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[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…

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.

"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.

The Information Technology Act, 2000 came into force on 17.10.2000 vide G.S.R No. 788(E) dated 17.10.2000 and for the first time, a legal definition of “Computer”, “Data”, “electronic record”, “Information” et al were provided. The said Act gave a legal recognition to the electronic records and digital signatures and in Chapter IX thereof provided for penalty and adjudication. Section 43 of the Act interalia provided that in case of unauthorised access, download or copying or damage to data etc, the person responsible shall be liable to pay damages by way of compensation not exceeding one crore rupees to the person affected.Apart from civil liability provided under Section 43, Chapter XI (Sections 63 to 78) of the Act of 2000 provided for criminal liability in cases of Tampering, Hacking, publishing or transmitting obscene material, misrepresentation etc. Apart from the same, Section 72 of the Act provided for penalty in case of bsignNow of confidentiality and privacy and laid that in case any person who has secured access to any electronic record, Data or information, discloses the same to any other person without obtaining the consent of the person concerned, he shall be punished with imprisonment upto two years or with fine upto Rupees one lakh or with both.However, the provisions of the Information Technology Act, 2000 were not adequate and the need for more stringent data protection measures were felt, the Information Technology (Amendment) Act, 2008 was enacted which came into force on 27.10.2009. The said Amendment Act brought in the concepts like cyber security in the statute book and widened the scope of digital signatures by replacing the words “electronic signature”. The amendment act also provided for secure electronic signatures and enjoined the central government to prescribe security procedures and practices for securing electronic records and signatures (Sections 15-16) The amendment Act also removed the cap of Rupees One Crore as earlier provided under Section 43 for damage to computer and computer systems and for unauthorised downloading/ copying of data. The said Amendment Act also introduced Section 43A which provides for compensation to be paid in case a body corporate fails to protect the data. Section 46 of the Act prescribes that the person affected has to approach the adjudicating officer appointed under Section 46 of the Act in case the claim for injury or damage does not exceed Rupees Five crores and the civil court in case, the claim exceeds Rupees Five crores. The amendment act also brought/ introduced several new provisions which provide for offenses such as identity theft, receiving stolen computer resource/ device, cheating, violation of privacy, cyber terrorism, pornography (Section 66A-F & 67A-C). The amendment act also brought in provisions directing intermediaries to protect the data/information and penalty has been prescribed for disclosure of information of information in bsignNow of lawful contract (Section 72A)With the enactment of the Amendment Act of 2008, India for the first time got statutory provisions dealing with data protection. However, as the ingredients of “sensitive personal data and information” as well as the “reasonable security practices and procedures” were yet to be prescribed by the Central Government, the Ministry of Communications and Information Technology vide Notification No. GSR 313 (E) dated 11th April 2011 made the Information Technology (Reasonable Security Practices and Procedures and Sensitive Personal Data or Information ) Rules, 2011 (the said rules). Rule 3 of the said rules defines personal sensitive data or information and provides that the same may include information relating to password, financial information such as bank account or credit card details, health condition, medical records etc. Rule 4 enjoins every body corporate which receives or deals with information to provide a privacy policy. Rule 5 prescribes that every body corporate shall obtain consent in writing from the provider of the sensitive information regarding purpose of usage before collection of such information and such body corporate will not collect such information unless it is collected for a lawful purpose connected with the function or activity of such body corporate and collection of such information or data is necessary and once such data is collected, it shall not be retained for a period longer than what is required. Rule 6 provides that disclosure of the information to any third party shall require prior permission from the provider unless such disclosure has been agreed to in the contract between the body corporate and the provider or where the disclosure is necessary for compliance of a legal obligation. The Body corporate has been barred to publish sensitive information and the third parties receiving such information have been barred to disclose it further. Rule 7 lays down that the body corporate may transfer such information to any other body corporate or person in India or outside, that ensure the same level of data protection and such transfer will be allowed only if it is necessary for performance of lawful contract between the body corporate and provider of information or where the provider has consented for data transfer. Rule 8 of the said rules further provide reasonable security practises and procedures and lays down that international standard IS/ISO/IEC 27001 on “Information Technology- Security Techniques- Information Security Management System- requirements “ would be one such standard.The Ministry of Communication and Information Technology further issued a press note dated 24th August 2011 and clarified that the said rules are applicable to the body corporate or any person located within India. The press note further provides that any body corporate providing services relating to collection or handling of sensitive personal data or information under contractual obligation with any other legal entity located within India or outside is not subject to requirements of Rules 5 &6 as mentioned hereinabove. A body corporate providing services to the provider of information under a contractual obligation directly with them however has to comply with Rules 5 &6. The said press note also clarifies that privacy policy mentioned in Rule 4 relates to the body corporate and is not with respect to any particular obligation under the contract. The press note at the end provides that the consent mentioned in Rule 5 includes consent given by any mode of electronic communication.Data Protection relates to issues relating to the collection, storage, accuracy and use of data provided by net users in the use of the World Wide Web. Visitors to any website want their privacy rights to be respected when they engage in e-Commerce. It is part of the confidence-creating role that successful e-Commerce businesses have to convey to the consumer. If industry doesn't make sure it's guarding the privacy of the data it collects, it will be the responsibility of the government and it's their obligation to enact legislation.Any transaction between two or more parties involves an exchange of essential information between the parties. Technological developments have enabled transactions by electronic means. Any such information/data collected by the parties should be used only for the specific purposes for which they were collected. The need arose, to create rights for those who have their data stored and create responsibilities for those who collect, store and process such data. The law relating to the creation of such rights and responsibilities may be referred to as ‘data protection’ law.The world’s first computer specific statute was enacted in the form of a Data Protection Act, in the German state of Hesse, in 1970.The misuse of records under the Nazi regime had raised concerns among the public about the use of computers to store and process large amounts of personal data.The Data Protection Act sought to heal such memories of misuse of information. A different rationale for the introduction of data protection legislation can be seen in the case of Sweden which introduced the first national statute in 1973.Here, data protection was seen as fitting naturally into a two hundred year old system of freedom of information with the concept of subject access (such a right allows an individual to find out what information is held about him) being identified as one of the most important aspects of the legislation.In 1995, the European Union adopted its Directive (95/46/EC) of the European Parliament and of the Council of 24 October 1995 on the protection of individuals with regard to the processing of personal data and on the free movement of such data (hereinafter, the Directive), establishing a detailed privacy regulatory structure. The Directive is specific on the requirements for the transfer of data. It sets down the principles regarding the transfer of data to third countries and states that personal data of EU nationals cannot be sent to countries that do not meet the EU “adequacy” standards with respect to privacy.In order to meet the EU “adequacy” standards, US developed a ‘Safe Harbour’ framework, according to which the US Department of Commerce would maintain a list of US companies that have self-certified to the safe harbor framework. An EU organization can ensure that it is sending information to a U.S. organization participating in the safe harbor by viewing the public list of safe harbor organizations posted on the official website.Data protection has emerged as an important reaction to the development of information technology. In India data protection is covered under the Information Technology Act, 2000 (hereinafter, the Act). The Act defines ‘data’ as, “‘data’ means a representation of information, knowledge, facts, concepts or instructions which are being prepared or have been prepared in a formalized manner, and is intended to be processed, is being processed or has been processed in a computer system or computer network, and may be in any form (including computer printouts magnetic or optical storage media, punched cards, punched tapes) or stored internally in the memory of the computer”. Protection of such data and privacy are covered under specific provisions in the Act. In the recent past, the need for data protection laws has been felt to cater to various needs. The following analyses the position of data protection law with respect to some of the needs.Data Protection Law In Respect of Information Technology Enabled Services (ITES)India started liberalizing its economy in the 1990’s and since then a huge upsurge in the IT business process outsourcing may be witnessed. Financial, educational, legal, marketing, healthcare, telecommunication, banking etc are only some of the services being outsourced into India. This upsurge of outsourcing of ITES into India in the recent past may be attributed to the large English-speaking unemployed populace, cheap labour, enterprising and hardworking nature of the people etc. Statistics have shown that the outsourcing industry is one of the biggest sources of employment. In a span of four years, the number of people working in call centers in the country supporting international industries has risen from 42,000 to 3,50,000. Exports were worth $5.2 billion in 2004-2005 and are expected to grow over 40% this fiscal year. US is currently the biggest investor in Indian ITES, taking advantage of cheap labour costs. Statistics indicate that software engineers with two-years experience in India are being paid about 1/5th of an equivalent US employee.Concerns about adequacy of lawBPO FraudsWith globalization and increasing BPO industry in India, protection of data warrants legislation. There are reasons for this. Every individual consumer of the BPO Industry would expect different levels of privacy from the employees who handle personal data. But there have been situations in the recent past where employees or systems have given away the personal information of customers to third parties without prior consent. So other countries providing BPO business to India expect the Indian government and BPO organizations to take measures for data protection. Countries with data protection law have guidelines that call for data protection law in the country with whom they are transacting.For instance, in, the European Union countries according to the latest guidelines, they will cease to part with data, which are considered the subject matter of protection to any third country unless such other country has a similar law on data protection. One of the essential features of any data protection law would be to prevent the flow of data to non-complying countries and such a provision when implemented may result in a loss of "Data Processing" business to some of the Indian companies.In the recent past, concerns have been raised both within the country as well as by customers abroad regarding the adequacy of data protection and privacy laws in the country. A few incidents have questioned the Indian data protection and privacy standards and have left the outsourcing industry embarrassed. In June 2005, ‘The Sun’ newspaper claimed that one of its journalists bought personal details including passwords, addresses and passport data from a Delhi IT worker for £4.25 each. Earlier BPO frauds in India include New York-based Citibank accounts being looted from a BPO in Pune and a call-center employee in Bangalore peddling credit card information to fraudsters who stole US$398,000 from British bank accounts.UK's Channel 4 TV station ran broadcast footage of a sting operation exposing middlemen hawking the financial data of 200,000 UK citizens. The documentary has prompted Britain's Information Commissioner's Office to examine the security of personal financial data at Indian call centers.In the absence of data protection laws, the kind of work that would be outsourced to India in the future would be limited. The effect of this can be very well seen in the health-care BPO business, which is estimated to be worth close to $45 billion. Lack of data protection laws have left Indian BPO outfits still stagnating in the lower end of the value chain, doing work like billing, insurance claims processing and of course transcription. Besides healthcare, players in the retail financial sector are also affected. Financial offshoring from banks is limited because of statutory compliance requirements and data privacy laws protecting sensitive financial information in accounts. In the Human Resource (HR) domain, there are many restrictions on sharing of personal information. In the medical domain, patient history needs to be protected. In credit card transactions, identity theft could be an issue and needs to be protected. Companies in the banking, financial services and insurance (BFSI) sector and healthcare have excluded applications/processes which use sensitive information from their portfolio for offshoring till they are comfortable about the data protection laws prevalent in the supplier country.Since there is lack of data protection laws in India, Indian BPO outfits are trying to deal with the issue by attempting to adhere to major US and European regulations. MNCs have to comply with foreign Regulations so that they don’t lose on their international partners. There are problems involved in this. Efforts by individual companies may not count for much if companies rule out India as a BPO destination in the first place in the absence of data protection law.Today, the largest portion of BPO work coming to India is low-end call centre and data processing work. If India has to exploit the full potential of the outsourcing opportunity, then we have to move up the value chain. Outsourced work in Intellectual Property Rights (IPR)-intensive areas such as clinical research, engineering design and legal research is the way ahead for Indian BPO companies. The move up the value chain cannot happen without stringent laws. Further, weak laws would act as deterrents for FDI, global business and the establishment of research and development parks in the pharmaceutical industry.Looking to the above scenario, we can say that for India to achieve heights in BPO industry stringent laws for data protection and intellectual property rights have to be made. . Thus, a law on data protection on India must address the following Constitutional issues on a "priority basis" before any statutory enactment procedure is set into motion:(1) Privacy rights of interested persons in real space and cyber space.(2) Mandates of freedom of information U/A 19 (1) (a).(3) Mandates of right to know of people at large U/A 21.Once the data protection rules are enforced in India, companies outsourcing to India are unlikely to dismantle the systems they have in place straightaway, and move data more freely to India. Hence ,the need for data protection laws would win over the confidence of international business partners; protect abuse of information; protection of privacy and personal rights of individuals would be ensured; there would be more FDI inflows, global business and the establishment of research and development parks in the pharmaceutical industry & impetus to the sector of e-Commerce at national and international levels would be provided.Data protection law in India (Present status):-Data Protection law in India is included in the Act under specific provisions. Both civil and criminal liabilities are imposed for violation of data protection.(1) Section 43 deals with penalties for damage to computer, computer system etc.(2) Section 65 deals with tampering with computer source documents.(3) Section 66 deals with hacking with computer system.(4) Section 72 deals with penalty for bsignNow of confidentiality and privacy. Call centers can be included in the definition of ‘intermediary’and a ‘network service provider’ and can be penalized under this section.These developments have put the Indian government under pressure to enact more stringent data protection laws in the country in order to protect the lucrative Indian outsourcing industry. In order to use IT as a tool for socio-economic development, employment generation and to consolidate India’s position as a major player in the IT sector,amendments to the IT Act, 2000 have been approved by the cabinet and are due to be tabled in the winter session of the Parliament.Proposed amendments:-The amendments relate to the following[22]:(i) Proposal at Sec. 43 (2) related to handling of sensitive personal data or information with reasonable security practices and procedures.(ii) Gradation of severity of computer related offences under Section 66, committed dishonestly or fraudulently and punishment thereof.(iii) Proposed additional Section 72 (2) for bsignNow of confidentiality with intent to cause injury to a subscriber.It is hoped that these amendments will strengthen the law to suffice the need.Data Protection Laws In Order To Invite ‘Data Controllers’.There has been a strong opinion that if India strengthens its data protection law, it can attract multi-national corporations to India. India can be home to such corporations than a mere supplier of services.In fact, there is an argument that the EU’s data protection law is sufficient to protect the privacy of its people and thus lack of strong protection under Indian law is not a hindrance to the outsourcing industry. To enumerate, consider a company established in EU (called the ‘data controller’) and the supplier of call center services (‘data processor’) in India. If the data processor makes any mistake in the processing of personal data or there are instances of data theft, then the data controller in the EU can be made liable for the consequences. The Indian data processor is not in control of personal data and can only process data under the instructions of the data controller. Thus if a person in EU wants to exercise rights of access and retrieve personal data, the data controller has to retrieve it from the data processor, irrespective of where the data processor is located. Thus a strong data protection law is needed not only to reinforce the image of the Indian outsourcing industry but also to invite multi-national corporations to establish their corporate offices here.Data Protection And TelemarketingIndia is faced with a new phenomenon-telemarketing. This is facilitated, to a large extent, by the widespread use of mobile telephones. Telemarketing executives, now said to be available for as low as US $70 per month, process information about individuals for direct marketing. This interrupts the peace of an individual and conduct of work. There is a violation of privacy caused by such calls who, on behalf of banks, mobile phone companies, financial institutions etc. offer various schemes. The right to privacy has been read into Article 21, Constitution of India, but this has not afforded enough protection. A PIL against several banks and mobile phone service providers is pending before the Supreme Court alleging inter alia that the right to privacy has been infringed.The EC Directive confers certain rights on the people and this includes the right to prevent processing for direct marketing. Thus, a data controller is required not to process information about individuals for direct marketing if an individual asks them not to. So individuals have the right to stop unwanted marketing offers. It would be highly beneficial that data protection law in India also includes such a right to prevent unsolicited marketing offers and protect the privacy of the people.Data Protection With Regard To Governance And PeopleThe Preamble to the Act specifies that, the IT Act 2000, inter alia, will facilitate electronic filing of documents with the Government agencies. It seeks to promote efficient delivery of Government services by means of reliable electronic records. Stringent data protection laws will thus help the Government to protect the interests of its people.Data protection law is necessary to provide protection to the privacy rights of people and to hold cyber criminals responsible for their wrongful acts. Data protection law is not about keeping personal information secret. It is about creating a trusted framework for collection, exchange and use of personal data in commercial and governmental contexts. It is to permit and facilitate the commercial and governmental use of personal data.The Data Security Council of India (DSCI) and Department of Information Technology(DIT) must also rejuvenate its efforts in this regard on the similar lines. However, the best solution can come from good legislative provisions along with suitable public and employee awareness. It is high time that we must pay attention to Data Security in India. Cyber Security in India is missing and the same requires rejuvenation. When even PMO's cyber security is compromised for many months we must at least now wake up. Data bsignNowes and cyber crimes in India cannot be reduced until we make strong cyber laws. We cannot do so by mere declaring a cat as a tiger. Cyber law of India must also be supported by sound cyber security and effective cyber forensics.Indian companies in the IT and BPO sectors handle and have access to all kinds of sensitive and personal data of individuals across the world, including their credit card details, financial information and even their medical history. These Companies store confidential data and information in electronic form and this could be vulnerable in the hands of their employees. It is often misused by unsurplous elements among them. There have been instances of security bsignNowes and data leakages in high profile Indian companies. The recent incidents of data thefts in the BPO industry have raised concerns about data privacy.There is no express legislation in India dealing with data protection. Although the Personal Data Protection Bill was introduced in Parliament in 2006, it is yet to see the light of day. The bill seems to proceed on the general framework of the European Union Data Privacy Directive, 1996. It follows a comprehensive model with the bill aiming to govern the collection, processing and distribution of personal data. It is important to note that the applicability of the bill is limited to ‘personal data’ as defined in Clause 2 of the bill.The bill applies both to government as well as private enterprises engaged in data functions. There is a provision for the appointment of, “Data Controllers”, who have general superintendence and adjudicatory jurisdiction over subjects covered by the bill. It also provides that penal sanctions may be imposed on offenders in addition to compensation for damages to victims.The stringency of data protection law, whether the prevailing law will suffice such needs, whether the proposed amendments are a welcome measure, whether India needs a separate legislation for data protection etc are questions which require an in-depth analysis of the prevailing circumstances and a comparative study with laws of other countries. There is no consensus among the experts regarding these issues. These issues are not in the purview of this write-up. But there can be no doubt about the importance of data protection law in the contemporary IT scenario and are not disputable.

The Information Technology Act 2000 (amended in 2008)The Information Technology Act was first drawn up in 2000, and has been revised most recently 2008. The Information Technology (Amendment) Bill, 2008 amended sections 43 (data protection), 66 (hacking), 67 (protection against unauthorised access to data), 69 (cyberterrorism), and 72 (privacy and confidentiality) of the Information Technology Act, 2000, which relate to computer/cybercrimes.Section 43 [Penalty and Compensation for damage to computer, computer system, etc.] amended vide Information Technology Amendment Act 2008 reads as under:If any person without permission of the owner or any other person who is in-charge of a computer, computer system or computer network:accesses or secures access to such computer, computer system or computer network or computer resource (ITAA2008)downloads, copies or extracts any data, computer data base or information from such computer, computer system or computer network including information or data held or stored in any removable storage medium;introduces or causes to be introduced any computer contaminant or computer virus into any computer, computer system or computer network;damages or causes to be damaged any computer, computer system or computer  network, data, computer data base or any other programmes residing in such computer, computer system or computer network;disrupts or causes disruption of any computer, computer system or computer network;denies or causes the denial of access to any person authorized to access any computer, computer system or computer network by any means;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;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;destroys, deletes or alters any information residing in a computer resource or diminishes its value or utility or affects it injuriously by any means (Inserted vide ITAA-2008); andSteals, 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, (Inserted vide ITAA 2008) he shall be liable to pay damages by way of compensation to the person so affected. (change vide ITAA 2008)Critique: In comparison to the laws enacted in other countries, this provision still falls short of a strong data protection law. In most other countries data protection laws specify:the definition and classification of data types;the nature and protection of the categories of data;that equal protection will be given to data stored offline and data stored manually;that data controllers and data processors have distinct roles;clear restrictions on the manner of data collection;clear guidelines on the purposes for which the data can be put and to whom it can be sent;standards and technical measures governing the collection, storage, access to, protection, retention, and destruction of data;that providers of goods or services must have a clear opt - in or opt - out option; andin addition, most countries provide strong safeguards and penalties against bsignNowes of any of the aboveSection 66 [Computer Related Offences] amended vide Information Technology Amendment Act 2008 reads as under: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.Explanation: For the purpose of this section,-the word "dishonestly" shall have the meaning assigned to it in section 24 of the Indian Penal Code;the word "fraudulently" shall have the meaning assigned to it in section 25 of the Indian Penal Code. [Section 66 A] [Punishment for sending offensive messages through communication service, etc.] (Introduced vide ITAA 2008):Any person who sends, by means of a computer resource or a communication device,-any information that is grossly offensive or has menacing character; orany 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;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 (Inserted vide ITAA 2008) shall be punishable with imprisonment for a term which may extend to three years and with fine.Explanation: For the purposes of this section, terms "Electronic mail" and "Electronic Mail Message" means a message or information created or transmitted or received on a computer, computer system, computer resource or communication device including attachments in text, image, audio, video and any other electronic record, which may be transmitted with the message.[Section 66 B] [Punishment for dishonestly receiving stolen computer resource or communication device] (Inserted Vide ITA 2008):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, 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] (Inserted Vide ITA 2008):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] (Inserted Vide ITA 2008):Whoever, by means of any communication device or computer resource cheats by personation, 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] (Inserted Vide ITA 2008):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, shall be punished with imprisonment which may extend to three years or with fine not exceeding two lakh rupees, or with bothExplanation - For the purposes of this section--“transmit” means to electronically send a visual image with the intent that it be viewed by a person or persons;“capture”, with respect to an image, means to videotape, photograph, film or record by any means;“private area” means the naked or undergarment clad genitals, pubic area, buttocks or female breast;“publishes” means reproduction in the printed or electronic form and making it available for public;“under circumstances violating privacy” means circumstances in which a person can have a reasonable expectation that:he or she could disrobe in privacy, without being concerned that an image of his private area was being captured; orany 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.[Section 66F] [Punishment for cyber terrorism]:(1) Whoever,-(A) 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 –denying or cause the denial of access to any person authorized to access computer resource; or attempting to penetrate or access a computer resource without authorisation or exceeding authorized access; orintroducing 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, or(B) knowingly or intentionally penetrates or accesses a computer resource without authorization or exceeding authorized access, and by means of such conduct obtains access to information, data or computer database that is restricted for reasons of the security of the State or foreign relations; or any restricted information, data or computer database, with reasons to believe that such information, data or computer database so obtained may be used to cause or likely to cause injury to the interests of the sovereignty and integrity of India, the security of the State, friendly relations with foreign States, public order, decency or morality, or in relation to contempt of court, defamation or incitement to an offence, or to the advantage of any foreign nation, group of individuals or otherwise, commits the offence of cyber terrorism.(2) Whoever commits or conspires to commit cyber terrorism shall be punishable with imprisonment which may extend to imprisonment for life’.Critique: We find the terminology in multiple sections too vague to ensure consistent and fair enforcement. The concepts of ‘annoyance’ and ‘insult’ are subjective. Clause (d) makes it clear that phishing requests are not permitted, but it is not clear that one cannot ask for information on a class of individuals.Section 67 [Publishing of information which is obscene in electronic form] amended vide Information Technology Amendment Act 2008 reads as under: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 which 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 67 A] [Punishment for publishing or transmitting of material containing sexually explicit act, etc. in electronic form] (Inserted vide ITAA 2008):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.Exception: This section and section 67 does not extend to any book, pamphlet, paper, writing, drawing, painting, representation or figure in electronic form-the publication of which is proved to be justified as being for the public good on the ground that such book, pamphlet, paper, writing, drawing, painting, representation or figure is in the interest of science, literature, art, or learning or other objects of general concern; orwhich is kept or used bona fide for religious purposes.[Section 67 B] 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 electronicform 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 inobscene or indecent or sexually explicit manner or(c) cultivates, entices or induces children to online relationship with one or more children forand 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:Provided that the provisions of section 67, section 67A and this section does not extend to any book, pamphlet, paper, writing, drawing, painting, representation or figure in electronic form-(i) The publication of which is proved to be justified as being for the public good on the ground that such book, pamphlet, paper writing, drawing, painting, representation or figure is in the interest of science, literature, art or learning or other objects of general concern; or(ii) which is kept or used for bonafide heritage or religious purposes Explanation: For the purposes of this section, "children" means a person who has not completed the age of 18 years. [Section 67 C] [Preservation and Retention of information by intermediaries]:(1) Intermediary shall preserve and retain such information as may be specified for such duration and in such manner and format as the Central Government may prescribe.(2) Any intermediary who intentionally or knowingly contravenes the provisions of sub section (1) shall be punished with an imprisonment for a term which may extend to three years and shall also be liable to fine.Critique: This provision adequately protects both the corporate and the citizen in a positive way.Section 69 [Powers to issue directions for interception or monitoring or decryption of any information through any computer resource] amended vide Information Technology Amendment Act 2008 reads as under:(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, 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 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 beintercepted 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 –(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 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.Explanation: For the purposes of this section,(i) "Computer Contaminant" shall have the meaning assigned to it in section 43(ii) "traffic data" means any data identifying or purporting to identify any person, computer system or computer network or location to or from which the communication is or may be transmitted and includes communications origin, destination, route, time, date, size, duration or type of underlying service or any other information.Critique: Though we recognize how important it is for a government to protect its citizens against cyberterrorism, we are concerned at the friction between these provisions and the guarantees of free dialog, debate, and free speech that are Fundamental Rights under the Constitution of India.Specifically:a) there is no clear provision of a link between an intermediary and the information or resource that is to be monitored.c)the penalties laid out in the clause are believed to be too harsh, and when read in conjunction with provision 66, there is no distinction between minor offenses and serious offenses.e) the ITA is too broad in its categorization of acts of cyberterrorism by including information that is likely to cause: injury to decency, injury to morality, injury in relation to contempt of court, and injury in relation to defamation.Section 72 [BsignNow of confidentiality and privacy] amended vide Information Technology Amendment Act 2008 reads as under:Save as otherwise provided in this Act or any other law for the time being in force, 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. [Section 72 A] Punishment for Disclosure of information in bsignNow of lawful contract (Inserted vide ITAA-2008):Save as otherwise provided in this Act or any other law for the time being in force, any person including an intermediary who, while providing services under the terms of lawful contract, has secured access to any material containing personal information about another person, with the intent to cause or knowing that he is likely to cause wrongful loss or wrongful gain discloses, without the consent of the person concerned, or in bsignNow of a lawful contract, such material to any other person shall be punished with imprisonment for a term which may extend to three years, or with a fine which may extend to five lakh rupees, or with both.General Notes and Critiques:As general notes on the ITA and data protection we find that the Act is lacking in many ways, including:there is no definition of “sensitive personal data or information” and that term is used indiscriminately without.the provisions and protections cover only electronic data and not stored data or non-electronic systems of mediain the absence of a data controller, liability is often imposed on persons who are not necessarily in a position to control datacivil liability for data bsignNow arises where negligence is involvedcriminal liability only applies to cases of information obtained in the context of a service contract.**I am neither a student of law nor attached in any way to the legal system. This is excerpted from Cybercrime and Privacy and merely reproduced here for the sake of convenience.

Mr SandsThe code phrase "Mr. Sands" was used in theatres, where sand buckets were used to put out fires, as a code for fire. The word "fire" backstage would cause alarm to either performers or the audience.I worked in a cinema in Edinburgh and I heard this, no one had ever told me what it was for, but the place cleared out.There are quite a few other interesting code your may or may not know about:Cruise ship codes"Operation Bright Star" -signals a medical emergency."Operation Rising Star" means a passenger has passed away.“PVI", which stands for "public vomiting incident", or "30-30", which is used by some cruise lines to ask for staff to assist with cleaning up a mess.Code Red - Outbreak of norovirus or illness. It means the ship must undergo deep cleaning and sick passengers should stay in their rooms. Code Green and Code Yellow indicate less severe problems.Mr Skylight; Alpha, Alpha, Alpha; Code Blue; or Star Code, Star Code, Star Code - Medical emergencyMr Mob or Oscar, Oscar, Oscar - Man overboardCharlie, Charlie, Charlie - Security threatEcho, Echo, Echo - Possible collision with another ship, or in other cases a warning of high winds.Red Parties, Red Parties, Red Parties; Alpha Team, Alpha Team, Alpha Team or Priority 1 - Possible fire on boardBravo, Bravo, Bravo - Fire or other serious incident.Delta - Damage to the ship.Papa - Pollution or oil spill.Priority 2 - Leak.Kilo - all staff to report to emergency posts.A fire or emergency may simply be indicated by a ringing of the general alarm bell. Seven or more short blast of the ship's whistle, followed by one long blast, means passengers should assemble at their muster stations.London Underground announcementsThe best known code is "Inspector Sands", or simply "Mr Sands", which refers to a potential emergency such as a fire or bomb scare. It is used on the Tube, as well as the wider UK rail network and at theatres ("Sands" because buckets of sand would be used to put out the fire).The numbered codes are nothing to be alarmed about, and simply refer to cleaning jobs.Code 1 - BloodCode 2 - Urine/FaecesCode 3 - VomitCode 4 - SpillageCode 5 - Broken GlassCode 6 - LitterCode 7 - Anything that doesn't fit into these categoriesAirport emergenciesCode Bravo - general security alert at an airport. Security officials will typically yell it at travellers, and may order them to "freeze!", to deliberately scare them and make it easier to pinpoint the source of the threat. More often than not, it will probably be a drill - as this amusing account explains.Code Adam may be used to alert staff of a missing child.Aircraft emergenciesMayday - which means an aircraft or ship is facing imminent danger. Fewer will know about pan-pan (from the French:panne, meaning a breakdown), which refers to a slightly less grave danger.7500 is a transponder code which means an aircraft has been, or is threatened with, hijacking.7700 is a more general emergency code; 7600 indicated a radio failure.Cabin crew jargonNot emergencies, but might be interesting:Arm and crosscheck - Prior to departure, the plane exits are put into emergency mode. If an "armed" door is opened, the emergency slide will inflate. The cabin crew will "crosscheck" to ensure that the opposite doors have been armed. Upon arrival, you're likely to hear "doors to manual".Debrief - Every little detail of every flight is recorded on the “debrief” - including medical situation, disruptive passengers or a catering problem.Hat bin - Another term for the overhead bins ("Why are these called hatbins? Surely they’re not used for hats? Well, in the 1960s, when flying was extremely glamorous, they actually were.")Hot bit - The heated part of an in-flight meal.Gash bag - The rubbish bag. ("Another military term, apparently if you were the gash man in the navy you got all the rubbish jobs").Landing lips - "That last slick of lippie we apply to look fresh as a daisy before we land."Plonkey kits - A bag of essentials carried by flight attendants. ("Apparently this originates from the ships’ galleys. Ours tend to contain ice tongs, oven gloves, small clippers, a sewing kit and a clothes brush".)Starburst - "You’ll see this happen when a service is started in the middle of the cabin and the trolleys work out towards the galleys."Pilot speakAll-call - "A request that each flight attendant report via intercom from his or her station - a sort of flight attendant conference call."Last-minute paperwork - "The flight is ready for pushback - then comes the wait for 'last minute paperwork'. Usually it’s something to do with the weight-and-balance record, a revision to the flight plan, or waiting for the maintenance guys to deal with a write-up and get the logbook in order."Flight level - "A fancy way of telling you how many thousands of feet you are above sea level. Just add a couple of zeroes. Flight level three-three zero is 33,000 feet."Thanks to Jim Lux for a better explanation:Flight Level is slightly different than altitude with a couple zeros removed. For altitude, you set the altimeter to the current barometric pressure, so it’s the actual heigh above sea level. FL is always done with the altimeter set to 29.92″, so the actual altitude(e.g. reported by GPS) will be a bit different. The actual term is “pressure altitude”.As long as everyone does the same thing, nobody runs into each other.Ground stop - "This is when departures to one or more destination are curtailed by air traffic control, usually due to a traffic backlog."EFC time - "The expect further clearance time, sometimes called a release time, is the point at which a crew expects to be set free from a holding pattern."Deadhead - "A deadheading pilot or flight attendant is one repositioning as part of an on-duty assignment. This is not the same as commuting to work or engaging in personal travel."Gatehouse - "An idiosyncratic way of saying the gate area or boarding lounge."Ramp - The aircraft parking zones.Alley - A taxiway.Apron - "Any expanse of tarmac that is not a runway or taxiway - areas where planes park or are otherwise serviced."At this time - "Example: 'At this time, we ask that you please put away all electronic devices'. Meaning: now, or presently. This is air travel's signature euphemism."

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?

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.