The new version of the Schrödinger's cat paradox

In a 2018 article in Nature Communications, the new version of Schrödinger's cat paradox was unveiled. This variation puts into difficulty the first and most common interpretation of quantum mechanics: that of Copenhagen. But before we understand how this was possible, let us take a step back to briefly recall what the interpretation in question consists of and what is the original version of the paradox.

The interpretation of Copenhagen

Broadly speaking, the physical quantities describing quantum particles are, in a sense, affected by uncertainties inherent in their very nature; there can be no measuring instruments capable of overcoming such uncertainties. We can describe such objects, therefore, only in probabilistic terms; the probabilities that a quantity has to assume certain values are mathematically decoded in the so-called 'wave function' (often indicated with the Greek letter Ψ). The latter, however, when for example a property such as the position of the electron is measured, always provides a precise value. And even immediately subsequent measurements give the same value.

The most common way of understanding the phenomenon just described, the Copenhagen interpretation, was formulated in the 1920s by the pioneers of quantum mechanics Niels Bohr and Werner Heisenberg, and takes its name from the city where the first of them lived. According to this interpretation, the act of observing a quantum system makes the wave function collapse from an extended curve on the possible values to a single point (that is, a precise value).

We have already explained in this post the original paradox.

The new version of the paradox

Infographic of the new version of Schrödinger’s cat paradox. Credit: Nature.

Already in 1967, the physicist Eugene Wigner proposed an alternative version of the paradox in which the cat and the poison are replaced with a friend of his who lived inside a box and a measuring device that can provide two results (for simplicity, as a macroscopic analogue, consider the toss of a coin, which can only give head or cross). The question now is: does the wave function collapse when Wigner’s friend learns of the result? If the laws of quantum theory, in addition to the measuring instrument, are to be applied to the friend, then he should be in an uncertain state that somehow combines both results until Wigner opens the box.

The variant proposed by physicists Daniela Frauchiger and Renato Renner is even more complicated than the previous one. They imagine they have two Wigners, each experimenting on a friend of their own, each locked in a different box. One of the two friends (let’s call her Alice) can, for example, 'throw a coin' and - using her knowledge of quantum physics - prepare a 'quantum message' to send to the other friend (let’s call him Bob). Using his knowledge of quantum theory, Bob can detect Alice’s message and guess the outcome of her launch. When the two Wigners open each other’s box, in some situations they may agree on the exit (head or tails), but other times they don’t. The paradox, then, is that in the second case a Wigner would get head and cross for the same coin toss.

We note, however, that currently the above is a mere mental experiment; in the future, however, it might be possible to play the roles of Alice and Bob two quantum computers. But there are still no quantum computers sophisticated enough to do that. 

Sources: Nature Communications, Nature, SpringerLink, Cambridge University Press.