# Bell's theorem & entanglement

## Main Question or Discussion Point

I've been studying Bell's theorem out of curiosity tonight after watching a BBC documentary about quantum mechanics (The secret of quantum physics - 1. Einsteins nightmare).

The episode ended on Bell's theorem disproving locality and showing Einstein to be wrong. So I went and did a little research into the experiment.

I found this great article by Gary Felder explaining how it worked and breaking it down into bitesize chunks, I'm sure many of you will have seen this before: http://www.felderbooks.com/papers/bell.html
I've only been studying this over the last couple of hours so let me know if my understanding is flaky in places!

Anyway, onto my question:

A photon that is entangled with another will change it's partners polarisation once it's reached the detector and measured along some orientation. I'm happy with that. So photon A is measured which instantly affects photon B.

Now, what would happen if we could measure the two photons at EXACTLY the same time. I realise this would be impossible to do in reality but I supposed we could explore it in theory.

So, photon A is measured and affects photon B, but at the same time the opposite is occurring; photon B is measured and is also affecting photon A. In my mind I have a kind of logic loop occurring, where the photons are constantly switching polarisation due to the change in it's entangled pair changing which in turn changes the photons again, plus this is all instantaneous, does physics break? If one measurement effects the other, which photon would be effecting which. Has this been scenario explored before?

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atyy
In the quantum formalism, it makes no difference whether A is measured before B, or B is measured before A, or A and B are simultaneously measured. When A and B are simultaneously measured, the measurement observable is the tensor product of the local observable at A and the local observable at B.

Ok, I think I follow. But with quantum I seem to continually get a disillusion of understanding!

So, is what you're saying: despite which photon passed through the detector first or if it was at the same time, photon A always changes photon B and photon B always changes photon A? Thus in doing so, always have the same orientation relative to each other?

Also, I'm a little confused in that you talk about the measurement observable, not measurements, i.e don't we get two measurements from each of the two detectors?

atyy
So, is what you're saying: despite which photon passed through the detector first or if it was at the same time, photon A always changes photon B and photon B always changes photon A? Thus in doing so, always have the same orientation relative to each other?
No, if A passes through the detector first, then A affects B. If B passes through the detector first, then B affects A. If A and B pass through the detector at the same time, one can think that they simultaneously affect each other, or that photons A and B should be considered one inseparable entity.

In the above, I used langauge in which the wave function of the photons is real. However, you should be aware that quantum mechanics distinguishes between absolute reality and the quantum reality of the wave function. Absolute reality is the everyday reality you see and includes the experimental outcomes that you observe, while quantum reality is a tool to calculate the probabilities of experimental outcomes.

Also, I'm a little confused in that you talk about the measurement observable, not measurements, i.e don't we get two measurements from each of the two detectors?
You can ignore the distinction for the moment, until you study the quantum formalism properly.

So photon A is measured which instantly affects photon B.
I would like to formulate it like this: "Photon A is measured which seems to instantly affect photon B." Why? Because there is no experimental evidence that clearly demonstrates that this "instant effect" actually is what happens.