Quantum mechanics or classical physics?

John Stewart Bell

The debate about which theory explains better the behavior of elementary particles, either quantum mechanics (with strange consequences such as state superposition and quantum collapse) or a still unknown classical physics-type theory that eliminates the need for such phenomena, has been going on since Bohr and Einstein started this debate almost one century ago.

The issue seemed to have been decided when John Steward Bell formulated in 1964 the famous Bell inequality, which I described in another post. However, as some physicists still raise the question, other means of distinguishing between the two types of theories are still being sought. One of them is the Leggett-Garg inequality (LGI), to which I will dedicate this post, based on a recent article in Physics World, dated August 12, 2024.

The difference between the two inequalities is this: Bell’s inequality affects two entangled particles, while LGI applies to a single object, and at first there is no entanglement. The object in question (for instance, a neutron) goes through three different situations (1, 2 and 3). In all of them, the state of the neutron can be measured. The experiment is then repeated many times and the value of the correlations between the results obtained in the three situations is calculated. Those correlations relate situations 2 and 1 (C₂₁), 3 and 2 (C₃₂), and 3 and 1 (C₃₁). Then the following value is computed:

K=C₂₁+C₃₂-C₃₁

Leggett and Garg showed that, if any form of classical physics were applicable to the object in question, K must be less than 1. On the other hand, if the object obeys quantum laws, the value of K must be greater than 1.

An experiment of this type was recently carried out at the Technical University of Vienna. A beam of neutrons is split in two when it hits a glass plate and then reunited into a single beam by redirecting the two beams onto a silicon plate. The device to do this is called a neutron interferometer. The three situations through which the neutron beam passes are the following:

1. The beam, before reaching the glass plate.
2. The two beams, after passing through the glass plate, but before reaching the silicon plate.
3. The reconstructed beam, beyond the silicon plate.

The Vienna team carried out various measurements on the three situations of the neutron beam and combined the values ​​obtained to calculate the correlations indicated above. The value of K turned out to be:

K=1.120±0.026

This value is greater than 1 throughout the interval, which shows that the behavior of the neutron beam cannot be explained by a classical theory, current or future. One of the researchers (Stephan Sponar) explains it in the following words:

There is no time [while the neutron is] inside the interferometer (i.e. when the neutron beam has been split) when the [neutron] is in a given state, that is, [only in one of the two beams; it is always in both at the same time].

In other words, the neutron is in a superposition of states, as predicted by quantum mechanics.

But I fear that there will always be physicists who insist, like Einstein, that quantum mechanics must be replaced by a classical theory, even though all attempts to overthrow it have failed.

The same post in Spanish

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Manuel Alfonseca