Interpretations of quantum mechanics

Ecrit par ColibrITD
Author : Phd. Marta Reina, Researcher at ColibrITD

The diatribe between realists and orthodox before Bell’s theorem

In quantum mechanics, the state of a particle can be determined through Schrödinger’s Equation, representing an analogous to the well-known Newton’s second law [1]. But, while from the classical counterpart, a deterministic expression for the position of the particle as a function of time x(t) can be deduced, in quantum mechanics, Schrödinger’s equation allows us only to obtain a wave function ψ(x, t), spread-out in space, that does not give us any certain information about the position of the particle.


The only information we can extract about the position from this wave function comes from its squared modulus, |ψ(x, t)|², and it is probabilistic. We only know how probable is that at a fixed time, the particle will be measured in the space interval [x, x+dx] [Fig. 1 — Unobserved].

Fig. 1 — On the left the probability density, |ψ|², before the measurement; on the right, the same quantity after the collapse of the wave function.

“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.” (A. Pais) [4]

“One should no more rack one’s brain about the problem of whether something one cannot know anything about exists all the same, than about the ancient question of how many angels are able to sit on the point of a needle. But it seems to me that Einstein’s questions are ultimately always of this kind.” (W. Pauli, 1954) [5]

Solvay congresses

Fig. 2— Fifth Solvay Congress (1927).

Fig. 3 — EPR\Bohm thought experiment configuration. A muon μ⁰ at rest decays in an electron e⁻ and a positron e⁺. Their spins are measured by the two parallel detectors.

According to the principle of conservation of angular momentum, we can affirm that electron and positron are in the singlet state, i.e. (|↑₋↓₊⟩-|↓₋↑₊⟩)/√2. They have for sure opposite spins, but you cannot tell which one between the electron and the positron will have spin up or down; all you can tell is that the two measures are correlated, which means that if the electron has spin up, the positron will be found in spin down and vice-versa.

It is now time to push this thought experiment a bit further. Since the muon was at rest, after its decay, the electron and the positron will fly apart from each other. What is crucial is that even if they fly 20 lightyears apart from each other, by measuring the spin-state of one of them, we will immediatelyknow the state of the other. How do we reconcile the fact that the electron knows that the spin of positron has been measured, even though they are separated by lightyears of space and far too little time has passed for information to have traveled to it according to the rules of special relativity?

According to Einstein, this peculiar behavior would be compatible only with a realist viewpoint: for the realistic school of thought, there is nothing weird, the angular momentum of the electron was down (or up), and the one of the positron was up (down) since the decay process happened. On the other hand, in the orthodox interpretation, neither the particle had spin up or down until the act of the measure forced it to choose; the measurement of the electron spin not only makes the electron wave function collapse but produces the collapse of the positron 20 lightyears away. For Einstein, Podolsky, and Rosen, this would lead to an infringement of the principle of locality: the two particles would be able to communicate faster than the speed of light.

Fig. 3 — Bell’s new configuration for the EPR\Bohm thought experiment. A muon μ⁰ at rest decays in an electron e⁻ and a positron e⁺. Their spins are measured by the two detectors oriented along the directions of the unit vectors a and b.

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