A simple quantum experiment: what have I got wrong?

[JollyOlly]

A source S of entangled photon pairs is placed between two polarised detectors A and B whose filters are placed at right angles. The source emits pairs of photons whose polarisation is the same but whose orientation is random. The detectors ring a bell whenever a photon is detected.

Now my understanding of the situation is as follows:

Under classical rules, if the emitted photon has its polarisation parallel to one of the detectors, that detector will ring its bell and the other will remain silent. If the emitted photon is polarised at 45deg to the detectors, then there is a 50% probability that each photon will pass through either filter and therefore a 25% probability that the two photons will pass through both filters. I haven't done the integration but my intuition tells me that, on average, with random polarisation, you would expect both bells to ring 12.5% of the time. You would certainly expect both bells to ring some of the time.

Under QT (as I understand it), the two photons are entangled and if one photon passes through filter A and rings the bell, it is impossible for photon B to pass through the other filter. In other words, QT forbids both bells from ringing at the same time.

Now this is such a simple experiment to describe (and do) and gives such an unequivocal difference in predicted behaviour that, if it were correct, it would be described in every book and be in every physics undergraduate practical course. The fact that it is not implies that I have misunderstood something.

I would be extremely grateful to you if someone could enlighten me!

 

[Simon Bridge]

What is it you are trying to demonstrate?

I suspect your stats are out though...
http://lesswrong.com/lw/q0/entangled_photons/

 

[JollyOlly]

Thanks, Simon, for that link. It was very interesting. I can't say that I followed the argument in detail but from what I can see, it bears out my calculations. The author says

The photons always have opposite polarizations, even though the prior probability of any particular photon having a particular polarization is 50%.

which I take to mean that in my experiment, QT predicts that it is impossible for both bells to ring at the same time.

Now I am pretty sure that under classical theory, both bells will ring at least some of the time so this simple experiment would be a vivid demonstration of non-locality in QT - much easier to describe and perform than violation of Bell's inequality.

So why have I never seen this experiment discussed in any book or textbook?

 

[DrChinese]

...which I take to mean that in my experiment, QT predicts that it is impossible for both bells to ring at the same time.

Now I am pretty sure that under classical theory, both bells will ring at least some of the time so this simple experiment would be a vivid demonstration of non-locality in QT - much easier to describe and perform than violation of Bell's inequality.

So why have I never seen this experiment discussed in any book or textbook?

You are correct that the bells will not ring at the same time. Actually, the experiment HAS been performed many times - look at the graphed results from any standard Bell test and you will see it. Look at theta=0 and 90 degrees.

However, that result does not lead to your assertion about non-locality. For that, you need Bell's Theorem and results from angle settings other than 90 degrees (or 0 degrees, etc). The reason is that a local hidden variable theory can explain your results, but it cannot explain Bell test results.

 

[Simon Bridge]

Thank's DrChinese.
Yep - this is why I wanted to be clear about what JollyOlly was trying to demonstrate.
The setup shows a difference between the quantum an classical statistics but does not demonstrate non-locality.

@JollyOlly: I suspect there are textbooks that discuss this experiment - you just haven't seen them. The ones you have seen presumably have other priorities. You are more likely to see ones like in the link done in detail in texts since they show more.

 

[JollyOlly]

DrChinese

I am having a bit of difficulty seeing how a hidden variable could ever explain the observed effects but I will take your word for it. But even if the experiment does not prove the non-locality of QT I am pleased to know that:

a) my description of the experimental facts was not wrong
b) the experiment does at least show that classical physics is seriously deficient in some respect

Thanks

 

[DrChinese]

DrChinese

I am having a bit of difficulty seeing how a hidden variable could ever explain the observed effects but I will take your word for it. ...

Imagine I have 2 random sets of red/black cards (A and B) numbered 0-89 (corresponding to angle settings in degrees). The sets correspond in the sense that when A's card is black, B's is red, and vice versa. This for all 90 cards. If we measure A at 36 degrees we pull out the card labelled 36. And do the same for B. Naturally, they will always be anti-correlated.

This is a local hidden variable model. If there were many components hidden inside a particle, it would support this method of yielding the correlations envisioned by EPR. Ie where the bells do not ring at the same time. (Of course there is no evidence anything like this actually exists, it is merely possible.)

Bell's Theorem goes beyond this, by showing there are no sets of cards that match the complete predictions of QM. Even though there are sets that do match this particular case.

 

[JollyOlly]

AHAH! I see what you mean.

A photon could have a parameter which takes the value YES or NO for every possible angle of polarization. A photon which is randomly polarized would have YES and NO values at random.

In the experiment I have described in which the polarizers A and B are at right angles, the experimental results can easily be explained if the entangled photon has the opposite value for every complementary angle.

If the polarizers were parallel, the entangled photons would have to have the same value at the same angles to reproduce the expected effects.

In order to prove non-locality, you would have to show that no set of values will work for all angles of the polarizers.

And this is exactly what Bell's theorem sets out to prove.

Have I got it now?

 

[DrChinese]

AHAH! I see what you mean.

A photon could have a parameter which takes the value YES or NO for every possible angle of polarization. A photon which is randomly polarized would have YES and NO values at random.

In the experiment I have described in which the polarizers A and B are at right angles, the experimental results can easily be explained if the entangled photon has the opposite value for every complementary angle.

If the polarizers were parallel, the entangled photons would have to have the same value at the same angles to reproduce the expected effects.

In order to prove non-locality, you would have to show that no set of values will work for all angles of the polarizers.

And this is exactly what Bell's theorem sets out to prove.

Have I got it now?

Exactly! Bell realized that there was something "wrong" in the cos(theta) (cos^2 for photons) relationship. It varies in a manner in which theta is key. Theta being the difference between 2 observers. But the second observer should not be altering the reality of the first, and the cos(theta) relationship allows for that! It was this point that set Bell on his path.

 

[San K]

But the second observer should not be altering the reality of the first, and the cos(theta) relationship allows for that! It was this point that set Bell on his path.

Well said DrChinese. So it rang a bell in Bell's mind?...:)

 

[DrChinese]

Well said DrChinese. So it rang a bell in Bell's mind?...:)

We got a lot of bells going off in this thread...