What is a superposition really like?

Here’s a longer version of the news story I just published in Scientific American, which includes more context and background. The interpretation of the outcomes of this thought experiment within the two-state vector formalism of quantum mechanics is by no means the only one possible. But what the experiment does show is that quantum mechanics suggests that superpositions are not always simply a case of a particle seeming to be in two places or states at once. A superposition, liker anything else in quantum mechanics, tells you about the possible outcomes of a measurement. All the rest is contingent interpretation. I’m reminded yet again today that it is going to take an awful lot to get media folks to accept this. I'm starting to see now that it was a mistake for me to assume that they didn't know any better; rather, I think there an active, positive desire for the "two places at once" to be true.

I should say also that I consciously decided to turn a blind eye to the use of the word “spooky” in the title of this piece, because it does perfectly acceptable work as it is. It does not imply that “spooky action at a distance” is a thing. It is not a thing, unless it is a disproved thing. Quantum nonlocality is the alternative to that Einsteinian picture.

______________________________________________________________________

It’s the central question in quantum mechanics, and no one knows the answer: what goes on for a particle in a superposition? All of the head-scratching oddness that seems to pervade quantum theory comes from these peculiar circumstances in which particles seem to be in two places or states at once. What that really means has provoked endless debate and argument. Now a team of researchers in Israel and Japan has proposed https://www.nature.com/articles/s41598-018-26018-y an experiment that should let us say something for sure about the nature of that nebulous state [A. C. Elitzur, E. Cohen, R. Okamoto & S. Takeuchi, Sci. Rep. 8, 7730 (2018)].

Their experiment, which they say could be carried out within a few months using existing technologies, should let us sneak a glance at where a quantum object – in this case a particle of light, called a photon – actually is when it is placed in a superposition of positions. And what the researchers predict is even more shocking and strange than the usual picture of this counterintuitive quantum phenomenon.

The classic illustration of a superposition – indeed, the central experiment of quantum mechanics, according to legendary physicist Richard Feynman – involves firing particles like photons through two closely spaced slits in a wall. Because quantum particles can behave like waves, those passing through one slit can ‘interfere’ with those going through the other, their wavy ripples either boosting or cancelling one another. For photons the result is a pattern of light and dark interference bands when the particles are detected on a screen on the far side, corresponding to a high or low number of photons reaching the screen.

Once you accept the waviness of quantum particles, there’s nothing so odd about this interference pattern. You can see it for ordinary water waves passing through double slits too. What is odd, though, is that the interference remains even if the rate of firing particles at the slits is so low that only one passes through at a time. The only way to rationalize that is to say each particle somehow passes through both slits at once, and interferes with itself. That’s a superposition.

To put it another way: when we ask the seemingly reasonable question “Where is the particle in a superposition?”, we’re using a notion of “where” inherited from our classical world, to which the answer can simply be “there”. But quantum mechanics is known now to be ‘nonlocal’, which means we have to relinquish the whole notion of locality – of “whereness”, you might say.

But that’s a hard habit to give up, which is why the ‘two places at once’ picture is commonly invoked to talk about quantum superpositions. Yet quantum mechanics doesn’t say anything about what particles are like until we make measurements on them. For the Danish physicist Niels Bohr, asking where the particle was in the double-slit experiment before it was measured has no meaning within quantum theory itself.

Why don’t we just look? Well, we can. We could put a detector in or just behind one slit that could register the passing of a particle without absorbing it. And in that case, the detector will show that sometimes the particle goes through one slit, and sometimes it goes through the other. But here’s the catch: there’s then no longer an interference pattern, but just the result we’d expect for particles taking one route or the other. Observing which route the particle takes destroys its ‘quantumness’.

This isn’t about measurements disturbing the particle, since interference is absent even in instances where a detector at one slit doesn’t see the particle, so that it ‘must’ have gone through the other slit. Rather, the ‘collapse’ of a superposition seems to be caused by our mere knowledge of the path.

We can try to be smarter. What if we wait until the particle has definitely passed through the slits before we measure the path? How could that delayed measurement affect what happened earlier at the slits themselves? But it does. In the 1960s the physicist John Wheeler proposed a way of doing this using an apparatus called a Mach-Zehnder interferometer, a modification of the double-slit experiment in which a partial mirror creates a superposition of photons that seems to send them along two different paths before they are brought back together to interfere (or not).

The result was that, just as Bohr had predicted, it makes no difference if we delay the detection. Still superposition and interference vanish if we detect the path before we measure the photons. It is as if the particle ‘knows’ our intention to measure it later.

Bohr’s argument that quantum mechanics is silent about ‘reality’ beyond what we can measure has long seemed deeply unsatisfactory to many researchers. “We know something fishy is going on in a superposition”, says physicist Avshalom Elitzur of the Israeli Institute for Advanced Research in Zichron Ya’akov. “But you’re not allowed to measure it”, he says – because then the superposition collapses. “This is what makes quantum mechanics so diabolical.”

There have been many attempts to develop alternative points of view to Bohr’s that restore an underlying reality in quantum mechanics – some description of the world before we look. But none seems able to restore the kind of picture we have in classical physics of objects that always have definite positions and paths.

One particular approach that aims to deduce something about quantum particles before their measurement is called the two-state-vector formalism (TSVF) of quantum mechanics, developed by Elitzur’s former mentor the Israeli physicist Yakir Aharonov and his collaborators. This postulates that quantum events are in some sense determined by quantum states not just in the past but also in the future: it makes the assumption that quantum mechanics works the same way both forwards and backwards in time. In this view, causes can seem to propagate backwards in time: there is retrocausality.

You don’t have to take that strange notion literally. Rather, in the TSVF you can gain retrospective knowledge of what happened in a quantum system by selecting the outcome: not, say, simply measuring where a particle ends up, but instead choosing a particular location in which to look for it. This is called post-selection, and it supplies more information than any unconditional peek at outcomes ever could, because it means that the particle’s situation at any instant is being evaluated retrospectively in the light of its entire history, up to and including measurement. But odd thing is that it looks as if, simply by you choosing to look for a particular outcome, the choice caused that outcome to happen.

“Normal quantum mechanics is about statistics”, Cohen says: what you see are average values, or what is generally called an expectation value of some variable you are measuring. But by looking at when a system produces some particular, chosen value, you can take a slice though the probabilistic theory and start to talk with certainty about what went on to cause that outcome. The odd thing is that it then looks as if your very choice of outcome was part of the cause.

“It’s generally accepted that the TSVF is mathematically equivalent to standard quantum mechanics,” says David Wallace of the University of Southern California, a philosopher who specializes in interpretations of quantum mechanics. “But it does lead to seeing certain things one wouldn’t otherwise have seen.”

Take, for instance, the version of the double-slit experiment devised using the TSVF by Aharonov and coworker Lev Vaidman in 2003. The pair described (but did not build) an optical system in which a single photon can act as a ‘shutter’ that closes a slit by perfectly reflecting another ‘probe’ photon that is doing the standard trick of interfering with itself as it passes through the slits. Aharonov and Vaidman showed that, by applying post-selection to the measurements of the probe photon, we should be able to see that a shutter photon in a superposition can close both (or indeed many) slits at once. So you could say with confidence that the shutter photon really was both ‘here’ and ‘there’ at once [Y. Aharonov & L. Vaidman, Phys. Rev. A 67, 1–3 (2003)] – a situation that seems paradoxical from our everyday experience but is one aspect of the so-called nonlocal properties of quantum particles, where the whole notion of a well-defined location in space dissolves.

In 2016, Ryo Okamoto and Shigeki Takeuchi of Kyoto University implemented Aharonov and Vaidman’s proposal experimentally using apparatus based on a Mach-Zehnder interferometer [R. Okamoto & S. Takeuchi, Sci. Rep. 6, 35161 (2016)]. The ability of a photon to act as a shutter was enabled by a photonic device called a quantum router, in which one photon can control the route taken by another. The crucial point is that this interaction is cleverly arranged to be completely one-sided: it affects only the probe photon. That way, the probe photon carries away no direct information about the shutter photon, and so doesn’t disturb its superposition – but nonetheless one can retrospectively deduce that the shutter photon was definitely in the position needed to reflect the probe.

The Japanese researchers found that the statistics of how the superposed shutter photon reflects the probe photon matched those that Aharonov and Vaidman predicted, and which could only be explained by some non-classical “two places at once” behaviour. “This was a pioneering experiment that allowed one to infer the simultaneous position of a particle in two places”, says Cohen.

Now Elitzur and Cohen have teamed up with Okamoto and Takeuchi to concoct an even more ingenious experiment, which allows one to say with certainty something about the position of a particle in a superposition at a series of different points in time before any measurement has been made. And it seems that this position is even more odd than the traditional “both here and there”.

Again the experiment involves a kind of Mach-Zehnder set-up in which a shutter photon interacts with some probe photon via quantum routers. This time, though, the probe photon’s route is split into three by partial mirrors. Along each of those paths it may interact with a shutter photon in a superposition. These interactions can be considered to take place within boxes labeled A, B and C along the probe photon’s route, and they provide an unambiguous indication that the shutter particle was definitely in a given box at a specific time.

Because nothing is inspected until the probe photon has completed the whole circuit and reached a detector, there should be no collapse of either its superposition or that of the shutter photon – so there’s still interference. But the experiment is carefully set up so that the probe photon can only show this interference pattern if it interacted with the shutter photon in a particular sequence of places and times: namely, if the shutter photon was in both boxes A and C at some time t1, then at a later time t2 only in C, and at a still later time t3 in both B and C. If you see interference in the probe photon, you can say for sure (retrospectively) that the shutter photon displayed this bizarre appearance and disappearance among the boxes at different times – an idea Elitzur, Cohen and Aharonov proposed as a possibility last year for a single particle superposed into three ‘boxes’ [Y. Aharonov, E. Cohen, A. Landau & A. C. Elitzur, Sci. Rep. 7, 531 (2017)].

Why those particular places and times, though? You could certainly look at other points on the route, says Elitzur, but those times and locations are ones where, in this configuration, the probability of finding the particle becomes 1 – in other words, a certainty.

So this thought experiment seems to lift part of the veil off a quantum superposition, and to let us say something definite beyond Bohr’s “Don’t ask” proscription. The TSVF opens up the story by considering both the initial and final states, which allows one to reconstruct what was not measured, namely what happens in between. “I like the way this paper frames questions about what is happening in terms of entire histories, rather than instantaneous states”, says physicist Ken Wharton of San Jose State University in California. “Taking about ‘states’ is an old pervasive bias, whereas full histories are generally far more rich and interesting.”

And the researchers’ interpretation of that intermediate history before measurement is extraordinary. The apparent vanishing of particles in one place at one time, and their reappearance in other times and places, suggests a new vision of what the underlying processes are that create quantum randomness and nonlocality. Within the TSVF, this flickering, ever-changing existence can be understood as a series of events in which a particle is somehow ‘cancelled’ by its own “counterparticle”, with negative energy and negative mass.

Elitzur compares this to the notion introduced by British physicist Paul Dirac in the 1920s that particles have antiparticles that can annihilate one another – a picture that seemed at first just a manner of speaking, but which soon led to the discovery that such antiparticles are real. The disappearance of quantum particles is not annihilation in this same sense, but it is somewhat analogous.

So while the traditional “two places at once” view of superpositions might seem odd enough, “it’s possible that a superposition is a collection of states that are even crazier”, says Elitzur. “Quantum mechanics just tells you about their average.” Post-selection then allows one to isolate and inspect just some of those states at greater resolution, he suggests. With just a hint of nervousness, he ventures to suggest that as a result, measurements on a quantum particle might be contingent on when you look even if the quantum state itself is unchanging in time. You might not find it here when you look – but had you looked a moment later, it might indeed have been there. Such an interpretation of quantum behaviour would be, Elitzur says, “revolutionary” – because it would entail a hitherto unguessed menagerie of real states underlying counter-intuitive quantum phenomena.

The researchers say that to do the actual experiment will require some refining of what quantum routers are capable of, but that they hope to have it ready to roll in three to five months. “The experiment is bound to work”, says Wharton – but he adds that it is also “bound to not convince anyone of anything, since the results are predicted by standard quantum mechanics.”

Elitzur agrees that this picture of a particle’s apparent appearance and disappearance at various points along the trajectory could have been noticed in quantum mechanics decades ago. But it never was. “Isn’t that a good indication of the soundness of the TSVF?” he asks. And if someone thinks they can formulate a different picture of “what is really going on” in this experiment using standard quantum mechanics, he says, “well, let them go ahead!”