Quantum paradoxes

The Copenhagen interpretation of quantum mechanics causes paradoxes, at least apparent, when one tries to apply it to the macroscopic world. These two are the best known:

• Schrödinger’s cat paradox. A live cat, a radioactive atom, a vial filled with hydrocyanic acid, and a device that breaks the vial if the radioactive atom decays are placed in an opaque box. If the vial is broken, the cat dies. If it isn’t broken, the cat lives. While the box is closed, the Copenhagen interpretation of quantum mechanics tells us that the radioactive atom is in a superposition of states, decayed and intact, until someone checks it, at which point the superposition of states collapses into one of them. But then, while the box is closed, the cat must be in a superposition of states: alive and dead. Can a cat be alive and dead at the same time? Intuition denies it, but the Copenhagen interpretation of quantum mechanics asserts it. As its name indicates, this paradox was proposed in 1935 by Erwin Schrödinger, one of the fathers of quantum mechanics.
• Wigner’s friend paradox. Wigner and his colleague friend are going to perform a quantum experiment by measuring the value of a qubit (a quantum bit of information), which can be read as 0 or 1 with probability ½. Initially, the value of the qubit is the superposition of the two states. The friend goes in the laboratory to perform the experiment and collapse the qubit. Wigner remains outside. What is the probability of the outcome of the experiment? For Wigner’s friend, before performing the experiment, the result would be 0 with 50% probability, and 1 with 50% probability. After it is performed, the probability is 100% for the measured value, and 0% for the other. For Wigner, who has remained outside, the system is still in a superposition of both states with 100% probability, even after Wigner knows that his friend has already performed the experiment, because he still does not know the result. For him, the probability will only change when his friend opens the door and tells him the result of the measurement. As its name indicates, this paradox was proposed in 1961 by Eugene Wigner, 1963 Nobel Prize winner in physics.

Eugene Wigner

Both paradoxes have baffled physicists for decades. Many have tried to find an explanation, although many experts have not been convinced.

The problem with Wigner’s friend paradox is this: According to the Copenhagen interpretation of quantum mechanics, both participants in the experiment are right. For each of them, the probability is as given in the previous explanation. But, seen from a macroscopic point of view, this clashes with intuition: How is it possible that the same physical situation, considered by two different people, one inside and the other outside the laboratory, can give rise to two different probability computations?

One recent proposal trying to explain Wigner’s friend paradox can be summarized as follows:

The two probabilities are different, because the two situations are different. For Wigner’s friend, the system whose probability should be calculated is the qubit. For Wigner, the system consists of his friend and the qubit. The first system collapses when Wigner's friend measures the value of the qubit. The second, made by Wigner’s friend and the qubit, collapses when the friend opens the door and informs Wigner of the result of the experiment. Therefore, there is no paradox, because two different systems can have different probabilities.

The authors of this explanation add the following:

The quantum formalism indicates Wigner and friend had consistent descriptions for two different states of affairs. This feels paradoxical only if we give in to our intuition and assume that it was the same system for Wigner and friend all along… Our classical intuition is that the system is the same for everyone. Quantum mechanics inclines us to think that we can have different systems without there being an inconsistency or be objective without needing to make all our descriptions identical.

As with the attempts to explain the Schrödinger’s cat paradox, this explanation may be controversial. But it is curious that the Copenhagen interpretation of quantum mechanics has resisted all attempts to overthrow it, especially those by Einstein.

The same post in Spanish

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Manuel Alfonseca