Suppose that we have a source that produces pairs of correlated photons, such that the polarization of the photons is opposite to each other.
Polarization Polarization
filter <-----photon 1 photon 2----> filter
We measure the polarization of each photon relative to a polarizarion filter. The output is either +1 or -1. The filters can be turned so that they are at an angle relative to each other.
https://en.m.wikipedia.org/wiki/Bell%27s_theorem
The famous theorem by John Bell states that the distribution of measurement results versus the angle cannot be reproduced if we assume that each photon already had its polarization determined before the measurements.
Some researcher claim that this shows there must be some kind of faster-than-light communication between the measuring devices.
Their claim is based on the following:
Assumption 1. The measuring devices make the wave function of the pair of photons to "collapse" at each end of the measurement apparatus. The measurement result can then be compressed to a single binary number +1 or -1 and sent to the scientist to tabulate and analyze.
Assumption 1 already highlights what is the error in this thinking: we make the wave function of the apparatus to collapse before the data is in the head of the observer, the scientist.
If we cut off part of the wave function of a system before the observer interacts with the system, then, of course, that will lead to strange behavior, like the need for faster-than-light communication or loss of unitarity.
The correct way to treat this experiment is to let the wave function propagate to the measurement devices and then to the head of the scientist. The interference pattern, that is, the table of measurement results, is formed in his head. There is no need for faster-than-light communication.
It is like a complex double-slit experiment where the screen is the head of the scientist. It is the screen where we finally let the wave function to collapse, if we use the Copenhagen interpretation.
If we use the Bohm model, then the hidden markers of the photons will sail on the wave function all the way to the head of the scientist where the markers finally "hit the shore" and determine in which of the many alternative worlds the observing subject will live in after the experiment. In the Bohm thinking, the wave function does not collapse at all. All the alternative worlds continue to exist. The markers just choose in which world our observing subject will be afterwards.
Open problem 2. The observing scientist receives the measurement outcomes from the different ends A and B of the apparatus at different times. For the interference pattern to form, the wave function must not collapse before the scientist has the outcome from both A and B in his head. How do we formalize this? Can the Bohm model help?
https://en.m.wikipedia.org/wiki/Entropy_of_entanglement
Entanglement is traditionally seen as a purely quantum phenomenon, but we can also interpret it classically. Entanglement just means that a classical wave was born in a single place in spacetime in a single process. When the classical wave propagates, there is correlation between its values in different points of spacetime. This correlation is called entanglement.
Entanglement entropy in quantum mechanics has the following meaning: if we have a combined system C & D in a pure state, and we measure C as accurately as we can, what is the von Neumann entropy of the mixed state in D after that?
Open problem 3. Can we really measure half of the system first and make its wave function to collapse, and later compare the result to the measured values in the rest of the system? That would require faster-than-light communication in the Bell inequality experiment. Does entanglement entropy have any physical meaning?
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