An international team of researchers from the University of Toronto, Griffith University (Brisbane), and the Institute for Quantum Computing (Waterloo) demonstrate "surrealistic" quantum trajectories in the lab

The Persistence of Memory, Salvador Dalí
Quantum mechanics, according to the common view, taught us that the world is uncertain: that in the quantum realm, you can't ask where a baseball was before you caught it. Electrons are described as "smeared out" in quantum waves, a sort of probability distribution, with no definite positions. But in fact, there is an alternate view, the "Bohm interpretation," in which quantum particles have definite positions, and are merely "guided" by these waves, like some kind of microscopic surfers. In 2011, a group at the University of Toronto succeeded in carrying out a measurement which reproduced the trajectories individual photons follow according to this interpretation. Meanwhile, another group of physicists had started raising objections to this picture about 20 years ago. They pointed out that in certain circumstances, a particle could follow one path according to the Bohm model, and yet cause a real detector to fire along an entirely different path -- they derided the Bohmian trajectories as being "surreal" in such cases. Now, by following the trajectories of entangled photons in an interferometer, the Toronto group has directly observed this strange behaviour of quantum trajectories, and offered data to try to explain how it arises. In particular, it is well known that quantum mechanics is not consistent with the kind of deterministic model that Einstein famously called for with his "God does not play dice!" The Bohm model is saved by violating one of Einstein's cherished principles, locality, or "no-action-at-a-distance." This experiment directly observes the non-local behaviour of the Bohm trajectories, and the authors suggest that this is how the "paradox" should be resolved.

If there is one "fact" about quantum mechanics that is most widely repeated at cocktail parties, it is probably that the world is "random" -- that even if Einstein didn't wish to believe it, "God throws dice with the Universe." Earlier this year, a triplet of remarkable papers convincingly closed the last major loopholes in testing "Bell's Theorem," which many reports described as the final proof that Einstein was wrong.

In fact, for more than half a century, there has been a consistent interpretation of quantum mechanics, due to Louis de Broglie, David Bohm, and others, which is completely deterministic: there is no randomness at all. But there is a price to pay if we wish to believe in these "Bohmian trajectories." It is that this theory is "nonlocal" -- that is, it says that a butterfly flapping its wings in Kuala Lumpur today might not just affect the weather in New York next year, but could affect something happening in the Orion nebula right now, a phenomenon known as "instantaneous action at a distance," which presents a real tension with Einstein's relativity.

In fact, what the tests of Bell's Theorem strictly confirmed was that any "realistic" model of the Universe must actually be nonlocal, not that no such model was possible.

While a sizable community has studied Bohm's approach for decades, most physicists are probably not even aware of it, and it receives relatively short shrift even in discussions of foundations of quantum mechanics. Nevertheless, in 1992, Englert, Scully, Süssman, and Walther ("ESSW") analyzed a fascinating gedankenexperiment, in which one particle travels through an example of the famous "double-slit interferometer" behind so many of Einstein's debates with Niels Bohr, while another system -- let us call it a "probe" -- interacts (and thereby becomes entangled) with it, to keep track of which slit the particle traversed. They found a contradiction, in some instances, between which slit examination of the probe would tell us that particle had chosen and the story recounted by the Bohmian trajectory of the particle. They concluded elegantly that what Bohmian mechanics offered was not a deeper "reality," but a "surrealistic trajectory," something unrelated to what was observably verifiable by looking at a probe. This conclusion led to widespread discussion among a very narrow group of people.

Meanwhile, in 2011, our group was able to demonstrate a method for directly reconstructing these previously hidden Bohm trajectories, mapping out the "average paths" taken by an ensemble of single photons flying through an interferometer. While this result cannot be used to "confirm" Bohm's interpretation -- like all interpretations, it gives precisely the same experimental predictions as any other view of the quantum theory -- it rekindled some discussion of this alternative perspective on reality.

Immediately, we began thinking about whether or not there was a way to extend our work to the "surrealistic" scenario, as did our colleagues Boris Braverman and Christoph Simon (see "for further reading"). Now, using pairs of entangled photons, one of which in essence "remembers" which path the other takes, we have implemented the ESSW idea, and for the first time, measured the trajectories for a particle going through an interferometer after interacting with a probe. Our first finding is that ESSW were entirely correct -- there are cases where if one reads the probe after the particle has reached a "screen" (or single-photon camera, in our experiment), it disagrees with the reconstructed Bohm trajectory as to which slit the particle went through. But we went further, and were able to watch the behaviour of the probe as its twin moved along its path, and find something more interesting -- the motion of one particle through the interferometer instantaneously affects the state of the other. A probe may begin having recorded the particle traversing the lower slit, but little by little change its state until at the end of the experiment, it seems to say it was the upper slit which was taken.

In other words, the disagreement arises not because Bohm's trajectories are "surrealistic" -- it arises because Einstein's "spooky action at a distance" is alive and well, and plays havoc with the probe's memory.

This work appears in Science Advances on Friday, February 19th, 2016.

We hope these results serve to bring Bohm's theory back out of the shadows, and make his view of the quantum world more visualizable, to demonstrate how it can be connected with real-life observations in the laboratory. Yet they also remind us that, as with all interpretations of quantum mechanics, there are pitfalls and tradeoffs and it's not always clear at the outset what the upshot is going to be. Susan Sontag once said "Interpretation is the revenge of the intellectual upon art." Perhaps the intellectuals can now take their revenge on nature as well.

For Further Reading

Our technical article, "Experimental nonlocal and surreal Bohmian trajectories" by Dylan Mahler, Lee Rozema, Kent Fisher, Lydia Vermeyden, Kevin Resch, Howard Wiseman, and Aephraim Steinberg, was published online in Science Advances on 19 February 2016.

See also

"Quantum weirdness may hide an orderly reality after all, Anil Ananthaswamy, New Scientist (2016)

"Surrealistic Bohm Trajectories," Berthold-Georg Englert, Marlan Scully, Georg Süssmann, and Herbert Walther, Z. Naturforsch. 47a, 1175 (1992)
"Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer," Sacha Kocsis, Boris Braverman, Sylvain Ravets, Martin Stevens, Richard Mirin, Krister Shalm, and Aephraim Steinberg, Science 332, 1170 (2011)
(or the musical version by Mitch Benn)
"The secret lives of photons revealed" (Physics World, 2011)
"Proposal to demonstrate the non-locality of Bohmian mechanics with entangled photons," Boris Braverman and Christoph Simon, Phys. Rev. Lett. 110, 060406 (2013)
"The Reality in Bohmian Quantum Mechanics or Can You Kill With an Empty Wave Bullet?", Lev Vaidman (contribution to the Jim Cushing Memorial Found. Phys. Issue, 2003)
"Quantum trajectories, real, surreal or an approximation to a deeper process?", B.J. Hiley, R.E. Callaghan, and O. Maroney (unpublished, 2000)
"Delayed-choice experiments and the Bohm approach", B.J. Hiley and R.E. Callaghan, Phys. Scr. 74, 336 (2006)
D. Bohm, B. Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Theory (Routledge, New York, 1993).

Back to Aephraim's home page