B Entangled Photons: Adam Becker's QM Book "What is Real?

[jeremyfiennes]

I'm reading Adam Becker's QM book "What is Real?" At one point he says:

"The single wave function shared by the two entangled photons guarantees that they will always behave in the same manner when encountering two polarizers with parallel axes. It does not specify what they will do. But merely that both will always do the same thing."

Is this correct? My understanding is the common wave function determines that the probability of a photon either passing or being blocked by its polarizing filter is the same for each. But this being a probabilistic relation, not necessarily that the outcomes will always be identical.

 

[Mentz114]

I'm reading Adam Becker's QM book "What is Real?" At one point he says:

"The single wave function shared by the two entangled photons guarantees that they will always behave in the same manner when encountering two polarizers with parallel axes. It does not specify what they will do. But merely that both will always do the same thing."

Is this correct? My understanding is the common wave function determines that the probability of a photon either passing or being blocked by its polarizing filter is the same for each. But this being a probabilistic relation, not necessarily that the outcomes will always be identical.

If something has a probability of 1 (of occurring) does that mean that it will certainly happen ? If one believes that then the outcomes can have 100% correlation or anti-correlation.

 

[PeterDonis]

My understanding is the common wave function determines that the probability of a photon either passing or being blocked by its polarizing filter is the same for each. But this being a probabilistic relation, not necessarily that the outcomes will always be identical.

Your understanding is incorrect. The outcome is always the same for both photons if the polarizers are parallel. Where probability comes in is that, depending on the angle of the polarizers, the probability of both photons passing the polarizers might not be 1. For example, you can pick a polarizer angle such that there is a 50-50 chance of the photons passing or not. So if you run the experiment many times, about half of the runs will show both photons passing their respective polarizers, and about half will show both photons not passing their respective polarizers. But for each run, the outcome for both photons (pass or not pass) will be the same.

 

[jeremyfiennes]

I'm interested in the individual case. Entangled photon A could arrive at polarizing filter A, with a 50% chance of passing, and pass. Entangled photon B could arrive at polarizing filter B, also with a 50% chance of passing, and be blocked. But Becker says that the two outcomes are always the same: if photon A passes then B will also pass, and vice versa. This on my understanding is wrong.

 

[PeterDonis]

Entangled photon A could arrive at polarizing filter A, with a 50% chance of passing, and pass. Entangled photon B could arrive at polarizing filter B, also with a 50% chance of passing, and be blocked.

Not if both filters are parallel; then it is impossible for the two outcomes to be different.

Becker says that the two outcomes are always the same: if photon A passes then B will also pass, and vice versa.

Yes.

 

[jeremyfiennes]

Not if both filters are parallel; then it is impossible for the two outcomes to be different

Why, given that the wave function only determines the probabilities of each passing or not passing?

 

[PeterDonis]

Why, given that the wave function only determines the probabilities of each passing or not passing?

The wave function describes the two-photon system, not either photon individually. So the probabilities given by the wave function are for joint measurements on the two-photon system. The entangled wave function tells you that there is a 100% probability that the two measurements will match if the polarizers are parallel. If the polarizers are not parallel, the entangled wave function tells you how the probability of the two measurements matching depends on the angle between the polarizers.

It's true that you can also compute, from the entangled wave function, probabilities for each individual photon to pass its respective polarizer. But the process by which you do this throws away information--information about how the two measurement results are correlated. So you can't draw inferences about how the two measurements are correlated from the probabilities that are computed for each individual photon. You have to look at the entangled wave function as a whole and what it says about the probabilities of joint measurements on the two-photon system.

 

[Mentz114]

Why, given that the wave function only determines the probabilities of each passing or not passing?

If the filters are aligned the same the probability of a coincidence is 1. It follows from the WF.
(Which is what PeterDonis is saying.)

 

[jeremyfiennes]

The entangled wave function tells you that there is a 100% probability that the two measurements will match if the polarizers are parallel.

So for parallel polarizers, the WF gives two pieces of information: 1) the probability of each photon passing its respective polarizer; 2) that if A passes, then B will also pass; and vice versa?

 

[PeterDonis]

So for parallel polarizers, the WF gives two pieces of information: 1) the probability of each photon passing its respective polarizer; 2) that if A passes, then B will also pass; and vice versa?

Yes. More precisely, the WF as a whole tells you the correlation between the A result and the B result (as a function of the angle between the polarizers), and the density matrix you get by tracing the wave function over B or A, respectively, gives you the probability of the A or B photon, respectively, passing its polarizer.

 

[jeremyfiennes]

Yes. More precisely, the WF as a whole tells you the correlation between the A result and the B result (as a function of the angle between the polarizers), and the density matrix you get by tracing the wave function over B or A, respectively, gives you the probability of the A or B photon, respectively, passing its polarizer.

Ok. thanks.