In one of my recent posts, I hinted at the practical paradox presented by the “electric” Aharonov-Bohm effect, in that such a phenomenon should affect charges traversing a region where an electric field existed previously. This singular and counter-intuitive effect of dissociation of time and space was extended a few years ago by the same Yakir Aharonov, with the idea that a physical property can be disembodied from its physical carrier. Our intuition suggests that an object should carry all of its physical properties with it, the properties which actually constitute its very definition. However, a quantum object may not act in such a manner, as it could temporarily leave some of its physical properties in a place where it never physically appeared. In their 2013 paper “Quantum Cheshire cats” (New J Phys 15, 113015) Aharonov and coworkers proposed that a quantum object can be separated from, and could even permanently discard, a physical property, and obtain a new one it did not initially have. In their proposed gedankenexperiment one would find the cat in one place and its grin in another place, akin to the scene of the Cheshire cat in the novel Alice in Wonderland: the cat could be a photon, while the grin could be its circular polarization.

Richard Feynman, for his part (sorry if I go back too often to Feynman, as you know by now he’s one of my two guide spirits, the other one being Freeman Dyson), maintained that all rarities of quantum mechanics can be traced back to the double slit experiment: I will take just this one experiment, which has been designed to contain all of the mysteries of quantum mechanics … Any other situation in quantum mechanics, it turns out, can always be explained by saying “Don’t you remember the case of that experiment with the two holes? They can give you a wider class of experiments than just the two slit interference experiment. But that is just repeating the same thing to drive it in.” (RPF, The Character of the Physical Law, MIT Press 1965). So are these quantum “paradoxes” just another different form of the familiar double-slit conundrum?

To see how the space-time splitting can be interpreted in this way, it is interesting to firstly rephrase the well-known double-slit experiment according to Feynman’s interpretation (Feynman’s Lectures in Physics, vol. III). Let us imagine an electron emitted by a source, that can reach some given point x on a screen by passing via two slits. Then, if the experimental apparatus is such that it is impossible to establish which of the two paths was taken, the probability of arriving at x is given by the square of the sum of the quantum amplitudes. If, on the other hand, the experiment allows to measure which slit the electron went through, then the probability of arriving at x is the sum of the two squared amplitudes. The fact that these two situations are mutually exclusive constitutes the so-called Feynman Uncertainty Principle (FUP), providing a measurable analog to the famous Schrödinger cat. From hereon, all the discussions about Bell’s inequalities, entanglement and the like, take the lead.

Now, the time variable enters the game.

Imagine that not only we want to know whether the electron is in x at the end of the experiment, but we also wish to measure a property of the electron, for example its spin up or down. Then we may arrange the experiment in such a way that we set to different probes, one on the slits and one on the screen. The measurements on the slits (1) and on the screen (2) necessarily take place at different times, t1<t2. Now the experiment has four possible outcomes: the electron in x at t2, with spin up or down, or the electron not in x at t2, also with spin up or down, whose respective probabilities can be calculated. However, if we want to know about the system’s past (t1) starting from the measurement in the present (t2), two conditions arise, mutually exclusive according to the FUP. If the measurement at t2 by probe 2 looks only at the value of electron spin, then the past situation at t1 can be determined by inspecting the state of the probe 1 after the experiment is finished. If, on the other hand, the measurement by probe 2 at t2 looks both at the electron position (x or not-x) and spin (up or down), then the record carried by probe 1 is permanently erased and, according to the FUP, it should be impossible to say whether the spin’s condition at t1 was up or down.

The FUP rule does not rely on human experience: for example, the mere existence of a photon scattered near one of the slits and carrying a record of the electron’s past, is enough to destroy the interference pattern, even if the photon is never observed. However, Eugene Wigner sharpened the Schrödinger cat paradox by claiming that a quantum measurement requires a conscious observer, without which nothing ever happens in the universe (or more modestly, nothing of what happens would be measurable). Wigner originally presented this extension of the paradox in a script entitled Remarks on the mind-body question, for a contributed volume, The Scientist speculates, edited by I. J. Good (London, Heinemann 1961). He imagined that a human friend of his were shut in a lab, where some equivalent of the two-slit experiment, or the Schrödinger cat test if you prefer, is being run. His friend makes the measurement at time t1, while Wigner waits outside and does not know the outcome. Until Wigner opens the door and asks his friend, at some time t2>t1, he sees his friend in a superposition of quantum states corresponding to all the possible experiment outcomes; however, at time t2 his friend already knows the result he obtained at time t1. So goes the original formulation of the paradox: did the “macroscopic” collapse of the laboratory (experiment+friend) wavefunction, and the attending definition of the final measured value, take place at time t1, or t2?

Originally, Wigner designed his thought experiment only to illustrate the (then popular) belief that consciousness is necessary to the quantum mechanical measurement process, and therefore, only consciousness must provide men (and women) their perception of ultimate reality, akin to Descartes’ famous sentence Cogito ergo sum. In the years that followed, such an extreme interpretation has been replaced by less “personalized” analyses, in the attempt to avoid making the last observer (that is, Wigner) a special one, who decides for the reality of an experiment independently done and measured by somebody else. The most exotic interpretation is the “many worlds” view, which says that reality splits whenever you make a quantum measurement, creating parallel universes to accommodate every possible outcome. Thus, Wigner’s friend would split into two copies and, with good enough supertechnology (ahem…) you could indeed measure that person to be in a superposition state of all possible results, when looking from outside the lab. Bohm-like hidden variables explanations contend that the friend has a uniquely defined value for the experiment, but Wigner may still measure him to be in a superposition state because of his own ignorance. And, among several others, we are not short of a “retrocausality” interpretation (in line with Aharonov-Bohm observation about the electric-AB effect) according to which Wigner’s friend absolutely does experience something at the point of measurement, but his experience can depend upon Wigner’s choice of how to observe that person at a later time (remember the brief discussion above, about the two probes measuring only spin, or both spin and position).

The trouble is that each of these theoretical interpretations is equally good (or bad) at predicting the outcome of quantum tests, so choosing between them in practice comes down to personal taste (maybe that’s a revival of the role of consciousness, that was swept under the carpet?). The only way out, eventually, is a theory that makes experimentally testable predictions. Ideally, such predictions should have a character of experimentum crucis, namely an experiment that gives only one or another possible outcome, to confirm or disprove the initial hypothesis. Unfortunately, quantum experiments are by their very nature probabilistic: even the famous Stern-Gerlach experiment, which indeed has such a yes/no character, relies on a probabilistic interpretation intrinsic to the quantum nature of the phenomenon.

For both the Cheshire cat and Wigner’s friend, there have been recent experimental implementations that seem to put things on a more right path. In their report A strong no-go theorem on the Wigner’s friend paradox (Nature Phys 16, 1199 (2020), Nora Tischler, Eric Cavalcanti and collaborators used polarization-encoded photon paths (that is, pair of photon qubits) as “friends”, whose quantum states can be mixed by manipulating a parameter. Their set up correspond to a double-Wigner friend experiment, in which two Wigners communicate with two friends in two separate laboratories, each accessing one half of the entangled state of the qubits (or the entangled state of a dead and alive cat). To make a long story short, their results support a view in which quantum theory may only describe observer-dependent facts, that is results that refer to private perceptions (if a photon can be imagined as perceiving something) of the participants held in sealed laboratories. Since in their experiment the photon paths can be isolated from each other, there is no danger of comparing the conflicting outcomes of a same experiment, and all perceived results are equally valid. Or, if you prefer, equally invalid.

In another recent report, Experimental exchange of grins between quantum Cheshire cats (Nature Comm 11, 3006 (2020)) a joint team of the chinese Heifei and Nankai universities prepared a non-unitary imaginary-time evolution on a photonic cluster quantum state. Their results reveal the counterintuitive phenomenon that two photons can exchange their spins without classically meeting each other: the grin passes from one cat to the other. Feynman reassures us that these two different experiments must both be safely interpreted in the light of his revised Uncertainty Principle, namely forbidding to use quantum amplitudes at a given time to deduce observables at earlier times. That is not, however, the only thing such experiments have in common. Can you suggest another? You’re right. Cats, obviously.

All the friends of Wigner

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