2), for reasons to be recorded in writing, by order, direct any agency of the appropriate Government to intercept, monitor or decrypt or cause to be intercepted or monitored or decrypted any information transmitted received or stored through any computer resource. (2) The Procedure and safeguards subject to which such interception or monitoring or decryption may be carried out, shall be such as may be prescribed. (3) The subscriber or intermediary or any person in charge of the computer resource shall, when called upon by any agency which has been directed under sub section (1), extend all facilities and technical assistance to -6. (a) provide access to or secure access to the computer resource generating, transmitting, receiving or storing such information; or (b) intercept or monitor or decrypt the information, as the case may be; or (c) provide information stored in computer resource. (4) The subscriber or intermediary or any person who fails to assist the agency referred to in sub-section (3) shall be punished with an imprisonment for a term which may extend to seven years and shall also be liable to fine. Section 69A - Power to issue directions for blocking for public access of any information through any computer resource (1) Where the Central Government or any of its officer specially authorized by it in this behalf is satisfied that it is necessary or expedient so to do in the interest of sovereignty and integrity of India, defense of India, security of the State, friendly relations with foreign states or public order or for preventing incitement to the commission of any cognizable offence relating to above, it may subject to the provisions of sub-sections (2) for reasons to be recorded in writing, by order direct any agency of the Government or intermediary to block access by the public or cause to be blocked for access by public any information generated, transmitted, received, stored or hosted in any computer resource. (2) The procedure and safeguards subject to which such blocking for access by the public may be carried out shall be such as may be prescribed. (3) The intermediary who fails to comply with the direction issued under sub-section (1) shall be punished with an imprisonment for a term which may extend to seven years and also be liable to fine. Section 69B. Power to authorize to monitor and collect traffic data or information through any computer resource for Cyber Security (1) The Central Government may, to enhance Cyber Security and for identification, analysis and prevention of any intrusion or spread of computer contaminant in the country, by notification in the official Gazette, authorize any agency of the Government to monitor and collect traffic data or information generated, transmitted, received or stored in any computer resource. (2) The Intermediary or any person in-charge of the Computer resource shall when called upon by the agency which has been authorized under sub-section (1), provide technical assistance and extend all facilities to such agency to enable online access or to secure and provide online access to the computer resource generating, transmitting, receiving or storing such traffic data or information. (3) The procedure and safeguards for monitoring and collecting traffic data or information, shall be such as may be prescribed. (4) Any intermediary who intentionally or knowingly contravenes the provisions of subsection (2) shall be punished with an imprisonment for a term which may extend to three years and shall also be liable to fine. Section 71. Penalty for misrepresentation Whoever makes any misrepresentation to, or suppresses any material fact from, the Controller or the signNowing Authority for obtaining any license or Electronic Signature Certificate, as the case may be, shall be punished with imprisonment for a term which may extend to two years, or with fine which may extend to one lakh rupees, or with both.7. Section 72 - BsignNow of confidentiality and privacy Any person who, in pursuant of any of the powers conferred under this Act, rules or regulations made there under, has secured access to any electronic record, book, register, correspondence, information, document or other material without the consent of the person concerned discloses such electronic record, book, register, correspondence, information, document or other material to any other person shall be punished with imprisonment for a term which may extend to two years, or with fine which may extend to one lakh rupees, or with both. These are the IPC Section codes : Section 499. Defamation Whoever, by words either spoken or intended to be read, or by signs or by visible representations, makes or publishes any imputation concerning any person intending to harm, or knowing or having reason to believe that such imputation will harm, the reputation of such person, is said, except in the cases hereinafter expected, to defame that person. It may amount to defamation to impute anything to a deceased person, if the imputation would harm the reputation of that person if living, and is intended to be hurtful to the feelings of his family or other near relatives. First Exception.—Imputation of truth which public good requires to be made or published Second Exception.—Public conduct of public servants Third Exception.—Conduct of any person touching any public question  Fourth Exception.—Publication of reports of proceedings of Courts Fifth Exception.-Merits of case decided in Court or conduct of witnesses and others concerned. Sixth Exception.—Merits of public performance Seventh Exception.—Censure passed in good faith by person having lawful authority over another. Eighth Exception.—Accusation preferred in good faith to authorised person. Ninth Exception.—Imputation made in good faith by person for protection of his or other’s interests Tenth Exception.—Caution intended for good of person to whom conveyed or for public good Section 500. Punishment for defamation Whoever defames another shall be punished with simple imprisonment for a term which may extend to two years, or with fine, or with both.8. CLASSIFICATION OF OFFENCE Para I Punishment—Simple imprisonment for 2 years, or fine, or both—Non-cognizable—Bailable—Triable by Court of Session—Compoundable by the person defamed. Para II Punishment—Simple imprisonment for 2 years, or fine, or both—Non-cognizable—Bailable—Triable by Magistrate of the first class—Compoundable by the person defamed with the permission of the court Section 420 Cheating and dishonestly inducing delivery of property Whoever cheats and thereby dishonestly induces the person deceived to deliver any property to any person, or to make, alter or destroy the whole or any part of a valuable security, or anything which is signed or sealed, and which is capable of being converted into a valuable security, shall be punished with imprisonment of either description for a term which may extend to seven years, and shall also be liable to fine.CLASSIFICATION OF OFFENCE Punishment—Imprisonment for 7 years and fine—Cognizable—Non-bailable—Triable by Magistrate of the first class—Compoundable by the person cheated with the permission of the court. Section 383. Extortion Whoever intentionally puts any person in fear of any injury to that person, or to any other, and thereby dishonestly induces the person so put in fear to deliver to any property or valuable security, or anything signed or sealed which may be converted into a valuable security, commits “extortion”. Example; (a) A threatens to publish a defamatory libel concerning Z unless Z give him money. He thus induces Z to give him money. A has committed extortion. (b) A threatens Z that he will keep Z’s child in wrongful confinement, unless Z will sign and deliver to A promissory note binding Z to pay certain monies to A. Z signs and delivers the note. A has committed extortion. (c) A threatens to send club-men to plough up Z’s field unless Z will sign and deliver to B bond binding Z under a penalty to deliver certain produce to B, and thereby induces Z to sing and deliver the bond. A has committed extortion. (d) A, by putting Z in fear of grievous hurt, dishonestly induces Z to sign or affix his seal to a blank paper and deliver it to A. Z signs and delivers the paper to A. Here, as the paper so signed may be converted into a valuable security. A has committed extortion. Section 384. Punishment for extortion Whoever commits extortion shall be punished with imprisonment of either description for a term which may extend to three years, or with fine or with both.9. CLASSIFICATION OF OFFENCE Punishment—Imprisonment for 3 years, or fine, or both—Cognizable—Non-bailable—Triable by any Magistrate—Non-compoundable.Section 463. Forgery Whoever makes any false documents or false electronic record or part of a document or electronic record, with intent to cause damage or injury], to the public or to any person, or to support any claim or title, or to cause any person to part with property, or to enter into any express or implied contract, or with intent to commit fraud or that fraud may be committed, commits forgery.Section 465. Punishment for forgery Whoever commits forgery shall be punished with imprisonment of either description for a term which may extend to two years, or with fine, or with both.CLASSIFICATION OF OFFENCE Punishment—Punishment for forgery of such document—Cognizable—Bailable—Triable by Magistrate of the first class—Non-compoundable. Section 503. Criminal intimidation Whoever threatens another with any injury to his person, reputation or property, or to the person or reputation of any one in whom that person is interested, with intent to cause alarm to that person, or to cause that person to do any act which he is not legally bound to do, or to omit to do any act which that person is legally entitled to do, as the means of avoiding the execution of such threat, commits criminal intimidation. Explanation A threat to injure the reputation of any deceased person in whom the person threatened is interested, is within this section. Illustration A, for the purpose of inducing B to desist from prosecuting a civil suit, threatens to burn B’s house. A is guilty of criminal intimidation. The following are the live cases : Section 43 Related Case: Mphasis BPO Fraud: 2005 In December 2004, four call centre employees, working at an outsourcing facility operated by MphasiS in India, obtained PIN codes from four customers of MphasiS’ client, Citi Group. These employees were not authorized to obtain the PINs. In association with others, the call centre employees opened new accounts at Indian banks using false identities. Within two months, they used the PINs and account information gleaned during their employment at MphasiS to transfer money from the bank accounts of CitiGroup customers to the new accounts at Indian banks.10. By April 2005, the Indian police had tipped off to the scam by a U.S. bank, and quickly identified the individuals involved in the scam. Arrests were made when those individuals attempted to withdraw cash from the falsified accounts, $426,000 was stolen; the amount recovered was $230,000. Verdict: Court held that Section 43(a) was applicable here due to the nature of unauthorized access involved to commit transactions. Section 65 Related Case: Syed Asifuddin and Ors. Vs. The State of Andhra Pradesh In this case, Tata Indicom employees were arrested for manipulation of the electronic 32- bit number (ESN) programmed into cell phones theft were exclusively franchised to Reliance Infocomm. Verdict: Court held that tampering with source code invokes Section 65 of the Information Technology Act.Section 66 Related Case: Kumar v/s Whiteley In this case the accused gained unauthorized access to the Joint Academic Network (JANET) and deleted, added files and changed the passwords to deny access to the authorized users. Investigations had revealed that Kumar was logging on to the BSNL broadband Internet connection as if he was the authorized genuine user and ‘made alteration in the computer database pertaining to broadband Internet user accounts’ of the subscribers. The CBI had registered a cyber crime case against Kumar and carried out investigations on the basis of a complaint by the Press Information Bureau, Chennai, which detected the unauthorised use of broadband Internet. The complaint also stated that the subscribers had incurred a loss of Rs 38,248 due to Kumar’s wrongful act. He used to ‘hack’ sites from Bangalore, Chennai and other cities too, they said. Verdict: The Additional Chief Metropolitan Magistrate, Egmore, Chennai, sentenced N G Arun Kumar, the techie from Bangalore to undergo a rigorous imprisonment for one year with a fine of Rs 5,000 under section 420 IPC (cheating) and Section 66 of IT Act (Computer related Offence). section 66 A Relevant Case #1: Fake profile of President posted by imposter On September 9, 2010, the imposter made a fake profile in the name of the Hon’ble President Pratibha Devi Patil. A complaint was made from Additional Controller, President Household, President Secretariat regarding the four fake profiles created in the name of Hon’ble President on social networking website, Facebook. The said complaint stated that president house has nothing to do with the facebook and the fake profile is misleading the general public. The First Information Report Under Sections 469 IPC and 66A Information Technology Act, 2000 was registered based on the said complaint at the police station, Economic Offences Wing, the elite wing of Delhi Police which specializes in investigating economic crimes including cyber offences. Relevant Case #2: Bomb Hoax mail In 2009, a 15-year-old Bangalore teenager was arrested by the cyber crime investigation cell (CCIC) of the city crime branch for allegedly sending a hoax e-mail to a private news channel. In the e-mail, he claimed to have planted five bombs in Mumbai, challenging the police to find them before it was too late. At around 1p.m. on May 25, the news channel received an e-mail that read: “I have planted five bombs in Mumbai; you have two hours to find it.” The police, who were alerted immediately, traced the Internet Protocol (IP) address to Vijay Nagar in Bangalore. The Internet service provider for the account was BSNL, said officials. section 66 C Relevant Cases: security number was exposed by Matt Lauer on NBC’s Today Show. Davis’ identity was used to obtain a $500 cash advance loan. University of Pennsylvania faked his own death, complete with a forged obituary in his local paper. Nine months later, Li attempted to obtain a new driver’s license with the intention of applying for new credit cards eventually.Section 66C: Punishment for identity theft Imprisonment upto three years and Fine upto Rs. 1 Lakhs.Section 66D: Punishment for cheating by personation by using computer resourceSection 66E: Punishment for violation of privacy Imprisonment upto three years and/or Fine upto Rs. 2 LakhsSection 66F: Punishment for cyber terrorism May extend to Life imprisonment -do- Non bailable.Section 67: Publishing obscene information in electronic form FirstConviction: Imprisonment upto three years and Fine upto Rs. 5 LakhsSecond or subsequent Conviction : Imprisonment upto five years and Fine upto Rs. 10 Lakhs -do- Bailable in case of first conviction only. Second or subsequent conviction shall be non bailableSection 67A: Punishment for publishing or transmitting of material containing sexually explicit act, etc. in electronic form First Conviction:Imprisonment upto Five years and Fine upto Rs. 10 LakhsSecond or subsequent Conviction : Imprisonment upto Seven years and Fine upto Rs. 10 Lakhs -do- Non-bailable in both first and second conviction.Section 67B: Punishment for publishing or transmitting of material depicting children in sexually explicit act, etc. in electronic form.Section 67C (2): Deliberate Failure by the intermediary to preserve and retain information as specified by the Central Government.Section 68 (2): Deliberate Failure to comply with the order/direction of controller.Section 69 (4): Failure to extend facilities to decrypt information to govt. notified agencySection 69A (3): Punishment for failure by the intermediary to comply with the order of the notified agency to block websites etc.Section 69B (4): Deliberate failure by the intermediary to provide the notified agency with the technical assistance or online access to the computer resource.Section 70: Unauthorized access to protected system directly or indirectly affects the facility of Critical Information Infrastructure.Section 72A: Punishment for Disclosure of information in bsignNow of lawful contract Indian Arms Act 1959 Imprisonment upto three years and Fine .Bailable Imprisonment for a term not exceeding two years or to a fine not exceeding one lakh rupees or to both Imprisonment for a term which may extend to seven years and fine Imprisonment for a term which may extend to three years and fine Imprisonment up to 10 years and fine Cognizable Non bailable Imprisonment for a term upto three years or to a fine upto Rs. 5 Lakhs or to both.Chapter V – Offences and Penalties Sec.25 – Punishment for certain offencesSec.26 – Secret contraventionsSec.27 – Punishment for using arms, etc. Non cognizable -do- Cognizable Non bailable Non Cognizable BailableSec.28 – Punishment for use and possession of firearms or imitation firearms in certain casesSec.29 – Punishment for knowingly purchasing arms, etc., from unlicensed person or for delivering arms, etc., to person not entitled to possess the sameSec.30 – Punishment for contravention of licence or ruleSec.31 – Punishment for subsequent offencesSec.32 – Power to confiscateSec.33 – Offence by companies NDPS ACT On 8th September, 2011, the Government introduced the NDPS (Amendment) Bill, 2011 in the Lok Sabha. The Bill was referred to the Parliamentary Standing Committee on Finance on 13th September, 2011 for further consideration. The Narcotic Drugs and Psychotropic Substances (NDPS) Act, 1985 is the central law on control, regulation and prohibition of narcotic and psychotropic drugs in India. The Act was last amended in 2001, to rationalize punishment and adopt a sentencing structure based on the quantity of drugs involved. The stringent penal structure and rigid implementation of the NDPS Act created many problems including non-availability of opioid medication and lack of access to drug dependence treatment. The Bill seeks to amend a number of provisions of the NDPS Act including:•Modification of the definitions of ‘small’ and ‘commercial’ quantity to include the entire amount of drugs involved and not only the pure drug content [Section 2(xxiiia) and Section 2(viia)]•Standardisation of punishment for consumption of drugs to a maximum of 6 months or fine [Section 27]•Transfer of power to regulate “poppy straw concentrate” from the State to the Central Government [Sections 9 and 10]•Widening provisions for forfeiture of illegally acquired property, wherein any property of a person who is alleged to be involved in illicit traffic whose source cannot be proved is termed as ‘illegally acquired property’ and liable to be seized [Sections 68-B, 68H and 68-O]•Addition of the term ‘management’ to provisions on treatment for drug dependence [Section 71] Concerns over the Bill The proposed quantity definitions would have far signNowing implications on sentencing for NDPS offences and may expose low-level drug offenders, including people who use drugs to stringent punishment. Despite standardisation of punishment for consumption of drugs, the policy of criminalisation of drug use remains unchanged. The overbroad scope of the forfeiture provision makes it susceptible to misuse and subject to constitutional challenges. Further still, the Bill fails to address key issues and contradictions that have arisen such as, death penalty for repeat offenders, immunity for treatment seeking, regulation of treatment centres, support for harm reduction measures and access to opioid medicines. Read more. The Lawyers Collective expressed these and other concerns to the Standing Committee on Finance through written and oral submissions on the NDPS (Amendment) Bill, 2011 My request to all the people is to be safe and to be alert and not involve in wrong activities.

Warning: Wave-particle duality gave birth to the mind-numbing world of quantum mechanics. Understanding it may mean upturning everything you believe about the world so that you are free to climb to a different perspective where it all makes sense. If you're willing to take that challenge on, then keep reading.“The voyage of discovery lies not in seeking new horizons, but in seeing with new eyes.” ~ Marcel ProustAn examination of the double-slit experiment is a great place to start. To make that examination worthwhile, we need to make sure that we are familiar with an important effect known as interference. [i]Interference applies universally to all interacting waves. A water wave, for instance, can be described as a disturbance in the shape of the water’s surface. This disturbance produces regions where the water level is higher and regions where it is lower than the undisturbed value. The highest part of each ripple is called a peak and the lowest part is called a trough. Typically waves involve periodic succession, peak followed by trough followed by peak and so on. In general, we can define a wavelength as the distance between identical parts of adjacent waves. Measurements from peak to peak, or trough to trough, for example, give the same value for wavelength.Figure 1 Peaks and troughs of wavesWhen waves interact in a medium, they interfere. For example, if we drop two rocks into spatially separated parts of a pond, their waves will interfere when they cross. (Figure 2) When a peak of one wave and a peak of another wave come together, the height of the water rises to a height equal to the sum of the two peaks. Similarly, when a trough of one wave and a trough of another wave cross, the depression of the water's surface dips to the sum of the two depressions. And when a peak of one wave crosses with a trough of another, the (at least partially) cancel each other out. The peak of one wave contributes a positive displacement while the trough of the other wave contributes a negative displacement. If the two waves have equal magnitude, then there will be perfect cancelation and the water's surface will be flat, just as it was before any wave existed.Figure 12-2 Constructive and destructive interference Keeping these rules of interference in mind, let’s turn our attention to light. If we take a laser emitting a single wavelength—a single color, and shine it on a screen that has a slit etched into it (Figure 3), what image should we expect to see on the wall behind the screen? [ii] Classically speaking, we would expect to see a stripe of light on the wall. (Classically means according to our four-dimensional intuition, or the rules of Euclidean geometry.) It turns out that this is what we see. In this sense light’s behavior correlates perfectly with our Euclidean intuition.Figure 12-3 Expected single slit projectionWhat image should we expect to see on the wall if we etch a second slit on our screen and cover the first slit with a black piece of tape? Well, our classical intuitions tell us to expect a line of light projected on the wall, just like we did before, except this line of light should be offset from the first. Again, this is exactly what we see when we perform the experiment. So far all of this is straightforward and conceptually trivial. But as it turns out, we are only one step away from a profound mystery. We discover this mystery by removing the piece of tape. To understand the impact of this mystery, ask yourself: What sort of projection do we expect to see on the wall when both slits are open?Classical intuition tells us that we should see two parallel bands of light on the wall (Figure 4).Figure 4 Expected double slit projectionBut this is where our classical training (our Euclidean intuition) lets us down. This is also where classical mechanics breaks down. When we perform this experiment, something completely counterintuitive happens, contradicting our Euclidean intuitions. A distinct interference pattern is projected on the wall (Figure 5).Figure 5 Actual double slit projection The bright and dark bands produced in this double-slit experiment are telltale signs that light propagates as a wave. [iii] Interference patterns are key signatures of waves. The problem is that this wavelike characteristic directly clashes with our observations of light’s particulate behavior. After all, photons are always found in point-like regions rather than spread out like a wave, and individual photons are always found to have very discrete amounts of energy. When measuring a wave, you would expect to find its energy spread out over a region instead of being concentrated in one location. So how are we supposed to make sense of this observation? What is going on?These diametrically opposed properties of light are verified facts. Contradictory as they may seem, they are here to stay. They have forced us to the seemingly paradoxical conclusion that light is both a wave and a particle. But how can this be? How can it be both? Although many scientists have found the wave-particle duality of light to be conceptually vague and schizophrenic, this description has persisted. In fact, after the wave-particle concept was adopted as an accurate description of light, it was extended to describe electrons and, eventually, all of matter. This transition was nothing short of a revolution.Up until 1910, atoms were simplistically viewed as miniature solar systems with the nucleus making up the “central star” and orbiting electrons being “planets”. [iv] The wave-particle duality of light and matter rejected this view and pointed to a signNowly different architecture for atoms. Of course, this conceptual transition did not take hold over night.In 1924, Prince Louis de Broglie found that in addition to their particle like character, [v] electrons also possessed a wavelike character. In 1927, Clinton Davisson and Lester Germer followed this up by firing a beam of electrons at a piece of nickel crystal, which acted as a barrier analogous to the one used in the double-slit experiment. A phosphor screen recorded the resultant pattern of electrons. [vi] When they examined the screen, they observed an interference pattern just like the one produced in the double-slit experiment, showing that even electrons have wavelike properties.These experiments shook the foundation of physics by threatening the structure of classical mechanics and destroying humanity’s intuitive framework of reality. But it didn’t stop there. The next step was to tune the beam of electrons down so that the electron gun fired just a single electron at a time. Similar experiments were later used with lasers wherein individual photons were fired seconds apart from each other. The results were mind-bending.Completely against expectation these experiments also produced interference patterns over time as the collection of electrons (or photons) continued to build (Figure 6).Figure 12-6 Over time individual photons construct an interference patternThese observations only added to the confusion. Waves are supposed to be a collective property—something that has no meaning when applied to separate, particulate ingredients. (A water wave, for example, involves a large number of water molecules.) So how can a single electron, or a single photon, be a wave? Furthermore, wave interference requires a wave from one place to interact with a wave from another place. So how can interference be relevantly applied to a single electron or photon? While we are considering such questions, we should also ask, if a single electron or photon is a wave, then what is it that is “waving”? [vii]To answer these questions, Erwin Schrödinger proposed that the stuff that makes up electrons might be smeared out in space and that this smeared electron essence might be what waves. If this idea was correct then we would expect to find all of the electron’s properties, spread out over a distance, but we never do. Every time we locate an electron, we find all of its mass and all of its charge concentrated in one tiny, point-like region. Max Born came up with a different idea. He suggested that the wave is actually a probability wave. [viii] Einstein tinkered with a similar idea when he hypothesized that these waves were optical observations that refer to time averages rather than instantaneous values.Inserting a probability wave (also called a state vector, or a wave function) as a fundamental aspect of Nature delivers another blow to our common-sense ideas about how things truly operate. It suggests that experiments with identical starting conditions do not necessarily lead to identical results because it claims that you can never predict exactly where an electron will be in a single instant. You can only define a probability that we will find it over here, or over there, at any given moment. Two situations with the same probabilistic starting conditions, say of a single particle, might not produce the same results, because the particle can be anywhere within that probability distribution. From a classical perspective, the discovery that the microscopic universe behaves this way is absolutely baffling. Nevertheless, it is how we have observed Nature to be.This leads us to a rather interesting precipice. It seems that the map we have been using to chart physical reality somehow dissolves when we look closely at it. The rules of four-dimensional geometry simply fail to accurately map Nature when we examine the smallest scales. Nature doesn’t strictly behave as our old Euclidean map dictates. Stumbling upon this discovery forces us to face a vital question. Is Nature ultimately and fundamentally probabilistic in a way that we may never understand, as many modern physicists have chosen to believe; or, is this probabilistic quality a byproduct of our reduced dimensional representation of Nature?After pondering these questions long and hard, some physicists have come to believe that the tapestry of spacetime is analogous to water: that the smooth appearance of space and time is only an approximation that must yield to a more fundamental framework when considering ultramicroscopic scales. As far as I can tell, however, up until now this point has only been entertained abstractly. Geometrically resolving a molecular structure for space might resolve our greatest quantum mechanical mysteries, but as of yet, no one has taken that final step. No one has developed a self-consistent picture from this geometric insight. No one has moved beyond the mathematical suggestion that spacetime is analogous to water, or interpreted the theoretical quanta of space as being physically real. Consequently, a framework that enables conceptualization of what is meant by the “molecules” or “atoms” of spacetime has not been developed.Eight decades of meticulous experiments have confirmed the predictions of quantum mechanics based on this wave function, or probability wave, description with amazing precision. “Yet there is still no agreed-upon way to envision what quantum mechanical probability waves actually are. Whether we should say that an electron’s probability wave is the electron, or that it’s associated with the electron, or that it’s a mathematical device for describing the electron’s motion, or that it’s the embodiment of what we can know about the electron is still debated.” [ix]Although quantum mechanics describes the universe as having an inherently probabilistic character, we don’t experience the effects of this character in our day-to-day lives. Why is this? The answer, according to quantum mechanics, is that we don't see quantum events like a chair being here now and then across the room in the next instant, because the probability of that occurring, although not zero, is absurdly miniscule. But what exactly makes the probability for large things to act, as electrons do, so small? At what scales do such effects become important? And, why should the macroscopic universe be so different from the microscopic universe?As if these newly uncovered characteristics of reality weren’t obscure enough, quantum physicists conceptually fuddle things further by suggesting that without observation things have no reality. They claim that until the position of an electron is actually measured the electron has no definite position. Before it is measured, the position exists only as a probability, and then suddenly, through the act of measuring, the electron miraculously acquires the property of position.Einstein acutely recognized the absurdity of this claim. When approached with this conjecture, he famously quipped, “Do you really believe that the moon is not there unless we are looking at it?” [x] To him everything in the physical world had a reality independent of our observations. Measurements that suggested otherwise were mere reflections of the incompleteness by which we currently map and comprehend physical reality. To many quantum physicists, however, the unobserved Moon’s existence became a matter of probability. To them, a discoverable, complete map of physical reality, with the ability to resolve an underlying determinism, became nothing more than a myth—a romantic dream.The mathematical projection of quantum mechanics can be statistically matched with our four-dimensional observations, but when it comes to a conceptual explanation of those observations, it completely lets us down. Intuitive explanations cannot be gleaned from a framework of physical reality that is assumed to be fundamentally probabilistic. By definition, randomness blurs causality. This vague description of physical reality keeps us from grasping a deeper truth by allowing what should be the most basic of concepts to drip into a realm of nonsense.As an example of the confusion that stems from swallowing the standard quantum mechanical interpretation “guts, feathers, and all,” consider the fact that a probabilistic treatment of quantum mechanics leads us to the conclusion that the double-slit experiment can be explained by assuming that a photon actually takes both paths. We can combine the two probability waves emerging from both slits to statistically determine where a photon will land on a screen. The result mimics an interference pattern.According to this, we can explain interference patterns by assuming that one photon somehow always manages to go through both slits, but is this really what is going on? Does a photon really travel along both paths? Can this count as an explanation if we have no coherent sense of what it means? You might notice that if we were to design our experiment with three slits, then we would have to consider whether or not the photon really travels all three routes. This question can be extended for as many slits as you like, but the fundamental conceptual problem remains the same.In order to solve this mystery, you may suggest that we place detectors in front of the slits to determine if the photons are actually going through both slits, or just one. When we do this, we always find that individual photons pass through one slit or the other—never both. But, when we measure the position of individual photons we no longer get an interference pattern and so the question retains its ambiguity. Some have taken this to mean that the act of observation forces wave properties to collapse into a particle, but how and why this theoretical collapse occurs still lacks explanation.Because probability waves are not directly observable and because photons (and electrons) are always found in one place or another when measured, we might be tempted to think that probability waves might not be real—that they were never really there. If that is true, then how are the interference patterns created? Surely these probability waves exist, but in what sense? What are they referencing? Why is it that whenever we know which path the photon takes, we get a classical image instead of an interference pattern? How does the detection of a photon, or an electron, change its behavior?To date, these questions have yet to be resolved. In fact, more clever experiments designed to solve these questions have only deepened the mystery. For example, let’s perform the double-slit experiment again, but this time let’s place devices in front of the slits, which mark (but do not stop or detect) the photons before they pass through the slits. This marking allows us to examine the photons that strike the screen and subsequently determine which slit they passed through. Thus we only gain knowledge of which path the photon takes after the path has been completed. For some reason, however, when we do this we find that the photons do not build up an interference pattern. They form a classical image (Figure 4).Once again, it seems that “which-path” information inhibits us from probing these ghostly waves. But is it really the fact that we gain the ability to determine which path a photon goes through—independent of when we gain that information—that disrupts the interference pattern? Or does our marking of the photon somehow disrupt its interference potential?To explore this question, we perform what’s known as the quantum eraser experiment. We start with the same set up we just described. Then we place another device between each slit and the screen, which completely removes the mark from the photon. We already know that the marked photons project a classical image. Will an interference pattern reemerge if we remove the effects of this mark—if we lose the ability to extract the which-path information?When we perform this experiment the interference pattern does return (Figure 7). Does this mean that photons somehow choose how to act, based on our knowledge of them? Or does it imply something even stranger—that the photons are always both particles and waves simultaneously? How are we to understand either conclusion?Figure 12-7 An interference pattern Another curiosity of Nature is known as the photoelectric effect. Philipp Lenard first discovered this effect through controlled experiments in 1900. When light shines on a metal surface, it causes electrons to be knocked loose and emitted. Knowing this, Lenard designed an experiment that allowed him to control the frequency of the incoming light. During the experiment, he increased the frequency of the light—moving from infrared heat and red light to violet and ultraviolet. Greater frequencies caused the emitted electrons to speed away with more kinetic energy. After discovering this, Lenard reconfigured his experiment to allow him to control the intensity of the incoming light. He used a carbon arc light that could be made brighter by a factor of 1,000.Because both experiments involved increasing the amount of incoming light energy he expected to have identical results. In other words, because the brighter, more intense light had more energy, Lenard expected that the electrons emitted would have more energy and speed away faster. But that’s not what happened. Instead, the more intense light produced more electrons, but the energy of each electron remained the same. [xi]In response to these experiments Einstein suggested that light is composed of discrete packets called photons. Under this assumption, light with higher frequency would cause electrons to be emitted with more energy, and light with higher intensity, that is, a higher quantity of photons, would result in emission of more electrons—just as we observe.The problem with this solution (a solution that is now universally accepted among physicists) is that it doesn’t provide us with a clear description for what the light quanta are. Why does light come in quantized packets? Near the end of his life Einstein lamented over this problem in a letter to his dear friend Michele Besso. He wrote, “All these fifty years of pondering have not brought me any closer to answering the question, what are light quanta?” [xii] It’s been another fifty years and we seem as confused as ever over how it is that light is quantized into little discrete packets called photons.In the midst of these enigmas lies the uncertainty principle, which states that knowledge of certain properties inhibits knowledge of other complimentary properties. For example, the more accurately we determine the position of an electron, the less we can determine its momentum, and vise versa.Heisenberg tried to explain the uncertainty principle by appealing to the observer effect; claiming that it was simply an observational effect of the fact that measurements of quantum systems cannot be made without affecting those systems. [xiii] Since then, the uncertainty principle has regularly been confused with the observer effect. [xiv] But the uncertainty principle is not a statement about the observational success of current technology. It has nothing to do with the observer effect. It highlights a fundamental property of quantum systems, a property that turns out to be inherent in all wave-like systems. [xv] Uncertainty is an aspect of quantum mechanics because of the wave nature it ascribes to all quantum objects.If our current description of quantum mechanics is fundamental, if there is nothing beneath the state vector—a claim that defines the heart of the standard interpretation of quantum mechanics—then this uncertainty principle may be a sharp enough dagger to kill our quest for an intuitive understanding of physical reality. The corrosive power of the uncertainty principle, when mixed with our current paradigm, is poignantly illustrated by an old story involving Niels Bohr. According to the story, Bohr was once asked what the complementary quality to truth is. After some thought he answered—“clarity.” [xvi] Unlike classical mechanics, which describes systems by specifying the positions and velocities of its components, quantum mechanics uses a complex mathematical object called a state vector (also called the wave function [xvii]) to map physical systems. Interjecting this state vector into the theory enables us to match its predictions to our observations of the microscopic world, but it also generates a relatively indirect description that is open to many equally valid interpretations. This creates a sticky situation, because to “really understand” quantum mechanics we need to be able to specify the exact status of and to have some sort of justification for that specification. At the present, we only have questions. Does the state vector describe physical reality itself, or only some (partial) knowledge that we have of reality? “Does it describe ensembles of systems only (statistical description), or one single system as well (single events)? Assume that indeed, is affected by an imperfect knowledge of the system, is it then not natural to expect that a better description should exist, at least in principle?” [xviii] If so, what would this deeper and more precise description of reality be?To explore the role of the state vector, consider a physical system made of N particles with mass, each propagating in ordinary three-dimensional space. In classical mechanics we would use N positions and N velocities to describe the state of the system. For convenience we might also group together the positions and velocities of those particles into a single vector V, which belongs to a real vector space with 6N dimensions, called phase space. [xix]The state vector can be thought of as the quantum equivalent of this classical vector V. The primary difference is that, as a complex vector, it belongs to something called complex vector space, also known as space of states, or Hilbert space. In other words, instead of being encoded by regular vectors whose positions and velocities are defined in phase space, the state of a quantum system is encoded by complex vectors whose positions and velocities live in a space of states. [xx]The transition from classical physics to quantum physics is the transition from phase space to space of states to describe the system. In the quantum formalism each physical observable of the system (position, momentum, energy, angular momentum, etc.) has an associated linear operator acting in the space of states. (Vectors belonging to the space of states are called “kets.”) The question is, is it possible to understand space of states in a classical manner? Could the evolution of the state vector be understood classically (under a projection of local realism) if, for example, there were additional variables associated with the system that were ignored completely by our current description/understanding of it?While that question hangs in the air, let’s note that if the state vector is fundamental, if there really isn’t a deeper-level description beneath the state vector, then the probabilities postulated by quantum mechanics must also be fundamental. This would be a strange anomaly in physics. Statistical classical mechanics makes constant use of probabilities, but those probabilistic claims relate to statistical ensembles. They come into play when the system under study is known to be one of many similar systems that share common properties, but differ on a level that has not been probed (for any reason). Without knowing the exact state of the system we can group all the similar systems together into an ensemble and assign that ensemble state to our system. This is done as a matter of convenience. Of course, the blurred average state of the ensemble is not as clear as any of the specific states the system might actually have. Beneath that ensemble there is a more complete description of the system’s state (at least in principle), but we don’t need to distinguish the exact state in order to make predictions. Statistical ensembles allow us to make predictions without probing the exact state of the system. But our ignorance of that exact state forces those predictions to be probabilistic.Can the same be said about quantum mechanics? Does quantum theory describe an ensemble of possible states? Or does the state vector provide the most accurate possible description of a single system? [xxi]How we answer that question impacts how we explain unique outcomes. If we treat the state vector as fundamental, then we should expect reality to always present itself in some sort of smeared out sense. If the state vector were the whole story, then our measurements should always record smeared out properties, instead of unique outcomes. But they don’t. We always measure well-defined properties that correspond to specific states. Sticking with the idea that the state vector is fundamental, von Neumann suggested a solution called state vector reduction (also called wave function collapse). [xxii] The idea was that when we aren’t looking, the state of a system is defined as a superposition of all its possible states (characterized by the state vector) and evolves according to the Schrödinger equation. But as soon as we look (or take a measurement) all but one of those possibilities collapse. How does this happen? What mechanism is responsible for selecting one of those states over the rest? To date there is no answer. Despite this, von Neumann’s idea has been taken seriously because his approach allows for unique outcomes.The problem that von Neumann was trying to address is that the Schrödinger equation itself does not select single outcomes. It cannot explain why unique outcomes are observed. According to it, if a fuzzy mix of properties comes in (coded by the state vector), a fuzzy mix of properties comes out. To fix this, von Neumann conjured up the idea that the state vector jumps discontinuously (and randomly) to a single value. [xxiii] He suggested that unique outcomes occur because the state vector retains only the “component corresponding to the observed outcome while all components of the state vector associated with the other results are put to zero, hence the name reduction.” [xxiv]The fact that this reduction process is discontinuous makes it incompatible with general relativity. It is also irreversible, which makes it stand out as the only equation in all of physics that introduces time-asymmetry into the world. If we think that the problem of explaining uniqueness of outcome eclipses these problems, then we might be willing to take them in stride. But to make this trade worthwhile we need to have a good story for how state vector collapse occurs. We don’t. The absence of this explanation is referred to as the quantum measurement problem.Many people are surprised to discover that the quantum measurement problem still stands. It has become popular to explain state vector reduction (wave function collapse) by appealing to the observer effect, asserting that measurements of quantum systems cannot be made without affecting those systems, and that state vector reduction is somehow initiated by those measurements. [xxv] This may sound plausible, but it doesn’t work. Even if we ignore the fact that this ‘explanation’ doesn’t elucidate howa disturbance could initiate state vector reduction, this isn’t an allowed answer because “state vector reduction can take place even when the interactions play no role in the process.” [xxvi] This is illustrated by negative measurements or interaction free measurements in quantum mechanics.To explore this point, consider a source, S, that emits a particle with a spherical wave function, which means its values are independent of the direction in space. [xxvii] In other words, it emits photons in random directions, each direction having equal probability. Let’s surround the source by two detectors with perfect efficiency. The first detector D1should be set up to capture the particle emitted in almost all directions, except a small solid angle θ, and the second detector D2 should be set up to capture the particle if it goes through this solid angle (Figure 8).Figure 8 An interaction-free measurement When the wave packet describing the wave function of the particle signNowes the first detector, it may or may not be detected. (The probability of detection depends on the ratio of the subtended angles of the detectors.) If the particle is detected by D1 it disappears, which means that its state vector is projected onto a state containing no particle and an excited detector. In this case, the second detector D2 will never record a particle. If the particle isn’t detected by D1 then D2 will detect the particle later. Therefore, the fact that the first detector has not recorded the particle implies a reduction of the wave function to its component contained within θ, implying that the second detector will always detect the particle later. In other words, the probability of detection by D2 has been greatly enhanced by a sort of “non-event” at D1. In short, the wave function has been reduced without any interaction between the particle and the first measurement apparatus.Franck Laloë notes that this illustrates that “the essence of quantum measurement is something much more subtle than the often invoked ‘unavoidable perturbations of the measurement apparatus’ (Heisenberg microscope, etc.).” [xxviii] If state vector reduction really takes place, then it takes place even when the interactions play no role in the process, which means that we are completely in the dark about how this reduction is initiated or how it unfolds. Why then is state vector reduction still taken seriously? Why would any thinking physicist uphold the claim that state vector reduction occurs, when there is no plausible story for how or why it occurs, and when the assertion that it does occur creates other monstrous problems that contradict central tenets of physics? The answer may be that generations of tradition have largely erased the fact that there is another way to solve the quantum measurement problem.Returning to the other option at hand, we note that if we assume that the state vector is a statistical ensemble, if we assume that the system does have a more exact state, then the interpretation of this thought experiment becomes straightforward; initially the particle has a well-defined direction of emission, and D2 records only the fraction of the particles that were emitted in its direction.Standard quantum mechanics postulates that this well-defined direction of emission does not exist before any measurement. Assuming that there is something beneath the state vector, that a more accurate state exists, is tantamount to introducing additional variables to quantum mechanics. It takes a departure from tradition, but as T. S. Eliot said in The Sacred Wood, “tradition should be positively discouraged.” [xxix] The scientific heart must search for the best possible answer. It cannot flourish if it is constantly held back by tradition, nor can it allow itself to ignore valid options. Intellectual journeys are obliged to forge new paths.So instead of asking whether of not wave-particle duality is an illusion, perhaps we should ask whether wave-particle duality implies that the state vector is the most fundamental description of a quantum mechanical system, or if a deeper level description exists? That's an open question, and at the moment there are many possible answers — interpretations of quantum mechanics that are equally aligned with the empirical evidence. My intuition is that a deeper level description of reality exists (something like Bohmian Mechanics yet deeper—like Superfluid vacuum theory).*This response is a modified excerpt from my book 'Einstein's Intuition'. Page on einsteinsintuition.com[i] The discussion on interference and the double-slit experiment that follows is further developed by Brian Greene, (2004). The Fabric of the Cosmos: Space, Time and the Texture of Reality. New York: Knopf, pp. 84–84. Greene’s discussion was used as a general guide here.[ii] In order to show diffraction (a fuzzy border of light on the projected image) the slit must have a width that does not greatly exceed the wavelength of the color of the light that we have chosen.[iii] Light’s wave nature was first revealed in the mid-seventeenth century through experiments performed by the Italian scientist Francesco Maria Grimaldi, and was later expanded upon by experiments performed in 1803 by the physician and physicist Thomas Young. (1807). Interference of Light; Alan Lightman. A Sense Of The Mysterious. pp. 51–52, 71.[iv] Before the “planetary model” of the atom, physicists pictured the atom being a plum-shaped blob (the nucleus) with tiny protruding springs that each had an electron stuck to its end. When the atom absorbed energy it was thought that these electrons would jiggle (oscillate) on the ends of their springs. Consequently, any atom that was above its ground state of energy was understood to be an “excited atomic oscillator,” This depiction of the atom wasn’t overthrown until 1900. At that point in history the physical existence of atoms was still controversial. It was replaced by the planetary model, which in turn was replaced by the electron cloud model we use today—a model that was initiated in 1910 and was secured by 1930. Gary Zukav. The Dancing Wu Li Masters, pp. 49–50.[v] Electrons can be individually counted and you can individually place them on a drop of oil and measure their electric charge. Richard Feynman. (1988). QED, The Strange Theory of Light and Matter. Princeton University Press, p. 84.[vi] According to de Broglie’s doctoral thesis all matter has corresponding waves. The wavelength of the “matter waves” that “correspond” to matter depends upon the momentum of the particle. Specifically, , which falls into an important group of equations along with Planck’s equation ) and the ever famous . (λ, pronounced “lambda,” stands for wavelength, h is Planck’s constant, and pronounced ‘nu’ represents the frequency of a photon) From this equation we are told to expect that when we send a beam of electrons (something we might traditionally think of as a stream of particles) through tiny openings, like the spacing between atoms in a piece of nickel crystal, the beam will diffract, just like light diffracts. The only requirement here is that the spacing between the atoms of the material must be as small, or smaller, than the electron’s corresponding wavelength—just like the slits in our double-slit experiment. When we perform the experiment, diffraction and therefore interference, occurs exactly as wave mechanics predicts.[vii] Part of the problem here is that in keeping with our four-dimensional intuition we tend to assume a particle aspect in the double-slit experiment without accounting for nonlocality. By doing this we are technically violating Heisenberg’s uncertainty principle and missing the bigger picture.[viii] M. Born. (1926). Quantenmechanik der Stossvorgänge. Zeitschrift für Physik 38, 803–827; (1926). Zur Wellenmechanik der Stossvorgänge. Göttingen Nachrichten 146–160.[ix] Brian Greene. (2004), p. 91.[x] Albert Einstein quoted in Einstein by Walter Isaacson.[xi] Walter Isaacson. Einstein, pp. 96–97.[xii] Ibid.[xiii] Werner Heisenberg. The Physical Principles of the Quantum Theory, p. 20.[xiv] Masano Ozawa. (2003). Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement. Physical Review A 67 (4), arXiv:quant-ph/0207121; Aya Furuta. (2012). One Thing Is Certain: Heisenberg’s Uncertainty Principle Is Not Dead. Scientific American.[xv] L. A. Rozema, A. Darabi, D. H. Mahler, A. Hayat, Y, Soudagar, & A. M. Steinberg. (2012). Violation of Heisenberg’s Measurement—Disturbance Relationship by Weak Measurements. Physical Review Letters 109 (10).[xvi] Steven Weinberg. Dreams Of A Final Theory, p. 74.[xvii] For a system of spinless particles with masses, the state vector is equivalent to a wave function, but for more complicated systems this is not the case. Nevertheless, conceptually they play the same role and are used in the same way in the theory, so that we do not need to make a distinction here. Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 7.[xviii] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. xxi.[xix] There are 6N dimensions in this phase space because there are N particles in the system and each particle comes with 6 data points (3 for its spatial position (x, y, z) and 3 for its velocity, which has x, y, zcomponents also).[xx] The space of states (complex vector space or Hilbert space) is linear, and therefore, conforms to the superposition principle. Any combination of two arbitrary state vectors and within the space of states is also a possible state for the system. Mathematically we write where & are arbitrary complex numbers.[xxi] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 19.[xxii] Chapter VI of J. von Neumann. (1932). Mathematische Grundlagen der Quantenmechanik, Springer, Berlin; (1955). Mathematical Foundations of Quantum Mechanics, Princeton University Press.[xxiii] It might be useful to challenge the logical validity of the claim that something can “cause a random occurrence.” By definition, causal relationships drive results, while “random” implies that there is no causal relationship. Deeper than this, I challenge the coherence of the idea that genuine random occurrences can happen. We cannot coherently claim that there are occurrences that are completely void of any causal relationship. To do so is to wisk away what we mean by “occurrences.” Every occurrence is intimately connected to the whole, and ignorance of what is driving a system is no reason to assume that it is randomly driven. Things cannot be randomly driven. Cause cannot be random.[xxiv] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 11.[xxv] Bohr preferred another point of view where state vector reduction is not used. D. Howard. (2004). Who invented the Copenhagen interpretation? A study in mythology. Philos. Sci. 71, 669–682.[xxvi] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 28.[xxvii] This example was inspired by section 2.4 of Franck Laloë’s book, Do We Really Understand Quantum Mechanics?, p. 27–31.[xxviii] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 28.[xxix] T. S. Eliot. (1921). The Sacred Wood. Tradition and the Individual Talent.

Thanks for the A2A.Jim Davis's answer to What are the differences between different music genres?Jim Davis's answer to Which music is the best?…and so my answer doesn’t get flagged for brevity:(alphabetically by genre/sub-genre; and no, not “every” genre is included. That would be physically impossible. This is closer to about 10% of all genres/sub-genres. You’re welcome.)Blues:Blues Rock; Similar to Electric Blues, but sometimes acoustic. Blues Rock can be played without having the power turned on. And it rocks. - Stoneground, Tommy Castro Band, Tom Waits, Jeff Healey, Chris Whitley, Paul Butterfield Blues BandChicago Blues; Sort of an urban blues using more piano and saxophone. These guys are quite often named Willie or "Big" something if not some kind of dog. Popular in Louisiana, strangely enough. - Willie Clarke, Willie Dixon, Willie Kent, Willie Murphy, Willie Nix, Big Bill Broonzy, Big Joe Turner, Big John Wrencher, Big Moose, Golden "Big" Wheeler, Eddie Shaw & The Wolf Gang, Hound Dog Taylor, Howlin' WolfDelta Blues; One of the earliest blues styles. The roots of the African-American styles honed in the Delta plains of the US in the midst of harsh mistreatment and soulful survival. Mostly acoustic guitar and harmonica. Best if played on the porch of an old, broken down shack. - Muddy Waters, Robert Johnson, Keb 'Mo', Memphis Jug Band, Johnny Shines, Tommy Johnson, Frank StokesElectric Blues; Blues that's plugged in and louder. Primarily guitar-based. When the power goes out it typically becomes Blues Rock.  - B.B. King, Eric Clapton, Magic Slim, Taj Mahal, John Lee Hooker, John Mayall, Charlie MusselwhiteJump Blues; Up-tempo with more swing. upright bass, piano, horns. One might jump if the mood strikes. - Magic Sam, Ruth Brown, Sugar Blue, Hal Singer, Amos Milburn, Ray Charles, Roy BrownNew Orleans Blues; More jazz and island influence. various drums and keyboard instruments. Popular in Texas, strangely enough. - Art Neville, Lloyd Price, Guitar Slim, Screamin' Jay Hawkins, T-Bone Burnett, Rockin' Sidney, Louisiana RedSt. Louis Blues; more piano based. similar to ragtime. Popular in Illinois, strangely enough. - Big Maybelle, Big Walter Horton, Roy Milton, Willie Mabon, Roosevelt Sykes, Yank Rachell, "Ma" Rainey, Percy MayfieldSwamp Blues; incorporates some Zydeco and more aggressive styles. Best when heard from the banks of a swamp and followed to an old, broken down shack. - Sonny Terry, Smiley Lewis, Luther Allison, Irma Thomas, Clifton Chenier, Doctor Ross, Bobby MarchanTexas Blues; more swing than Electric Blues, but more guitar than Jump Blues. Popular in Missouri, strangely enough. - Albert King, Lightnin' Hopkins, Tutu Jones, T-Bone Walker, Smokin' Joe Kubek, Grady Gains, Lafayette LeakeZydeco; more Creole influence. Accordion and alternative percussion instruments. You can't understand a word these guys are saying. - Al Rapone, Zydeco Boneshakers, Wayne Toups, Dr. John, The Mavericks, Buckwheat ZydecoGospel: somewhere between Blues and Country. Dominantly Christian in lyrical form.  - The Staple Singers, Shirley Caesar, Mahalia Jackson, Ira Tucker & The Dixie Hummingbirds, The Golden Gate Quartet, Fisk Jubilee Singers, The Blind Boys of AlabamaCountry:Bluegrass; up-tempo roots country using fiddle, banjo, jug, washtub bass. Should wear one-strap overalls and/or chew on a wheat stalk whilst playing. - Bill Monroe, Doc Watson, Laurie Lewis, The Del McCoury Band, The Cox Family, Don Reno, Carl Story, New Grass RevivalCountry Pop; pop-oriented country without the believable sadness. Mostly fifth and sixth generation Country for the sake of making money. - Carrie Underwood, Faith Hill, Lonestar, Pam Tillis, Juice Newton, Dixie Chicks, Martina McBrideHonky Tonk; up-tempo like Bluegrass, but more party-oriented and public. Drunken out-of-tune pianos and bar fights abound. Mostly second generation Country. - Rex Griffin, Lefty Frizzell, Hank Williams, Ernest Tubb, Jim Edward Brown, Red FoleyMountain; vocal harmonies, fast-pickin', nostalgia, and "ya gotta have a fiddle in the band". Judging by their names, they're usually related to someone if not each other.  - Alabama, Oak Ridge Boys, Roy Acuff, The Forester Sisters, The Louvin Brothers, The Stanley Brothers, The Burch Sisters, The Cook Family SingersNeotraditional; the sort of "we wish we'd been alive before country was cool" artists. True to their form, but still "new". Mostly fifth generation Country. - Alan Jackson, Brad Paisley, Garth Brooks, Vince Gill, Mark ChesnuttOutlaw; the real deal. These guys invented the country themes; heartache, loss, being broke, depressed, lonely and/or in jail. Third and Fourth generation Country with no fancy band or artist names; just straight-forward actual names with lots of "N"s and "L"s.  - Johnny Cash, Willie Nelson, Merle Haggard, Waylon Jennings, Hank Williams Jr., Charlie Daniels, David Allan Coe, Rodney Crowell, Leon RussellTraditional; the realer deal. Country for the sake of true mountain/southern expression. Hard workin' white trash sadness and hard times with an occasionally poppy feel later in the genre. Third and Fourth generation Country with lots of steel guitar twang, dobro, wailing fiddle and soft yet straight-forward 4/4 back beats that keep audiences clappin' on 1 and 3.  - Loretta Lynn, Emmylou Harris, Porter Wagoner, Kenny Rogers, George Jones, Tanya Tucker, Ronnie Milsap, Dolly PartonWestern; Out on the range/prairie. Cowboy music of the American Frontier Mostly campfire sing-alongs with little to no percussion. Bouncy rhythms reminiscent of horse galloping. Mostly second generation Country and frequently named a group belonging to an individual.  - Jean Shepard, Kitty Wells, Gene Autry, Tex Ritter, Skeets McDonald, Bob Wills & His Texas Playboys, Curly Williams and His Georgia Peach Pickers, Hank Penny and His Rodeo Cowboys, Leon McAuliffe and His Western Swing Band, Noel Boggs and His Day Sleepers, Tex Williams and His Western Caravan, Jack Guthrie and His Oklahomans, Milton Brown and His Brownies, Johnnie Lee Willis and His BoysElectronica:Acid Breaks; utilizes breakbeats and sampling of small rhythmic grooves to create longer song patterns. It is not a complete sentence explaining how acid reacts when dropped on the floor. - Zak Baney, DJ Icey, K-Swing, NAPT, Vigi, The Sables, Rozalla, C2CAggrotech; darker lyrics than most electronica, using high-mixed synth/saw leads and aggressive bass frequency oscillation. - Lights of Euphoria, Alien Vampires, Amduscia, Cenobita, Unter NullAmbient; emphasizes atmosphere and overall tone over song structure. Mood music.... if you're in the mood to feel ambient. - Etro Anime, Sneaker Pimps, Ceasefire, Aphex Twin, Kinobe, HalcyonColdwave; sort of industrial, electronic, punk. Angst ridden and aggressive, yet nebulous and icy in it’s emotional exposition. Often politically or socially oriented; and usually in an irreverent manner. - Artefact, Jacno, Museum of Devotion, Pavilion 7BDrone; minimalistic, repetitive, clustered patterns sustained throughout a piece with few, if any, alterations to chord/harmonic structure. Imagine a 100′ diameter, futuristic, spherical, steel eyeball floating around a city. The sound that would make? That’s drone. - Faust, Neu!, Phil Niblock, Yoshi WadaDubstep; characterized by sub-bass frequency oscillation and warbling along with broken beats, syncopation and "the drop". If you don't like it you're obviously too old. - Skrillex, Plastician, Magnetic Man, Nero, Deadmau5, SkreamElectronicore; electronic metalcore. There. make sense? A lot of sequencing, auto-tuning and screaming. Angry and “in-your-face” lyrics and breakbeats that figuratively knock your teeth out. But sometimes literally. - Abandon All Ships, Palisades, Himwaterdragon, Fall Emotions, Eskimo CallboyElectropop; Electronic music more accepted by the masses and general public. Deep, grinding electronic tones, frequencies and breakbeats coupled with more pop-friendly vocals and lyrics. Usually fronted by a female. - Elly Jackson, Ke$ha, Lady Gaga, Demi Lovato, PerfumeGrime; sort of a dirty, wet-floor, smoke-in-the-air, acrid B.O. type of Jungle or grimey-House music. Not music that might be played in a grimey house; but House music that is also grimey. - Boy Better Know, Ghetts, Kano, Newham Generals, Ruff Squad, SkeptaHouse; a style of electronic dance music that grew from disco production and reggae beats. Don't know why it's called "House". Maybe it just sounded cool.  - Chemical Brothers, Daft Punk, MARRS, Sonique, Dirty VegasTechno; a form of EDM synthesizing funk, jazz, African rhythms and a general party-type atmosphere. This music is often directly from the future or outerspace.  - Arab Strap, Rednex, Technotronic, LeClick, Culture Beat, RozallaTrance; repetition repetition repetition. Beats between 125 and 140 with lots of repetition. Melodic themes slowly layer and build to climaxes and then, you guessed it, repeat.  - Life on Mars, Enigma, Blue States, B12, Craig Armstrong, AirTrip Hop; a more experimental style of electronic music that utilizes soul, funk, jazz, and blues forms. Sometimes danceable. Sometimes commercial. But always 100% hip-hop/ambient/soul/jazz/acid/dub/electronica. Or something...  - Moby, Bossa Nostra, Fatboy Slim, Vanja Lazarova, Seph, Electric ChairsFolk:American Roots; 1800s' pre-Country acoustic. Not as upbeat as bluegrass. More akin to Mountain ballads stemming from Irish/Scottish roots in the Appalachian Mountains of the USA.  - The Civil Wars, Mac Wiseman, Pete Seeger, The Wallin Family, Bass Mountain Boys, The Chuck Wagon GangFolk Pop; softer than folk rock. Folk music that people actually like while sober. - John Denver, Simon & Garfunkel, Don McLean, Leonard Cohen, Sonny and Cher, Partridge FamilyFolk Rock; slightly heavier than Folk Pop. Somewhat more instrument-based yet audience-friendly.  - Dave Matthews Band, Indigo Girls, Joan Osborne, Mumford & Sons, KT Tunstall, Suzanne VegaJam; 20 minute dual guitar solos while singer stands, looking at the stage floor, head-bobbing slightly using the microphone stand to keep from falling over. Best enjoyed while under the influence of some sort of psychotropic substance. If sober, turn around and watch the crowd. Usually pretty fun shows but pretty boring albums.  - The Grateful Dead, Bela Fleck & The Flecktones, Phish, Sister Hazel, The Pat McGee BandJazz:Acid Jazz; Jazz....on acid. Or with acid poured over it. I can't quite figure out which but there's definitely some form of actual acid involved and it's likely more potent than lactic or citric. Plus "acid" is a really cool word. Even cooler than "house".  - Exodus Quartet; Medeski, Martin & Wood; DJ Logic, Count Basie, Quiet Boys, RadBebop; up-tempo, exemplifying instrumental mastery while not actually showing off. Lots of improvisation and elements that leant themselves eventually to the progressive rock styles; unison melodies, shrink/grow rhythm backings, solo breaks, etc.  - Charlie Parker, Chet Baker, Dizzy Gillespie, Thelonious Monk, Bud Powell TrioBig Band; larger than a small band. Incorporating strong brass, woodwinds and dominant percussion throughout. Typically more happy and bouncy. And big.  - Squirrel Nut Zippers, Glenn Miller Orchestra, Duke Ellington, Chickenhawks, Benny GoodmanJazz Funk; more of a solid back-beat groove than other jazz styles. Makes use of synthesizers and analog tone generation. More groove than pure jazz but more jazz than pure funk.  - Wynton Marsalis, Grover Washington, The Whitefield Brothers, The Woo Woos, Entourage, Joe AugustineJazz Fusion; sort of Progressive Jazz. Fuses jazz with other styles like funk, R&B, rock, etc. "Fuse" is a cool jazzy sounding word. Almost as cool as "acid".  - Plunge, Soulive, Tom Scott, Weather Report, Manhattan Transfer, NiacinLatin Jazz; exactly that. Utilizes latin beats and rhythms along with multiple and various percussion-centric structures. Incorporates anything from Bolero to Rhumba but doesn't quite "fuse" them.....I guess.... - Acoustic Alchemy, Gare Du Nord, Yutaka, Mas Mamones, Kim Pensyl, Al Di Meola, BrasiliaRagtime; socially and chronologically bridged the gap between classical and jazz. Strong syncopated rhythms and metric patterns pulled from African-American music from the early 20th Century. Primarily piano based.  - Scott Joplin, Gene Austin, Ernest Hogan, Dorsey Brothers, Nora Bayes, Ted LewisSmooth Jazz; the music you listen to when you're winding down after a hard day of yoga classes and meditation. Relaxation akin to whale sounds and trickling rivers.  - Yellowjackets, Kenny G, Where There's Smoke, J. Spencer, Ricky Ford, Dave KozSoft Jazz; see Smooth Jazz, but softer. Imagine winding down after a day of winding down after a day of yoga classes and...... you get the picture.  - Mark Baldwin, Victor Goines, Ziggy Elfman, Eric Darken, Pat Coil, Phil WoodsTraditional Jazz; music for music's sake. The guys who originally broke the rules and continue to do so. They even broke the rules of jazz itself with their category name; since "Traditional Jazz" is itself oxymoronic.  - Dave Brubeck, Lord Buckley, Diana Krall, Al Jolson, Elmer Bernstein, Chick WebbVocal Jazz; not all scat and beedoppadoops. The voice as an instrument. Focus on virtuosity of the voice and expression through vocal timbre and fluidity. The best ones were female. Sorry, Louis.  - Nina Simone, Etta James, Louis Armstrong, Billie Holiday, Ethel Waters, Nat King ColeMetal:Avant-Garde Metal; the weird crap. The stuff that people either love or hate. Typically not as talented as the Progressive guys, but less heavy and hardcore than the pure metal guys.  - System of a Down, Faith No More, Buckethead, King Crimson, Sikth, IntronautClassic Metal; where it all started. The first down-tuned, high-action riffs building from the oppressive industrial age in mid-century Great Britain. And the need to kick ass following all that rockabilly crap. - Scorpions, Black Sabbath, Judas Priest, Iron Maiden, Dio, Rainbow, Iron Butterfly, MotörheadDark Metal: including…Black Metal; similar to death metal, but slightly more atmospheric and extreme. These guys wear skull face-paint and dress like dead demons and other scary stuff. Lo-fi recordings with tremolo guitar and screeching, wailing vocals atop fast tempos/beats and low, thrumming bass. -Aurora Borealis, Behemoth, Setherial, Satanic Slaughter, Noctuary, Watain, Ethereal WoodsDeath Metal; metal about death. Or metal that sounds like it's dying or killing. Lots of blast beats and atonalities. Fast double-bass drums and down-tuned guitars. Screaming and growling. These guys don't play too many Bar Mitzvahs. - Napalm Death, Abysmal Dawn, Mortification, Dethklok, Fleshgore, Beneath the MassacreDoom Metal; like death metal but more ominous using slower tempos and more atmospheric tones. Lyrics are typically depressing and morose and will leave you wanting to kill others; including yourself. - Thergothon, Orodruin, The Hidden Hand, Mindrot, The Obsessed, Unholy, Witchfinder GeneralGoth Metal; somewhat of a horror theme pervades this category. Often times skull makeup or zombie/vampire/werewolf themes will be prevalent. Names often include prepositions. - In This Moment, Cradle of Filth, Within Temptation, Theatre of Tragedy, Cadaveria, AgathodaimonSludge Metal; usually has a somewhat dirtier, grimier feel to it. Slower deep-tuned crunchy riffs and distortion. Sometimes screaming and growling mixed with somewhat southern rock feeling styles. Themes include pessimism, hopelessness, anger.  - Black Label Society, Rollins Band, Mastodon, Corrosion of Conformity, Haste, Soilent Green, EyehategodEmo Metal; usually pretty heavy and angst-ridden, but with some clear-voice singing and wailing throughout. Not all screams and growls like Metalcore; and sometimes no screaming or growling at all. Just sort of, “Life is tough and I’m gonna bitch about it” music - but good. -Anberlin, Good Charlotte, Motionless in White, My Chemical Romance, SkilletFusion Metal: including…Folk Metal: including…Celtic Metal; reminiscent of ancient Celtic/Irish battle music. Heavy and grinding, but with an air of ambient atmosphere and possibly pan flutes. Yes definitely pan flutes. One must paint one’s face blue and wear a loin cloth to fully appreciate this genre. - Agalloch, Cruachan, Finntroll, Eluveitie, Mael Mórdha, Geasa, SuidrakaGypsy Metal; crunchy, heavy guitars with fiddles and percussion instruments that might be found hanging in the fortune teller’s wagon of a traveling circus. Some themes get pretty heavy and mythological and really make little sense. But hey…it’s Metal. - Inspirit, Kultur Shock, Stella Arja, Tribe of Gypsies, The Crooked Fiddle BandMedieval Metal; similar to Doom Metal in that the mood is more somber and morose and oppressive. Imagine metal that’s been living in a dungeon for 650 years and has just now stepped out into the sun. Yeah. That. - Heimataerde, In Extremo, Letzte Instanz, Morgenstern, Saltatio Mortis, SkycladPagan Metal; Metal that stays true to the original pagan/wiccan image. Metal that rails against organized religion; especially monotheism. Metal that revels in worldly idolatry and basks in the indulgence of the physical. Lots of symbolism and iconography used on album covers. - Arkona, Asmergin, Finsterforst, Korpiklaani, Obtest, MoonsorrowPirate Metal; exactly what it sounds like. Swashbuckling, rum-guzzling, peg-legged, patch-eyed, hook-armed, parrot-perched ne’er-do-wells prowling the waters in wooden ships carrying gold, gems and ghosts of the sea. At least that’s what they sing about. I think in real life they’re just normal people who drive cars and pay taxes like the rest of us. - Alestorm, Blaxon Stone, Cat O’ Nine Tails, Iron Seawolf, Red Rum, Silverbones, SwashbuckleViking Metal; metal having to do with Vikings (mostly lyrically) and their respective culture. Many reminders that Vikings are likely the most "metal" culture in the history of the world. - Mortiis, Heidevolk, Hel, Turisas, Wolfchant, Grand Magus, BorknagarFunk Metal; relatively self-explanatory. Metal, with some funk. Or funk with a heavier vibe. Heavy crunchy; yet funky and danceable; grooves. slap-bass and wah-wah guitar often rear their heads. Tightly tuned snare drums and snappy bass drums with a lot of emphasis on the hi-hat; usually. -Infectious Grooves, Living Colour, Mordred, Primus, Fishbone, Mind FunkJazz Metal; metal with an air of pretense. Not as esoteric as Avant-Garde Metal and more artsy than Funk Metal. Elements of Jazz like improvisation and off-kilter chord structures prevail. -Conflux, Gru, Sithu Aye, Shining, Naked CityNeoclassical Metal; these guys would be composing for their respective local monarchs had they lived 200 years ago. This is metal with classical tendencies, but not necessarily classical instrumentation. Mostly guitar virtuosi hang out here. Their bands are typically comprised of musical over-achievers who don’t quite have what it takes to be fully progressive. -Yngwie Malmsteen, Vinnie Moore, Timmo Tolkki, Joshua Perahia, Marty FriedmanRap Metal; Pretty self-explanatory. Combines rap and metal.  - Linkin Park, P.O.D., Kid Rock, Rage Against The Machine, Papa Roach, Crazy Town, Limp BizkitSymphonic Metal; - again, pretty self-explanatory. Metal guys don't like to waste time with esoteric nomenclature like "Trip Hop" or "Bluegrass".  - After Forever, Dimmu Borgir, Blind Guardian, Nightwish, Seraphim, Interfector, AyreonGlam Metal; including…Hair Metal; all about glitz and glamour. Make-up, hair-spray, tight red leather pants and ripped-off blues riffs. I love it. So do you. Many names include animals or a reference to something white. Or both.  - Whitesnake, White Lion, Great White, Ratt, Def Leppard, Zebra, Bon Jovi, Firehouse, PoisonSleaze Metal; akin to Hair Metal, but with more grime. More about sex and drugs in the deviant and slimy way. Not really about partying, but about the actual sex and drugs. More leather and fringe than hairspray and makeup. Though you will find some hairspray. And makeup. -Billy Idol, Guns ’n’ Roses, Skid Row, Mötley Crüe, L.A. Guns, ExtremeGroove Metal; Metal with slightly more funk than pure Metal, slightly more balls than Jazz Metal and slightly more balls than pure Funk Metal. Imagine Funk Metal more laid back and less aggressive. Like….if Motown made Metal. Channel Zero, Soulfly, Tad, Fight, DevilDriver, Byzantine, Bleed From WithinIndustrial Metal; more digital sound than raw analog metal. Sometimes just one or two guys doing it all. Can become over-commercialized due to its attainability by the masses.  - Rob Zombie, Front Line Assembly, God Lives Underwater, Skinny Puppy, NIN, Filter, The Union UndergroundMetalcore; growling, screaming and yelling. Angry people reside here; somewhere between extreme metal and hardcore punk. Hey wait.....Metalpunk? no....Extrard? no.....Punkstreme? no. Metalcore! There. That works.  - SOiL, Drowning Pool, Biohazard, The Agonist, Trivium, HelmetNu Metal; guys who use digital production techniques and a more refined sound. Good hardcore stuff, but not raw and dirty. Often have numbers or present tense verbs/gerunds in their names. - 10 Years, 3 Days Grace, 30 Seconds To Mars, Breaking Benjamin, Dropping Daylight, Shinedown, Sevendust, Finger Eleven, KoЯnPower Metal; metal that combines the powerful elements of classic metal, speed metal and a bit of symphonic metal for added drama. These guys are in your face but not in a Death/Doom/Black Metal way. There’s more life and less death here. Not always happy, but driven and motivational. -Alestorm, Powerwolf, Metal Church, Iced Earth, Kamelot, HelloweenProgressive Metal; including…Classical Prog; Heavy, yet classical virtuosity runs rampant. Complex orchestrations and thematic derivatives abound. Their album covers are usually pretty Dungeons & Dragons-esque. - Adagio, Blind Guardian, Symphony X, Triumph, The Devin Townsend ProjectDjent; pretty much onomatopoeiaic. Those crunchy guitar sounds that are mimicked by Metalheads using their voices to project “DJENT DJENT DJENT DJENT….” as they mouth along with the kickass guitar riffs. - Animals As Leaders, Meshuggah, Mnemic, Periphery, Sikth, TesseracTMathcore; the guys who are more into technique than groove. Music that exhibits what a theoretical physicist’s chalkboard might sound like if transferred to aural perception. - Benea signNow, Botch, Daughters, Ion Dissonance, Psyopus, Spiral ArchitectMelodic Prog; the guys who are more about melody and tonality than about technical virtuosity. Don’t get me wrong, they’re still damn good, but they produce more memorable and catchy tunes than some other Progressive groups. - Crimson Glory, A Perfect Circle, Tool, Queensrÿche, Rhapsody of Fire, Shadow GalleryOmni Prog; the guys who can do it all. Classical, Rock, Jazz, Funk, Groove, Technique, Passion, Virtuosity, Acoustic, Electric, Slow, Fast, Flamenco, Baroque, etc. Pretty much the embodiment of “Musicians’ Bands”. - Dream Theater, Fates Warning, King’s X, Pain of Salvation, Liquid Tension Experiment, PlatypusPower Prog; virtuosity tempered with sheer power. Hard-driving beats and riffs with high-volume, in-your-face ass-kicking. - Adrenaline Mob, Frameshift, Nevermore, Orden Ogan, Ne Obliviscaris, Seventh WonderTechnical Death Metal; similar to the Mathcore guys but heavier. That’s about it. There are lots of prime numbered time signatures in this genre. - Cynic, Green Carnation, Obscura, Odious Mortem, PsycropticPunk: including…Garage Punk; early sixties punk that was raw, lo-fi, scratchy, distorted and fuzzy. Simple chords (I mean…it IS Punk…) and even simpler lyrics. - Black Lips, The Hives, The Humpers, The Mummies, TeengenerateGlam Punk; Punk railing against the status quo with high shock value. Makeup and crazy hair and facial prosthetics abound. - Cherry Vanilla, Flash Bastard, The Hot Dogs, New York Dolls, Shady Lady, Sick Six CrushHardcore; faster, more aggressive Punk. Same simple chords and song themes, but played faster and with more aggression. Usually very fast and/or aggressive. Basically…fast and aggressive Punk. With lyrical themes occasionally treated a bit more seriously for the sake of actual social commentary. - Bad Religion, Black flag, Fugazi, Sworn Enemy, Raised Fist, Social DistortionOi!; the UK scene that tried to bring Punk back to its roots and steal it back from all the spoiled, rich-kid wannabes that had started to become “punkers”. Music is raw, unproduced, natural; yet maintains an honesty that’s rare in a lot of musical styles. - Last Resort, Peter and the Test Tube Babies, Public Enemy, Street Dogs, SuperYob, Toy DollsPop Punk; music by and for the spoiled, rich-kid wannabes that had started to become “punkers”. Punk in the mainstream. The use of Punk stylings and techniques for the sake of selling albums and making money and becoming famous and rich. - American Hi-Fi, The Ataris, Green Day, OffspringPost-Punk; the evolution of Punk into a more personally stylistic and individually nuanced style. More experiementation and removal from the classic Punk traditions created a sort of Avant-Garde Punk movement which culminated in Post-Punk. - 23 Skidoo, Au Pairs, Bauhaus, Big Black, The Chills, The Cult, The StranglersProto-Punk; the ones who started it all. The original punks. The artists who originally went against the grain of the conventional Rock or Pop of their day to create what would become the Punk movement. - Iggy & The Stooges, MC5, NEU!, The Patti Smith Group, The Sonics, TelevisionPunk Rock; those groups that don’t really fit into any subgenre of Punk and just encapsulate what the common culture knows as “Punk”. - The Clash, The Jam, The Ramones, Sex Pistols, Sprung MonkeySpeed Metal; exactly that. Speed. Even the band names are so fast they only use one word.  - Helloween, Overkill, Impellitteri, Cranium, Atomkraft, Annihilator, Sodom, Kreator, GravediggerThrash Metal; the guys you likely know best. The original Bay-Area metalheads themselves. - Metallica, Megadeth, Anthrax, Sepultura, Pantera, Slayer, Metal Church, Exodus, TestamentOrchestral:Broadway; the music that's played during those plays on Broadway in NYC. - Les Miserables, Phantom of the Opera, Miss Saigon, Jesus Christ SuperstarClassical; the dominant Western music from 1750 to 1830.  - (composers) Antonin Dvořák, Claude Debussy, Franz Schubert, Hector Berlioz, Ludwig Van Beethoven, Wolfgang Mozart, Frédéric Chopin - (performers) Yo-Yo Ma, Mike Wollenberg, Lang Lang, Andre Rieu, The London Philharmonic, Woody PhillipsMovie Scores; the music that's played during those movies you watch sometimes. Either in NYC or elsewhere. - Alan Silvestri (Back to the Future, Forrest Gump); Danny Elfman (Batman, Beetlejuice, Pee-Wee's Big Adventure); James Horner (Titanic, Braveheart); John Williams (Star Wars, Indiana Jones, E.T., Jaws, Jurassic Park, Superman); Hans Zimmer (Gladiator, The Rock); Harold Faltermeyer (Beverly Hills Cop, Fletch, Top Gun)New Age; the music you listen to during your hard day of yoga classes and meditation. - Andreas Wollenweider, Jordan Rudess, Turin Brakes, Yanni, Gordon HemptonVocal; the vocal instrument applied to the rigors of Classical instrumentation - Andrea Bocelli, Josh Groban, Sarah Brightman, Luciano Pavarotti, Il Divo, Brooklyn Tabernacle ChoirPop:Adult Contemporary; a fancy name for the lame music your parents probably listened to. Mostly maudlin tunes about the lives and thoughts of privileged, white, middle-aged hipsters.  - Anne Murray, Barry Manilow, Wilson Phillips, Neil Diamond, Carly SimonBeat Pop; the British invasion of back-beat driven pop icons of the late 50s and early 60s. Most bands are "The" something.  - The Beatles, The Lovin' Spoonful, The Kingsmen, The Turtles, The Byrds, The Cuff Links, The Hollies, The Newbeats, The Left Banke, The Zombies, Gunhill RoadDance Pop; the popular music to dance to. Not as counter-culture as EDM, but slightly heavier than Bubble Gum Pop; which I didn't list as a category.  - Bananarama, Billy Ocean, Katy Perry, Lady Gaga, Debbie Gibson, EMF, Will to Power, TiffanyDisco; formed from funk, psychedelic and soul; this style rebelled against the rock music of the day in a more visceral, primal way. All about body movement, dancing and the human spectacle, it stole colorful clothing and drugs from the Hippies, up-beat driven rhythms from the Beatniks and combined them in a sexy, seductive libido-based production praising dance and expressive human life. It is currently "dead".  - ABBA, The Bee Gees, The Village People, KC & The Sunshine Band, Gloria Gaynor, Lipps Inc.Doo Wop; yet another mainstream derivative of African-American music, doo wop uses more nonsensical phrases and sounds to emphasize harmony and melody over lyrical substance. These names also are often "The" something.  - The Dominoes, The Platters, The Tune-Weavers, The Casinos, The Dreamlovers, The Passions, The Penguins, The Rivieras, The Esquires, Bob & Earl.Indie Pop; somewhat contradictory, the emphasis on self-reliance and the whole DIY perspective is exploited to assure popularity and mainstream success. But somehow it works. - The Ting Tings, Fine Young Cannibals, Nil Lara, Karry Walker, Sundays, Hang UpsLatin Pop; exactly that. Pop with better beats and more complex rhythms that actually force you to dance even if you are unwilling.  - Ricky Martin, Enrique Iglesias, Pit Bull, Shakira, Miami Sound Machine, Lou BegaPop Rock; slightly edgier pop. Or slightly more commercialized rock. Take your pick. - Fiona Apple, Jewel, Avril Lavigne, Natalie Imbruglia, Eric Carmen, Maroon 5Power Pop; high production music for the sake of performance. - Journey, Rick Springfield, Survivor, Duran Duran, Huey Lewis & The News, Go-Gos, Cutting Crew, The B52sSurf Pop; the music you listen to while watching people surf. Somehow this style became separate from other closely related similar styles and is audibly evident in every group it houses. - The Ventures, The Beach Boys, The Surfaris, Jan and Dean, The Rip-Chords, Dick DaleSynthpop; like power pop, but with the emphasis on synthesizers.  - Tears For Fears, OMD, Herbie Hancock, When In Rome, Falco, Dead or Alive, Thomas DolbyTraditional Pop; the crooners. The original pop vocalists whose reputations continue to dazzle and impress. The Rat Pack. The Vegas Lounge Lizards. No, those aren't band names. - Perry Como, Wayne Newton, Tom Jones, Bobby Vinton, Frank Sinatra, Mel TormeR&B:Alternative Hip Hop; Hip Hop that doesn't quite fit the mold of standard R&B. Somewhat left of center and progressive by R&B standards. - Outkast, Black Eyed Peas, Jurassic 5, Wu-Tang Clan, Jadakiss, N.E.R.D., Insane Clown PosseFunk; emphasis on rhythm and groove rather than melody and harmony. Chords aren't as important as the bass line underneath them or the drum beat behind them.  - The Brothers Johnson, Commodores, Kool & The Gang, George Clinton & the P-Funk All Stars, Curtis MayfieldNeo Soul; Soul, but newer. Neo is just a cool word for "new". Though not as cool as "acid". OOH!!! Acid Soul! Is that a genre?! If it isn't then it should be.  - Jamiroquai, Amy Winehouse, Beyonce, Bruno Mars, Christina Aguilera, Terence Trent d'ArbyNew Jack Swing; "Neo Jack Swing" would sound pretentious and the R&B genre is anything but pretentious. And "Acid Jack Swing" would sound like drug or sex slang. These guys combined Urban Contemporary beats and Dance Pop composition to create a very catchy sound that showcased a lot of soulful melodies and harmonies. This was "The bomb" in the late '80s and early '90s.  - Boyz II Men, Bel Biv DeVoe, En Vogue, DJ Jazzy Jeff & The Fresh Prince, New Edition, Kid 'n' Play, MC Hammer, Paula AbdulRap; talking. mostly. Though talking very well and rhyming with complex rhythms and rhyme schemes on top of looped beats and melody lines.  - Eminem, Cypress Hill, Timbaland, Snoop Dogg, Grandmaster Flash, Digital Underground, Ludacris, Beastie BoysSoul; the s%*t that makes you wanna f%*k.  - Teddy Pendergrass, The Righteous Brothers, Lionel Richie, Aaron Neville, Hall & Oates, Luther Vandross, John LegendUrban Contemporary; a combination of EDM, Reggae, Dance Pop, Soul and Rap that creates a very broad range of styles and expressions.  - Usher, Nikki Minaj, Justin Timberlake, Missy Elliott, Trey Songz, Rihanna, Ne-Yo, Flo-Rida, DrakeReggae:Dancehall; Jamaican pop that strips down Reggae to the most crucial dance vibes necessary, though it added more digital instrumentation and faster rhythms. - Leonard Dillon, Toots Hibbert, Wailing Souls, Ebony Steelband, Aswad, Big MountainDub; mostly instrumental remixes of existing Reggae recordings. - Third World, Black Uhuru, Yellowman, Sly & Robbie, Freddie McGregorRagga; primarily electronic Reggae. Slower and more laid back than Dancehall, but more produced and digitized than Roots. - Steel Pulse, Trinidad Steel Drum Band, Inner Circle, Desmond Williams, Lasana Bandelé, Joe HiggsRoots; spiritual Rastafarian expression of life and experiences. Primal, raw and unmistakably catchy. - Bob Marley & The Wailers, Greyhound, Dhaima, Crucial Vibes, Kojak & Liza, Shorty the PresidentRock:Alternative; not quite squeezed into the "Rock" definition, but not quite squeezed out of it either.  - Soul Asylum, U2, The Wallflowers, Jesus Jones, Beck, Toad the Wet SprocketAmericana; the music about the working class. The hopes and dreams of the free American people. Driving rock that you can hear in bars and stadiums alike. - Bruce Springsteen, Bryan Adams, The Traveling Wilburys, John Mellencamp, Tom Petty, John FogertyClassic Rock; the original rockers. If you haven't heard of these guys you haven't heard of Rock.  - Led Zeppelin, The Who, Steve Miller Band, Queen, Eagles, Fleetwood Mac, The Rolling Stones, The TroggsCollege Rock; rock for the sake of getting laid in college. These guys pandered to the more sensitive female audience, thereby creating the necessity for the male audience to like them as well. Typically pretty stupid and nonsensical sounding names. - Vertical Horizon, Iffy, Counting Crows, Hoobastank, Goo Goo Dolls, Fastball, Dishwalla, Hootie & The Blowfish, Matchbox 20, Emmet SwimmingDark Wave; slightly more despondent and depressed. More morose and well......dark.  - The Church, The Cure, Blue October, Depeche Mode, The Stone Roses, Joy DivisionFunk Rock; pretty self-explanatory. - Primus, Red Hot Chili Peppers, Spin Doctors, 311, Mother's Finest, Tina & The B-side MovementGrunge; these guys killed Glam Metal. But it was already beginning to show signs of weakness. This music stripped away all image and pretense and left us with guys who were just good enough at their instrument to still allow every high-school boy in America to be able to play along...... to all their pretty songs......and shoot his gun.  - Nirvana, Pearl Jam, Soundgarden, Alice In Chains, Garbage, L7, Mudhoney, Stone Temple Pilots, Local H, Love Battery, The MelvinsHard Rock; not Classic. But not Soft. Or Grungy. Just hard. Though not as hard as Metal. So maybe really hard wood or stone. Yeah that's it. Hard Rock. - Velvet Revolver, Audioslave, Midnight Oil, Pat Benatar, Billy Squier, Drivin' 'N' Cryin', LoverboyIndie Rock; rock that does it's own thing despite what the industry tells it to do. - R.E.M., Florence + The Machine, Monks Of Doom, The Connells, Cake, Juliette & The Licks, They Might Be GiantsNew Wave; more frenetic and impulsive than former rock, disco and punk. More guitar licks and rhythms that didn't just sit you down and leave you there. Somewhat electronic and experimental. Some might say, "new".  - INXS, The Police, Crowded House, Spandau Ballet, Oingo Boingo, Shiny Toy Guns, Corey HartPost-Grunge; came after grunge, and was slightly more produced than grunge, but still held on to some of that Grunge angst that made it so successful. - Stone Sour, Ugly Kid Joe, Hinder, Collective Soul, Nickelback, Flyleaf, Candlebox, GodsmackProgressive Rock: including…1970s; Progressive Rock artists of the 1970s. Pretty self-explanatory. These guys were near the birth of what is known as Progressive Rock. Some of the earliest pioneers and trailblazers of the genre.- Deep Purple, Emerson Lake & Palmer, Rush, Kansas, Jethro Tull, Frank Zappa, GenesisArt Rock; Slightly skewed but still rock. More experimental and “out there”. Costumes are common. As is make-up and characterization. -David Bowie, Peter Gabriel, David Byrne, Velvet Underground, Radiohead, Incubus, Talking HeadsCanterbury Scene; named after a bunch of improvisational dudes from Canterbury got someone’s attention. These guys shifted into and out of each other’s bands all the time. Constantly changing and altering their lineups. - Caravan, Short Wave, Supersister, In Cahoots, Gong, Egg, GilgameshPost-Progressive; the spawn of and next generation following 1970s Progressive Rock. These guys adapted to the current zeitgeist and pushed the boundaries even more than their predecessors. I mean….that IS the definition of Progressive. - Attention Deficit, Bozzio Levin Stevens, Somnambulist, Transatlantic, Dali’s Dilemma, Chroma Key, BravePsychedelic Rock (Acid Rock); quirky, drugged-out hysterical nonsense rock with a lot of outward expression against normalcy. Fun shows that led to a lot of deaths; by drug and alcohol consumption; and pregnancies......by drug and alcohol consumption.  - Big Brother & The Holding Company, The Doors, Quicksilver Messenger Service, Moody Blues, Sopwith Camel, Vanilla Fudge, DonovanRIO (Rock In Opposition); akin to the Canterbury guys I mentioned earlier, these Progressive musicians got pissed that no one was recognizing their talent and banded together against the music industry itself. Surprise: they still didn’t get very popular. - Aksak Maboul, Etron Fou Lelouban, Henry Cow, Art Bears, Stormy Six, Art ZoydPunk; the rebels who hated society and weren't afraid to let it be known. They'd bleed on stage, rip off their clothes and surf the crowd naked, dump buckets of sweat and other bodily fluids on the crowd while screaming and railing against authority and tradition. Oh and they sometimes held instruments too. - Sex Pistols, Bad Religion, Ramones, Iggy & The Stooges, The Clash, American Hi-FiRockabilly; what some call the original Rock & Roll. A combination of hillbilly and rock containing a western swing and a bouncing party vibe. With elements of piano-based Jump Blues and electric boogie woogie, it made it's mark on the music scene indelibly. Almost everyone's named contained a "Y".  - Elvis Presley, Chuck Berry, Buddy Holly, Tommy Sands, Johnny Rivers, Jerry Lee Lewis, Freddy Cannon, Chubby Checker, Little RichardSka; rock with horns. This provided all those high school kids who chose to play brass in the school band a way to be cool... For about 18 months in the late '90s.  - No Doubt, Fighting Gravity, Dispatch, Blue Meanies, Toots & The Maytals, Jack FridaySoft Rock; the rock you listen to on the radio when driving to your yoga or meditation class.  - Traffic, Glenn Frey, Linda Ronstadt, Don Henley, Kim Carnes, Gerry RaffertySouthern Rock; rock from the south. Lots of twang and rough gravelly vocals mixed with two-step rhythms that keep audiences head-bobbin' and wavin' confederate flags. When "Free Bird" is yelled at one of these shows, it will be played.  - Lynyrd Skynyrd, 38 Special, Blackfoot, Pride & Glory, Molly Hatchet, The Georgia SatellitesWorld: (please forgive my American/Euro-Centric categorizations. And please don't be offended if I've misplaced something that you feel should go elsewhere; in all the previous categories or in the following geographic generalizations. These are mostly all regional folk or traditional music of general locations named accordingly, and just those that I am familiar with and like. I know full well that many and various styles and cultures exist within the overall regions I’ve specified here.)African  - Zap Mama, Zwabesho Sibisi, Eleja Choir, Turtle Island String Quartet, Habib Koité and Bamada, Coco LeeMiddle Eastern  - Nusrat Fateh Ali Khan; Kaila Flexer; Ilhan Ersahin; Ighigou Haile; S-Tone, Inc.Asian  - Liu Huan, Yungchen Lhamo, Itsuki No Komoriuta, Bhoora Singh and Party, Hoang Vuy, Imperial Household OrchestraEastern European  - Goralska Orkestra, Stephanya G. Penchevya, Nikollë Nikprelaj, Raderman Beckerman Orchestra, Efta Botoca, Petrică PaşcaIrish/Celtic/Gaelic  - Loreena McKennitt, Michael O'Suilleabhain, The Pogues, Enya, The Chieftains, The Tannahill Weavers, WolfstoneIsland  - Sean Na'auao, Les Tamaru, Israel Kamakawiwo'ole, Andi Thakambau, Lord Composer, Kealoha KonoLatin/Hispanic  - Ruben Blades, Tu Abandono, Adam Del Monte, Brian Keane, Elvis Crespo, Los UmbrellosMediterranean  - Triki Triki, Stellákis Perpiniádhis, La Nina Del Los Peines, Márkos Vamvakáris, Effisio Melis, Marika KanaropoulouScandinavian  - Värttinä, Hållbus Totte Mattson, Arto Järvelä, Gjallarhorn, Angelit, Annbjørg Lien, Sari Kaasinen...and that's all I can think of off the top of my head.

Hello, I've find an excellent article which will solve your query. I am copy pasting it here or if you want you can go with link. The requiem for Ramsay's horror | Latest News & Updates at Daily News & Analysis The disembodied zombies of the season’s word-of-mouth-hit, Go Goa Gone, can’t but remind us of the lords of horror in India — the Ramsay brothers, who entertained and horrified millions much before special effects and lifelike props made their once-scary monsters look like something the cat dragged in. Google the name ‘Ramsay brothers’ and a listing with all possible contact numbers and email addresses of Tulsi Ramsay, one of seven siblings that made up the Ramsay Brothers, pops up everywhere.It’s clear he wants to be found. A phone call to request an interview, and there is excitement in Tulsi Ramsay’s voice. “Yes! Of course. Do you know where I live?” He calls on the day of the meeting, to confirm if the interview is still on. “Sometimes, people forget,” he says, by way of explanation. At the lobby of the high-rise Ramsay lives in (where Hema Malini, Sunny Deol, Akshay Kumar’s mother and sister also have flats, he says), teenagers fan themselves while waiting for drivers to bring cars; a struggling actor, script in his hand, talks animatedly on the phone; a bunch of nannies take kids to the pool, and a production crew steps out discussing edits. Inside his 15th floor apartment, the almost 69-year-old Tulsi Ramsay sits in a corner of his cream, brown and gold couch, nervous. Very odd for someone who’s made it his business to scare others.Introduction to cinema“Are you speaking only to me?” he asks with hesitation. “Yes.” “Oh, there was a journalist who interviewed me and then went and spoke to others,” he says. He has next to him, an old, grey plastic briefcase from which he removes a document and hands it over. It’s an introduction to his production house, and his resume. Tulsi is clearly nostalgic about the good old days, with good reason perhaps. His father Fatehchand U Ramsinghani moved to Mumbai from Karachi after Partition and started an electronics business on Lamington Road. When the industry wasn’t doing too well, he started looking at the movie business. When his second film Rustom Sohrab (1963), a historical epic, did well, Ramsay Sr decided to stay in the business.But the Ramsays really took off in the ’70s and ’80s when they churned out their signature, low-budget horror films, most of which were panned by anyone with any sense of aesthetics. But that hardly mattered — the audience the films were intended for loved it. Discovering horror Throughout the three-hour interview, one gets the sense that Tulsi knows what journalists are looking for. He almost anticipates the questions and eagerly delivers one anecdote after another.He narrates one on how he and his brothers convinced their father to produce horror films.When FU Ramsay’s third film Ek Nanhi Munni Ladki Thi (1970), starring Prithviraj Kapoor, didn’t do very well, brothers Tulsi and Shyam visited a theatre to gauge the audience’s reaction. That’s when they realised a 10 minute sequence in which Prithviraj Kapoor went to a museum to steal a dagger that belonged to his ancestors got the loudest cheers. In the scene, the actor wore an elaborate costume comprising eight inch boots, a scary mask, a cape and a furry costume inside which he was wearing an armour. “He looked just like a monster. When the police shoot at him, the bullets bounce off and people around look shocked and scared. The audience loved it,” says Tulsi. The brothers then convinced their father to focus on horror.Tulsi drops names of the famous stars who he worked with. “Shatrughan Sinha started out with us in Ek Nanni Munhi Ladki Thi. Kishore Kumar loved our films. He would have a lot of fun in recordings. Once, he came to the studio with fake vampire teeth and refused to take them off till the end of the recording. Another time, we went to his house and he refused to come out and was making scary sounds instead.” Those were the times when Rekha would visit the sets in Mahabaleshwar, where most of the films were shot. “Rekha would come just watch Kiran Kumar.They had a romance going, he was so handsome, so attractive. Now, she is still so glamorous and he is an old man,” laughs Tulsi.After the high of the ‘70s and ‘80s, Ramsay produced five shows for Zee TV. The insanely popular Zee Horror Show ran for seven years with record TRPs. But now Tulsi’s clearly hungry for another break. When he realises dna is part of the Essel Group that also owns Zee, he insists we write about his association with Zee and Subhash Chandra, chairman, Essel Group and Zee. “You must write about Subhashji and my association. He was a mastermind, I tell you. If you do, the story will go big,” he says, helpfully.At their peak Talking about the Ramsay focus on horror, Tulsi states the obvious: “It (horror) was our USP. We started it. People lapped it up. It’s what made us. There was sex, drama, songs in between the horror.” He narrates an incident in which one of their most popular films gave a big-budget Bachchan film a run for its money in the early ’80s. “Our cult film Purana Mandir released on the same day as the big budget Bachchan (Amitabh) starrer Laawaris. We were in Delhi then and we saw people lining up for our film. No one wanted to watch Laawaris. We couldn’t enter the theatre to watch our own film. Indira Gandhi was killed few days later and there was a bandh. Two days later, theatres were packed again. It was the second biggest hit of 1984,” he says. The success of their films at the time is still paying off. “It still runs our kitchens,” says Tulsi.The fall and the hunger to rise The lull came because of an overkill of Ramsay-style horror. “People overdid it. After us, several people started to make bad horror films and every channel picked up the horror show idea. The audiences got sick of it.” But has he retired yet? No, he quickly responds. “I am going to start a project in a month or so. But I won’t tell you details. People nowadays copy your ideas If I tell you now, tomorrow someone will shoot it in two days and it will be showing in a four-part series on some channel,” he says. His phone rings in between, he answers and says, “I can’t talk right now.I am in a very, very important meeting… No, no, you don’t get it. Yeh bahut zaroori hai mere liye, aap kal phone karna.” He hangs up and says: “I want to go out with a bang. I want to be remembered.” “Will you let me know when this will be out? This Sunday? I’ll buy some extra copies. Thank you for your time,” he concludes, looking relaxed for the first time in three hours.What’s in a name?Fatehchand U Ramsinghani ran an electronics store in Karachi before Independence. He was a radio engineer and foreigners who visited the store mangled his surname. “My father then realised that foreigners had a problem pronouncing Ramsinghani and changed his surname and the name of the shop to Ramsay,” says Tulsi Ramsay.Radio dealers to movie makersFU Ramsay moved to Bombay after Partition with his wife and four sons and two daughters. Three more sons were born in India. Ramsay Sr re-established his shop on Mumbai’s Lamington Road and became a dealer of the famous Murphy Radio. When the electronics business was doing badly, he decided to give the movie business a shot. He co-produced Shaheed-E-Azam Bhagat Singhin 1954. It was India’s first film on the martyr but it didn’t do too well. “India had just gained Independence and people didn’t care much about Bhagat Singh,” says Tulsi. His second film, Rustom Sohrab (1963), was a historical epic. It did well and Ramsay Sr decided to stay in the business.All in the familyIn the 1950s, to be part of a film crew, one had to be a member of the film workers’ union. “So my father decided to enroll us into the union keeping in mind our interests and talents,” says Tulsi Ramsay. Gangu was a good photographer so he was enrolled as an assistant to a cinematographer, Keshu assisted Gangu. Kiran liked music, so he got to be the sound assistant, and Kumar, “a double graduate,” was the screenwriter Shyam and Tulsi were directors and Arjun worked on edits. The crew of seven brothers were then recognised as the Ramsay Brothers.Tiffin box productions FU Ramsay wanted to train his sons in all aspects of filmmaking. So he took them to Kashmir for a workshop. “We hired a houseboat on the Jhelum and held a four-month long workshop where our father trained us in various aspects of filmmaking. We read books, discussed plots and practiced cinematography,” says Tulsi. Post the workshop, the brothers set out to do what was then unheard of in Indian Cinema. They boarded a bus with unknown actors and family members who doubled up as crew and went to Mahabaleshwar to shoot Do Gaz Zameen Ke Neeche. They lived in a government guesthouse and shot on location so they saved on the cost to put up a set.The ladies in the family cooked for the crew and helped with make-up and the costumes came from their own or the actors’ wardrobes. The film was shot in a 40-day schedule. “My father called it Tiffin Box Productions. He said jab ghar mein khana bana sakte hain, toh hotel se kyun mangayein,” says Tulsi. The film was a rage at the box office and the brothers repeated this model to make over 30 superhit films.Regards,

For almost all practical purposes, space is homogeneous and isotropic. Philip Warren AndersonBasic Notions of Condensed Matter Physics ( 1984 )Look, I am going to make a hypothesis :: Frank Wilczek is playing a massive joke on all of us, to see if we've gone collectively crazy. He is one of the great physicists of the last century. Saying the words perpetual motion machine was meant, I think, as a marketing gimmick - that worked, through the noise of Twitter and Wired. The man is a genius. He wears awesome T shirts full of math and physics wisdom and humor.. He also says funny things while also saying quite profound things. And he totally looks like what you would expect from Paul Giamatti's uncle. I made that up. As far as, I know, he is not Paul Giamatti's uncle. However, that does not mean that his papers will not lead to something incredibly awesome. Here is why.Why does spontaneous time symmetry breaking not imply a perptual motion machine?A perpetual motion machine of the first kind in common lore is a device that accomplishes more work than is put into it. A perpetual motion machine of the second kind extracts work from a thermal bath, like Maxwell's demon. Wilczek is referring to the first kind. The limiting case of the second kind was resolved in a paper on the thermodynamics of computation by Charles H. Bennett - IBM Research, where Bennett calculated the entropic cost of the erasure of memory. An analogous phenomena is persistent currents in normal metals, where non-superconducting electrons can flow through resistive metals without dissipation when their wave functions have the appropriate boundary conditions. The Jack Harris Lab at Yale did a beautiful experiment demonstrating the phenomena of persistent currents in aluminum, measuring them on silicon cantilevers through their angular mechanical signatures instead of through their magnetic signatures via SQUIDS.  Persistent Currents in Normal Metal RingsDid Jack create a time crystal? Maybe. There is a sense in which something is moving in the experiments and Jack measures that movement, persistently. But, perhaps a more correct statement would be to say that he observed a momentum crystal. Did Jack observe perpetual motion?Well, yes, sort of, but you could not power anything with it, though, because the persistence is in the ground state. None of the above involves perpetual motion, in the sense of a perpetual motion machine, of the first kind, because you cannot extract any work from the systems - they are already in their lowest energy state. Another way to think about conservation of energy and time crystals is to note, analogously, you cannot extract infinite momentum from a space crystal, even though conservation of momentum in a space crystal is not strictly conserved and only conserved under modular arithmetic - that is, mod the inverse of the lattice spacing. That is the summary. ----Here is a proposal to investigate the physics in the paper. Does an atom exist with an electronic ground state with non-zero angular momentum that is not rotationally symmetric?We know that atoms exist that have ground states - lowest energy states - that  have non-zero angular momentum, in analogy with persistent currents in  normal metals. The main difference between Jack's experiment and Wilczek's proposal is that Jack did not break rotational symmetry. As far as we know, persistent currents in normal metals actually depend on not breaking that symmetry, by extending the wavefunction of the free electron in the metal symmetrically around the ring. Think of a circle. Now, rotate the circle a bit. Looks the same. Now, put a dot on the circle. Rotate the circle a bit. Looks different. That dot can be used to track the motion precisely. But, of course, not too precisely, because their exists an uncertainty relation between measuring space and momentum. You could imagine using a different material for the ring that had interactions between the electrons appropriate and strong enough - or even tunable by a magnetic field - to produce a soliton ( the dot), or some rotational symmetry breaking, like a p wave, in the ground state. Then, you could measure the soliton or whatever moving around the ring, persistently or not. That would also be a time crystal, in the sense Wilczek defined it, just the solid state version rather than the cold atom version. The uneven distribution around the ring would create a wobble behavior, like an imbalanced spinning plate, that would certainly show up in the resonance coupling to the cantilever. The problem with localizing anything into a soliton is that you might lose the global boundary conditions necessary for the persistent current. That is the real issue here, mathematically. In the normal metal ring, the electron wave function wraps around the ring and the current is enforced by the requirement that the wavefunction be continuous where the electron meets itself on the other side. The question is whether or not you can have some stable kink as you wrap around the ring while maintaining the persistent boundary conditions. I do not know of any principle that says by creating a soliton, which itself depends on special boundary conditions, you also need to lose the boundary conditions that allow for persistent currents. If it exists, it's probably a theorem in topology, either way. We already know and observe momentum crystals, which yield perpetual or persistent motion, all the time in quantum coherent phenomena like superconductors, superfluids and coherent electron persistent motion in normal metals. If you think of a spatial crystal lattice being a system collapsing around a single spatial vector that defines the lattice, then these persistent flow quantum coherent phenomena all are momentum crystals where the system of particle collapses around a single momentum vector that defines the flow. All the electron pairs that compose a superconductor, for example, flow together with the same momentum. That crystallization in momentum space gives the superconductor the rigidity to flow without dissipation, just as a solid like copper exhibits a certain rigidity. That is, of course, relevant because the quantum mechanical model used by Wilczek is basically the same model used to describe superconductivity, macroscopically. Also interesting to note that the other mathematical models studied in the papers show striking resemble to PT symmetric quantum mechanical models of Carl Bender, if one were to complexity them by adding a complex real space variable in addition to the higher derivatives of momentum. Physics Video Archive COLLOQ_BENDERI think that is an extremely promising way to look at these models, since they are the discrete ( reflection ) symmetry versions of the proposals that want to break continuous time and spatial symmetry separately, but maintain some remaining combined symmetry. In the PT symmetric models, an extremely precise mathematical relationships is developed between systems that have balance gain and loss and systems that do not, related to the PT symmetry itself being broken or unbroken. Such systems have been realized in many experiments, quantum and classical, and have subtle and critical boundary condition relationships. Finally, PT symmetric models are deeply related to the more general CPT symmetry, which is essential for Lorentz invariance. The proposal by Wilczek is strikingly reminiscent at a schematic level of CPT Violation Experiments. By the way, I have a time crystal for you that exhibits perpetual motion and periodicity in time. Light. Photons have a well defined frequency and never rest. Speaking of light, note that though Wilczek was inspired by the Lorentz symmetry between time and space to look for time crystals, none of his models are relativistic. They cannot be, in the manner he is investigating time crystals, because all the models are non-relativistic with non-linear dispersion relations.---- FUTURE RADIO EDIT :: Almost everything below that is not referenced is pure speculation. Read for enjoyment, not for physical accuracy. All lot above this line is speculative. I am going to continue to edit and learn about this area, because it is a fascinating area of physics. I might do that in a blog, and get more detailed with the mathematics. The answer is redundant in some places and certainly incorrect or poorly written in others, but I wanted to get it up so you could enjoy and learn from pieces of it; and hopefully, explore some of the questions yourself with more powerful tools and analogies. You should also check out Carver Mead's book Collective Electrodynamics: Quantum Foundations of Electromagnetism: Carver A. Mead: 9780262133784: Amazon.com: Books because it takes as its logical foundation the following coherent quantum phenomena. 1911 Superconductivity1933 Persistent Current in Superconducting Ring1954 Maser1960 Atomic Laser1961 Quantized Flux in Superconducting Ring1962 Semiconductor Laser1980 Integer Quantum Hall Effect1981 Fractional Quantum Hall Effect1995 Bose-Einstein Condensate2009 Persistent Currents in Normal Metal Rings ----Four dimensional crystallography is a different path to investigate the idea ::Ordinary crystallography deals with regular, discrete, static arrangements in space. Of course, dynamic considerations— and thus the additional dimension of time—must be introduced when one studies the origin of crystals (since they are emergent structures) and their physical properties such as conductivity and compressibility. The space and time of the dynamics in which the crystal is embedded are assumed to be those of ordinary continuous mechanics. In this paper, we take as the starting point a spacetime crystal, that is, the spacetime structure underlying a discrete and regular dynamics. A dynamics of this kind can be viewed as a “crystalline computer.” After considering transformations that leave this structure invariant, we turn to the possible states of this crystal, that is, the discrete spacetime histories that can take place in it and how they transform under different crystal transformations. This introduction to spacetime crystallography provides the rationale for making certain definitions and addressing specific issues; presents the novel features of this approach to crystallography by analogy and by contrast with conventional crystallography; and raises issues that have no counterpart there. Tommaso ToffoliA pedestrian’s introduction to spacetime crystallography ( 2004 )Lets use the same analogy that Wilczek used to come up with the idea of time crystals by looking at spatial crystals. Here's the key analogical observation to make ::Solids spontaneously break the continuous symmetry of space down to periodic discrete symmetry, yet we cannot extract infinite momentum from them, even though momentum is not strictly conserved in the solid. Noether's theorem tells us that in mechanical and quantum mechanical systems describable by a Lagrangian, any symmetry transformation that leaves the Lagrangian invariant leads to a conservation law. Continuous time translation symmetry yields conservation of energy. Continuous space translation symmetry yield conservation of momentum. Continuous rotation translation symmetry yields conservation of energy. Sometimes, however, that symmetry is broken naturally, as in a solid state crystal. As Wilczek says, "When a physical solution of a set of equations displays less symmetry than the equations themselves, we say the symmetry is spontaneously broken by that solution." Similarly, a time crystal does not imply that we can extract infinite energy from the system even if the system spontaneously breaks the continuous symmetry of time down to periodic discrete symmetry. As Wilczek says, " ... one interesting case, that will concern us here, is of the lowest energy solutions of a time-independent,conservative, classical dynamical system. If such a solution exhibits motion, we will have broken time translation symmetry spontaneously ... Speaking broadly, what we’re looking for seems perilously close to perpetual motion." [ emphasis mine ]A crystal lattice formed by atoms in a solid is a great example of spontaneous symmetry breaking. The fundamental equations describing the dynamics of the nuclei and electrons of the atoms have continuous time, space and rotational symmetry. However, at low enough average energy ( related to temperature ), elemental atoms may form solutions to these equations that do not exhibit that full symmetry. Specifically, a solid state lattice exhibits discrete rather than continuous translation symmetry such that conversation of momentum is no longer strictly conserved, but rather only conserved modulo a specific value related to the inverse of the lattice spacing. For example ...At 2,835 degrees Kelvin, Copper atoms transition from a gas state to a liquid state. At 1,357.77 K, copper atoms will solidify naturally into a face centered cubic lattice crystal structure of the cubic crystal system. The type of lattice a particular atom will solidify into is determined by its electronic structure; however, the group theory of crystallography mandates that only, starting with the 14 Bravais lattice and keeping one point of the lattice fixed, one obtains the 32 Point groups. If the latter are combined with translations, one obtains the 230 Space groups (ascertained in 1891).  Image :: The Bauhinia blakeana flower on the Hong Kong flag has C5 symmetry; the star on each petal has D5 symmetry. A beautiful book on symmetry is The Symmetries of Things by the great mathematician John Horton Conway. What happens in a solid is that [ a ] the symmetry breaking results in a "rigidity" of the system in space and [ b ] the dynamics particles flowing through that solid - electrons or phonons, for example - only conserve momenta under modular arithmetic. What do I mean by that?The easiest way to see what is happening to conservation of momentum in a crystal that break spontaneously breaks spatial symmetry is to look at a Bloch wave, which simply describes the wave function of a particle such as an electron in any periodic potential, like that found in a solid state crystal.First, lets temporarily remove the lattice atoms completely and just analyze free space. Say you took an electron in free space and applied an electric field. The electron would accelerate and gain momentum and energy. Note that you are not creating a perpetual motion machine. The electric field comes from somewhere and you had to do work to create it. If you remove the electric field at some point, the electron will continue to move with the same momentum and energy for eternity, precisely because free space is homogeneous and isotropic. That means, if you shift free space a little in time or space, or rotate free space slightly, nothing changes about free space. It's like if you moved an infinite line a little to the left or right. It looks exactly the same. Well, a particle moving along a line is exactly the same as a line moving along a particle. Momentum conservation reduces to tautology if you think about it correctly. If something is symmetric, it does not change. If something is conserved, it does not change. By Noether's Theorem, free space being homogenous and isotropic means all physical systems conserve momentum, energy and angular momentum. Just because the particle moves forever - perpetually - after you've removed the electric field does not make it a perpetual motion machine, either. It's actually just Newton's first law of motion, dressed up in a little more sophistication. Now, lets put the face centered cubic arrangement of atoms of copper, or whatever, and assume they fill all of the universe. A giant block of solid copper. Now, apply an electric field. Remember again that we had to create the electric field, so we are putting work into the system. For those in the know, I am about to describe Bloch oscillations, which clearly demonstrate the modular arithmetic of momenta in solid state crystals. As you apply an electric field on the electron in the copper lattice, the momentum of the electron increases. However, the crystal lattice structure puts an upper limit on the momenta that is the inverse of the lattice spacing. Lets say in appropriate units that upper limit is 12. After applying the extremely weak electric field for 1 hour, the momentum of the electron is now 1; and so on. Now imagine the clock you are using to measure time. When you signNow 12, you start back again at zero. That's modular arithmetic. And that's what happens to momentum in a solid. Actually, a better way to think of the clock is starting at minus 6 at the bottom, zero at the top and plus six approaching the bottom clockwise. The momentum of a particle in a solid literally goes from plus six to minus six instantly due to the symmetry breaking of the lattice. That is because momentum is only conserved mod 12. So, plus and minus six are equivalent. However, there is absolutely no way to exploit that momentum jump to extract infinite momentum outside the solid because from the perspective of the lattice plus and minus 6 are smoothly connected in momentum space, which takes the shape of a 3-torus for a cubic lattice. ( By the way, a circle is a 1-torus and a torus is a 2-torus. )That is, you cannot simply apply an electron field to silicon and copper and extract infinite momentum in a perpetual motion machine. Intel and Samsung would have a field day with that, if you could, and your Apple iPhone would power your city. What you can do is interpret the seemingly large momentum shift as an interference scattering effect of the electron wave function off the periodic lattice, recalling that on the atomic scale, electron dynamics behave according the quantum mechanical wave equations. And, of course, the lattice nuclei are much much heavier than the electrons, so the electrons hitting the lattice is like a ball bouncing off a wall. Modular arithmetic is extremely useful and powerful in number theory. For me, it's fascinating to see it arise in quantum mechanics as a result of discrete symmetry in Bloch waves. Now, lets play some games here.Ironically, the relativistic notion of mixing time and space through Lorentz transformation was used as a motivation for the work. However, the theory of special relativity requires a linear relationship between energy and momentum. That allows linear transformations between energy and momentum to occur and allows energy and momentum to be combined into a single, highly compact energy-momentum four vector. At low energy, you can expand out any relativistic equation with the speed of light in the denominator of any terms and extract non-relativistic physics by ignoring those terms, since their effect will be very small. What you end up with is a relationships between energy and momentum that is parabolic rather than linear, if no interactions between particles or other objects in the theory add any further complexity. The papers take as a starting point a relationship between energy and momentum - a dispersion relation - that is both non-linear, as noted, and exhibits a cusp singularity. The dispersion relation looks a swallow's tail, like the shape of the swallowtail butterfly in the images above at the beginning of the answer. The curve shows a crossing where the body of the butterfly rests. They have a parabolic term and a quartic term. Guess what the dispersion relation of Bloch waves are?The cosine function. The cosine function is non-linear and periodic. Guess what the first two terms Taylor series expansion of a cosine function yields up to an overall constant?A parabolic with a negative coefficient and a quartic term with a positive coefficient. The same form as in Wiczek's papers. Guess how you get from electric field to magnetic fields in electromagnetism? Lorentz transformations. The basis of the spacetime physics that inspired Wilczek to write his papers. And note that the primary example used in his papers is a particle oscillating around a circular lattice in a weak magnetic field. I am playing with the idea that Wilczek "discovered" the "time version" of Bloch oscillations. And, just as Bloch waves in a solid ( aka a "space crystal" ) do not violate conservation of momentum in a manner that enables a perpetual motion machine, Wilczek waves in a "time crystal" do not violate conservation of energy in a manner that enables a perpetual motion machine. I do not even think it's appropriate to call them the time version, in the experiment being proposed in cold atoms. The appropriate name for the experiment being proposed would be magnetic Bloch oscillations. A space-time crystal actually implies that the lattice atoms disappear for a well-defined time step; just as in a space crystal, matter disappears for a well defined spatial step called the lattice spacing in a well defined crystallographic arrangement. Have we found a system that breaks continuous time translation symmetry such that matter blinks in and out of existence periodically? I do not think we have. That would be a true time crystal, in my mind.That system would require a quantum field that oscillates in time between a ground state with a mass gap and a ground state that is gapless. Such a system would also not allow you to build a perpetual motion machine, even though it violates conservation of matter and energy.That is, you could not extract energy by coherently scattering from a time crystal just as you cannot extract momentum by coherent scattering off a space crystal. Furthermore, given the analogy with Bloch oscillations, which is nearly mathematically equivalent to the example used by Wilczek, a system that exhibits periodic motion in the ground state is not actually that surprising. Actually, it turns out that what Wilczek is saying is even less surprising when you think about superconductivity in the right way. Superconductors are essentially crystals in momentum space. Just as atoms condense to a specific spatial lattice vector in solids that are "rigid," electron pairs condense to a specific momentum lattice vector in superconductors, yielding persistent currents that are, in their own way, "rigid." That observation is, in fact, how London developed his London equations of superconductors. A superconducting condensate exhibits a persistent current because the condensate collapses to a momentum vector, which implies motion. That motion may be angular, around a ring and periodic with a magnetic field. So, not only is Wilczek simply describing the magnetic version of Bloch oscillations in his papers; he is also simply describing the persistent currents of superconductors. The requirement he posits to break a cylindrical spatial symmetry of a persistent current condensate in order to then break time symmetry by making the motion in the ground state more salient does not actually make any difference. In non relativistic quantum mechanics, we have real space and momentum space, which are simply related by Fourier transforms. The reason you cannot isolate the location of a superconductor condensate is because the Fourier transform of a single momentum vector is completely and evenly spread out in real space. Conversely, in a solid state lattice, the momentum distribution is relatively spread out. If you want to create a time crystal in the sense Wilczek is after, you have to be in the relativistic regime. However, to be in the relativistic regime, you need a linear dispersion relation. But, the only way that you can create a time crystal in the way Wilczek wants to is by being in a highly non-linear, non-relativistic regime.  What would be interesting is if someone could describe and experimentally realize a state that naturally interpolated back and forth between a solid ground state, collapsed on a spatial vector, and a superconducting ground state, collapsed on a momentum vector, in a closed, non-relativistic quantum mechanical system that was both naturally conservative and time independent.You could then watch the momentum and space vectors of the state collapses and expand, periodically in time.  It actually turns out that someone has done that, in a sense,Greiner - Mott Insulator to Superfluid transitionbut that transition was still driven rather than occurring naturally in a conservative, time independent system. Perpetual motion machines are out. Time crystals have not been created. What specifically is going on in the time crystal papers that is interesting?The basic mathematical problem that arises in Wilczek's papers is that the energy is multivalued in the momentum. That, actually, is a fascinating area of physics. There is, I should mention, an entire book on multivalued quantum fields ::Multivalued Fields: In Condensed Matter, Electromagnetism, and Gravitation: Hagen Kleinert: 9789812791719: Amazon.com: Booksbut, I have not yet read it. I've been meaning to for a while. Any book with a Riemann surface on the cover with detailed mathematical descriptions of superconductors and gravity in the interior should be read by people like me.So, I will, now, within the decade. In fact, the quantum mechanical equation to be solved is the non-linear, non-relativistic Schrödinger equation that is used in Ginzburg–Landau theory to describe the Cooper pair condensate in superconductors in a single wavefunction. The non-linearity of the theory results from the emergent physics of superconductivity and leads to topological objects like flux vortices, as discovered by Alexei Alexeyevich Abrikosov. The theory includes a momentum term that is parabolic and a momentum term that is quartic when related to energy. The mathematical qualities of the coefficients of these terms matter greatly. The non-linear theory is emergent because it evolves via a process of renormalization from a completely linear quantum mechanical theory of electrons interacting with each other via repulsive Coloumb forces and with phonons - excitations of the underlying solid state lattice. At low enough temperatures, the interactions between the electrons and the phonons effectively switch the interactions between the electrons to be attractive rather than repulsive. The electrons pair up to form bound states that are bosons, the electromagnetic field mediating the interaction between electrons attains a mass gap and the boson condense into a collective state describable by the theory mentioned above. Topologically, Wilczek's swallowtail curve looks like the curve on the cover of the book Elliptic Tales: Avner Ash, Robert Gross: Amazon.com: Kindle Store. It's very similar to the curves found in Jack Huizenga's answer ::Given two low-degree polynomials defined on the integers, how can one find the integers which are in the range of both polynomials?In that answer, Jack gives a procedure for analyzing the intersection of two curves :: complexify, projectify ( to infinity and beyond), and normalize ( that is, smooth over the singularities).You might immediately object to apply anything like that procedure to analyzing a Hamiltonian system. If you are a physicist you know that the Hamiltonian of a quantum system must be Hermitian - that is, both real and probability conserving. However, as Carl Bender shows us in [quant-ph/9809072] PT-Symmetric Quantum Mechanics, we can relax that mathematical condition and replace it with a physical condition of PT symmetry and find some interesting results. The PT symmetry physical condition relaxes the constraint that the Hamiltonian is real; for example, [math] H = p^2 + i x^3 [/math]is PT symmetric, but obviously not Hermitian since it is complex. That is a hugely powerful constraint to relax and opens up an entire new world of mathematics to explore. You can actually see the mathematics that Bender is revealing to us in any power of the momentum. That is, he already solved Wilczek's problem, by the process - complexify, projectify, normalize. That work started with something known as the Yang Lee edge singularity. I do not know what that is, yet. Why do I care?Wilczek's class on topological quantum physics at MIT was by far my favorite course while I was in graduate school at Harvard. I wrote a paper on trying to extend Alexei Kitaev's K-theory classification in [0901.2686] Periodic table for topological insulators and superconductors to strongly interacting topological condensed matter systems using the success of the Seiberg–Witten invariants that survive strong coupling in supersymmetric QCD as a guide, which can be embedded in string theory [hep-th/9611190] Introduction to Seiberg-Witten Theory and its Stringy Origin. What Seiberg Witten theory describes is the electromagnetic dual of a superconductor. In fact, it describes a condensation of magnetic monopoles that allow electric flux tubes to form as a simplified model of QCD, as opposed to the condensation of electron ( pairs ) that allow magnetic flux tubes to form in a real superconductor. The face they used complex curve theory to solve their equations always fascinated me. Why?I wanted to somehow use the idea of a coobordism to track how the structure of the theory evolved under the tuning of the interaction strength; and, to show that certain invariant quantities survived that the tuning of the interaction strength in the topological electronic systems. The topological invariants would tell you if two different topological phases were connected through a strongly interacting regime, which would otherwise be hidden you by traditional analytic calculations involving an expansion in a small parameter. Seiberg-Witten theory is one of the few strongly interacting theories that is completely soluble, due to the strong supersymmetry in the theory. My paper completely failed to do that. He still gave me an "A" in the class, though everything I said was complete nonsense. I think he is returning the favor to the rest of us now. Kitaev later wrote a paper accomplishing what I had hoped to accomplish in [0904.2197] The effects of interactions on the topological classification of free fermion systems. Actually, that paper only identified a problem in the previous classification with small interactions. But, the problem of understanding topological phases still remains largely a mystery, though recent progress was made by Xiao-Gang Wen, now at the Perimeter Institute, in his paper [1106.4772] Symmetry protected topological orders and the group cohomology of their symmetry group. That's important because, from everything we know about M / string theory and topological quantum field theory ( which by the way has no dynamics and a Hamiltonian of zero ) understanding black holes and quantum gravity requires a deep understanding of topological phases. Wilczek's analysis showing up in the news gave me a different idea, one related to my M theory ideas here ::What do theoretical physicists think of Mark Morales' answer about M-theory?Whatever the case, I cannot wait to see someone create a Calabi Yau manifold in their laboratory hologram.Postscript :: If you followed my link above, you'll see that I proposed a general shift in mathematical approach to M theory. Along those lines, I found a good introduction to Elliptic Curves and Cryptography from Josh Alman ::Good introduction to elliptic curves?

Edit: I wrote this answer for “must have Android apps” but these are same apps which have changed the way I used to live my life. Each and every App has helped me in one or the other way. I hope you will also find them helpful and a bit life changing. So here is the list: 10. Psiphon For those who use WiFi with proxy settings. So Psiphon bypasses and tunnel the websites or app through a different IP Address. 9. Mirror It's a simple app to record your mobile screen. Based on the concept of CamStudio in PC where you can record your screen, Mirror offers recording of your Mobile screen. 8. NTES- National Train Enquiry System If you are from India and you want to know the running status, cancelled train (partial or fully), Live Station and other features, this App is a must have. 7. VOLT Simple but effective for those who want to learn new vocabulary. That's too obvious, then why not others? Coz here you get the “memory key” which helps you relate the words and easier to remember them. 6. Parchi It a note making app. But here’s a catch. You can view, review, edit and add right from your lockscreen without need to open the app. Isn't that amazing! I personally find this app very useful. 5. edX If you are student or a learner who wants learn something new everyday, and cannot afford to go in the prestigious institutions like MIT, Harvard University, Cambridge, IITM, etc ten it is a must have app. Enroll yourself in any course and Bazinga!! You are ready to learn from the most amazing professors. Similar to edX, we have Coursera. 4. Walnut Manage your expenses on your finger tips. Its easier then that. It shows you your monthly expenditure, ATM locations, bill remainders and many more features. Its a must have app. 3. CamScanner Everyone doesn’t own a scanner but most of us have camera. So click the pic, upload to CamScanner and voila you are done. You have the scanned copy of your documents, notes, Marksheet and upload them on your DigiLocker. 2. inshorts Till now you all must be knowing this app. The tagline is also simple “News in 60 words” and trust me it is worth having. In this “I don't have time” world, you need news to be fast and accurate so here it is. 1. DigiLocker If you have this app then you don’t need to carry your personal documents like driving license, Adhar card, voter ID card, or even your Marksheets. Keep them safe in actual locker and leave the rest to your DigiLocker. And the best part is that it is acceptable as the original ones at every governmental or non governmental institution because it is developed under Digital India initiative. That's it for the day. Thank you and Enjoy !!! Update 1: Today I came across two new apps which I found useful. Hope it would help you all. 1.Forest : Stay focused Features • A self-motivated and interesting way to help you beat phone addiction • Stay focused and get more things done • Share your forest and compete with friends • Track your history in a simple and pleasant way • Earn reward and unlock more tree species • Customize your whitelist : Leaving Forest and using apps in whitelist won’t kill your tree. 2. Swachh Bharat Toilet Locator Swachh Bharat Toilet Locator is specifically useful for Indians who're committed for Swachh Bharat. Update 2: So I am back with yet another interesting app for you all. And trust me it is worth hanving. You are bored just go through it and kaboooom !!! You are into a black hole. Enjoy the ride. 3. Curiosity It is the latest app I installed but got addicted to it. It’s exactly works like its name, generates a curiosity which inturn increases your knowledge. It covers a large field of scope from Humanity to science to faith and many more. This app deserves more snapshots but why to increase the length of my answer. Comment below if you think the list should be updated? Thank you.