Olena Shmahalo/Quanta Magazine

Olena Shmahalo/Quanta Magazine

Of the many counterintuitive features of quantum mechanics, perhaps the most challenging to our notions of common sense is that particles do not have locations until they are observed. This is exactly what the standard view of quantum mechanics, often called the Copenhagen interpretation, asks us to believe. Instead of the clear-cut positions and movements of Newtonian physics, we have a cloud of probabilities described by a mathematical structure known as a wave function. The wave function, meanwhile, evolves over time, its evolution governed by precise rules codified in something called the Schrödinger equation. The mathematics are clear enough; the actual whereabouts of particles, less so. Until a particle is observed, an act that causes the wave function to “collapse,” we can say nothing about its location. Albert Einstein, among others, objected to this idea. As his biographer Abraham Pais wrote: “We often discussed his notions on objective reality. I recall that during one walk Einstein suddenly stopped, turned to me and asked whether I really believed that the moon exists only when I look at it.”

But there’s another view — one that’s been around for almost a century — in which particles really do have precise positions at all times. This alternative view, known as pilot-wave theory or Bohmian mechanics, never became as popular as the Copenhagen view, in part because Bohmian mechanics implies that the world must be strange in other ways. In particular, a 1992 study claimed to crystalize certain bizarre consequences of Bohmian mechanics and in doing so deal it a fatal conceptual blow. The authors of that paper concluded that a particle following the laws of Bohmian mechanics would end up taking a trajectory that was so unphysical — even by the warped standards of quantum theory — that they described it as “surreal.”

Nearly a quarter-century later, a group of scientists has carried out an experiment in a Toronto laboratory that aims to test this idea. And if their results, first reported earlier this year, hold up to scrutiny, the Bohmian view of quantum mechanics — less fuzzy but in some ways more strange than the traditional view — may be poised for a comeback.

Saving Particle Positions

Bohmian mechanics was worked out by Louis de Broglie in 1927 and again, independently, by David Bohm in 1952, who developed it further until his death in 1992. (It’s also sometimes called the de Broglie–Bohm theory.) As with the Copenhagen view, there’s a wave function governed by the Schrödinger equation. In addition, every particle has an actual, definite location, even when it’s not being observed. Changes in the positions of the particles are given by another equation, known as the “pilot wave” equation (or “guiding equation”). The theory is fully deterministic; if you know the initial state of a system, and you’ve got the wave function, you can calculate where each particle will end up.

That may sound like a throwback to classical mechanics, but there’s a crucial difference. Classical mechanics is purely “local” — stuff can affect other stuff only if it is adjacent to it (or via the influence of some kind of field, like an electric field, which can send impulses no faster than the speed of light). Quantum mechanics, in contrast, is inherently nonlocal. The best-known example of a nonlocal effect — one that Einstein himself considered, back in the 1930s — is when a pair of particles are connected in such a way that a measurement of one particle appears to affect the state of another, distant particle. The idea was ridiculed by Einstein as “spooky action at a distance.” But hundreds of experiments, beginning in the 1980s, have confirmed that this spooky action is a very real characteristic of our universe.

In the Bohmian view, nonlocality is even more conspicuous. The trajectory of any one particle depends on what all the other particles described by the same wave function are doing. And, critically, the wave function has no geographic limits; it might, in principle, span the entire universe. Which means that the universe is weirdly interdependent, even across vast stretches of space. The wave function “combines — or binds — distant particles into a single irreducible reality,” as Sheldon Goldstein, a mathematician and physicist at Rutgers University, has written.

The differences between Bohm and Copenhagen become clear when we look at the classic “double slit” experiment, in which particles (let’s say electrons) pass through a pair of narrow slits, eventually reaching a screen where each particle can be recorded. When the experiment is carried out, the electrons behave like waves, creating on the screen a particular pattern called an “interference pattern.” Remarkably, this pattern gradually emerges even if the electrons are sent one at a time, suggesting that each electron passes through both slits simultaneously.

Those who embrace the Copenhagen view have come to live with this state of affairs — after all, it’s meaningless to speak of a particle’s position until we measure it. Some physicists are drawn instead to the Many Worlds interpretation of quantum mechanics, in which observers in some universes see the electron go through the left slit, while those in other universes see it go through the right slit — which is fine, if you’re comfortable with an infinite array of unseen universes.

By comparison, the Bohmian view sounds rather tame: The electrons act like actual particles, their velocities at any moment fully determined by the pilot wave, which in turn depends on the wave function. In this view, each electron is like a surfer: It occupies a particular place at every specific moment in time, yet its motion is dictated by the motion of a spread-out wave. Although each electron takes a fully determined path through just one slit, the pilot wave passes through both slits. The end result exactly matches the pattern one sees in standard quantum mechanics.

Lucy Reading-Ikkanda for Quanta Magazine

For some theorists, the Bohmian interpretation holds an irresistible appeal. “All you have to do to make sense of quantum mechanics is to say to yourself: When we talk about particles, we really mean particles. Then all the problems go away,” said Goldstein. “Things have positions. They are somewhere. If you take that idea seriously, you’re led almost immediately to Bohm. It’s a far simpler version of quantum mechanics than what you find in the textbooks.” Howard Wiseman, a physicist at Griffith University in Brisbane, Australia, said that the Bohmian view “gives you a pretty straightforward account of how the world is…. You don’t have to tie yourself into any sort of philosophical knots to say how things really are.”

But not everyone feels that way, and over the years the Bohm view has struggled to gain acceptance, trailing behind Copenhagen and, these days, behind Many Worlds as well. A significant blow came with the paper known as “ESSW,” an acronym built from the names of its four authors. The ESSW paper claimed that particles can’t follow simple Bohmian trajectories as they traverse the double-slit experiment. Suppose that someone placed a detector next to each slit, argued ESSW, recording which particle passed through which slit. ESSW showed that a photon could pass through the left slit and yet, in the Bohmian view, still end up being recorded as having passed through the right slit. This seemed impossible; the photons were deemed to follow “surreal” trajectories, as the ESSW paper put it.

The ESSW argument “was a striking philosophical objection” to the Bohmian view, said Aephraim Steinberg, a physicist at the University of Toronto. “It damaged my love for Bohmian mechanics.”

But Steinberg has found a way to rekindle that love. In a paper published in Science Advances, Steinberg and his colleagues — the team includes Wiseman, in Australia, as well as five other Canadian researchers — describe what happened when they actually performed the ESSW experiment. They found that the photon trajectories aren’t surrealistic after all — or, more precisely, that the paths may seem surrealistic, but only if one fails to take into account the nonlocality inherent in Bohm’s theory.

The experiment that Steinberg and his team conducted was analogous to the standard two-slit experiment. They used photons rather than electrons, and instead of sending those photons through a pair of slits, they passed through a beam splitter, a device that directs a photon along one of two paths, depending on the photon’s polarization. The photons eventually reach a single-photon camera (equivalent to the screen in the traditional experiment) that records their final position. The question “Which of two slits did the particle pass through?” becomes “Which of two paths did the photon take?”

Importantly, the researchers used pairs of entangled photons rather than individual photons. As a result, they could interrogate one photon to gain information about the other. When the first photon passes through the beam splitter, the second photon “knows” which path the first one took. The team could then use information from the second photon to track the first photon’s path. Each indirect measurement yields only an approximate value, but the scientists could average large numbers of measurements to reconstruct the trajectory of the first photon.

The team found that the photon paths do indeed appear to be surreal, just as ESSW predicted: A photon would sometimes strike one side of the screen, even though the polarization of the entangled partner said that the photon took the other route.

But can the information from the second photon be trusted? Crucially, Steinberg and his colleagues found that the answer to the question “Which path did the first photon take?” depends on when it is asked.

At first — in the moments immediately after the first photon passes through the beam splitter — the second photon is very strongly correlated with the first photon’s path. “As one particle goes through the slit, the probe [the second photon] has a perfectly accurate memory of which slit it went through,” Steinberg explained.

But the farther the first photon travels, the less reliable the second photon’s report becomes. The reason is nonlocality. Because the two photons are entangled, the path that the first photon takes will affect the polarization of the second photon. By the time the first photon reaches the screen, the second photon’s polarization is equally likely to be oriented one way as the other — thus giving it “no opinion,” so to speak, as to whether the first photon took the first route or the second (the equivalent of knowing which of the two slits it went through).

The problem isn’t that Bohm trajectories are surreal, said Steinberg. The problem is that the second photon says that Bohm trajectories are surreal — and, thanks to nonlocality, its report is not to be trusted. “There’s no real contradiction in there,” said Steinberg. “You just have to always bear in mind the nonlocality, or you miss something very important.”

Faster Than Light

Some physicists, unperturbed by ESSW, have embraced the Bohmian view all along and aren’t particularly surprised by what Steinberg and his team found. There have been many attacks on the Bohmian view over the years, and “they all fizzled out because they had misunderstood what the Bohm approach was actually claiming,” said Basil Hiley, a physicist at Birkbeck, University of London (formerly Birkbeck College), who collaborated with Bohm on his last book, The Undivided Universe. Owen Maroney, a physicist at the University of Oxford who was a student of Hiley’s, described ESSW as “a terrible argument” that “did not present a novel challenge to de Broglie–Bohm.” Not surprisingly, Maroney is excited by Steinberg’s experimental results, which seem to support the view he’s held all along. “It’s a very interesting experiment,” he said. “It gives a motivation for taking de Broglie–Bohm seriously.”

On the other side of the Bohmian divide, Berthold-Georg Englert, one of the authors of ESSW (along with Marlan Scully, George Süssman and Herbert Walther), still describes their paper as a “fatal blow” to the Bohmian view. According to Englert, now at the National University of Singapore, the Bohm trajectories exist as mathematical objects but “lack physical meaning.”

On a historical note, Einstein lived just long enough to hear about Bohm’s revival of de Broglie’s proposal — and he wasn’t impressed, dismissing it as too simplistic to be correct. In a letter to physicist Max Born, in the spring of 1952, Einstein weighed in on Bohm’s work:

Have you noticed that Bohm believes (as de Broglie did, by the way, 25 years ago) that he is able to interpret the quantum theory in deterministic terms? That way seems too cheap to me. But you, of course, can judge this better than I.

But even for those who embrace the Bohmian view, with its clearly defined particles moving along precise paths, questions remain. Topping the list is an apparent tension with special relativity, which prohibits faster-than-light communication. Of course, as physicists have long noted, nonlocality of the sort associated with quantum entanglement does not allow for faster-than-light signaling (thus incurring no risk of the grandfather paradox or other violations of causality). Even so, many physicists feel that more clarification is needed, especially given the prominent role of nonlocality in the Bohmian view. The apparent dependence of what happens here on what may be happening there cries out for an explanation.

“The universe seems to like talking to itself faster than the speed of light,” said Steinberg. “I could understand a universe where nothing can go faster than light, but a universe where the internal workings operate faster than light, and yet we’re forbidden from ever making use of that at the macroscopic level — it’s very hard to understand.”

This article was reprinted on Wired.com.

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  • Sternberg: “I could understand a universe where nothing can go faster than light, but a universe where the internal workings operate faster than light, and yet we’re forbidden from ever making use of that at the macroscopic level — it’s very hard to understand.”

    I don't see why this is particularly difficult for the Bohm picture. Entanglement and Bell's theorem show that it has to be true no matter what model of QM you choose to follow. The other models just leave "the faster than light internal workings" implicit.

  • What an embarrassing piece of pseudoscience. The article "Experimental nonlocal and surreal Bohmian trajectories" in the Science Magazine that is described by the Quanta Magazine text above actually says the following in the "Discussion":

    "We have verified the effect pointed out by ESSW that for a WWM with a delayed readout, Bohmian trajectories originating at the lower slit may be accompanied by WWM results associated with either the upper or the lower slit. …"

    So they have verified that everything that ESSW predicted in their criticism of the Bohmian mechanics. These new authors also claim that they have simultaneously verified "nonlocality". That's nonsense – an experimental verification of nonlocality would require to be able to send some information or influence faster than light. Aside from all physics prizes for "proving Einstein completely wrong", they could also earn billions of dollars for fast trading between London and New York, giving the sell and buy orders before everyone else.

    Physicists have known for sure since 1905 that there can't be any nonlocal influence in Nature, i.e. no experimental verification of any nonlocality. So the only thing that actually happened was that proper (Copenhagen) quantum quantum mechanics was totally confirmed again, like millions of times in the past, while its would-be alternative was killed, like many times before that.

    No seriouos physicist may take Bohmian mechanics seriously now, in the 21st century. It's a totally discredited and forgotten chapter from the dumping ground of the history of physics.

  • Sternberg: “I could understand a universe where nothing can go faster than light, but a universe where the internal workings operate faster than light, and yet we’re forbidden from ever making use of that at the macroscopic level — it’s very hard to understand.”

    I would take analogy with a computer simulation: the values of states within the simulation can be calculated with respect to one another in a way that seems instantaneous from the perspective of simulation time; put another way, there can be an arbitrary amount of computation beween each tick of the simulation.

    This, of course, implies discrete time.

  • @Lubos Motl:

    You're about 10 years behind the science:


    Most working scientists hold fast to the concept of 'realism'—a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affected by actions in space-like separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of 'spooky' actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned.

  • Interesting report. I wonder if pilot waves could be thought of as hints of Stephen Wolfram's network of space? http://blog.stephenwolfram.com/2015/12/what-is-spacetime-really/

  • Oh Lubos, you're always such a delight. You're right that the verified the predictions of ESSW, and those predictions were allegedly "surreal" trajectories. Since those trajectories were actually observed, I guess reality is a little surreal and Bohmian mechanics isn't so unbelievable after all, a point which apparently flew right over your head.

    This surreality shouldn't be surprising to you though, considering you apparently believe in the completely unphysical Copenhagen interpretation. Although I'm mystified at your skepticism about non-locality considering Copenhagen is itself non-local. Of course, anyone who knows anything about QM knows that "non-locality" in this context does not refer to FTL signalling, so your rant against it says much about you.

    But rest assured, Copenhagen is well on its way to that dumping ground of physics you mentioned. From near universal dominance as an interpretation, now less than half of physicists working on QM fundamentals actually believe in Copenhagen. It's really only textbook inertia keeping it going now.

  • Nietzsche introduced the idea of perspectivism: in the final analysis, all we really have is a manifold of interlocking perspectives. For example, consider the following toy model. If humans are small finite, represent each possible human perspective by a small non-empty subset of {1,…,n} where n is a large natural number. Then, there are minimal perspectives, but no maximal human perspective. Still, there is an ideal finite perspective which sees everything! If n=infinity, then there is still an ideal infinite perspective which sees everything! (God's eye-view!) If one accepts the standard quantum logic then one has a manifold of perspectives which cannot-by Gleason's Theorem-be embedded into any single perspective! There are now maximal perspectives, but no universal perspective! (Theologically, this requires accepting polytheism!! Alternatively: Even God suffers from cognitive dissonance!!)

    Dr. David A. Edwards
    Department of Mathematics
    University of Georgia
    Athens, Georgia 30602
    [email protected]

  • The canon of science should be dynamic, vibrant and always open to differing ideas, old or new. Let scientific method prevail, not the guttural grunts of some close minded kangaroo court. Science is not a religion based on dogma, but an ever improving understanding of the universe in which we are born, live, grow old and hopefully learn before we die. The pilot-wave theory, and many other theories that have been left by the wayside as science marches on, should, and rightly so, be revisited from time to time. The reason for this is self evident. The more we expand the empirical understanding of our universe, the more important it is to look backward, as well as forward, constantly reevaluating theoretical models in the light of new empirical data.
    Humanity is still in its cradle, not yet processing omniscience. I applaud Quanta Magazine and its editorial staff for making this excellent article available to the ever curious scientists and thinkers of our time.

  • The two comments here (by Pradeep Mutalik and Lubos Motl) nicely illustrate the problem with terminology in this area, a problem I've addressed a number of times, most recently in
    "Causarum Investigatio and the two Bell's Theorems of John Bell"
    to be published in

    For Mutalik, nonlocality is demonstrated whenever a Bell's inequality is violated for space-like separated events. I maintain we should call that a violation of *local causality* (a notion defined by Bell in 1976) rather than of locality. The "causality" element here is appropriate because this notion is built on the assumption that correlated events must have a common cause that explains the correlation. This is not the case in a purely operational interpretation of quantum mechanics.

    For Motl, nonlocality means signalling faster than light. I maintain we should call that a violation of *signal locality* rather than of locality.

    The nonlocality we address in this experiment is neither of these. It is the violation of *locality*, in the sense (I maintain) that Bell used it in 1964, and that various philosophers of physics (Jon Jarrett, Don Howard) have used it since. It is also known by the ugly name of "parameter independence". You could think of it as signalling at the hidden-variable level. Because we as experimenters don't have access to the hidden variable level, violation of locality does *not* mean we can signal faster than light.

  • An interesting report. I've noted Aephraim Steinberg et al before, see the physicsworld breakthroughs of 2011 (http://physicsworld.com/cws/article/news/2011/dec/16/physics-world-reveals-its-top-10-breakthroughs-for-2011). Jeff Lundeen et al were in second place doing related "weak measurement" work.

    Having looked into this general topic, I'd say that the problem here is that the Copenhagen interpretation is wrong because it's cargo-cult claptrap: the E=hf photon is not some wave of probability that determines the location of a point-particle. But on top of that, the Bohmian interpretation is missing the trick: the photon isn't some speck that has a pilot wave. See Jeff Lundeen's semi-technical explanation (http://www.photonicquantum.info/Research/SemiTechnical_Wavefunction.html) where he says wavefunction is real. It's like the photon IS the pilot wave. But when you detect it at one of the slits, you perform something akin to an optical Fourier transform on it. So you convert it into something pointlike and it goes through that slit only. Then when you detect it at the screen, you again convert it into something pointlike, so you see a dot on the screen.

    It's similar for the electron. The electron isn't some speck that has a field, it IS field. In atomic orbitals electrons "exist as standing waves". Standing wave, standing field. We made the electron out of a photon in pair production, we can diffract electrons, it IS a wave, in a closed path. For an analogy, think of a hurricane. The eye of the storm is not what the storm is. That's where there is no wind. That's where there is no storm. In similar vein the pilot wave IS the electron, not the thing in the middle.

  • I'm with my Czech realist above 🙂

    Nothing I've read here (or elsewhere) is contrary to the experimental predictions of the quantum mechanics of the 1930s. Yet, you have a more complicated interpretation (Bohmian mechanics) which has serious difficulties with aspects of relativity, let alone quantum field theory, all developed because of an anthropocentric need to save determinism without any good reasoning.

    Lacking any differences in experimental outcomes, I'd personally go with the simpler theory which is consistent with relativity and is not motivated by this human bias. Decoherence, which isn't any new physics from the 1930s, seems to me a natural way out of this endless pseudo-paradox claiming that Copenhagen folks need to address some discontinuous wavefunction collapse.

  • In support of the Standard Motl, here's a common aphorism: "Most working scientists hold fast to the concept of ‘realism’—a viewpoint according to which an external reality exists independent of observation."

    But the "realism" in this report goes beyond that and implies the non-Copenhagen view that the observed polarisation of a photon pre-existed the observation. Such an implication is a direct route to the claimed and fanciful nonlocality.

  • Non-locality. Mysterious pilot waves. Particle and wave at the same time depending on observation. Sounds like it's a 5 player game and we're observing only 2 players and trying to piece together "the table".

    Meaning, like Howard Wiseman says, this feels strongly like there are hidden variables in QM. Likely "many more" hidden variables than just one.

    This happened before. Without deeper understanding of forms of energy and periodic tables, ancient theories split the world into elements like "earth, water, air, fire and the myserious aether".

    If our understanding of all "fundamental forces & particles", are missing parts. It will exactly be like the ancients' trying to explain the world via the 5 elements. It'll have gyrations and holes and "spooky actions".

    If astrophysics can have "dark matter" and "dark energy", what makes us think that QM doesn't have "dark something, or two" that apparently causes "non-locality" or "wave/particle" insanity. What if these QM-Dark-Whatever, are at the "edge of existence", so they defy measurement and capture (our main tools of experimentation)

    A fish cannot fathom vacuum even if it can figure out the existence of air (outside it's own water which it lives in). Something immediately outside our perception can be figured out, but if it is several orders of magnitude/layer outside our perception, or even experiment-able constructs. Those are much harder to even think about, let alone experiment on.

  • In the Bohmian view…The trajectory of any one particle depends on what all the other particles described by the same wave function are doing. And, critically, the wave function has no geographic limits; it might, in principle, span the entire universe. Which means that the universe is weirdly interdependent, even across vast stretches of space. The wave function “combines — or binds — distant particles into a single irreducible reality,”

    I'm just wildly speculating, but what if space is quantized, and these particles of space are the smallest possible size (e.g., they have no component pieces). So, if you push one end of this particle, the other end starts to move right away. If all of space is made of these particles, then when a photon goes through a slit/beam slitter, it can be thought of as interacting instantaneously with all other particles of space, and vice versa. It's kind of like when you push one end of a stick, and the other end seems to move at the same time. It doesn't because the things the stick are made of aren't the smallest possible particle size. But, in the case of a photon interacting with the other particles of space, maybe the "other end of the stick" does move and interact instantaneously? Also, these particles of space that the moving photon is pushing could be thought of as a pilot wave?

    Just wild speculation, but I thought I'd throw it out there. Thanks.

  • Amazingly, most people still don’t understand that sending signals faster than light requires that commutators of operators do not vanish outside the light cone. In QFT, they do, while correlation functions (expectation values of time ordered products of operators) do not vanish at all outside the light cone. In fact they can be very strong there. It’s the correlation functions, not the commutators, that cause the violation of Bell inequalities and the like. Once you realize this, all weirdness of qm goes away. No need for pilot waves or all those ugly concoctions some people come up with to explain “wave function collapse” etc.
    Unfortunately, we probably first have to understand how to quantize gravity in order to discover models that show in detail what happens. As long as we don’t, people will continue to worry about “superdeterminism”, “conspiracy” and the like.

  • I agree with John Duffield's eye-of-the-hurricane analogy; I have always pictured the wave(field)/particle duality as a whirlpool. In this way, the field and the particle-like observations are the result of the interaction of whirlpools. The extended field (spiraling waves) of the electron or photon interact with those of a 'particle' (e/m field) of the slit's material as it passes through, which would then convert the particle (concentrated) attribute of the electron/photon to a wave-like attribute while converting the wave (extended) attribute of the electron/photon to a particle-like attribute.

    Further, since 'entanglement' refers to the simultaneous measure of the state (a partial attribute) of two particles, it may be that the extended attributes of the two entangled particles overlap across the large distance, and it is the transformation of the attribute (such as spin state) across this overlap that happens 'immediately'. After all, it is the rho component of the whirlpool (photon) that is measured as constant 'c', and the theta component of the whirlpool (transformation of field/particle) that may be observed as 'immediate', or simultaneous.

    The analogy of interacting whirlpools also lends itself well to relativity, with the exchanging of space and time attributes modeled as rho and theta components of whirlpools.

  • @Howard Wiseman

    Love that you hopped into the comments section to help explicate some things. I'm a big fan of realist conceptions of the quantum wavefunction (whether Bohmian, MWI, or others). Keep up the good work and ignore those like Lubos Motl.

    Anyone who actually considers the Copenhagen Interpretation to be the final word on QM needs to get his/her head examined.

    Great article as well

  • @G. ’t Hooft "It’s the correlation functions, not the commutators, that cause the violation of Bell inequalities and the like. Once you realize this, all weirdness of qm goes away."

    How does the weirdness go away? Isn't this just a more precise restatement of the weirdness? The question remains, why should events outside one another's lightcones be correlated at all when they have no common cause?

  • This is definitely a great article with great discussion. Thank you, Dan Falk, and all commenters here.

    @Howard Wiseman,
    I agree completely with your exhortation to follow proper terminology, and I went through your illuminating paper. I still don’t quite grasp your subtle differentiation of “local causality” and “parameter independence – signaling at the hidden-variable level,” though. Is it that the latter applies only to realist theories, whereas the former applies to operationalist theories as well?

    In this connection it is a little amusing to see George Opletal referring to Luboš Motl as a “Czech realist.” No doubt he means a realist in the sense of “pragmatist” and not in the philosophical sense ̶ Luboš seems to be definitely an operationalist of the “shut up and calculate” variety.

    I am all for developing realist models like Bohm’s. While I understand the need for practicing physicists to use the mathematically most elegant formulations, we do not need to make QM weirder than it is by confusing mathematical descriptions of reality with reality itself ̶ the map in NOT the territory. I can accept the existence of any kind of weird physical objects/fields that can play within time and space dimensions (any number of them) such as waves that can instantaneously spread out their essence across the universe, entangled composite objects that internally violate relativistic signaling limits in a way we cannot, space quantization a la Roger’s comment, Bob’s whirlpool model and so on. Yes, there could be objects of this type – who are we to proscribe them, with our limited experience in the micro domain? But to claim that mathematical models such as the wave functions existing in multidimensional complex Hilbert spaces, and objective probabilities, are real objects, is to break with all other science, and should not be done unless all else fails. I think we are far from that point. When we postulate sub-quantum objects, it will, of course, be necessary to postulate hidden features that we cannot experimentally access today and may never be able to – that is fine, and to be expected, as long as it is done in a principled and parsimonious way. Who knows, a successful model of this type may actually one day extend QM. That being said, we await a realist model that reflects the elegance of the quantum formalism.

    I have some questions for commenters here who are better versed in QM than I am. Please forgive and point out any obvious things that are off-base – I’m trying to understand these things more deeply. 

    @ Joshua McMichael
    Thanks for posting this interesting abstract. The abstract states, “Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned.” My question is: does the Bohm pilot wave model have features that need to be abandoned or is it compatible with the Leggett inequality?

    @George Opletal
    As I understand it, decoherence doesn’t explain why one particular alternative is selected, unless you accept the hyperpromiscuous baggage of the Many Worlds theory. Is there any objection to a sub-quantum randomizing mechanism at a scale far below the Planck scale which kicks in whenever the degree of entanglement exceeds a certain threshold?

    @John Duffield
    If the photon is really the pilot wave, isn’t it correct to say that it’s unlike any wave we know, because the wave completely disappears from everywhere when “something akin to an optical Fourier transform” is applied to it. Don’t we need to have to have a physical model of how something so dispersed becomes pointlike across spatial dimensions instantly? All this seems to indicate that quantum objects are truly timeless or outside of time in some way.

    @ G. ’t Hooft
    Very interesting comment. I want to echo Jim’s comment. Your answer will probably go over my head, but please try. Thanks!

    @Anyone who wants to answer
    (I might be completely off-base here)
    Bohm’s pilot waves are internal features of the model that have to violate relativity in order to be compatible with QM. Why should these internal features need to be made compatible with relativity? They obviously cannot. As long as QM is compatible with relativity, that’s all that matters: after all, on the surface Bohm’s model is compatible with QM isn’t it? Only the surface needs to be compatible with relativity, the internals don't. Is this wrong?

  • A couple of thoughts from a layperson:

    • Two other Quanta Magazine articles, "How Quantum Pairs Stitch Space-Time" (April 28, 2015) and "Quantum Weirdness Now a Matter of Time" (January 19, 2016) may provide some insight as we interpret the results of the Sternberg, et. al. experiment. The first article addresses spacetime connectedness, which could possibly provide a "quantum network" for nonlocal information transfer. Now let's add in the observations from the second article, in which the quantum entanglement is temporal rather than spatial. Could a temporal entanglement be perceived as a nonlocal (superluminal) spatial effect as observed by Sternberg, et. al.?

    • If the "reliability" of quantum entanglement degrades as the particles disperse in spacetime ("…the farther the first photon travels, the less reliable the second photon’s report becomes…"), what are the implications for quantum computing and quantum encryption?

  • Correction: I referred to Aephraim Steinberg as "Sternberg" in my previous post — I apologize for the error.

  • I'm a little confused as to the logic of many of the comments. The ESSW paper demonstrated that the Bohmian version of QM implied a "surreal" path for the deterministic real particle in two slit experiments. They then concluded an impossible path constituted a self-refutation of the Bohmian interpretation, revealing an inconsistency with its notion there is an independent (albeit non-local) reality of deterministic particles following "simple" trajectories. The thing here is, although it may reasonably be argued that Bohmianism isn't Bohmianism if the trajectories aren't simple, the Bohmian system predicts surreal paths will be observed.

    Steinberg et al. report they have found that sometimes experiment finds the predicted surreal path predicted by the Bohmian system, at later phases of the experimental set up. But at earlier phases they find the simple trajectory ESSW thought characteristic of
    the Bohmian system. In their experimental set up, the path of the entangled particle is detected by indirect measurement using polarization. Steinberg et al. suggest that the polarization changes because the pilot wave changes, inevitably, since its nature depends upon the spatial separation between moving particles.

    The first thing I notice is that the experimental results match the Bohmian predictions explicated by ESSW. It is unclear how this refutes Bohm, comments to the contrary.

    [The surreal path prediction reminds me of the Feynman approach, in which the phase contributions from all the possible paths are summed to predict experimental results. Some of those possible paths include some very surreal possibilities as I understand it. I've been a little confused about whether Bohm's system, designed to give the same results as the usual version of QM, isn't as a natural consequence mathematically equivalent, little more than deciding that one can always decide that one of Feynman's virtual particles is *the* real particle, with the pilot wave (which actually seems to be a field?) providing the phase interference information Feynman conceived as coming from the whole ensemble of virtual particles.]

    The second thing I notice is that what needs to be explained is the difference in the correlations at different stages of the experimental set up. Steinberg et al.'s proposal that the changes in the pilot wave change the polarization making the surreal path a false appearance does seem to do that. Whether that is really successful in explaining away experimental contradiction of simple trajectories depends I suppose on how essential you think that picture is for the Bohmian system? It seems more important for those who adhere to Copenhagen to explain that I think, for a start. If there isn't, then this experiment stands as evidence against Copenhagen.

    It's not clear at all to me that this experiment does that. At this point, the thing is that the Copenhagenists seem largely to be represented by Motl's abuse. In particular is is quite unclear how t'Hooft's comment bears on the changes in polarization.

  • Do I have it right that the motivation for the concept of inflation in cosmology is that the cosmological microwave background is too uniform to be explained by information transfer at the speed of light? If so, could non-local quantum effects explain the uniformity without resort to inflation? If the big bang is nothing but a high energy quantum fluctuation, wouldn't one expect quantum effects in the decay of that fluctuation?

  • We have another mysterious theoretical field that spans across the universe: gravity (seen as a force field). Newton was its inceptor (well aware of the issue). Einstein its next serious innovator. Perhaps de Broglie's wave-particle model just illustrates another facet of the same theoretical issue, that of an infinite reach.

  • I have difficulty comprehending how a de Broglie-Bohm (dBB) approach using a 'pilot wave' (essentially a 'wave function') to 'guide' the motion of a particle can duplicate the results of normal QM – at least in the case of many particles, since in that case the 'wave function' exists in a multi-dimensional Hilbert Space – not in real space! Moreover, if the supposed primary advantage of the dBB approach is to provide one with a more classical or realistic visualization/ontology of reality, through what critical physical mechanism does the pilot wave actually affect the particle(s) – and, correspondingly, how does the particle affect the pilot wave? Moreover, if the pilot wave is somehow causing changes in direction to a charged particle, why doesn't the particle radiate EM? The additional conceptual 'baggage' and unspoken questions associated with dBB seems more than a little debilitating!

  • Interesting to see this being talked about. Our FEM simulations are based somewhat on this idea of a "pilot wave", so its cool to see that we are kind of keeping with the pack on this one.

    Just sharing but we don't describe it in terms of a modified probability function like how it was described here, but the methodology is quite similar. We use terms like "torsion", and "curvature".

    Thanks again for new insights into what's going on in the world of physics.

  • I have read a bit about the Holographic Principle, which states that the description of a region of space can be thought of as encoded on the boundary of the region. I understand that the principle somehow arises in string theory and if it holds in reality I think it implies non-locality (a point on the boundary is not associated with a single point in the region but encodes some information associated with the entire region).

  • I found this article on wired.com I hope that you get payed something for the use of your article as there is a crazy amount of advertizment on that web site. Thanks for your content.

  • I only wish I knew enough to understand the mathematical basis for all of this discussion. I understand some of this to a point. My simpleton question: why are the pilot waves effected by the slits? (I assume the electric field of the atoms composing the slits?) Is there a meta-material or other formulation of double-slits (virtual double-slit or analogous double-slits) that can separate the wave and particle? (I guess that was the purpose of the beam splitting experiment)

    I am sure this is an absurd question to those with enough understanding, but I am curious.

  • As an outsider, I see the article as a suggestion that reality might be deterministic in nature after all.

    One development here is to have learnt that "there is no real contradiction in there," as Steinberg puts it, in his defence of the Bohmian trajectories (or the Bohmain view as a whole) against its main criticism made by ESSW.

    As for Englert's beef with the Bohmian view (that its trajectories lack physical meaning), I kind of agree with him but only up to a point, because personally, I do care if Laplace's Demon will be resurrected. For knowing whether the universe's fate has been pre-determined or not is like to affect how I live my life.

  • A universe where nothing can go faster than light speed at the macroscopic level THAT WE KNOW ABOUT. I'm 100% sure that in the next 100 years we will figure out how to do quantum entangled networking and not need an ISP at all.

  • The debate might benefit by moving on from the double-slit problem to consider the Clauser et al. double polarizing beam splitting experiments.

  • If you combine the theories of the respected physicists Carlo Rovelli who argues for an atemporal universe where time is derived and not fundamental, Julian Barbour who argues for an aspatial universe where relative position defines separation, and John Cramer who posited the Transactional Interpretation of QM where "pilot" waves traverse an atemporal/aspatial universe, the mysteries of QM disappear. The certainty of quantum entanglement means that either this approach is correct, or we live in a universe where no existing theory represents a rational model.

  • Interesting stuff but I think there needs to be a clear understanding of what the word "observed" means.
    Like with the moon for a basic example. Observation of which could be in the form of tides and so long as there's something capable of sensing the tide or even the rainfall, there is a clear observation of the existence of the moon. Similarly with any much smaller particle such as a photon which has mass and will interact with the entire universe gravitationally.
    So where can the line of observation be drawn between gravitational fields of a photon and a moon, or a galaxy for that matter?
    Either gravity does not reach the limits of space or the line between observation and non observation is drawn in perceptual cognition and the universe's overall advances in observation technology?

  • Would this theory, if indeed true, have any effect on the possibility of building a quantum computer?

  • "Because the two photons are entangled, the path that the first photon takes will affect the polarization of the second photon."

    Unless I keep reading about fake results, experiments (lots of them) show that the first photon's path does NOT "affect" the second photon. That is precisely the single most important thing the experiments all show, as a matter of fact. The correlation of results occurs when the information about each photon is compared using classical communication (at the end). Entanglement is interesting, however, because information about various outcomes is present and hidden locally (made inaccessible) when a measurement occurs. If I can learn this, why can scientists and science journalists?

    I keep seeing science articles that follow the same pattern. They describe experiments which show one thing – the same thing, over and over – which is good. Somewhere in the middle or near the end of the article the writer gets lost in a description of "nonlocality," then they express a hope of one day having the experiment show the OPPOSITE of what is actually shown (FTL communication, etc.), and they begin discussing it as a possibility. Why bother doing an experiment?


  • What the double slit experiment proves is that the photon acts as an "Orthogonal, Quadratic, Oscillator. Its orthogonal and quadratic because at the double slit, it has the probability to oscillate left or right but also to oscillate up or down (simultaneously). The up/down probability always goes through the same slit (the pattern of hits on the screen is always random). The left/right probability can go through the same slit as the up/down or through the opposite slit. When the probability goes through the opposite slit, extra stripes appear on the detector screen. This eliminates the Many Worlds model since we can have the up/down and left probability go through one slit while the right probability, only, goes through the opposite slit, or vice versa. With one slit closed, all probability goes through the same slit leaving a completely random pattern on the detector screen both vertically and horizontally. The splitting of the left/right probability is what gives rise to the idea of the pilot wave.

  • Excellent!

    And, in their meetings in Copenhagen, Bohr was a loud bully to the mild Einstein.

  • I feel inspired to give a crazy answer to the photon slit. Einstein would forgive me. I believe that the poor photon goes splat against the barrier and flattens out like silly putty so it is stretched wide enough to be detected through two slits simultaneously if the observer is far enough away! Then the photon recontracts to it's original shape and goes on its merry way. It depends on the observer's point of view. May Einstein and all other great physicists forgive my levity and actually give my point of view a moment of thought.

  • It is sad that science and physics going down by introducing a strange things like philosophy, theology, para-physics, witchcraft etc, where two atoms communicate to each other even if they are on the opposite side of universe. Then there is probability that I am Elvis Presley reincarnated in some 10th dimension, etc. Or 4th dimension is curled so small that we do not see it??. isn't that still 3D?, doesn't meter how small. There must be some real science and we should stick to it. Like an example that famous double slit experiment could have very simple explanation. What if electron has a kinetic energy (me*v2/2) and some device fire it axially towards slits? Its path will become helical (starting vector will be resultant, composed with tangential and axial starting speed of electron) and that means its destination point will never be the same. It will depend on starting location and power of the device (starting speed). Eventually after firing so many electrons we will get a infringed pattern.

    Sorry gents, sooner you give up stupidities like Schrodinger cut, etc, the sooner we will get back to real science.

  • The deBroglie-Bohmian view is very similar to the famous walkers experiments, except the "guiding wave" comes with its own equation and its' source is obscure (deBroglie wanted standing waves and just hypothesized them)."
    COMMENTS: Similarly than in the case of the "guiding waves" of the walkers, in my new lattice theory of everything (translated by Marc Fleury in www.gerardgremaud.ch) , the real particles (lattice singularities) are also associated with "guiding waves" which are simply local gravitational vibrations, of which behaviours follow opportunely the Schrödinger equations!

  • That a particle does noy have a defined place when not observed is nonsense. But a free particle that is not bound by some force may be ditributed within a kind of extended space in some way, or may wiggle from point to point faster than the speed of light. Before the particle can be observed it must interact with something that shrinks the space the particle has at its disposal. In the doubleslitexperiment this happens when the particle hits the screen and is fixed to a specific point in the screeen. And then it can be observed. If you close one of the slits, the particle is also bound to a more narrow space when it passes, and this effects its subsequent trajectory. There is thus nothing in this experiment that supports the Copenhagen interpretation. But having a definite place does not imply deterministic behavior. A particle may be at some place at one time, whithout that definitely determines its placement at a later time.

  • When thinking about deBroglie-Bohm, it is most important to keep in mind the measurement is part of the system's wave function, as Holland explains in detail in
    "The Quantum Theory of Motion."

    Also, the quantum potential is not so mysterious when you consider a particle can only be influenced by another particle, as explained by Parmenter and DiRienzo:

  • “The universe seems to like talking to itself faster than the speed of light,” said Steinberg. “I could understand a universe where nothing can go faster than light, but a universe where the internal workings operate faster than light, and yet we’re forbidden from ever making use of that at the macroscopic level — it’s very hard to understand.”

    This is why we can't agree on one quantum solution. We dictate what should the particle do instead of letting it tell us what it wants to do. If all are bounded by the field of gravity, can the observer's geometry, mass, acceleration, and time of observation moving from a non-observing state affect the field where the particle is and randomness occurs? I guess the pilot-wave theory will gain traction in the coming years.

  • Can all the weirdness of double slit experiment be explained by the fact that we are only looking at it from a stationary frame perspective? If you look at the special relativity equation for total energy you see that it has a velocity of the speed of light. In that perspective it looks entirely like a wave of light and would defract and interfere just like light. In our reference frame we observe the momentum energy component and the rest energy component of the total energy separately as the velocity of a particle with rest mass. So it looks like you can have a wave and a particle at the same time.

  • “…when we look at the classic “double slit” experiment, in which particles (let’s say electrons) pass through a pair of narrow slits,…”

    Isn’t it assumed that in the DSE particles are sent one after another in sequence? Do we have the engineering technology to produce a beam of single electron? It appears that the narrowest beam of electrons, that we can generate today, will send millions of electrons simultaneously.

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