Question

After watching this video on Bell’s inequality, it mentions that if you have a process for pair production, in this case a photon pair where the photons travel in opposite directions, the polarization of each photon will be the same. In the video, he uses this example to eventually show what Bell’s inequality is and how it is violated in experiments ruling out hidden variables that are local.

However, the analysis depends upon two things. First, he says that the polarization of each photon would be the same, and that this has been demonstrated experimentally.

Secondly, he says that if there was a hidden variable that determined whether each photon will go through a particular kind of polarization filter, the determination should be the same for each photon if they were measured at different locations. So for example, suppose that Alice and Bob in different locations had three kinds of polarization filters at different angles. Let’s call these 1,2, and 3.

If there was a hidden variable in one photon in a pair that determined that it will pass through Alice’s polarization filter 1, the other photon in the pair must also pass through Bob’s polarization filter 1. This is because, as he states, the hidden variables in each photon, must be the same.

My question is how do we know this? What if the hidden variable is different in each photon of the same pair? How do we rule this out?

Answer 1

Experiments show that outcomes of measurements on entangled particles violate Bell's inequality, suggesting that any hidden variables cannot be both local and deterministic. It implies that entangled particles are linked in a way that cannot be explained by independent hidden variables for each particle, supporting quantum mechanics over local hidden variable theories.

Step-by-step explanation:

The question you are asking relates to the physical concept known as quantum entanglement and how it is related with Bell's theorem. Bell's inequality tests whether the concept of local hidden variables is coherent with the predictions of quantum mechanics. The key experiments that test Bell's inequality use pairs of particles that are entangled, meaning that their properties are correlated in such a way that the state of one (even when separated by a large distance) can instantaneously affect the state of the other.

The hypothesis of local hidden variables would suggest that there are predetermined states (or "hidden variables") that dictate the outcomes of measurements on these particles. However, experiments repeatedly demonstrate that the results of measurements on entangled particles violate Bell's inequality. This violation implies that the hidden variables cannot be both local and deterministic, as that would result in correlations that fall within the bounds of Bell's inequality, which is not the case.

If one poses the hypothesis that hidden variables could differ between the photons in an entangled pair, this would not be consistent with the observed violations of Bell's inequality in experiments. These violations suggest a link between the properties of the particles that cannot be explained by independent hidden variables for each particle. This is one of the cornerstones of quantum mechanics, highlighting non-locality and the entanglement of particles.