Schrödinger's cat



2019/12/3
[List]
Published 2004/12/25

I will explain a mysterious problem called Schrödinger's cat.

Schrödinger's cat

The Copenhagen interpretation of Bohr

Niels Bohr and Werner Heisenberg proposed the following things in 1927.

  1. Non-existence: A wave function does not exist and just represents the knowledge of the system.
  2. Uncertainty principle: Generaly a particle does not have a definite location.
  3. Reduction of wave function: The wave function reduces when the device makes a measurement.
  4. Born rule: The result given by the wave function is probability.
  5. Classical system: We need classical system to get the final measuring result.

Though Bohr did not state the position of boundary between quantum system and classical system, he stated that the photon-box can be quantum system when he debated with Einstein.

This claim is called the Copenhagen interpretation because the Niels Bohr Institute is in Copenhagen of Denmark. This is the mainstream interpretation of quantum mechanics.

Von Neumann–Wigner interpretation

John von Neumann and Eugene Paul Wigner elaborated the Copenhagen interpretation and proposed the following thing in 1932.

  1. Non-existence: A wave function does not exist and just represents the knowledge of the system.
  2. Uncertainty principle: Generaly a particle does not have a definite location.
  3. Reduction of wave function: The wave function reduces when the device makes a measurement.
  4. Born rule: The result given by the wave function is probability.
  5. Necessity of consciousness: We need consciousness to get the final measuring result.
  6. von Neumann Chain: We can expand the boundary between quantum system and classical system as much as we want.

This claim is called Von Neumann–Wigner interpretation. Austrian physicist Erwin Schrödinger thought that the interpretation had a problem. Then, he proposed the thought experiment, Schrödinger's cat in 1935.

Paradox of Schrödinger's cat

We put a cat in a box. And we put observational equipment of decay of the radioisotope. We connect this observational equipment to a poison gas jet machine. When a radioisotope collapses, observation equipment sends a signal to the poison gas jet machine. As a result, the poison gas erupted and the cat will die.

The decay phenomenon of the radioisotope is described by a wave function. In other words, the state of the radioisotope becomes the superposition of the state that it collapsed and the state that it does not collapse, when the time passed. Therefore, we do not know whether the radioisotope decays until we observe it.

If Von Neumann–Wigner interpretation is correct, human consciousness causes reduction of the wave function. Therefore, the cat becomes the superposition of the life and death until the human observes it. We call this cat Schrödinger's cat.

The superposition of the life and death is lack of common sense. Therefore, Von Neumann–Wigner interpretation is not correct. This is the claim of Schrödinger.

The Von Neumann–Wigner interpretation is elaborated Copenhagen interpretation. Schrödinger proposed the paradox of Schrödinger's cat in order to argue against the Von Neumann–Wigner interpretation.

Schrödinger's cat

Solution of Schrödinger's cat

According to the Copenhagen interpretation, there is no problem because the wave function does not exist and just represents the knowledge of the system.

On the other hand, a living cat and a dead cat exist in other worlds in the many-worlds interpretation of Everett. However, there is still no experimental evidence indicating many-worlds interpretation being correct.

It is not resolved which interpretation is correct. I would like to wait for the future solution.


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