Entanglement, correlation and randomness

[entropy1]

I was wondering. In this example I use polarized photons, but maybe it is applicable to electrons and spin also.

We can prepare two completely unentangled polarized photons, and send them in opposite directions to two detectors preceded by a filter at particular angles. Both of them will show a correlation between their individual prepared polarization, the angle at which each filter is oriented, and the probability the photon is detected at that side. The measurements are, of course, independent.

Alternatively, we can prepare two completely entangled polarized photons, and send them in opposite directions to two detectors. This time, there will be a correlation between the relative probabilities a photon will of will not be detected, and the relative orientations of the filters.

There is even a possibility to prepare the photons in some mixed state, in which some degree of both scenario´s is applicable simultaneously.

So what I´m wondering about is this: To which extent is a probable outcome purely random if there is correlation in play? It seems that, at least in this particular example, entangled or not, randomness always has an amount of correlation, which in my eyes seems the opposite of randomness, to it.

 

[andrewkirk]

Both of them will show a correlation between their individual prepared polarization, the angle at which each filter is oriented, and the probability the photon is detected at that side.

Correlation does not apply in this case. Correlation is defined between two random variables. In the case of each photon there is only one random variable, and all the other amounts (angles, preparation) are deterministic.

 

[entropy1]

Correlation does not apply in this case. Correlation is defined between two random variables.

I don´t see that? If you set one variable, another can be correlated to it. The term ¨correlation¨ applies because there is a statistical relation between the setting and the detection of quanta rather than a direct causal relation.

 

[Demystifier]

Entropy1, your argument looks to me as the following one. If I win lottery, I become rich. If I don't win lottery, I don't become rich. Therefore winning lottery is correlated with becoming rich. Therefore winning lottery is not random.

Do you see a similarity with your own argument? Do you see what is wrong with my argument? If both answers are "yes", then can you tell now what was wrong with your argument?

 

[Demystifier]

The term ¨correlation¨ applies because there is a statistical relation between the setting and the detection of quanta rather than a direct causal relation.

The term "correlation" applies even when there is a direct causal relation, as in my case above where winning lottery directly causes me to become rich.

 

[entropy1]

Entropy1, your argument looks to me as the following one. If I win lottery, I become rich. If I don't win lottery, I don't become rich. Therefore winning lottery is correlated with becoming rich. Therefore winning lottery is not random.

Do you see a similarity with your own argument? Do you see what is wrong with my argument? If both answers are "yes", then can you tell now what was wrong with your argument?

I think I was misguided by the cos²(φ) -shaped curve of the filter orientation/polarization direction correlation. I took this as an inate property of the photons being detected. An experimental setup of course shapes any measured correlation also! It´s like pushing water through a sprinkler: the water forms a nice fountain but the water molecules themselves of course behave like water molecules (randomness).

But: In my example I am considering individual photons. So, each photon contributes to the cos²(φ) -shaped curve. Each individual photon does not exhibit this correlation in its own! In this respect, the passing of the photon is random! However, a collection of measurements on photons do exhibit the cos²(φ) correlation. It´s like pushing individual water molecules through a sprinkler: a collection of them should measure a nice fountain again! Does this mean the water molecules do not behave randomly? No. The sprinkler shapes the randomness into a fountain! However: This would mean total locality, and we don´t have that at subatomic level! (since Bell´s inequality) After all, if the experimental setup (the sprinkler) shapes the correlation (the fountain), then the thing being shaped, in this case the photon, was acted on locally! (and this is not the case)

To make my view on this clear to be complete: As I understand it, entanglement in general corresponds to an exchange of subatomic information. So, if we have information contents A and B respectively, and B exchanges an amount b with A, then we end up with A+b and B-b, right? So, the total information content remains preserved! Is this right? (I am wondering)

 

[Demystifier]

But: In my example I am considering individual photons. So, each photon contributes to the cos²(φ) -shaped curve. Each individual photon does not exhibit this correlation in its own! In this respect, the passing of the photon is random! However, a collection of measurements on photons do exhibit the cos²(φ) correlation. It´s like pushing individual water molecules through a sprinkler: a collection of them should measure a nice fountain again! Does this mean the water molecules do not behave randomly? No. The sprinkler shapes the randomness into a fountain!

That's a good analogy. Indeed, we have something similar in QM within the Bohmian interpretation. According to the Bohmian interpretation, the wave function shapes the randomness into an interference pattern (or cos²(φ) pattern in your case), while each individual particle is a pointlike object which does not exhibit any interference pattern.

However: This would mean total locality, and we don´t have that at subatomic level! (since Bell´s inequality) After all, if the experimental setup (the sprinkler) shapes the correlation (the fountain), then the thing being shaped, in this case the photon, was acted on locally! (and this is not the case)

You seem to be mistaken about the Bell's inequality.

First, we have non-locality only when the particles are entangled. But in your example you seem to be talking about non-entangled photons, in which case a local description is perfectly possible.

Second, if you consider the case of entangled photons, then you are right that one needs a non-local description. But QM in the Bohmian interpretation gives a clear picture of the origin of non-locality. The source of non-locality is a non-local (or more precisely non-separable) wave function, which can be thought of as a sort of non-local sprinkler.

To make my view on this clear to be complete: As I understand it, entanglement in general corresponds to an exchange of subatomic information. So, if we have information contents A and B respectively, and B exchanges an amount b with A, then we end up with A+b and B-b, right? So, the total information content remains preserved! Is this right? (I am wondering)

Not quite. When I tell you what I know about physics, I don't forget that information. I am sharing my information with you, so that nobody looses anything. The same is the case with sub-quantum information associated with entanglement.

 

[entropy1]

I still can't get my head around it very well: I am not familiar with the Bohmian model, but if the guidewave introduces randomness, isn't that randomness?

I can picture the non-local imparitive for the guidewave though. Is that like throwing a dice for the entangled pair as a whole as opposed to two dice for unentangled photons separately?

 

[Demystifier]

but if the guidewave introduces randomness ...

The guiding wave does not introduce randomness. Think of guiding wave as a roulette wheel. Does the roulette wheel introduce randomness for the roulette ball?

I can picture the non-local imparitive for the guidewave though. Is that like throwing a dice for the entangled pair as a whole as opposed to two dice for unentangled photons separately?

Something like that. But try to develop your intuition in terms of a roulette wheel and roulette ball, it is a much better analogy for Bohmian mechanics.

 

[entropy1]

Does the roulette wheel introduce randomness for the roulette ball?

In the case of the roulette wheel, for me it is hard to say whether there is randomness or not; it suggests not and too at the same time, as if we can't in principle make out if there is randomness involved or not. It obscures the matter to my opinion. Why do you prefer that analogy?

 

[DrChinese]

In the case of the roulette wheel, for me it is hard to say whether there is randomness or not; it suggests not and too at the same time, as if we can't in principle make out if there is randomness involved or not. It obscures the matter to my opinion. Why do you prefer that analogy?

Because it makes sense for the Bohmian Interpretation. What you describe is the desired analogy in this case: a causal mechanism that appears to deliver random results.

 

[Demystifier]

In the case of the roulette wheel, for me it is hard to say whether there is randomness or not; it suggests not and too at the same time, as if we can't in principle make out if there is randomness involved or not. It obscures the matter to my opinion. Why do you prefer that analogy?

As DrChinese said, I prefer this analogy because randomnnes (or its absence) in the roulette case is almost identical to that in the Bohmian case. If you find one obscure, then the other is obscure too for exactly the same reason. But the case of roulette is much simpler, so I would suggest you to resolve that case first.

 

[entropy1]

If we consider electrons hitting a detector screen after passing a double slit, each electron has to impact the screen somewhere, but not anywhere! After all, the collective of electrons must form an interference pattern! So, each impact is not entirely random. Somewhere in the setup, there is information present about the interference pattern that allows it to emerge! Am I right?

If an electron meets the detector screen, it has to appear somewhere. So it has to 'decide' where! Is this decision random or deterministic? Or a little of both? Or is it a matter of taste?

 

[Demystifier]

If we consider electrons hitting a detector screen after passing a double slit, each electron has to impact the screen somewhere, but not anywhere! After all, the collective of electrons must form an interference pattern! So, each impact is not entirely random. Somewhere in the setup, there is information present about the interference pattern that allows it to emerge! Am I right?

You are right.

If an electron meets the detector screen, it has to appear somewhere. So it has to 'decide' where! Is this decision random or deterministic? Or a little of both? Or is it a matter of taste?

Are those rhetorical questions? Anyway, the answers depend on the interpretation. Whether the choice of interpretation is a matter of taste or not is a matter of taste itself.

 

[entropy1]

Somewhere in the setup, there is information present about the interference pattern that allows it to emerge! Am I right?

You are right.

I am wondering, since the only thing that can carry that information from the exit of the double slit to the screen are the particles/EM radiation itself, that is where that information must be, right? Does that make sense?

So, speculating forth, since the shape of the interference pattern is fixed, that information must be determined and the impacts on the screen are either determined or random within that pattern. Does that make sense?

Or alternatively, there must be some mechanism that results in the emergence of an interference pattern as a result of properties of the particles/EM radiation.

Does any of these approaches prevail?

Are those rhetorical questions?

Not to me, haha!

Anyway, the answers depend on the interpretation.

Thank you. That is exactly what I needed to get confirmed.

 

[Demystifier]

I am wondering, since the only thing that can carry that information from the exit of the double slit to the screen are the particles/EM radiation itself, that is where that information must be, right?

No. The information about interference is in the wave function. But depending on interpretation, the particle may or may not be identified with the wave function.

 

[entropy1]

the particle may or may not be identified with the wave function.

...but I think that the wavefunction describes properties of the particle? Or does it also incorporate properties of the experimental setup?

If the particle didn't interact with the double slit, the screen would show a different pattern. So I think the double slit, when interacting with the particle, induces its properties into the particle, thereby adding properties to (or properties changing in) the particle?

 

[Demystifier]

...but I think that the wavefunction describes properties of the particle? Or does it also incorporate properties of the experimental setup?

First define what do you mean by "particle". That word, for instance, has very different meanings in standard and Bohmian interpretation.

If the particle didn't interact with the double slit, the screen would show a different pattern. So I think the double slit, when interacting with the particle, induces its properties into the particle, thereby adding properties to (or properties changing in) the particle?

I cannot answer that before we agree on the definition of particle.

 

[entropy1]

First define what do you mean by "particle".

In my naivety I have to resort to the notion of 'electron', but I suspect that definition depends on the interpretation too. My knowledge of QM is still very basic.