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Is wave-particle duality an illusion?
"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.
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What is wave-particle duality?
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.
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What is your review of Osho?
What is your review of Osho? I’ve thought about this question on and off for over twenty-five years. Now I mostly see him as a tragic figure, a man of immense talent who fell victim to the fruits of his own abilities.I think he was seduced by the dark side of his power, and many of the fruits of his labor turned to poison.Lots of people make a big deal out of the sex thing. Osho was very ‘sex-positive’ and there was a tremendous amount of sex happening at his ashrams. By current [2019] San Francisco standards this kind of behavior is ‘so what?’, or ‘who cares?’ His attitudes about sex didn’t work so well for him in Pune, then they didn’t work for him in Montclair, NJ, and they definitely didn’t work well in rural Oregon. But, again, so what?He obviously had tremendous presence, and something about his energy had a huge impact on people around him. It seems likely that he had some spiritual awakening. He definitely had siddhis. He was a tremendous charmer, and could sit down and talk ‘off the cuff’ (unprepared) for hours and keep an audience spell-bound. An amazing talent. His books and lectures have inspired thousands of people to pursue spiritual goals.It wasn’t until years later that I went back and re-read many of his books and realized how careless he was with facts, how many things he said were wrong (even about religion and philosophy) [2] and how extensively he slammed or talked down anyone who could remotely be considered a rival or competitor.I was quite taken aback when I found out about his decades of extensive, personal, recreational drug use (nitrous oxide) and his addiction(?) to valium. I found his obsession with expensive baubles (exotic watches and Rolls Royces) very disturbing. As far as I can tell, he insisted that the community spend money on these when the money was badly needed for other things - like lawyers.Many people claim that Osho was extremely perceptive, and could effectively read the minds of people around him. How then was it that he missed the numerous plots by his senior disciples, all of which was happening within yards of him. For example, the senior sanyassin plotted to murder at least three people:US Attorney Charles H. Turner - Wikipedia;Osho's caretaker and girlfriend, Ma Yoga Vivek; andOsho’s personal physician, Swami Devaraj (Dr. George Meredith).How could Osho not know about the laboratory at Rajneeshpuram where some of the sannyasin cultured the salmonella bacteria that was used to poison 751 people? This is all a matter of public record, and court testimony. You can read about it on wikipedia - 1984 Rajneeshee bioterror attack - Wikipedia. While Osho steadfastly denied that he had any knowledge of the illegal activities taking place at Rajneeshpuram, some of his students testified otherwise. There is court testimony about a tape of a conversation between Sheela and Osho, that tape was played for the senior sannyasin, this is what the listeners believed it said:And the gist of Bhagwan's response, yes, it was going to be necessary to kill people to stay in Oregon. And that actually killing people wasn't such a bad thing. And actually Hitler was a great man, although he could not say that publicly because nobody would understand that. Hitler had great vision." [2]I’ll close with a quote from American neuroscientist and philospher Sam Harris - Wikipedia.He [Osho] was by no means the worst that the New Age had to offer. He undoubtedly harmed many people in the end—and, perhaps, in the beginning and middle as well—but he wasn’t merely a lunatic or a con artist as many other gurus have been. Osho always seemed like a genuinely insightful man who had much to teach, but who grew increasingly intoxicated by the power of his role, and then finally lost his mind in it. When you spend your days sniffing nitrous oxide, demanding fellatio at 45-minute intervals, making sacred gifts of your fingernail clippings, and shopping for your 94th Rolls Royce… you should probably know that you’ve wandered a step or two off the path. Sam HarrisFootnotes, etc.[1] According to court testimony by Ma Ava (Ava Avalos), a prominent disciple, [Ma Anand] Sheela played associates a tape recording of a meeting she had had with Rajneesh about the "need to kill people" in order to strengthen wavering sannyasins resolve in participating in her murderous plots: "She came back to the meeting and […] began to play the tape. It was a little hard to hear what he was saying. […] And the gist of Bhagwan's response, yes, it was going to be necessary to kill people to stay in Oregon. And that actually killing people wasn't such a bad thing. And actually Hitler was a great man, although he could not say that publicly because nobody would understand that. Hitler had great vision."[2] Academic assessments of Rajneesh's work have been mixed and often directly contradictory.Uday Mehta saw errors in his interpretation of Zen and Mahayana Buddhism, speaking of "gross contradictions and inconsistencies in his teachings" that "exploit" the "ignorance and gullibility" of his listeners. [222]The sociologist Bob Mullan wrote in 1983 of "a borrowing of truths, half-truths and occasional misrepresentations from the great traditions"... often bland, inaccurate, spurious and extremely contradictory".[223]Hugh B. Urban also found Rajneesh's teaching neither original nor especially profound and concluded that most of its content had been borrowed from various Eastern and Western philosophies.[171]Rajneesh - Wikipedia - Appraisals by Scholars of ReligionIf you would like to learn more, here are three places to start. Many of Osho’s senior students have written books about their experiences with him, documenting both the good and the bad.25 years after Rajneeshee commune collapsed, truth spills out -- Part 1 of 5Rajneesh - WikipediaPromise of Paradise: : A Woman's Intimate Life With 'Bhagwan' Osho Rajneesh by Satya Bharti Franklin. She was a sannyasin and student of Osho’s for decades. Franklin left for what was intended to be a three-week visit to India. Instead, it was the beginning of her intimate involvement with the Bhagwan Rajneesh, one of the most infamous spiritual teachers of recent decades. In this extraordinary and passionate memoir, Franklin provides an insider’s view of the manipulation, sexual exploitation, and internecine struggles, as well as the more publicized joys and ecstasies, that characterized one of the most talked-about religious experiments of the 20th century.
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What likely happened to Kris Kremers and Lisanne Froon after getting lost in the Panamanian jungle?
My personal guess is that they were murdered. And that they had been dead since April 1st. The photos taken on April 8th was taken by the murderer to mislead the police. So was those cellphone signal checking and calling 112/911.April 1st morning: The two girls were enjoying their hike.Picture #505Picture #507Picture #508: Last “happy” “regular” picture the girls took.April 1st afternoon/evening: Girls went missing.April 1st-6th: Cellphone activities and signal checks, attempts to call the emergency but the cellphones has no signal.April 3rd: Search for the girls began.…(7 days after their disappearance.)…April 8th 1 am to 4 am: 90 photos taken in the dark by Lisanne’s Canon SX270. First was picture #510 (#509 missing/deleted).Some of the many night time pictures.April 11th: Last attempt of signal check on Kremers’ cellphone.My thought:1)Where did picture #509 went?That is the critical pictures between the last happy picture #508, and the first of the night time photos #510 seven days later.The investigators have noted that the girls didn’t delete any other pictures, except #509. So they do not know why they would delete #509, which in this situation would be very crucial to the investigation.Another interesting thing is that the #509 picture was totally deleted and cannot be restored. When a camera deletes a picture, usually it can be restored. It would take a PC computer to totally delete a picture. If so this would mean foul play.2) No goodbye messages.When people know that it is hopeless, and they will die, they would leave behind goodbye massages to love ones. This is done to let their love ones know that they love them, and to explain how they got themselves into the life threatening situation.They can write something down. And in this case, the girls could have made a goodbye video with their camera or cellphone. At the very least, they would have taken a goodbye picture of themselves on their camera or cellphone.The only reason the girls didn’t leave any goodbye message is that they weren’t able to. However given that “they” can take 90 photos on the 7th days after they disappeared, on April 8th, it shows that “they” easily could have left a goodbye message.And by “they”, perhaps I am no longer referring to the 2 girls, but their murderer.It takes only a few minutes to leave one goodbye video. “Mama, Papa, I love you!” Certainly by April 8th, it must come upon the girls that this might be it, and they should leave a goodbye message (if they were alive). They know they were in grave danger, and they were still strong enough to take 90 photos at night, so why didn’t they leave a goodbye message?3) Not a single picture of the girlsThe only picture we have is the back of the head of one of the girls at night. It was almost as if the girls don’t want their face to be seen at all. Why all the secrecy?That picture of one of the girls’ back of the head at night, unfortunately, does not prove that she was still alive. And if she was dead, why would the other girl take a picture of the back of her dead friend’s head?4) Who took those 90 night time photos on April 8th? Who was checking the cellphone signals and calling 112/911 between April 1st and 11th?Given the above, it seems unlikely that those pictures were taken by the 2 girls. Once again, why no goodbye messages then? Some people suspect it was an animal or monkey that took the pictures. But I say it was their murderer(s).The cellphone signal checking thing can easily be done by the murderer, to “pretend” that the girls were alive when they were already murdered. It is no rocket science. The murderer knew there was no signal in that location so the calls will never go through. That’s why the murderer was confident to call the police, because he knew he would not actually need to talk to the police. And the murdered did this for 6 days from April 1st to 6th, and then return one more time on April 11th.5) There were other murders in the area after these 2 girls.The area that they hiked in was not the safest place. There were other “unrelated” murders in the same area. Could be the cartel. Could be some tribes.Conclusion:The rainforest is a very dangerous place. These 2 girls could have died of natural cause easily. However in this case, being in a naturally dangerous location does not automatically mean it wasn’t a murder. There are evidence that indicates foul play. However even so, we might never catch the killer.
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Which NIN albums are the best?
Tough question as answers will be so subjective.Personally, The Downward Spiral takes centre stage. Many reasons spring to mind:Angry, disillusioned young man signNowing a zenith in his abilities to express these difficult emotions in musical terms with utter laser guided precision. The resultant album crystallised the turmoil of his inner spirit with such jaw dropping efficiency and aggression. The album has proven to be timeless and a gift that keeps on giving.Fun with time signatures - no shying away from breaking away from 4/4 song structures. The results were incredible - think March of The Pigs, I do Not Want This, as leading examples.The alchemical nature of its production. Nine Inch Nails may well be Trent Reznor (and more recently Atticus Ross) however at the time TDS was being recorded, it was the alchemy of others such as Chris Vrenna, Robin Finck, Danny Lohner, Flood, Adrian Belew and to an extent the house 10050 Ceilo Drive where the infamous Manson Murders took place. I’d argue that the sound of the album could never have sounded as it does without the characters and location surrounding its productionFourteen tracks where nothing is wasted - not a beat or sample out of place. Not a single disposable song or instrumental. Genius manipulation of layers and sonics. 25 years later, I still notice things that I hadn’t before.For many the album remains misunderstood - TDS had garnered descriptions of being an ‘industrial metal album’ at times. While the shoe can fit superficially, the core of the album is electronic. It always was and always will be. Given how organic and abrasive the sound design was, it is easier to see why it was incorrectly pigeon holed, but drilling deeper into the production sonics, it becomes harder to not be mind blown by the stunning and meticulously crafted electronic production standards buried deep within it. Sampling mastery at its finest.I said this was going to be subjective…I was 23 when this album came out. Thinking of myself as something of a music aficianado, I remember clearly feeling rattled with such a deep unease during the first three plays of TDS. I thought that I’d developed a broad vocabulary for the kind of music I appreciated, thought I could describe it easily. TDS came out and I became lost for words as to what It was. I’d never head music that had got under my skin as much as this before. I remember Eraser being particularly horrifying upon first listen, it actually invoked something close to fear. I haven’t heard a record since then that could affect me in the way that this album did. When I reflect upon this now (an this probably ties back to point 4) the whole album has a deeply unsettling personality, there is the alchemy of the tracks and their sequential arrangement. Because of this detail, with all parts connecting to make the final sum, the album skilfully pulls the listener through a ‘heart of darkness’ and cleverly taps into a variety of dark emotions, concluding with a delicate thread of hope.I could probably continue with an ongoing list in this TDS TL;DR monologue of praise, but I’ll leave it here.I also rate The Slip for being up there in the cream of NIN albums. I found the immediacy of the album incredibly superb. The album is sharp and mostly punchy, therefore has another particular energy characteristic. I know that it was recorded in the spirit of quick production, allowing for imperfections.As a result, The Slip is a fun listen in some respects, it’s the sound of Trent and co-conspirators going Bang-Bang-Bang! firing out tracks in a short space of time compared to other NIN releases. It somehow feels lighter, very lean, attitudinal and unselfconscious. As NIN albums go, this one is as close in sentiment to the saying ‘Dance like nobody is looking, sing like nobody is listening’ There is an inherent rawness to the character of The Slip, making it (in my opinion) one of the best NIN albums in a generally impressive collection. Noteworthy mention here is that The Slip was a ‘Free’ download at the time of release. I still bought a physical copy though.Best of three.I surprise myself by choosing the most recent trilogy of e.p’s - ‘What about the Fragile?!’ Some of you say. I know that a lot of people rate it as the best of NIN, there was a time where with fewer albums under their belt, it would have been in the top three for me. However, further down the line of time, while I acknowledge moments of sublimity, brilliance, menace and beauty, I also have to acknowledge that there are a few tracks that just jar, for personal reasons.The recent trilogy: Not the Actual Events, Add Violence , and Bad Witch on the other hand, can and should be viewed as an album in three acts. I adored NTAE for returning to an earlier almost TDS sound in places, the self referential sonic nuances were a delight, especially as this sounded closer in spirit to what the imagined Hesitation Marks would sound like when pre-release articles mentioned NIN returning to earlier, familiar sound palettes (or words to that effect)The beauty of the e.p trilogy was that it was clear that however the final tracks were honed down and chosen, those that made it were succinct, blunt-force to the point and admirably exploratory in their presentation.Trent and Atticus may often tear up the rule book of what NIN should sound like, which is always refreshing. Sometimes this attitude works brilliantly, at other times you can sense that they just wanted to get something out of their system (Hesitation Marks being a good example)The trilogy presents a plethora of new NIN material, from the familiar to brazenly strange. What I liked the most about this collection was that It never settled on one identity and a consequence of this was that listened to as a whole, this felt like a brand new era of a revived NIN, bursting with imagination and new ideas. I particularly enjoyed the Bad Witch e.p for really taking me out of my comfort zone of what I think NIN should sound like. Those odd moments of Sax or Trent’s alternative approach to vocal delivery at first seemed alien and partly jarring, but then I think It worked on a deeper level, touching upon something Trent had mentioned in interviews at the time where he was recalling ‘working with an album that you may not like at first, but grow to love with each listen’ This is how it turned out for me and for the reasons stated above, the trilogy has cemented itself for being worthy of being in a subjective ‘best NIN albums’ trilogy.Noteworthy also were the first two e.p ‘Physical Components’ I absolutely loved the care and thought that went into the presentation of these two releases. I loved that the additional materials begged to be explored, examined, discussed. It was a masterclass in generating ‘user engagement’ beyond the commonplace boundaries of just playing an mp3/aac etc I hope that this spirit continues in future NIN releases. I personally don’t mind paying a little bit more for having an ‘experience’ that accompanies and extends the scope of the music.
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