[math-fun] Quantum Mechanical Pilot waves: they're baaaack !
FYI -- Follow the link to also see the pix. http://www.wired.com/2014/06/the-new-quantum-reality/ Have We Been Interpreting Quantum Mechanics Wrong This Whole Time? By Natalie Wolchover, Quanta Magazine 06.30.14 6:30 am For nearly a century, Âreality has been a murky concept. The laws of quantum physics seem to suggest that particles spend much of their time in a ghostly state, lacking even basic properties such as a definite location and instead existing everywhere and nowhere at once. Only when a particle is measured does it suddenly materialize, appearing to pick its position as if by a roll of the dice. This idea that nature is inherently probabilistic  that particles have no hard properties, only likelihoods, until they are observed  is directly implied by the standard equations of quantum mechanics. But now a set of surprising experiments with fluids has revived old skepticism about that worldview. The bizarre results are fueling interest in an almost forgotten version of quantum mechanics, one that never gave up the idea of a single, concrete reality. The experiments involve an oil droplet that bounces along the surface of a liquid. The droplet gently sloshes the liquid with every bounce. At the same time, ripples from past bounces affect its course. The dropletÂs interaction with its own ripples, which form whatÂs known as a pilot wave, causes it to exhibit behaviors previously thought to be peculiar to elementary particles  including behaviors seen as evidence that these particles are spread through space like waves, without any specific location, until they are measured. Particles at the quantum scale seem to do things that human-scale objects do not do. They can tunnel through barriers, spontaneously arise or annihilate, and occupy discrete energy levels. This new body of research reveals that oil droplets, when guided by pilot waves, also exhibit these quantum-like features. To some researchers, the experiments suggest that quantum objects are as definite as droplets, and that they too are guided by pilot waves  in this case, fluid-like undulations in space and time. These arguments have injected new life into a deterministic (as opposed to probabilistic) theory of the microscopic world first proposed, and rejected, at the birth of quantum mechanics. ÂThis is a classical system that exhibits behavior that people previously thought was exclusive to the quantum realm, and we can say why, said John Bush, a professor of applied mathematics at the Massachusetts Institute of Technology who has led several recent bouncing-droplet experiments. ÂThe more things we understand and can provide a physical rationale for, the more difficult it will be to defend the Âquantum mechanics is magic perspective. Magical Measurements The orthodox view of quantum mechanics, known as the ÂCopenhagen interpretation after the home city of Danish physicist Niels Bohr, one of its architects, holds that particles play out all possible realities simultaneously. Each particle is represented by a Âprobability wave weighting these various possibilities, and the wave collapses to a definite state only when the particle is measured. The equations of quantum mechanics do not address how a particleÂs properties solidify at the moment of measurement, or how, at such moments, reality picks which form to take. But the calculations work. As Seth Lloyd, a quantum physicist at MIT, put it, ÂQuantum mechanics is just counterintuitive and we just have to suck it up. A classic experiment in quantum mechanics that seems to demonstrate the probabilistic nature of reality involves a beam of particles (such as electrons) propelled one by one toward a pair of slits in a screen. When no one keeps track of each electronÂs trajectory, it seems to pass through both slits simultaneously. In time, the electron beam creates a wavelike interference pattern of bright and dark stripes on the other side of the screen. But when a detector is placed in front of one of the slits, its measurement causes the particles to lose their wavelike omnipresence, collapse into definite states, and travel through one slit or the other. The interference pattern vanishes. The great 20th-century physicist Richard Feynman said that this double-slit experiment Âhas in it the heart of quantum mechanics, and Âis impossible, absolutely impossible, to explain in any classical way. Some physicists now disagree. ÂQuantum mechanics is very successful; nobodyÂs claiming that itÂs wrong, said Paul Milewski, a professor of mathematics at the University of Bath in England who has devised computer models of bouncing-droplet dynamics. ÂWhat we believe is that there may be, in fact, some more fundamental reason why [quantum mechanics] looks the way it does. Riding Waves The idea that pilot waves might explain the peculiarities of particles dates back to the early days of quantum mechanics. The French physicist Louis de Broglie presented the earliest version of pilot-wave theory at the 1927 Solvay Conference in Brussels, a famous gathering of the founders of the field. As de Broglie explained that day to Bohr, Albert Einstein, Erwin Schrödinger, Werner Heisenberg and two dozen other celebrated physicists, pilot-wave theory made all the same predictions as the probabilistic formulation of quantum mechanics (which wouldnÂt be referred to as the ÂCopenhagen interpretation until the 1950s), but without the ghostliness or mysterious collapse. The probabilistic version, championed by Bohr, involves a single equation that represents likely and unlikely locations of particles as peaks and troughs of a wave. Bohr interpreted this probability-wave equation as a complete definition of the particle. But de Broglie urged his colleagues to use two equations: one describing a real, physical wave, and another tying the trajectory of an actual, concrete particle to the variables in that wave equation, as if the particle interacts with and is propelled by the wave rather than being defined by it. For example, consider the double-slit experiment. In de BroglieÂs pilot-wave picture, each electron passes through just one of the two slits, but is influenced by a pilot wave that splits and travels through both slits. Like flotsam in a current, the particle is drawn to the places where the two wavefronts cooperate, and does not go where they cancel out. De Broglie could not predict the exact place where an individual particle would end up  just like BohrÂs version of events, pilot-wave theory predicts only the statistical distribution of outcomes, or the bright and dark stripes  but the two men interpreted this shortcoming differently. Bohr claimed that particles donÂt have definite trajectories; de Broglie argued that they do, but that we canÂt measure each particleÂs initial position well enough to deduce its exact path. In principle, however, the pilot-wave theory is deterministic: The future evolves dynamically from the past, so that, if the exact state of all the particles in the universe were known at a given instant, their states at all future times could be calculated. At the Solvay conference, Einstein objected to a probabilistic universe, quipping, ÂGod does not play dice, but he seemed ambivalent about de BroglieÂs alternative. Bohr told Einstein to Âstop telling God what to do, and (for reasons that remain in dispute) he won the day. By 1932, when the Hungarian-American mathematician John von Neumann claimed to have proven that the probabilistic wave equation in quantum mechanics could have no Âhidden variables (that is, missing components, such as de BroglieÂs particle with its well-defined trajectory), pilot-wave theory was so poorly regarded that most physicists believed von NeumannÂs proof without even reading a translation. More than 30 years would pass before von NeumannÂs proof was shown to be false, but by then the damage was done. The physicist David Bohm resurrected pilot-wave theory in a modified form in 1952, with EinsteinÂs encouragement, and made clear that it did work, but it never caught on. (The theory is also known as de Broglie-Bohm theory, or Bohmian mechanics.) Later, the Northern Irish physicist John Stewart Bell went on to prove a seminal theorem that many physicists today misinterpret as rendering hidden variables impossible. But Bell supported pilot-wave theory. He was the one who pointed out the flaws in von NeumannÂs original proof. And in 1986 he wrote that pilot-wave theory Âseems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored. The neglect continues. A century down the line, the standard, probabilistic formulation of quantum mechanics has been combined with EinsteinÂs theory of special relativity and developed into the Standard Model, an elaborate and precise description of most of the particles and forces in the universe. Acclimating to the weirdness of quantum mechanics has become a physicists rite of passage. The old, deterministic alternative is not mentioned in most textbooks; most people in the field havenÂt heard of it. Sheldon Goldstein, a professor of mathematics, physics and philosophy at Rutgers University and a supporter of pilot-wave theory, blames the Âpreposterous neglect of the theory on Âdecades of indoctrination. At this stage, Goldstein and several others noted, researchers risk their careers by questioning quantum orthodoxy. A Quantum Drop Now at last, pilot-wave theory may be experiencing a minor comeback  at least, among fluid dynamicists. ÂI wish that the people who were developing quantum mechanics at the beginning of last century had access to these experiments, Milewski said. ÂBecause then the whole history of quantum mechanics might be different. The experiments began a decade ago, when Yves Couder and colleagues at Paris Diderot University discovered that vibrating a silicon oil bath up and down at a particular frequency can induce a droplet to bounce along the surface. The dropletÂs path, they found, was guided by the slanted contours of the liquidÂs surface generated from the dropletÂs own bounces  a mutual particle-wave interaction analogous to de BroglieÂs pilot-wave concept. In a groundbreaking experiment, the Paris researchers used the droplet setup to demonstrate single- and double-slit interference. They discovered that when a droplet bounces toward a pair of openings in a damlike barrier, it passes through only one slit or the other, while the pilot wave passes through both. Repeated trials show that the overlapping wavefronts of the pilot wave steer the droplets to certain places and never to locations in between  an apparent replication of the interference pattern in the quantum double-slit experiment that Feynman described as Âimpossible  to explain in any classical way. And just as measuring the trajectories of particles seems to Âcollapse their simultaneous realities, disturbing the pilot wave in the bouncing-droplet experiment destroys the interference pattern. Droplets can also seem to Âtunnel through barriers, orbit each other in stable Âbound states, and exhibit properties analogous to quantum spin and electromagnetic attraction. When confined to circular areas called corrals, they form concentric rings analogous to the standing waves generated by electrons in quantum corrals. They even annihilate with subsurface bubbles, an effect reminiscent of the mutual destruction of matter and antimatter particles. In each test, the droplet wends a chaotic path that, over time, builds up the same statistical distribution in the fluid system as that expected of particles at the quantum scale. But rather than resulting from indefiniteness or a lack of reality, these quantum-like effects are driven, according to the researchers, by Âpath memory. Every bounce of the droplet leaves a mark in the form of ripples, and these ripples chaotically but deterministically influence the dropletÂs future bounces and lead to quantum-like statistical outcomes. The more path memory a given fluid exhibits  that is, the less its ripples dissipate  the crisper and more quantum-like the statistics become. ÂMemory generates chaos, which we need to get the right probabilities, Couder explained. ÂWe see path memory clearly in our system. It doesnÂt necessarily mean it exists in quantum objects, it just suggests it would be possible. The quantum statistics are apparent even when the droplets are subjected to external forces. In one recent test, Couder and his colleagues placed a magnet at the center of their oil bath and observed a magnetic ferrofluid droplet. Like an electron occupying fixed energy levels around a nucleus, the bouncing droplet adopted a discrete set of stable orbits around the magnet, each characterized by a set energy level and angular momentum. The Âquantization of these properties into discrete packets is usually understood as a defining feature of the quantum realm. If space and time behave like a superfluid, or a fluid that experiences no dissipation at all, then path memory could conceivably give rise to the strange quantum phenomenon of entanglement  what Einstein referred to as Âspooky action at a distance. When two particles become entangled, a measurement of the state of one instantly affects that of the other. The entanglement holds even if the two particles are light-years apart. In standard quantum mechanics, the effect is rationalized as the instantaneous collapse of the particles joint probability wave. But in the pilot-wave version of events, an interaction between two particles in a superfluid universe sets them on paths that stay correlated forever because the interaction permanently affects the contours of the superfluid. ÂAs the particles move along, they feel the wave field generated by them in the past and all other particles in the past, Bush explained. In other words, the ubiquity of the pilot wave Âprovides a mechanism for accounting for these nonlocal correlations. Yet an experimental test of droplet entanglement remains a distant goal. Subatomic Realities Many of the fluid dynamicists involved in or familiar with the new research have become convinced that there is a classical, fluid explanation of quantum mechanics. ÂI think itÂs all too much of a coincidence, said Bush, who led a June workshop on the topic in Rio de Janeiro and is writing a review paper on the experiments for the Annual Review of Fluid Mechanics. Quantum physicists tend to consider the findings less significant. After all, the fluid research does not provide direct evidence that pilot waves propel particles at the quantum scale. And a surprising analogy between electrons and oil droplets does not yield new and better calculations. ÂPersonally, I think it has little to do with quantum mechanics, said Gerard Ât Hooft, a Nobel Prize-winning particle physicist at Utrecht University in the Netherlands. He believes quantum theory is incomplete but dislikes pilot-wave theory. Many working quantum physicists question the value of rebuilding their highly successful Standard Model from scratch. ÂI think the experiments are very clever and mind-expanding, said Frank Wilczek, a professor of physics at MIT and a Nobel laureate, Âbut they take you only a few steps along what would have to be a very long road, going from a hypothetical classical underlying theory to the successful use of quantum mechanics as we know it. ÂThis really is a very striking and visible manifestation of the pilot-wave phenomenon, Lloyd said. ÂItÂs mind-blowing  but itÂs not going to replace actual quantum mechanics anytime soon. In its current, immature state, the pilot-wave formulation of quantum mechanics only describes simple interactions between matter and electromagnetic fields, according toDavid Wallace, a philosopher of physics at the University of Oxford in England, and cannot even capture the physics of an ordinary light bulb. ÂIt is not by itself capable of representing very much physics, Wallace said. ÂIn my own view, this is the most severe problem for the theory, though, to be fair, it remains an active research area. Pilot-wave theory has the reputation of being more cumbersome than standard quantum mechanics. Some researchers said that the theory has trouble dealing with identical particles, and that it becomes unwieldy when describing multiparticle interactions. They also claimed that it combines less elegantly with special relativity. But other specialists in quantum mechanics disagreed or said the approach is simply under-researched. It may just be a matter of effort to recast the predictions of quantum mechanics in the pilot-wave language, said Anthony Leggett, a professor of physics at the University of Illinois, Urbana-Champaign, and a Nobel laureate. ÂWhether one thinks this is worth a lot of time and effort is a matter of personal taste, he added. ÂPersonally, I donÂt. On the other hand, as Bohm argued in his 1952 paper, an alternative formulation of quantum mechanics might make the same predictions as the standard version at the quantum scale, but differ when it comes to smaller scales of nature. In the search for a unified theory of physics at all scales, Âwe could easily be kept on the wrong track for a long time by restricting ourselves to the usual interpretation of quantum theory, Bohm wrote. Some enthusiasts think the fluid approach could indeed be the key to resolving the long-standing conflict between quantum mechanics and EinsteinÂs theory of gravity, which clash at infinitesimal scales. ÂThe possibility exists that we can look for a unified theory of the Standard Model and gravity in terms of an underlying, superfluid substrate of reality, said Ross Anderson, a computer scientist and mathematician at the University of Cambridge in England, and the co-author of a recent paper on the fluid-quantum analogy. In the future, Anderson and his collaborators plan to study the behavior of Ârotons (particle-like excitations) in superfluid helium as an even closer analog of this possible Âsuperfluid model of reality. But at present, these connections with quantum gravity are speculative, and for young researchers, risky ideas. Bush, Couder and the other fluid dynamicists hope that their demonstrations of a growing number of quantum-like phenomena will make a deterministic, fluid picture of quantum mechanics increasingly convincing. ÂWith physicists itÂs such a controversial thing, and people are pretty noncommittal at this stage, Bush said. ÂWeÂre just forging ahead, and time will tell. The truth wins out in the end.Â
I hope to better understand the curious case of the photon. It has no frame of reference and, were it conscious, would perceive itself to be emitted and absorbed simultaneously, i.e. no time passing between the events. With zero time between emission and absorption, whimsy allows me to think of emitter and absorber as in some sense touching, albeit one is an ancient star and the other a cone in my living eye. Zero time means zero distance, in my book, although applying that rule to the no-frame-of-reference photon is probably a category error. Cramer's transactional interpretation, inspired by Wheeler-Feynman time-symmetric theory, has both forward and backward-in-time waves between emitter and absorber, agreeing upon the transaction before (as? timey-wimey words ...) it takes place, which leaves precious little room for the free will electrons have if you or I do, John Conway and Simon Kocken say, and leaving no room at all for deciding whether or not to slide a detector into a photon's path after the photon has been emitted. Emitters, detectors and photons have united, and their agreements will be kept! At least, in this regime, Rietdijk–Putnam–Penrose can be resolved in the affirmative. And now pilot waves. Bohm still stirs. Rod Sutherland combines pilot waves and the transactional interpretation in "Causally Symmetric Bohm Model", http://arxiv.org/pdf/quant-ph/0601095v2.pdf.
Jeff, this sounds ultra-interesting, but my lack of background prevents me from understanding what you've written. Can you please include some more detail? Like, what are the Cramer thing, the Wheeler-Feynman thing, the Conway-Kochen thing, the Rietdijk–Putnam–Penrose thing, and the Bohm thing that "still stirs" ? Thanks, Dan On Jun 30, 2014, at 2:12 PM, Jeff Caldwell <jeffrey.d.caldwell@gmail.com> wrote:
I hope to better understand the curious case of the photon. It has no frame of reference and, were it conscious, would perceive itself to be emitted and absorbed simultaneously, i.e. no time passing between the events. With zero time between emission and absorption, whimsy allows me to think of emitter and absorber as in some sense touching, albeit one is an ancient star and the other a cone in my living eye. Zero time means zero distance, in my book, although applying that rule to the no-frame-of-reference photon is probably a category error. Cramer's transactional interpretation, inspired by Wheeler-Feynman time-symmetric theory, has both forward and backward-in-time waves between emitter and absorber, agreeing upon the transaction before (as? timey-wimey words ...) it takes place, which leaves precious little room for the free will electrons have if you or I do, John Conway and Simon Kocken say, and leaving no room at all for deciding whether or not to slide a detector into a photon's path after the photon has been emitted. Emitters, detectors and photons have united, and their agreements will be kept! At least, in this regime, Rietdijk–Putnam–Penrose can be resolved in the affirmative.
And now pilot waves. Bohm still stirs. Rod Sutherland combines pilot waves and the transactional interpretation in "Causally Symmetric Bohm Model", http://arxiv.org/pdf/quant-ph/0601095v2.pdf.
Hi Dan, Thanks for asking. Very few things are my field, and none of these are, but I, like you, think they are indeed fascinating. John Cramer is a U of WA physicist who proposed TI, the transactional interpretation of Quantum Mechanics as an alternative to the wave-collapse Copenhagen interpretation. TI claims to be objective and explicitly non-local. From Cramer's 1986 paper, which can be found at http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html, "The basic element of the transactional interpretation is an emitter-absorber transaction through the exchange of advanced and retarded waves, as first described by Wheeler and Feynman (1945, 1949) [see also (Feynman, 1967b)]. Advanced waves are solutions of the electromagnetic wave equation and other similar wave equations which contain only the second time derivative. Advanced waves have characteristic eigenvalues of negative energy and frequency, and they propagate in the negative time direction. Fig. 2 illustrates the propagation of advanced and retarded waves. The advanced wave solutions of the electromagnetic wave equation are usually ignored as unphysical because they seem to have no counterpart in nature. ... There is a second application of the Wheeler-Feynman approach which was introduced by the author in a previous publication (Cramer, 1980). The WF description of radiative processes can be applied to the microscopic exchange of a single quantum of energy, momentum, etc., between a present emitter and a single future absorber through the medium of a transaction, a Wheeler-Feynman exchange of advanced and retarded waves. Fig. 3 illustrates a simplified form (one space dimension and one time dimension) of the the transaction process. The emitter, e.g., a vibrating electron or atom in an excited state, attempts to radiate by producing a field. This field, according to the Wheeler-Feynman description, is a time-symmetric combination of a retarded field which propagates into the future and an advanced field which propagates into the past. For simplicity let us first consider the net field to consist of a retarded plane wave of the form F1 ~ exp[i(k.r- t)] for tT1 (T1 is the instant of emission) and an advanced plane wave of the form G1 ~ exp[-i(k.r- t)] for tT1. Since the retarded wave F1has eigenvalues characteristic of positive energy and momentum k, while the advanced wave G1 has eigenvalues of negative energy - and momentum - k, the net loss of energy and momentum by the emitter in producing the pair of waves (F1 + G1) is zero, as might be expected from the time-symmetry of the composite wave." And so forth. The idea is that there is a transaction between the emitter and the absorber and that the transaction is "negotiated" "at the instant" (whatever that means given that we have waves traveling backward in time) it is executed. Cramer uses TI when teaching quantum mechanics. In "The Plane of the Present and the New Transactional Paradigm of Time", he claims that TI doesn't imply no free will, but it is hard for me to see how e.g. forward and retarded waves communicating over the time span from the formation of the CMB to today leaves room for non-determinism. http://arxiv.org/abs/quant-ph/0507089 So that's Cramer and Wheeler-Feynman. John Conway and Simon Kochen wrote about their theorem that can be phrased loosely as "If we have free will, then so do electrons". They argue that quantum mechanics has done away with the deterministic universe forever, but that whatever we humans have in us that we can define as free will is also an attribute of fundamental particles. The Free Will Theorem http://arxiv.org/abs/quant-ph/0604079 "On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications." The Strong Free Will Theorem http://www.ams.org/notices/200902/rtx090200226p.pdf?q=will Can't copy/paste here so loosely quoted: If the experimenter is free to choose the orientation of his aparatus, the particle's response (more precisely, the universe's response near the particle's location) is not determined by the entire previous history of the universe. Reitdijk-Putnam-Penrose started with an argument from Reitdijk and Putnam, based upon special relativity, and extended by Penrose in what is called the Andromeda Paradox. From http://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument "If special relativity is true, then each observer will have their own plane of simultaneity, which contains a unique set of events that constitutes the observer's present moment. Observers moving at different relative velocities have different planes of simultaneity hence different sets of events that are present. Each observer considers their set of present events to be a three-dimensional universe, but even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content. If each three-dimensional universe exists, then the existence of multiple three-dimensional universes suggests that the universe is four-dimensional. The argument is named after the discussions by Rietdijk (1966)[1] and Putnam (1967).[2] It is sometimes called the Rietdijk–Putnam–Penrose argument.[3] Roger Penrose[4] advanced a form of this argument that has been called the Andromeda paradox in which he points out that two people walking past each other in the street could have very different present moments. If one of the people were walking towards the Andromeda Galaxy, then events in this galaxy might be hours or even days advanced of the events on Andromeda for the person walking in the other direction. If this occurs, it would have dramatic effects on our understanding of time. Penrose highlighted the consequences by discussing a potential invasion of Earth by aliens living in the Andromeda Galaxy. As Penrose put it:[5] people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability. In fact neither of the people can yet know of the launching of the space fleet. They can know only later, when telescopic observations from earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter, and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past. Was there then any uncertainty about that future? Or was the future of both people already "fixed"?" After reading about the Andromeda Paradox, I played a bit with the relevant special relativity equation, the Lorentz transformation for time, with which synchronized clocks, if in relative motion to you, cease to be synchronized. Distance, i.e. the amount of space between event A and event B, is a factor in the equation, so the greater the spatial separation, the greater the time dilation. If I recall correctly, t' = (t-vx/c^2)/sqrt(1-v^2/c^2) The distance to Andromeda is about 2.5 x 10^6 light years or about 2.4 x 10^22 meters. Walking speed is about 1.4 m/s. If one person is standing and the other is walking by at a time when Andromeda is directly on the horizon, I calculate a difference of around 373850 seconds, or 4.3 days, between the two people in the time of simultaneity. It would be 8.6 days difference if each were walking past one another. Then, they simply could turn and each walk the other way, past one another once again, and their times of simultaneity would have switched! It's difficult for me to see how special relativity, simultaneity and a non-deterministic universe (and hence free will as most people define it) all survive with their common meanings, given the math. It gets worse, for me. The observable universe is about 4.4 x 10^26 meters away on all sides. The space shuttle travels about 1 x 10^11 m/s. Even at 1 x 10^8 m/s, the equation gives me a difference of around 5 x 10^17 seconds. Not bad for a universe that's 1.4 x 10^17 seconds old! I have no idea what it means to have a time of simultaneity between two observable objects that implies that one of those times is before the Big Bang. (Yes, I know about the Hubble Flow and how we can have a 46 million light-year distance between us and a visible object in only 14 billion years or so. I don't know how the increased distances due to the Hubble Flow play into special relativity.) Well, enough, Dan, about all that. The key point relevant to your inquiry is that the Andromeda Paradox is another nail helping to pin down the evidence I see against free will as I knew it as a child. And regarding the Bohm thing that still stirs .... that was just me, saying something like "Bohm is rolling over in his grave" except in a good way, i.e. Bohm's ideas still have power. I apologize for making you think there was something even more interesting to learn about ... But I'm glad you asked for explanations, thanks! Jeff On Mon, Jun 30, 2014 at 5:22 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Jeff, this sounds ultra-interesting, but my lack of background prevents me from understanding what you've written.
Can you please include some more detail? Like, what are the Cramer thing, the Wheeler-Feynman thing, the Conway-Kochen thing, the Rietdijk–Putnam–Penrose thing, and the Bohm thing that "still stirs" ?
Thanks,
Dan
On Jun 30, 2014, at 2:12 PM, Jeff Caldwell <jeffrey.d.caldwell@gmail.com> wrote:
I hope to better understand the curious case of the photon. It has no frame of reference and, were it conscious, would perceive itself to be emitted and absorbed simultaneously, i.e. no time passing between the events. With zero time between emission and absorption, whimsy allows me to think of emitter and absorber as in some sense touching, albeit one is an ancient star and the other a cone in my living eye. Zero time means zero distance, in my book, although applying that rule to the no-frame-of-reference photon is probably a category error. Cramer's transactional interpretation, inspired by Wheeler-Feynman time-symmetric theory, has both forward and backward-in-time waves between emitter and absorber, agreeing upon the transaction before (as? timey-wimey words ...) it takes place, which leaves precious little room for the free will electrons have if you or I do, John Conway and Simon Kocken say, and leaving no room at all for deciding whether or not to slide a detector into a photon's path after the photon has been emitted. Emitters, detectors and photons have united, and their agreements will be kept! At least, in this regime, Rietdijk–Putnam–Penrose can be resolved in the affirmative.
And now pilot waves. Bohm still stirs. Rod Sutherland combines pilot waves and the transactional interpretation in "Causally Symmetric Bohm Model", http://arxiv.org/pdf/quant-ph/0601095v2.pdf.
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The quantum mechanical wave function for a system of n particles is a function on a 3n-dimensional space. If these pilot waves are something real, where do they live, in ordinary 3-space or in 3n-space? How is spin handled? When a measurement is made on one of two separated entangled particles, does the pilot wave of the other particle change instantaneously, faster than the speed of light? The Bohmians need to answer these questions if they hope to be taken seriously. While these fluid dynamics experiments are nice, those waves are real waves that can be measured. There is no way to measure a wave function. If the Bohmians wish to reify (make real) the wave function, they should either show us how to measure it, or be very clever in explaining why it can't be measured. The true significance, to me at least, of the Einstein-Podolsky-Rosen paper is that it demonstrates that the wave function cannot be reified, not without violating causality. One should separate the physical part from the interpretive part. The physical part is what can be experimentally measured, and the standard theory does that job admirably. The interpretive part fills the gap in our intuition, our lack of understanding why physics should be quantum mechanical, our dissatisfaction with its foundations. It's not like, once you see F=ma, you say, "but of course, it could not be any other way." Interpretations are personal opinions, as long as their predictions agree with experiment. Most physicists go with the Copenhagen interpretation since it appears to be the least problematical. This is the interpretation which posits that the wave function is a probability amplitude, possessing the same kind of reality as classical probability. -- Gene
On Mon, Jun 30, 2014 at 5:24 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
Most physicists go with the Copenhagen interpretation since it appears to be the least problematical. This is the interpretation which posits that the wave function is a probability amplitude, possessing the same kind of reality as classical probability.
All of the interpretations say that, as far as I'm aware. Copenhagen says that the wave function "collapses" randomly when it's observed. The collapse postulate, in my opinion, is clearly wrong. If it actually behaved that way, it would be - The only non-linear evolution in all of quantum mechanics. - The only non-unitary evolution in all of quantum mechanics. - The only non-differentiable (in fact, discontinuous) phenomenon in all of quantum mechanics. - The only phenomenon in all of quantum mechanics that is non-local in the configuration space. - The only phenomenon in all of physics that violates CPT symmetry. - The only phenomenon in all of physics that violates Liouville's Theorem (has a many-to-one mapping from initial conditions to outcomes). - The only phenomenon in all of physics that is acausal / non-deterministic / inherently random. - The only phenomenon in all of physics that is non-local in spacetime and propagates an influence faster than light. (http://lesswrong.com/lw/q6/collapse_postulates/) -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
________________________________ From: Mike Stay <metaweta@gmail.com> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Monday, June 30, 2014 5:31 PM Subject: Re: [math-fun] Quantum Mechanical Pilot waves: they're baaaack !
On Mon, Jun 30, 2014 at 5:24 PM, Eugene Salamin via math-fun
<math-fun@mailman.xmission.com> wrote:
Most physicists go with the Copenhagen interpretation since it appears to be the least problematical. This is the interpretation which posits that the wave function is a probability amplitude, possessing the same kind of reality as classical probability.
All of the interpretations say that, as far as I'm aware. Copenhagen says that the wave function "collapses" randomly when it's observed. The collapse postulate, in my opinion, is clearly wrong. If it actually behaved that way, it would be
- The only non-linear evolution in all of quantum mechanics. - The only non-unitary evolution in all of quantum mechanics. - The only non-differentiable (in fact, discontinuous) phenomenon in all of quantum mechanics. - The only phenomenon in all of quantum mechanics that is non-local in the configuration space. - The only phenomenon in all of physics that violates CPT symmetry. - The only phenomenon in all of physics that violates Liouville's Theorem (has a many-to-one mapping from initial conditions to outcomes). - The only phenomenon in all of physics that is acausal / non-deterministic / inherently random. - The only phenomenon in all of physics that is non-local in spacetime and propagates an influence faster than light.
(http://lesswrong.com/lw/q6/collapse_postulates/)
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
No, The Copenhagenists assert that the wave function represents a state of knowledge. Wave function collapse is not a physical process obeying an evolution equation. It is an update to our knowledge.
-- Gene
On Mon, Jun 30, 2014 at 5:44 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
No, The Copenhagenists assert that the wave function represents a state of knowledge. Wave function collapse is not a physical process obeying an evolution equation. It is an update to our knowledge.
No, you're describing a Bayesian interpretation. From http://en.wikipedia.org/wiki/Quantum_Bayesianism : -------- Quantum Bayesianism applies the Bayesian approach to the fundamentals of quantum mechanics. The Bayesian approach is a mode of statistical inference. It introduces the concept of "degree of belief"... Quantum Bayesianism is an alternative to the (more) popular Copenhagen interpretation of quantum mechanics, which is built upon the idea of wavefunction collapse. The Copenhagen interpretation does not assume a specific interpretation of probability. -----------
From http://en.wikipedia.org/wiki/Copenhagen_interpretation :
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics.[1] It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta, entities that fit neither the classical idea of particles nor the classical idea of waves. The act of measurement causes the set of probabilities to immediately and randomly assume only one of the possible values. This feature of mathematics is known as wavefunction collapse. The essential concepts of the interpretation were devised by Niels Bohr, Werner Heisenberg and others in the years 1924-27. -----------
"When the Copenhagen interpretation was first expressed, Niels Bohr postulated wave function collapse to cut the quantum world from the classical.[5] This tactical move allowed quantum theory to develop without distractions from interpretational worries. Nevertheless it was debated, for if collapse were a fundamental physical phenomenon, rather than just the epiphenomenonof some other process, it would mean nature was fundamentally stochastic, i.e. nondeterministic, an undesirable property for a theory.[3][6] This issue remained until quantum decoherence entered mainstream opinion after its reformulation in the 1980s.[3][4][7]" ----------- Decoherence is what happens when you trace out a subsystem that doesn't interest you or over which you have no control. Given a density matrix [A B] [C D], tracing out a qubit gives [A+D]. In particular, an EPR pair (fully entangled pair of particles) has a density matrix 1/2 * [1 0 0 1] [0 0 0 0] [0 0 0 0] [1 0 0 1] but when you trace out one of the particles, the result is the mixed state 1/2 * [1 0] [0 1]. A photon that bounces off a semisilvered mirror so that part of the wavefunction amplitude gets reflected and part goes into a human's eye entangles the human's brain with the photon. Mathematically, there's no reason to choose the basis "human sees photon" (x) /"human doesn't see photon" (y) as opposed to (x + y) / (x - y), but because brains evolved only to perceive information they could use, decoherence pretty much means a human's never going to be aware of being in a superposition. I think, on the other hand, it's likely that viruses could exploit superposition somehow. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
I think it's better to say that most physicists view the Copenhagen interpretation as convenient for calculation --- we don't believe the collapse is a physical event. A "measurement" is just an interaction, like any other physical interaction. When a small system interacts with a larger one, the two systems become entangled and have a joint wave function. This is true whether the larger system is the brain of an experimenter, a photographic plate, or any other macroscopic system. In theory, if we could account for all the interactions we could reverse them, and disentangle the two systems. The smaller system would then be "unmeasured". But this is rather like unscrambling an egg. If the interactions are difficult to control or reverse --- which is generally true when the larger system has a huge number of particles --- then the system's wave function effectively collapses. - Cris On Jun 30, 2014, at 6:31 PM, Mike Stay <metaweta@gmail.com> wrote:
On Mon, Jun 30, 2014 at 5:24 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
Most physicists go with the Copenhagen interpretation since it appears to be the least problematical. This is the interpretation which posits that the wave function is a probability amplitude, possessing the same kind of reality as classical probability.
All of the interpretations say that, as far as I'm aware. Copenhagen says that the wave function "collapses" randomly when it's observed. The collapse postulate, in my opinion, is clearly wrong. If it actually behaved that way, it would be
- The only non-linear evolution in all of quantum mechanics. - The only non-unitary evolution in all of quantum mechanics. - The only non-differentiable (in fact, discontinuous) phenomenon in all of quantum mechanics. - The only phenomenon in all of quantum mechanics that is non-local in the configuration space. - The only phenomenon in all of physics that violates CPT symmetry. - The only phenomenon in all of physics that violates Liouville's Theorem (has a many-to-one mapping from initial conditions to outcomes). - The only phenomenon in all of physics that is acausal / non-deterministic / inherently random. - The only phenomenon in all of physics that is non-local in spacetime and propagates an influence faster than light.
(http://lesswrong.com/lw/q6/collapse_postulates/)
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Isn't `wavefunction collapse' just a lazy shorthand for `the system we're interested in interacts with the observer, who is so huge and complex that decoherence occurs and thus the observer never sees the superposition'? Sincerely, Adam P. Goucher
All of the interpretations say that, as far as I'm aware. Copenhagen says that the wave function "collapses" randomly when it's observed. The collapse postulate, in my opinion, is clearly wrong. If it actually behaved that way, it would be
- The only non-linear evolution in all of quantum mechanics. - The only non-unitary evolution in all of quantum mechanics. - The only non-differentiable (in fact, discontinuous) phenomenon in all of quantum mechanics. - The only phenomenon in all of quantum mechanics that is non-local in the configuration space. - The only phenomenon in all of physics that violates CPT symmetry. - The only phenomenon in all of physics that violates Liouville's Theorem (has a many-to-one mapping from initial conditions to outcomes). - The only phenomenon in all of physics that is acausal / non-deterministic / inherently random. - The only phenomenon in all of physics that is non-local in spacetime and propagates an influence faster than light.
(http://lesswrong.com/lw/q6/collapse_postulates/)
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Tue, Jul 1, 2014 at 12:00 AM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Isn't `wavefunction collapse' just a lazy shorthand for `the system we're interested in interacts with the observer, who is so huge and complex that decoherence occurs and thus the observer never sees the superposition'?
That's not how it was originally proposed, and not how some physicists like Penrose believe it happens. See http://en.wikipedia.org/wiki/Objective_collapse_theory . -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
On 7/1/2014 2:18 PM, Mike Stay wrote:
On Tue, Jul 1, 2014 at 12:00 AM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Isn't `wavefunction collapse' just a lazy shorthand for `the system we're interested in interacts with the observer, who is so huge and complex that decoherence occurs and thus the observer never sees the superposition'? That's not how it was originally proposed,
Orignally, i.e. by Bohr, QM was just about what we can calculate. He adopted a kind of mystical idea of "complementarity" which limited what we can say about the world. The classical world had to exist in order that we can have records/knowledge, there was no "quantum world", it was just a useful mathematical fiction. "Collapse" was just part of the mathematics. Heisenberg actually mentions the possibility that interaction with the environment defines the classical/quantum boundary, but he didn't work out decoherence. Brent
and not how some physicists like Penrose believe it happens. See http://en.wikipedia.org/wiki/Objective_collapse_theory .
The trouble is that the pilot wave has to change faster-than-light (per Bell type experiments), so relativistic quantum field theory doesn't work with Bohmian QM. Brent Meeker On 6/30/2014 11:59 AM, Henry Baker wrote:
FYI -- Follow the link to also see the pix.
http://www.wired.com/2014/06/the-new-quantum-reality/
Have We Been Interpreting Quantum Mechanics Wrong This Whole Time?
By Natalie Wolchover, Quanta Magazine 06.30.14 6:30 am
For nearly a century, “reality” has been a murky concept. The laws of quantum physics seem to suggest that particles spend much of their time in a ghostly state, lacking even basic properties such as a definite location and instead existing everywhere and nowhere at once. Only when a particle is measured does it suddenly materialize, appearing to pick its position as if by a roll of the dice.
This idea that nature is inherently probabilistic — that particles have no hard properties, only likelihoods, until they are observed — is directly implied by the standard equations of quantum mechanics. But now a set of surprising experiments with fluids has revived old skepticism about that worldview. The bizarre results are fueling interest in an almost forgotten version of quantum mechanics, one that never gave up the idea of a single, concrete reality.
The experiments involve an oil droplet that bounces along the surface of a liquid. The droplet gently sloshes the liquid with every bounce. At the same time, ripples from past bounces affect its course. The droplet’s interaction with its own ripples, which form what’s known as a pilot wave, causes it to exhibit behaviors previously thought to be peculiar to elementary particles — including behaviors seen as evidence that these particles are spread through space like waves, without any specific location, until they are measured.
Particles at the quantum scale seem to do things that human-scale objects do not do. They can tunnel through barriers, spontaneously arise or annihilate, and occupy discrete energy levels. This new body of research reveals that oil droplets, when guided by pilot waves, also exhibit these quantum-like features.
To some researchers, the experiments suggest that quantum objects are as definite as droplets, and that they too are guided by pilot waves — in this case, fluid-like undulations in space and time. These arguments have injected new life into a deterministic (as opposed to probabilistic) theory of the microscopic world first proposed, and rejected, at the birth of quantum mechanics.
“This is a classical system that exhibits behavior that people previously thought was exclusive to the quantum realm, and we can say why,” said John Bush, a professor of applied mathematics at the Massachusetts Institute of Technology who has led several recent bouncing-droplet experiments. “The more things we understand and can provide a physical rationale for, the more difficult it will be to defend the ‘quantum mechanics is magic’ perspective.”
Magical Measurements
The orthodox view of quantum mechanics, known as the “Copenhagen interpretation” after the home city of Danish physicist Niels Bohr, one of its architects, holds that particles play out all possible realities simultaneously. Each particle is represented by a “probability wave” weighting these various possibilities, and the wave collapses to a definite state only when the particle is measured. The equations of quantum mechanics do not address how a particle’s properties solidify at the moment of measurement, or how, at such moments, reality picks which form to take. But the calculations work. As Seth Lloyd, a quantum physicist at MIT, put it, “Quantum mechanics is just counterintuitive and we just have to suck it up.”
A classic experiment in quantum mechanics that seems to demonstrate the probabilistic nature of reality involves a beam of particles (such as electrons) propelled one by one toward a pair of slits in a screen. When no one keeps track of each electron’s trajectory, it seems to pass through both slits simultaneously. In time, the electron beam creates a wavelike interference pattern of bright and dark stripes on the other side of the screen. But when a detector is placed in front of one of the slits, its measurement causes the particles to lose their wavelike omnipresence, collapse into definite states, and travel through one slit or the other. The interference pattern vanishes. The great 20th-century physicist Richard Feynman said that this double-slit experiment “has in it the heart of quantum mechanics,” and “is impossible, absolutely impossible, to explain in any classical way.”
Some physicists now disagree. “Quantum mechanics is very successful; nobody’s claiming that it’s wrong,” said Paul Milewski, a professor of mathematics at the University of Bath in England who has devised computer models of bouncing-droplet dynamics. “What we believe is that there may be, in fact, some more fundamental reason why [quantum mechanics] looks the way it does.”
Riding Waves
The idea that pilot waves might explain the peculiarities of particles dates back to the early days of quantum mechanics. The French physicist Louis de Broglie presented the earliest version of pilot-wave theory at the 1927 Solvay Conference in Brussels, a famous gathering of the founders of the field. As de Broglie explained that day to Bohr, Albert Einstein, Erwin Schrödinger, Werner Heisenberg and two dozen other celebrated physicists, pilot-wave theory made all the same predictions as the probabilistic formulation of quantum mechanics (which wouldn’t be referred to as the “Copenhagen” interpretation until the 1950s), but without the ghostliness or mysterious collapse.
The probabilistic version, championed by Bohr, involves a single equation that represents likely and unlikely locations of particles as peaks and troughs of a wave. Bohr interpreted this probability-wave equation as a complete definition of the particle. But de Broglie urged his colleagues to use two equations: one describing a real, physical wave, and another tying the trajectory of an actual, concrete particle to the variables in that wave equation, as if the particle interacts with and is propelled by the wave rather than being defined by it.
For example, consider the double-slit experiment. In de Broglie’s pilot-wave picture, each electron passes through just one of the two slits, but is influenced by a pilot wave that splits and travels through both slits. Like flotsam in a current, the particle is drawn to the places where the two wavefronts cooperate, and does not go where they cancel out.
De Broglie could not predict the exact place where an individual particle would end up — just like Bohr’s version of events, pilot-wave theory predicts only the statistical distribution of outcomes, or the bright and dark stripes — but the two men interpreted this shortcoming differently. Bohr claimed that particles don’t have definite trajectories; de Broglie argued that they do, but that we can’t measure each particle’s initial position well enough to deduce its exact path.
In principle, however, the pilot-wave theory is deterministic: The future evolves dynamically from the past, so that, if the exact state of all the particles in the universe were known at a given instant, their states at all future times could be calculated.
At the Solvay conference, Einstein objected to a probabilistic universe, quipping, “God does not play dice,” but he seemed ambivalent about de Broglie’s alternative. Bohr told Einstein to “stop telling God what to do,” and (for reasons that remain in dispute) he won the day. By 1932, when the Hungarian-American mathematician John von Neumann claimed to have proven that the probabilistic wave equation in quantum mechanics could have no “hidden variables” (that is, missing components, such as de Broglie’s particle with its well-defined trajectory), pilot-wave theory was so poorly regarded that most physicists believed von Neumann’s proof without even reading a translation.
More than 30 years would pass before von Neumann’s proof was shown to be false, but by then the damage was done. The physicist David Bohm resurrected pilot-wave theory in a modified form in 1952, with Einstein’s encouragement, and made clear that it did work, but it never caught on. (The theory is also known as de Broglie-Bohm theory, or Bohmian mechanics.)
Later, the Northern Irish physicist John Stewart Bell went on to prove a seminal theorem that many physicists today misinterpret as rendering hidden variables impossible. But Bell supported pilot-wave theory. He was the one who pointed out the flaws in von Neumann’s original proof. And in 1986 he wrote that pilot-wave theory “seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored.”
The neglect continues. A century down the line, the standard, probabilistic formulation of quantum mechanics has been combined with Einstein’s theory of special relativity and developed into the Standard Model, an elaborate and precise description of most of the particles and forces in the universe. Acclimating to the weirdness of quantum mechanics has become a physicists’ rite of passage. The old, deterministic alternative is not mentioned in most textbooks; most people in the field haven’t heard of it. Sheldon Goldstein, a professor of mathematics, physics and philosophy at Rutgers University and a supporter of pilot-wave theory, blames the “preposterous” neglect of the theory on “decades of indoctrination.” At this stage, Goldstein and several others noted, researchers risk their careers by questioning quantum orthodoxy.
A Quantum Drop
Now at last, pilot-wave theory may be experiencing a minor comeback — at least, among fluid dynamicists. “I wish that the people who were developing quantum mechanics at the beginning of last century had access to these experiments,” Milewski said. “Because then the whole history of quantum mechanics might be different.”
The experiments began a decade ago, when Yves Couder and colleagues at Paris Diderot University discovered that vibrating a silicon oil bath up and down at a particular frequency can induce a droplet to bounce along the surface. The droplet’s path, they found, was guided by the slanted contours of the liquid’s surface generated from the droplet’s own bounces — a mutual particle-wave interaction analogous to de Broglie’s pilot-wave concept.
In a groundbreaking experiment, the Paris researchers used the droplet setup to demonstrate single- and double-slit interference. They discovered that when a droplet bounces toward a pair of openings in a damlike barrier, it passes through only one slit or the other, while the pilot wave passes through both. Repeated trials show that the overlapping wavefronts of the pilot wave steer the droplets to certain places and never to locations in between — an apparent replication of the interference pattern in the quantum double-slit experiment that Feynman described as “impossible … to explain in any classical way.” And just as measuring the trajectories of particles seems to “collapse” their simultaneous realities, disturbing the pilot wave in the bouncing-droplet experiment destroys the interference pattern.
Droplets can also seem to “tunnel” through barriers, orbit each other in stable “bound states,” and exhibit properties analogous to quantum spin and electromagnetic attraction. When confined to circular areas called corrals, they form concentric rings analogous to the standing waves generated by electrons in quantum corrals. They even annihilate with subsurface bubbles, an effect reminiscent of the mutual destruction of matter and antimatter particles.
In each test, the droplet wends a chaotic path that, over time, builds up the same statistical distribution in the fluid system as that expected of particles at the quantum scale. But rather than resulting from indefiniteness or a lack of reality, these quantum-like effects are driven, according to the researchers, by “path memory.” Every bounce of the droplet leaves a mark in the form of ripples, and these ripples chaotically but deterministically influence the droplet’s future bounces and lead to quantum-like statistical outcomes. The more path memory a given fluid exhibits — that is, the less its ripples dissipate — the crisper and more quantum-like the statistics become. “Memory generates chaos, which we need to get the right probabilities,” Couder explained. “We see path memory clearly in our system. It doesn’t necessarily mean it exists in quantum objects, it just suggests it would be possible.”
The quantum statistics are apparent even when the droplets are subjected to external forces. In one recent test, Couder and his colleagues placed a magnet at the center of their oil bath and observed a magnetic ferrofluid droplet. Like an electron occupying fixed energy levels around a nucleus, the bouncing droplet adopted a discrete set of stable orbits around the magnet, each characterized by a set energy level and angular momentum. The “quantization” of these properties into discrete packets is usually understood as a defining feature of the quantum realm.
If space and time behave like a superfluid, or a fluid that experiences no dissipation at all, then path memory could conceivably give rise to the strange quantum phenomenon of entanglement — what Einstein referred to as “spooky action at a distance.” When two particles become entangled, a measurement of the state of one instantly affects that of the other. The entanglement holds even if the two particles are light-years apart.
In standard quantum mechanics, the effect is rationalized as the instantaneous collapse of the particles’ joint probability wave. But in the pilot-wave version of events, an interaction between two particles in a superfluid universe sets them on paths that stay correlated forever because the interaction permanently affects the contours of the superfluid. “As the particles move along, they feel the wave field generated by them in the past and all other particles in the past,” Bush explained. In other words, the ubiquity of the pilot wave “provides a mechanism for accounting for these nonlocal correlations.” Yet an experimental test of droplet entanglement remains a distant goal.
Subatomic Realities
Many of the fluid dynamicists involved in or familiar with the new research have become convinced that there is a classical, fluid explanation of quantum mechanics. “I think it’s all too much of a coincidence,” said Bush, who led a June workshop on the topic in Rio de Janeiro and is writing a review paper on the experiments for the Annual Review of Fluid Mechanics.
Quantum physicists tend to consider the findings less significant. After all, the fluid research does not provide direct evidence that pilot waves propel particles at the quantum scale. And a surprising analogy between electrons and oil droplets does not yield new and better calculations. “Personally, I think it has little to do with quantum mechanics,” said Gerard ’t Hooft, a Nobel Prize-winning particle physicist at Utrecht University in the Netherlands. He believes quantum theory is incomplete but dislikes pilot-wave theory.
Many working quantum physicists question the value of rebuilding their highly successful Standard Model from scratch. “I think the experiments are very clever and mind-expanding,” said Frank Wilczek, a professor of physics at MIT and a Nobel laureate, “but they take you only a few steps along what would have to be a very long road, going from a hypothetical classical underlying theory to the successful use of quantum mechanics as we know it.”
“This really is a very striking and visible manifestation of the pilot-wave phenomenon,” Lloyd said. “It’s mind-blowing — but it’s not going to replace actual quantum mechanics anytime soon.”
In its current, immature state, the pilot-wave formulation of quantum mechanics only describes simple interactions between matter and electromagnetic fields, according toDavid Wallace, a philosopher of physics at the University of Oxford in England, and cannot even capture the physics of an ordinary light bulb. “It is not by itself capable of representing very much physics,” Wallace said. “In my own view, this is the most severe problem for the theory, though, to be fair, it remains an active research area.”
Pilot-wave theory has the reputation of being more cumbersome than standard quantum mechanics. Some researchers said that the theory has trouble dealing with identical particles, and that it becomes unwieldy when describing multiparticle interactions. They also claimed that it combines less elegantly with special relativity. But other specialists in quantum mechanics disagreed or said the approach is simply under-researched. It may just be a matter of effort to recast the predictions of quantum mechanics in the pilot-wave language, said Anthony Leggett, a professor of physics at the University of Illinois, Urbana-Champaign, and a Nobel laureate. “Whether one thinks this is worth a lot of time and effort is a matter of personal taste,” he added. “Personally, I don’t.”
On the other hand, as Bohm argued in his 1952 paper, an alternative formulation of quantum mechanics might make the same predictions as the standard version at the quantum scale, but differ when it comes to smaller scales of nature. In the search for a unified theory of physics at all scales, “we could easily be kept on the wrong track for a long time by restricting ourselves to the usual interpretation of quantum theory,” Bohm wrote.
Some enthusiasts think the fluid approach could indeed be the key to resolving the long-standing conflict between quantum mechanics and Einstein’s theory of gravity, which clash at infinitesimal scales.
“The possibility exists that we can look for a unified theory of the Standard Model and gravity in terms of an underlying, superfluid substrate of reality,” said Ross Anderson, a computer scientist and mathematician at the University of Cambridge in England, and the co-author of a recent paper on the fluid-quantum analogy. In the future, Anderson and his collaborators plan to study the behavior of “rotons” (particle-like excitations) in superfluid helium as an even closer analog of this possible “superfluid model of reality.”
But at present, these connections with quantum gravity are speculative, and for young researchers, risky ideas. Bush, Couder and the other fluid dynamicists hope that their demonstrations of a growing number of quantum-like phenomena will make a deterministic, fluid picture of quantum mechanics increasingly convincing.
“With physicists it’s such a controversial thing, and people are pretty noncommittal at this stage,” Bush said. “We’re just forging ahead, and time will tell. The truth wins out in the end.”
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Since Bell supposedly supported the pilot wave idea in 1986 (according to the article quoted below), Bell (at least) thought that it was consistent with relativity and other experiments (presumably the Alain Aspect experiments). At 07:23 PM 6/30/2014, meekerdb wrote:
The trouble is that the pilot wave has to change faster-than-light (per Bell type experiments), so relativistic quantum field theory doesn't work with Bohmian QM.
Brent Meeker
On 6/30/2014 11:59 AM, Henry Baker wrote:
FYI -- Follow the link to also see the pix.
http://www.wired.com/2014/06/the-new-quantum-reality/
Have We Been Interpreting Quantum Mechanics Wrong This Whole Time?
By Natalie Wolchover, Quanta Magazine 06.30.14 6:30 am
For nearly a century, Âreality has been a murky concept. The laws of quantum physics seem to suggest that particles spend much of their time in a ghostly state, lacking even basic properties such as a definite location and instead existing everywhere and nowhere at once. Only when a particle is measured does it suddenly materialize, appearing to pick its position as if by a roll of the dice.
This idea that nature is inherently probabilistic  that particles have no hard properties, only likelihoods, until they are observed  is directly implied by the standard equations of quantum mechanics. But now a set of surprising experiments with fluids has revived old skepticism about that worldview. The bizarre results are fueling interest in an almost forgotten version of quantum mechanics, one that never gave up the idea of a single, concrete reality.
The experiments involve an oil droplet that bounces along the surface of a liquid. The droplet gently sloshes the liquid with every bounce. At the same time, ripples from past bounces affect its course. The dropletÂs interaction with its own ripples, which form whatÂs known as a pilot wave, causes it to exhibit behaviors previously thought to be peculiar to elementary particles  including behaviors seen as evidence that these particles are spread through space like waves, without any specific location, until they are measured.
Particles at the quantum scale seem to do things that human-scale objects do not do. They can tunnel through barriers, spontaneously arise or annihilate, and occupy discrete energy levels. This new body of research reveals that oil droplets, when guided by pilot waves, also exhibit these quantum-like features.
To some researchers, the experiments suggest that quantum objects are as definite as droplets, and that they too are guided by pilot waves  in this case, fluid-like undulations in space and time. These arguments have injected new life into a deterministic (as opposed to probabilistic) theory of the microscopic world first proposed, and rejected, at the birth of quantum mechanics.
ÂThis is a classical system that exhibits behavior that people previously thought was exclusive to the quantum realm, and we can say why, said John Bush, a professor of applied mathematics at the Massachusetts Institute of Technology who has led several recent bouncing-droplet experiments. ÂThe more things we understand and can provide a physical rationale for, the more difficult it will be to defend the Âquantum mechanics is magic perspective.Â
Magical Measurements
The orthodox view of quantum mechanics, known as the ÂCopenhagen interpretation after the home city of Danish physicist Niels Bohr, one of its architects, holds that particles play out all possible realities simultaneously. Each particle is represented by a Âprobability wave weighting these various possibilities, and the wave collapses to a definite state only when the particle is measured. The equations of quantum mechanics do not address how a particleÂs properties solidify at the moment of measurement, or how, at such moments, reality picks which form to take. But the calculations work. As Seth Lloyd, a quantum physicist at MIT, put it, ÂQuantum mechanics is just counterintuitive and we just have to suck it up.Â
A classic experiment in quantum mechanics that seems to demonstrate the probabilistic nature of reality involves a beam of particles (such as electrons) propelled one by one toward a pair of slits in a screen. When no one keeps track of each electronÂs trajectory, it seems to pass through both slits simultaneously. In time, the electron beam creates a wavelike interference pattern of bright and dark stripes on the other side of the screen. But when a detector is placed in front of one of the slits, its measurement causes the particles to lose their wavelike omnipresence, collapse into definite states, and travel through one slit or the other. The interference pattern vanishes. The great 20th-century physicist Richard Feynman said that this double-slit experiment Âhas in it the heart of quantum mechanics, and Âis impossible, absolutely impossible, to explain in any classical way.Â
Some physicists now disagree. ÂQuantum mechanics is very successful; nobodyÂs claiming that itÂs wrong, said Paul Milewski, a professor of mathematics at the University of Bath in England who has devised computer models of bouncing-droplet dynamics. ÂWhat we believe is that there may be, in fact, some more fundamental reason why [quantum mechanics] looks the way it does.Â
Riding Waves
The idea that pilot waves might explain the peculiarities of particles dates back to the early days of quantum mechanics. The French physicist Louis de Broglie presented the earliest version of pilot-wave theory at the 1927 Solvay Conference in Brussels, a famous gathering of the founders of the field. As de Broglie explained that day to Bohr, Albert Einstein, Erwin Schrödinger, Werner Heisenberg and two dozen other celebrated physicists, pilot-wave theory made all the same predictions as the probabilistic formulation of quantum mechanics (which wouldnÂt be referred to as the ÂCopenhagen interpretation until the 1950s), but without the ghostliness or mysterious collapse.
The probabilistic version, championed by Bohr, involves a single equation that represents likely and unlikely locations of particles as peaks and troughs of a wave. Bohr interpreted this probability-wave equation as a complete definition of the particle. But de Broglie urged his colleagues to use two equations: one describing a real, physical wave, and another tying the trajectory of an actual, concrete particle to the variables in that wave equation, as if the particle interacts with and is propelled by the wave rather than being defined by it.
For example, consider the double-slit experiment. In de BroglieÂs pilot-wave picture, each electron passes through just one of the two slits, but is influenced by a pilot wave that splits and travels through both slits. Like flotsam in a current, the particle is drawn to the places where the two wavefronts cooperate, and does not go where they cancel out.
De Broglie could not predict the exact place where an individual particle would end up  just like BohrÂs version of events, pilot-wave theory predicts only the statistical distribution of outcomes, or the bright and dark stripes  but the two men interpreted this shortcoming differently. Bohr claimed that particles donÂt have definite trajectories; de Broglie argued that they do, but that we canÂt measure each particleÂs initial position well enough to deduce its exact path.
In principle, however, the pilot-wave theory is deterministic: The future evolves dynamically from the past, so that, if the exact state of all the particles in the universe were known at a given instant, their states at all future times could be calculated.
At the Solvay conference, Einstein objected to a probabilistic universe, quipping, ÂGod does not play dice, but he seemed ambivalent about de BroglieÂs alternative. Bohr told Einstein to Âstop telling God what to do, and (for reasons that remain in dispute) he won the day. By 1932, when the Hungarian-American mathematician John von Neumann claimed to have proven that the probabilistic wave equation in quantum mechanics could have no Âhidden variables (that is, missing components, such as de BroglieÂs particle with its well-defined trajectory), pilot-wave theory was so poorly regarded that most physicists believed von NeumannÂs proof without even reading a translation.
More than 30 years would pass before von NeumannÂs proof was shown to be false, but by then the damage was done. The physicist David Bohm resurrected pilot-wave theory in a modified form in 1952, with EinsteinÂs encouragement, and made clear that it did work, but it never caught on. (The theory is also known as de Broglie-Bohm theory, or Bohmian mechanics.)
Later, the Northern Irish physicist John Stewart Bell went on to prove a seminal theorem that many physicists today misinterpret as rendering hidden variables impossible. But Bell supported pilot-wave theory. He was the one who pointed out the flaws in von NeumannÂs original proof. And in 1986 he wrote that pilot-wave theory Âseems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored.Â
The neglect continues. A century down the line, the standard, probabilistic formulation of quantum mechanics has been combined with EinsteinÂs theory of special relativity and developed into the Standard Model, an elaborate and precise description of most of the particles and forces in the universe. Acclimating to the weirdness of quantum mechanics has become a physicists rite of passage. The old, deterministic alternative is not mentioned in most textbooks; most people in the field havenÂt heard of it. Sheldon Goldstein, a professor of mathematics, physics and philosophy at Rutgers University and a supporter of pilot-wave theory, blames the Âpreposterous neglect of the theory on Âdecades of indoctrination. At this stage, Goldstein and several others noted, researchers risk their careers by questioning quantum orthodoxy.
A Quantum Drop
Now at last, pilot-wave theory may be experiencing a minor comeback  at least, among fluid dynamicists. ÂI wish that the people who were developing quantum mechanics at the beginning of last century had access to these experiments, Milewski said. ÂBecause then the whole history of quantum mechanics might be different.Â
The experiments began a decade ago, when Yves Couder and colleagues at Paris Diderot University discovered that vibrating a silicon oil bath up and down at a particular frequency can induce a droplet to bounce along the surface. The dropletÂs path, they found, was guided by the slanted contours of the liquidÂs surface generated from the dropletÂs own bounces  a mutual particle-wave interaction analogous to de BroglieÂs pilot-wave concept.
In a groundbreaking experiment, the Paris researchers used the droplet setup to demonstrate single- and double-slit interference. They discovered that when a droplet bounces toward a pair of openings in a damlike barrier, it passes through only one slit or the other, while the pilot wave passes through both. Repeated trials show that the overlapping wavefronts of the pilot wave steer the droplets to certain places and never to locations in between  an apparent replication of the interference pattern in the quantum double-slit experiment that Feynman described as Âimpossible  to explain in any classical way. And just as measuring the trajectories of particles seems to Âcollapse their simultaneous realities, disturbing the pilot wave in the bouncing-droplet experiment destroys the interference pattern.
Droplets can also seem to Âtunnel through barriers, orbit each other in stable Âbound states, and exhibit properties analogous to quantum spin and electromagnetic attraction. When confined to circular areas called corrals, they form concentric rings analogous to the standing waves generated by electrons in quantum corrals. They even annihilate with subsurface bubbles, an effect reminiscent of the mutual destruction of matter and antimatter particles.
In each test, the droplet wends a chaotic path that, over time, builds up the same statistical distribution in the fluid system as that expected of particles at the quantum scale. But rather than resulting from indefiniteness or a lack of reality, these quantum-like effects are driven, according to the researchers, by Âpath memory. Every bounce of the droplet leaves a mark in the form of ripples, and these ripples chaotically but deterministically influence the dropletÂs future bounces and lead to quantum-like statistical outcomes. The more path memory a given fluid exhibits  that is, the less its ripples dissipate  the crisper and more quantum-like the statistics become. ÂMemory generates chaos, which we need to get the right probabilities, Couder explained. ÂWe see path memory clearly in our system. It doesnÂt necessarily mean it exists in quantum objects, it just suggests it would be possible.Â
The quantum statistics are apparent even when the droplets are subjected to external forces. In one recent test, Couder and his colleagues placed a magnet at the center of their oil bath and observed a magnetic ferrofluid droplet. Like an electron occupying fixed energy levels around a nucleus, the bouncing droplet adopted a discrete set of stable orbits around the magnet, each characterized by a set energy level and angular momentum. The Âquantization of these properties into discrete packets is usually understood as a defining feature of the quantum realm.
If space and time behave like a superfluid, or a fluid that experiences no dissipation at all, then path memory could conceivably give rise to the strange quantum phenomenon of entanglement  what Einstein referred to as Âspooky action at a distance. When two particles become entangled, a measurement of the state of one instantly affects that of the other. The entanglement holds even if the two particles are light-years apart.
In standard quantum mechanics, the effect is rationalized as the instantaneous collapse of the particles joint probability wave. But in the pilot-wave version of events, an interaction between two particles in a superfluid universe sets them on paths that stay correlated forever because the interaction permanently affects the contours of the superfluid. ÂAs the particles move along, they feel the wave field generated by them in the past and all other particles in the past, Bush explained. In other words, the ubiquity of the pilot wave Âprovides a mechanism for accounting for these nonlocal correlations. Yet an experimental test of droplet entanglement remains a distant goal.
Subatomic Realities
Many of the fluid dynamicists involved in or familiar with the new research have become convinced that there is a classical, fluid explanation of quantum mechanics. ÂI think itÂs all too much of a coincidence, said Bush, who led a June workshop on the topic in Rio de Janeiro and is writing a review paper on the experiments for the Annual Review of Fluid Mechanics.
Quantum physicists tend to consider the findings less significant. After all, the fluid research does not provide direct evidence that pilot waves propel particles at the quantum scale. And a surprising analogy between electrons and oil droplets does not yield new and better calculations. ÂPersonally, I think it has little to do with quantum mechanics, said Gerard Ât Hooft, a Nobel Prize-winning particle physicist at Utrecht University in the Netherlands. He believes quantum theory is incomplete but dislikes pilot-wave theory.
Many working quantum physicists question the value of rebuilding their highly successful Standard Model from scratch. ÂI think the experiments are very clever and mind-expanding, said Frank Wilczek, a professor of physics at MIT and a Nobel laureate, Âbut they take you only a few steps along what would have to be a very long road, going from a hypothetical classical underlying theory to the successful use of quantum mechanics as we know it.Â
ÂThis really is a very striking and visible manifestation of the pilot-wave phenomenon, Lloyd said. ÂItÂs mind-blowing  but itÂs not going to replace actual quantum mechanics anytime soon.Â
In its current, immature state, the pilot-wave formulation of quantum mechanics only describes simple interactions between matter and electromagnetic fields, according toDavid Wallace, a philosopher of physics at the University of Oxford in England, and cannot even capture the physics of an ordinary light bulb. ÂIt is not by itself capable of representing very much physics, Wallace said. ÂIn my own view, this is the most severe problem for the theory, though, to be fair, it remains an active research area.Â
Pilot-wave theory has the reputation of being more cumbersome than standard quantum mechanics. Some researchers said that the theory has trouble dealing with identical particles, and that it becomes unwieldy when describing multiparticle interactions. They also claimed that it combines less elegantly with special relativity. But other specialists in quantum mechanics disagreed or said the approach is simply under-researched. It may just be a matter of effort to recast the predictions of quantum mechanics in the pilot-wave language, said Anthony Leggett, a professor of physics at the University of Illinois, Urbana-Champaign, and a Nobel laureate. ÂWhether one thinks this is worth a lot of time and effort is a matter of personal taste, he added. ÂPersonally, I donÂt.Â
On the other hand, as Bohm argued in his 1952 paper, an alternative formulation of quantum mechanics might make the same predictions as the standard version at the quantum scale, but differ when it comes to smaller scales of nature. In the search for a unified theory of physics at all scales, Âwe could easily be kept on the wrong track for a long time by restricting ourselves to the usual interpretation of quantum theory, Bohm wrote.
Some enthusiasts think the fluid approach could indeed be the key to resolving the long-standing conflict between quantum mechanics and EinsteinÂs theory of gravity, which clash at infinitesimal scales.
ÂThe possibility exists that we can look for a unified theory of the Standard Model and gravity in terms of an underlying, superfluid substrate of reality, said Ross Anderson, a computer scientist and mathematician at the University of Cambridge in England, and the co-author of a recent paper on the fluid-quantum analogy. In the future, Anderson and his collaborators plan to study the behavior of Ârotons (particle-like excitations) in superfluid helium as an even closer analog of this possible Âsuperfluid model of reality.Â
But at present, these connections with quantum gravity are speculative, and for young researchers, risky ideas. Bush, Couder and the other fluid dynamicists hope that their demonstrations of a growing number of quantum-like phenomena will make a deterministic, fluid picture of quantum mechanics increasingly convincing.
ÂWith physicists itÂs such a controversial thing, and people are pretty noncommittal at this stage, Bush said. ÂWeÂre just forging ahead, and time will tell. The truth wins out in the end.Â
It is consistent in the sense that you can't use it to signal FTL. But it violates the spirit of relativity (having a preferred frame) and this has prevented it from being extended to quantum field theory where the number of particles is indefinite. I really don't see how a liquid model is going to accomplish the FTL changes in the pilot waves; which are necessary in the theory even though they can't be used for communication. Brent On 6/30/2014 9:00 PM, Henry Baker wrote:
Since Bell supposedly supported the pilot wave idea in 1986 (according to the article quoted below), Bell (at least) thought that it was consistent with relativity and other experiments (presumably the Alain Aspect experiments).
At 07:23 PM 6/30/2014, meekerdb wrote:
The trouble is that the pilot wave has to change faster-than-light (per Bell type experiments), so relativistic quantum field theory doesn't work with Bohmian QM.
Brent Meeker
On 6/30/2014 11:59 AM, Henry Baker wrote:
FYI -- Follow the link to also see the pix.
http://www.wired.com/2014/06/the-new-quantum-reality/
Have We Been Interpreting Quantum Mechanics Wrong This Whole Time?
By Natalie Wolchover, Quanta Magazine 06.30.14 6:30 am
For nearly a century, “reality” has been a murky concept. The laws of quantum physics seem to suggest that particles spend much of their time in a ghostly state, lacking even basic properties such as a definite location and instead existing everywhere and nowhere at once. Only when a particle is measured does it suddenly materialize, appearing to pick its position as if by a roll of the dice.
This idea that nature is inherently probabilistic — that particles have no hard properties, only likelihoods, until they are observed — is directly implied by the standard equations of quantum mechanics. But now a set of surprising experiments with fluids has revived old skepticism about that worldview. The bizarre results are fueling interest in an almost forgotten version of quantum mechanics, one that never gave up the idea of a single, concrete reality.
The experiments involve an oil droplet that bounces along the surface of a liquid. The droplet gently sloshes the liquid with every bounce. At the same time, ripples from past bounces affect its course. The droplet’s interaction with its own ripples, which form what’s known as a pilot wave, causes it to exhibit behaviors previously thought to be peculiar to elementary particles — including behaviors seen as evidence that these particles are spread through space like waves, without any specific location, until they are measured.
Particles at the quantum scale seem to do things that human-scale objects do not do. They can tunnel through barriers, spontaneously arise or annihilate, and occupy discrete energy levels. This new body of research reveals that oil droplets, when guided by pilot waves, also exhibit these quantum-like features.
To some researchers, the experiments suggest that quantum objects are as definite as droplets, and that they too are guided by pilot waves — in this case, fluid-like undulations in space and time. These arguments have injected new life into a deterministic (as opposed to probabilistic) theory of the microscopic world first proposed, and rejected, at the birth of quantum mechanics.
“This is a classical system that exhibits behavior that people previously thought was exclusive to the quantum realm, and we can say why,” said John Bush, a professor of applied mathematics at the Massachusetts Institute of Technology who has led several recent bouncing-droplet experiments. “The more things we understand and can provide a physical rationale for, the more difficult it will be to defend the ‘quantum mechanics is magic’ perspective.”
Magical Measurements
The orthodox view of quantum mechanics, known as the “Copenhagen interpretation” after the home city of Danish physicist Niels Bohr, one of its architects, holds that particles play out all possible realities simultaneously. Each particle is represented by a “probability wave” weighting these various possibilities, and the wave collapses to a definite state only when the particle is measured. The equations of quantum mechanics do not address how a particle’s properties solidify at the moment of measurement, or how, at such moments, reality picks which form to take. But the calculations work. As Seth Lloyd, a quantum physicist at MIT, put it, “Quantum mechanics is just counterintuitive and we just have to suck it up.”
A classic experiment in quantum mechanics that seems to demonstrate the probabilistic nature of reality involves a beam of particles (such as electrons) propelled one by one toward a pair of slits in a screen. When no one keeps track of each electron’s trajectory, it seems to pass through both slits simultaneously. In time, the electron beam creates a wavelike interference pattern of bright and dark stripes on the other side of the screen. But when a detector is placed in front of one of the slits, its measurement causes the particles to lose their wavelike omnipresence, collapse into definite states, and travel through one slit or the other. The interference pattern vanishes. The great 20th-century physicist Richard Feynman said that this double-slit experiment “has in it the heart of quantum mechanics,” and “is impossible, absolutely impossible, to explain in any classical way.”
Some physicists now disagree. “Quantum mechanics is very successful; nobody’s claiming that it’s wrong,” said Paul Milewski, a professor of mathematics at the University of Bath in England who has devised computer models of bouncing-droplet dynamics. “What we believe is that there may be, in fact, some more fundamental reason why [quantum mechanics] looks the way it does.”
Riding Waves
The idea that pilot waves might explain the peculiarities of particles dates back to the early days of quantum mechanics. The French physicist Louis de Broglie presented the earliest version of pilot-wave theory at the 1927 Solvay Conference in Brussels, a famous gathering of the founders of the field. As de Broglie explained that day to Bohr, Albert Einstein, Erwin Schrödinger, Werner Heisenberg and two dozen other celebrated physicists, pilot-wave theory made all the same predictions as the probabilistic formulation of quantum mechanics (which wouldn’t be referred to as the “Copenhagen” interpretation until the 1950s), but without the ghostliness or mysterious collapse.
The probabilistic version, championed by Bohr, involves a single equation that represents likely and unlikely locations of particles as peaks and troughs of a wave. Bohr interpreted this probability-wave equation as a complete definition of the particle. But de Broglie urged his colleagues to use two equations: one describing a real, physical wave, and another tying the trajectory of an actual, concrete particle to the variables in that wave equation, as if the particle interacts with and is propelled by the wave rather than being defined by it.
For example, consider the double-slit experiment. In de Broglie’s pilot-wave picture, each electron passes through just one of the two slits, but is influenced by a pilot wave that splits and travels through both slits. Like flotsam in a current, the particle is drawn to the places where the two wavefronts cooperate, and does not go where they cancel out.
De Broglie could not predict the exact place where an individual particle would end up — just like Bohr’s version of events, pilot-wave theory predicts only the statistical distribution of outcomes, or the bright and dark stripes — but the two men interpreted this shortcoming differently. Bohr claimed that particles don’t have definite trajectories; de Broglie argued that they do, but that we can’t measure each particle’s initial position well enough to deduce its exact path.
In principle, however, the pilot-wave theory is deterministic: The future evolves dynamically from the past, so that, if the exact state of all the particles in the universe were known at a given instant, their states at all future times could be calculated.
At the Solvay conference, Einstein objected to a probabilistic universe, quipping, “God does not play dice,” but he seemed ambivalent about de Broglie’s alternative. Bohr told Einstein to “stop telling God what to do,” and (for reasons that remain in dispute) he won the day. By 1932, when the Hungarian-American mathematician John von Neumann claimed to have proven that the probabilistic wave equation in quantum mechanics could have no “hidden variables” (that is, missing components, such as de Broglie’s particle with its well-defined trajectory), pilot-wave theory was so poorly regarded that most physicists believed von Neumann’s proof without even reading a translation.
More than 30 years would pass before von Neumann’s proof was shown to be false, but by then the damage was done. The physicist David Bohm resurrected pilot-wave theory in a modified form in 1952, with Einstein’s encouragement, and made clear that it did work, but it never caught on. (The theory is also known as de Broglie-Bohm theory, or Bohmian mechanics.)
Later, the Northern Irish physicist John Stewart Bell went on to prove a seminal theorem that many physicists today misinterpret as rendering hidden variables impossible. But Bell supported pilot-wave theory. He was the one who pointed out the flaws in von Neumann’s original proof. And in 1986 he wrote that pilot-wave theory “seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored.”
The neglect continues. A century down the line, the standard, probabilistic formulation of quantum mechanics has been combined with Einstein’s theory of special relativity and developed into the Standard Model, an elaborate and precise description of most of the particles and forces in the universe. Acclimating to the weirdness of quantum mechanics has become a physicists’ rite of passage. The old, deterministic alternative is not mentioned in most textbooks; most people in the field haven’t heard of it. Sheldon Goldstein, a professor of mathematics, physics and philosophy at Rutgers University and a supporter of pilot-wave theory, blames the “preposterous” neglect of the theory on “decades of indoctrination.” At this stage, Goldstein and several others noted, researchers risk their careers by questioning quantum orthodoxy.
A Quantum Drop
Now at last, pilot-wave theory may be experiencing a minor comeback — at least, among fluid dynamicists. “I wish that the people who were developing quantum mechanics at the beginning of last century had access to these experiments,” Milewski said. “Because then the whole history of quantum mechanics might be different.”
The experiments began a decade ago, when Yves Couder and colleagues at Paris Diderot University discovered that vibrating a silicon oil bath up and down at a particular frequency can induce a droplet to bounce along the surface. The droplet’s path, they found, was guided by the slanted contours of the liquid’s surface generated from the droplet’s own bounces — a mutual particle-wave interaction analogous to de Broglie’s pilot-wave concept.
In a groundbreaking experiment, the Paris researchers used the droplet setup to demonstrate single- and double-slit interference. They discovered that when a droplet bounces toward a pair of openings in a damlike barrier, it passes through only one slit or the other, while the pilot wave passes through both. Repeated trials show that the overlapping wavefronts of the pilot wave steer the droplets to certain places and never to locations in between — an apparent replication of the interference pattern in the quantum double-slit experiment that Feynman described as “impossible … to explain in any classical way.” And just as measuring the trajectories of particles seems to “collapse” their simultaneous realities, disturbing the pilot wave in the bouncing-droplet experiment destroys the interference pattern.
Droplets can also seem to “tunnel” through barriers, orbit each other in stable “bound states,” and exhibit properties analogous to quantum spin and electromagnetic attraction. When confined to circular areas called corrals, they form concentric rings analogous to the standing waves generated by electrons in quantum corrals. They even annihilate with subsurface bubbles, an effect reminiscent of the mutual destruction of matter and antimatter particles.
In each test, the droplet wends a chaotic path that, over time, builds up the same statistical distribution in the fluid system as that expected of particles at the quantum scale. But rather than resulting from indefiniteness or a lack of reality, these quantum-like effects are driven, according to the researchers, by “path memory.” Every bounce of the droplet leaves a mark in the form of ripples, and these ripples chaotically but deterministically influence the droplet’s future bounces and lead to quantum-like statistical outcomes. The more path memory a given fluid exhibits — that is, the less its ripples dissipate — the crisper and more quantum-like the statistics become. “Memory generates chaos, which we need to get the right probabilities,” Couder explained. “We see path memory clearly in our system. It doesn’t necessarily mean it exists in quantum objects, it just suggests it would be possible.”
The quantum statistics are apparent even when the droplets are subjected to external forces. In one recent test, Couder and his colleagues placed a magnet at the center of their oil bath and observed a magnetic ferrofluid droplet. Like an electron occupying fixed energy levels around a nucleus, the bouncing droplet adopted a discrete set of stable orbits around the magnet, each characterized by a set energy level and angular momentum. The “quantization” of these properties into discrete packets is usually understood as a defining feature of the quantum realm.
If space and time behave like a superfluid, or a fluid that experiences no dissipation at all, then path memory could conceivably give rise to the strange quantum phenomenon of entanglement — what Einstein referred to as “spooky action at a distance.” When two particles become entangled, a measurement of the state of one instantly affects that of the other. The entanglement holds even if the two particles are light-years apart.
In standard quantum mechanics, the effect is rationalized as the instantaneous collapse of the particles’ joint probability wave. But in the pilot-wave version of events, an interaction between two particles in a superfluid universe sets them on paths that stay correlated forever because the interaction permanently affects the contours of the superfluid. “As the particles move along, they feel the wave field generated by them in the past and all other particles in the past,” Bush explained. In other words, the ubiquity of the pilot wave “provides a mechanism for accounting for these nonlocal correlations.” Yet an experimental test of droplet entanglement remains a distant goal.
Subatomic Realities
Many of the fluid dynamicists involved in or familiar with the new research have become convinced that there is a classical, fluid explanation of quantum mechanics. “I think it’s all too much of a coincidence,” said Bush, who led a June workshop on the topic in Rio de Janeiro and is writing a review paper on the experiments for the Annual Review of Fluid Mechanics.
Quantum physicists tend to consider the findings less significant. After all, the fluid research does not provide direct evidence that pilot waves propel particles at the quantum scale. And a surprising analogy between electrons and oil droplets does not yield new and better calculations. “Personally, I think it has little to do with quantum mechanics,” said Gerard ’t Hooft, a Nobel Prize-winning particle physicist at Utrecht University in the Netherlands. He believes quantum theory is incomplete but dislikes pilot-wave theory.
Many working quantum physicists question the value of rebuilding their highly successful Standard Model from scratch. “I think the experiments are very clever and mind-expanding,” said Frank Wilczek, a professor of physics at MIT and a Nobel laureate, “but they take you only a few steps along what would have to be a very long road, going from a hypothetical classical underlying theory to the successful use of quantum mechanics as we know it.”
“This really is a very striking and visible manifestation of the pilot-wave phenomenon,” Lloyd said. “It’s mind-blowing — but it’s not going to replace actual quantum mechanics anytime soon.”
In its current, immature state, the pilot-wave formulation of quantum mechanics only describes simple interactions between matter and electromagnetic fields, according toDavid Wallace, a philosopher of physics at the University of Oxford in England, and cannot even capture the physics of an ordinary light bulb. “It is not by itself capable of representing very much physics,” Wallace said. “In my own view, this is the most severe problem for the theory, though, to be fair, it remains an active research area.”
Pilot-wave theory has the reputation of being more cumbersome than standard quantum mechanics. Some researchers said that the theory has trouble dealing with identical particles, and that it becomes unwieldy when describing multiparticle interactions. They also claimed that it combines less elegantly with special relativity. But other specialists in quantum mechanics disagreed or said the approach is simply under-researched. It may just be a matter of effort to recast the predictions of quantum mechanics in the pilot-wave language, said Anthony Leggett, a professor of physics at the University of Illinois, Urbana-Champaign, and a Nobel laureate. “Whether one thinks this is worth a lot of time and effort is a matter of personal taste,” he added. “Personally, I don’t.”
On the other hand, as Bohm argued in his 1952 paper, an alternative formulation of quantum mechanics might make the same predictions as the standard version at the quantum scale, but differ when it comes to smaller scales of nature. In the search for a unified theory of physics at all scales, “we could easily be kept on the wrong track for a long time by restricting ourselves to the usual interpretation of quantum theory,” Bohm wrote.
Some enthusiasts think the fluid approach could indeed be the key to resolving the long-standing conflict between quantum mechanics and Einstein’s theory of gravity, which clash at infinitesimal scales.
“The possibility exists that we can look for a unified theory of the Standard Model and gravity in terms of an underlying, superfluid substrate of reality,” said Ross Anderson, a computer scientist and mathematician at the University of Cambridge in England, and the co-author of a recent paper on the fluid-quantum analogy. In the future, Anderson and his collaborators plan to study the behavior of “rotons” (particle-like excitations) in superfluid helium as an even closer analog of this possible “superfluid model of reality.”
But at present, these connections with quantum gravity are speculative, and for young researchers, risky ideas. Bush, Couder and the other fluid dynamicists hope that their demonstrations of a growing number of quantum-like phenomena will make a deterministic, fluid picture of quantum mechanics increasingly convincing.
“With physicists it’s such a controversial thing, and people are pretty noncommittal at this stage,” Bush said. “We’re just forging ahead, and time will tell. The truth wins out in the end.”
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