Entanglement: which properties are entangled?

[iamcj]

Hi,

So far I understand that when two particles are entangled measuring the state will provide the same result for both particles. But what I can't figure out: a particle has multiple properties like spin and momentum etc, are all these properties the same (or opposite), or only the one measured? Can one be sure that all properties are the same? Or can one be sure that if spin is equal, momentum is always not equal? Or is it unknown?

For example two entangled photons with the same polarization, do the two photons always have opposite momentum?

I hope some one can shed some light on this point or point me in the right direction.

 

[DrChinese]

So far I understand that when two particles are entangled measuring the state will provide the same result for both particles. But what I can't figure out: a particle has multiple properties like spin and momentum etc, are all these properties the same (or opposite), or only the one measured? Can one be sure that all properties are the same? Or can one be sure that if spin is equal, momentum is always not equal? Or is it unknown?

For example two entangled photons with the same polarization, do the two photons always have opposite momentum?

Whether the measurement results will be the same, opposite, or sum to a constant value entirely depends on the setup. There are also considerations that vary for the observable you are measuring. And finally, the entanglement can be on one basis or on multiple bases.

For example: Type II entangled photons may be entangled such that momentum/frequency is conserved. They would also be polarization entangled, with opposite (orthogonal) polarization.

It is possible to measure a photon's polarization and leave its momentum entangled. The momentum is not specifically opposite, but as I mention, conserved in total. Assuming you know initial momentum: A momentum measurement on one will yield the value of the other.

 

[iamcj]

Whether the measurement results will be the same, opposite, or sum to a constant value entirely depends on the setup. There are also considerations that vary for the observable you are measuring. And finally, the entanglement can be on one basis or on multiple bases.

For example: Type II entangled photons may be entangled such that momentum/frequency is conserved. They would also be polarization entangled, with opposite (orthogonal) polarization.

It is possible to measure a photon's polarization and leave its momentum entangled. The momentum is not specifically opposite, but as I mention, conserved in total. Assuming you know initial momentum: A momentum measurement on one will yield the value of the other.

Many tnx for you answer. So if momentum is between -1 and 1. If I measure particle A at 0.2, particle B has -0.2 ? My real question is: for any entangled photon can I say: if the polarization is entangled ( the same) , there is always a property like momentum that moves like this for the two photons?

 

[DrChinese]

Many tnx for you answer. So if momentum is between -1 and 1. If I measure particle A at 0.2, particle B has -0.2 ? My real question is: for any entangled photon can I say: if the polarization is entangled ( the same) , there is always a property like momentum that moves like this for the two photons?

View attachment 222791

Most quantum observables cannot be said to oscillate as implied. If they did, time of measurement would be a factor... and it is not.

It can be difficult (in QM) to assign values to unmeasured quantities. Especially entangled ones.

 

[iamcj]

Most quantum observables cannot be said to oscillate as implied. If they did, time of measurement would be a factor... and it is not.

It can be difficult (in QM) to assign values to unmeasured quantities. Especially entangled ones.

I don't understand...

https://en.wikipedia.org/wiki/Photon

p = h/lambda, that means for momentum there is a relation to frequency thus to time? Or is momentum constant for a given frequency?

Can we even measure with the kind of the accuracy that we can observe photons at exactly the same time interval?

 

[DrChinese]

I don't understand...

https://en.wikipedia.org/wiki/Photon

1. p = h/lambda, that means for momentum there is a relation to frequency thus to time?

2. Can we even measure with the kind of the accuracy that we can observe photons at exactly the same time interval?

1. Frequency yes, time no.

2. Yes, you can measure some attributes to a very high degree of time resolution. But what purpose would it serve? Any polarization measurement on the entangled pair has no dependency on time whatsoever. Ditto for momentum. So a little time here or there makes no difference to the expected results.

I think what you are picturing is that a photon oscillates as it moves. In a basic way, that is correct. And indeed you can construct experiments (using a Mach-Zehnder Interferometer, for example) that depend on that element. But that is not something that can be exploited in the manner of a water wave, sound wave, etc.

We are talking quantum particles, and analogies are notoriously difficult to extend to this realm. Most of the time, you end up going in circles trying to make the analogy hold - when it is of limited application in the first place.

 

[DrChinese]

To be more specific about what I said above about oscillation of a photon: What do you think is oscillating? Do you think there is a little piece of a photon that flaps back and forth? If it did, then a photon would have a shape. What is that shape? How big is it? Is it like a tail?

When you attempt to use an analogy to describe a quantum particle, you usually fall into a vat pretty quick. The spatial extent of many/some/most photons covers a vast volume of spacetime. So they couldn't look like your analogy. (That is why our cellphones, which receive light transmissions as part of the receiving function, continue to operate no matter where you are in the room. I assure you there aren't that many individual, separate photons floating around to fill a room. They become localized upon arrival at the antenna.)

On the other hand: it is possible to localize a photon to a very small volume of space too. As far as anyone knows, it has no internal structure. That a photon can be described in both ways is essentially a contradiction. And yet, the quantum model is successful.

 

[iamcj]

1. Frequency yes, time no.

2. Yes, you can measure some attributes to a very high degree of time resolution. But what purpose would it serve? Any polarization measurement on the entangled pair has no dependency on time whatsoever. Ditto for momentum. So a little time here or there makes no difference to the expected results.

I think what you are picturing is that a photon oscillates as it moves. In a basic way, that is correct. And indeed you can construct experiments (using a Mach-Zehnder Interferometer, for example) that depend on that element. But that is not something that can be exploited in the manner of a water wave, sound wave, etc.

We are talking quantum particles, and analogies are notoriously difficult to extend to this realm. Most of the time, you end up going in circles trying to make the analogy hold - when it is of limited application in the first place.

I indeed visualize a photon vibrating in some way.

And if I interpret this information, +-h is based on time as you also point out?

https://en.wikipedia.org/wiki/Spin_angular_momentum_of_light#/media/File:Sam_v1.png
https://en.wikipedia.org/wiki/Spin_angular_momentum_of_light

Thanks for the example of the Mach-Zehnder Interferometer.

Has there ever been experiments with (entangled) photons using an interval of exact k * lambda? Only then you are sure you are not measuring photons with a "random" momentum?

Do we no why photons are absorbed by a filter or not?

 

[DrChinese]

1. I indeed visualize a photon vibrating in some way.
...
2. Has there ever been experiments with (entangled) photons using an interval of exact k * lambda? Only then you are sure you are not measuring photons with a "random" momentum?

3. Do we no why photons are absorbed by a filter or not?

1. Don't. There is no pointer as shown in the picture. It is useful for general study, but should not be taken literally. Quantum mechanics is considered a mathematical theory. Only the math is part of the theory, the pictures are not.

2. As a result of what I said in 1.: It makes no sense to ask for probing experiments to back up a picture. Virtually any kind of experiment that would verify any element of Quantum Theory has been performed, or alternately there may be plans to perform them as feasible. But you can see logically that if QM does not have a time dependency on entanglement predictions, there is actually nothing to test related to time. The predictions of QM are confirmed without any concern for "an interval of exact k * lambda"; so what would we be looking for? That there is no time dependency has been clearly validated precisely because the measurement times of Alice and Bob were not precisely measured as to phase.

3. As to why photons are absorbed by a filter: This apparently simple question is complicated to answer. There are both classical and quantum treatments of the subject. It also relates to spin, a quantum property which can be difficult to model in a fully satisfying manner visually. I will recommend you follow up on this subject by reading some additional treatments. From https://en.wikipedia.org/wiki/Photon_polarization to https://arxiv.org/pdf/quant-ph/0101074.pdf there is much to learn and appreciate.

Perhaps another would care to take a crack at this as well.

 

[Tracer]

DrChinese posted:
"1. Don't. There is no pointer as shown in the picture. It is useful for general study, but should not be taken literally. Quantum mechanics is considered a mathematical theory. Only the math is part of the theory, the pictures are not.
2. As a result of what I said in 1.: It makes no sense to ask for probing experiments to back up a picture. Virtually any kind of experiment that would verify any element of Quantum Theory has been performed, or alternately there may be plans to perform them as feasible. But you can see logically that if QM does not have a time dependency on entanglement predictions, there is actually nothing to test related to time. The predictions of QM are confirmed without any concern for "an interval of exact k * lambda"; so what would we be looking for? That there is no time dependency has been clearly validated precisely because the measurement times of Alice and Bob were not precisely measured as to phase.

Reference https://www.physicsforums.com/threads/entanglement-which-properties-are-entangled.943178/"

The reference explains a lot but does not address timing of entanglement events. Can you explain why entanglement events have no time dependency?
Regards. Tracer

 

[Mentz114]

The reference explains a lot but does not address timing of entanglement events. Can you explain why entanglement events have no time dependency?
Regards. Tracer

When two particles become entangled their quantum state becomes a single state (immediately) . Any change to this state affects both members of the pair (immediately). QT tells us nothing about times for individual entangled particles.
Also, if there was a delay, would the first particle to be affected change state or would that happen when the other one does ?
Theory and experiments show that it makes no difference which ordering is chosen ( as predicted ).

 

[Derek P]

Has there ever been experiments with (entangled) photons using an interval of exact k * lambda? Only then you are sure you are not measuring photons with a "random" momentum?

Any finite wavepacket has a spectrum of spatial frequencies and therefore an uncertainty in the momentum. Chopping it to a precise number of wavelengths doesn't give you a pure single frequency; on the contrary it introduces more sidebands by ordinary modulation theory. So, far from getting an exact momentum, you make the uncertainty greater. Which is hardly surprising as lopping the ends of a wavepacket off makes the position more defined.

 

[iamcj]

When two particles become entangled their quantum state becomes a single state (immediately) . Any change to this state affects both members of the pair (immediately). QT tells us nothing about times for individual entangled particles.
Also, if there was a delay, would the first particle to be affected change state or would that happen when the other one does ?
Theory and experiments show that it makes no difference which ordering is chosen ( as predicted ).

Any finite wavepacket has a spectrum of spatial frequencies and therefore an uncertainty in the momentum. Chopping it to a precise number of wavelengths doesn't give you a pure single frequency; on the contrary it introduces more sidebands by ordinary modulation theory. So, far from getting an exact momentum, you make the uncertainty greater. Which is hardly surprising as lopping the ends of a wavepacket off makes the position more defined.

Tnx for your answers. It makes things somewhat more clear to me.

I would like for you to join me in a thought experiment where time does play a role. The real big question for me is why in the Bell experiments photon A gets absorbed and B gets not. From QM we can predict the percentage, but we can’t say much about the why, other than it is undecided until it happens.

“A finite wavepacket has a spectrum of spatial frequencies and therefore an uncertainty in the momentum”.

My first assumption is that, although we may or may not know the momentum at a specific time interval, for two entangled photons a property (let us say momentum) is exactly opposite. Two photons are entangled on their polarization and are part of the Bell experiment.

No please have an open mind and let me oversimplify the spectrum of spatial frequencies to a single one, just to visualize that they are opposite at any moment in time. So we get something like the picture below, where the left value is the value for let’s say the momentum and the picture just indicates the opposite value of the property for both photons. So in this picture I assume we have 64 pairs of polarized photons distributed by their state. With high amplitude momentum they are absorbed and with low momentum they are polarized.

This picture would indicate that the two particle should always behave the same and both will pass the filter or not depending on the moment of impact. This is contradicting the results of QM experiments, so this can’t be.

No I make a second assumption that only in specific cases, for example when momentum is building up the photons are absorbed or not. This does not have to be the reason, but there are states that lead to absorption and there are states that lead to polarization. So that is what this means.

When we do this assumption we get the picture below that correspond with the passing rate between a polarized photon and a filter at an angle difference, at cos2(θ). So in the picture below at 60 degrees angle difference 50% passes and 50% is absorbed. Please hang on a little longer and keep that open mind.

Now we put in the entangled opposite brother into the picture with its mirrored momentum state:

So what do we see here: 64 pairs of polarized entangled photons approaching Alice and Bob filters, but all distributed in their state of momentum over time. As you can see in the picture in 25% of the cases we have the same result (2 blue or red balls) and in 75% we have different results, matching QM predictions.

Is this deterministic reasoning opposing Bell? No, the “hidden variable” is opposite and not always equal over, there we have it, time…. it is just following a simple wave function. (I can produce these images for other angles). Some times they are both in the same (opposite) state to get polarized and some times not.

I would say that if one could influence or time an experiment in such a way that you are sure every photon hits the polarizer in the same state, you would always get the same result. No we throw all these cases below on one big pile and get the average as a result, as in my opinion we should try to look at only one to get more understanding. The picture below gives 4 possible representations of the photon momentum value a the moment of impact on a filter.

http://[url=https://imgbb.com/]https://image.ibb.co/cJhPAS/4.jpg[ATTACH=full]222897[/ATTACH]

Now you can think of me as some stupid brat that should first start learning all the math to think about this stuff, but please don’t close this topic and please discuss with me why this is wrong or better be inspired and think about how this rough idea can fit within known physics.

 

[DrChinese]

Can you explain why entanglement events have no time dependency?

If you have Alice and Bob measuring entangled Type I PDC photons (same polarization) at angles A and B, the match % function is:

M=cos^(A-B)

Note that time is not a factor in the equation. That's probably the easiest way to understand the issue. Note that the difference between the angles is the only relevant factor, and the distance between the settings is NOT a factor either.

 

[iamcj]

If you have Alice and Bob measuring entangled Type I PDC photons (same polarization) at angles A and B, the match % function is:

M=cos^(A-B)

Note that time is not a factor in the equation. That's probably the easiest way to understand the issue. Note that the difference between the angles is the only relevant factor, and the distance between the settings is NOT a factor either.

So we have two guys over here. One is holding the pendulum that he will be swinging and keep it in motion. The guy with the red T-shirt will put the ball on the spot at random times. 50% of the cases the ball goes forward and is hit with the point of the shoe. 50% of the cases the ball goes backwards and is hit with the back of the shoe. If I understand you correctly you say time is not a factor in this picture because M = number of tries / 2, so there is no time in the formula. But if the guy in the red shirt gets his timing right, all balls will go forward, so time is a factor.

 

[Mentz114]

Tnx for your answers. It makes things somewhat more clear to me.

I would like for you to join me in a thought experiment where time does play a role. The real big question for me is why in the Bell experiments photon A gets absorbed and B gets not. From QM we can predict the percentage, but we can’t say much about the why, other than it is undecided until it happens.

“A finite wavepacket has a spectrum of spatial frequencies and therefore an uncertainty in the momentum”.

My first assumption is that, although we may or may not know the momentum at a specific time interval, for two entangled photons a property (let us say momentum) is exactly opposite. Two photons are entangled on their polarization and are part of the Bell experiment.

http://[url=https://imgbb.com/]https://image.ibb.co/cJhPAS/4.jpg

Now you can think of me as some stupid brat that should first start learning all the math to think about this stuff, but please don’t close this topic and please discuss with me why this is wrong or better be inspired and think about how this rough idea can fit within known physics.
[]
[/QUOTE]
You misunderstand entanglement and there is nothing to discuss.
[QUOTE="iamcj, post: 5967889, member: 563104"]So we have two guys over here. One is holding the pendulum that he will be swinging and keep it in motion. The guy with the red T-shirt will put the ball on the spot at random times. 50% of the cases the ball goes forward and is hit with the point of the shoe. 50% of the cases the ball goes backwards and is hit with the back of the shoe. If I understand you correctly you say time is not a factor in this picture because M = number of tries / 2, so there is no time in the formula. But if the guy in the red shirt gets his timing right, all balls will go forward, so time is a factor.

[ATTACH=full]222903[/ATTACH][/QUOTE]
You cannot reproduce quantum mechanics using naive mechanical models. Everyone is trying to tell you this.
Please go away and do some physics study.

 

[Tracer]

Mentz114 said
When two particles become entangled their quantum state becomes a single state (immediately) . Any change to this state affects both members of the pair (immediately). QT tells us nothing about times for individual entangled particles. Also, if there was a delay, would the first particle to be affected change state or would that happen when the other one does ? Theory and experiments show that it makes no difference which ordering is chosen ( as predicted ). I accept that as a fact and without any dispute. However, I believe time does play a role in the observation of entangled events as follows. In addition to the contents of your post, I believe events which happen to one photon of an entangled pair affect only the photon's entangled partner and has no effect on any other photons in the entangled partner's photon stream. Consider the following scenario:

A continuous stream of entangled photons is generated at position D0. Each entangled photon follows a path in a direction opposite to that of its entangled partner to either D1 or D2. There are observers at both D1 and D2 who are able to place filters in their stream of photons from D0 and measure the results. Let the distance between D0 to either D1 or D2 be several light seconds. Then if D1 is greater than D2 and the observer at D1 inserts a filter into the stream of photons from D0 and measures the Quantum state of the entangled photons now received at D1, then the quantum state of the entangled photons in beam from D0 to D2 will also be changed. However, The entangled partner photons will already have passed D2 and therefore no change of quantum states will be observed at D2. However, If D1 is less than D2, then the observer at D2 might have to wait a few seconds for the altered quantum state, partner photons to reach D2 before the altered quantum states can be determined. The observer at D2 will see the affects of the filter placed in D1's stream of photons from D0 immediately only if D1 is exactly equal tp D2.
If Quantum entanglement doesn't work that way then it really is "Spooky action at a distance". I think I have given you enough of my beliefs about entanglement to enable you to point out where I am wrong. Please do.
Tracer.

 

[iamcj]

You misunderstand entanglement and there is nothing to discuss.

You cannot reproduce quantum mechanics using naive mechanical models. Everyone is trying to tell you this.
Please go away and do some physics study.

I am sorry to have offended you. Please tell me where I am wrong, so I can get these ideas out of my head.

 

[DrChinese]

I would like for you to join me in a thought experiment where time does play a role. The real big question for me is why in the Bell experiments photon A gets absorbed and B gets not. ...

Please discuss with me why this is wrong or better be inspired and think about how this rough idea can fit within known physics.

The issue is that descriptions of experiments invariably leave out many things that it is assumed that everyone knows. Of course, not everyone knows these things...

Unfortunately, your premise is not correct. It is NOT a factor that A gets absorbed by the polarizer and B does not. About half of all Bell tests have this attribute, so no surprise that it looks relevant initially. But the other half of experiments do not work that way. Instead: in those, a beam splitter is used instead of a polarizer. So neither polarization is absorbed, and both are positively detected. I.e. there are 2 detectors on Alice's side, and 2 on Bob's side. All Alice+Bob pairs are considered.

Not trying to pick your logic apart at all, as there is no way you would be aware of some of these details.

Don't forget that there are 2 types of photon polarization entanglement: symmetric (same) and anti-symmetric (opposite). Also: polarization entanglement and momentum entanglement are 2 completely independent bases of entanglement. A photon pair can be entangled on either basis, both bases, or neither basis. There is no connection between these two bases because they commute.

And I can assure you the polarization and/or momentum of a photon does NOT fluctuate as you imply. If it did, then time WOULD be a factor. And it clearly is not. You should be able to see that from the fact that there is no calibration performed of the type you think should occur. Because if it were a factor, and the calibration was not performed, the correlations would not persist at the time of measurement.

 

[Mentz114]

Mentz114 said
When two particles become entangled their quantum state becomes a single state (immediately) . Any change to this state affects both members of the pair (immediately). QT tells us nothing about times for individual entangled particles. Also, if there was a delay, would the first particle to be affected change state or would that happen when the other one does ? Theory and experiments show that it makes no difference which ordering is chosen ( as predicted ).

I accept that as a fact and without any dispute. However, I believe time does play a role in the observation of entangled events as follows. In addition to the contents of your post, I believe events which happen to one photon of an entangled pair affect only the photon's entangled partner and has no effect on any other photons in the entangled partner's photon stream. Consider the following scenario:

A continuous stream of entangled photons is generated at position D0. Each entangled photon follows a path in a direction opposite to that of its entangled partner to either D1 or D2. There are observers at both D1 and D2 who are able to place filters in their stream of photons from D0 and measure the results. Let the distance between D0 to either D1 or D2 be several light seconds. Then if D1 is greater than D2 and the observer at D1 inserts a filter into the stream of photons from D0 and measures the Quantum state of the entangled photons now received at D1, then the quantum state of the entangled photons in beam from D0 to D2 will also be changed. However, The entangled partner photons will already have passed D2 and therefore no change of quantum states will be observed at D2. However, If D1 is less than D2, then the observer at D2 might have to wait a few seconds for the altered quantum state, partner photons to reach D2 before the altered quantum states can be determined. The observer at D2 will see the affects of the filter placed in D1's stream of photons from D0 immediately only if D1 is exactly equal tp D2.
If Quantum entanglement doesn't work that way then it really is "Spooky action at a distance". I think I have given you enough of my beliefs about entanglement to enable you to point out where I am wrong. Please do.
Tracer.

I don't follow the logic of the stream of entangled photons with multiple filtering thought experiment. I have nothing to add to what I said because that is all there is. Interpretation is your problem.

 

[Mentz114]

I am sorry to have offended you. Please tell me where I am wrong, so I can get these ideas out of my head.

No offence taken. Listen to Dr Chinese.

 

[DrChinese]

So we have two guys over here. ... so time is a factor.

What I believe you are trying to say: time is a factor in entanglement tests, it just doesn't appear that way to any scientist who has ever done this type of experiment. Oh, and it is not a factor in theoretical predictions.

Do you see what is wrong with your concept? I call that the "unicorn" fallacy. You don't see them either.

While we have been trying to help you understand entanglement, I must point out: discussion of personal speculative ideas are actually not appropriate on this site. So in all fairness, this line of discussion should come to a halt now. Ask a question about the generally accepted science instead.

 

[iamcj]

What I believe you are trying to say: time is a factor in entanglement tests, it just doesn't appear that way to any scientist who has ever done this type of experiment. Oh, and it is not a factor in theoretical predictions.

Do you see what is wrong with your concept? I call that the "unicorn" fallacy. You don't see them either.

While we have been trying to help you understand entanglement, I must point out: discussion of personal speculative ideas are actually not appropriate on this site. So in all fairness, this line of discussion should come to a halt now. Ask a question about the generally accepted science instead.

Tnx for your perspective. I am not English so maybe in the translation some nuances that are there for you I don't get. What I meant is that your explanation that time is not in the formula itself is not enough to rule out time and just a fun example. I appreciate your help and patience with me. I can't help that I still have an unsatisfied feeling about this, but that is probably has to do with a lack of knowledge on my side. Getting to know all the proper math will take me many year as I already have a family. I have to give this a rest as hard as it is :), maybe if I have more time.

I think there should be a place for farmer speculation because a stupid question or idea from another view can bring an new way of thinking for the expert even if in 999 of 1000 times it won't. And that was my only goal.

I hope one day, Einstein will be proven to be right after all :)

 

[DrChinese]

I think there should be a place for [...] speculation because a stupid question or idea from another view can bring an new way of thinking for the expert even if in 999 of 1000 times it won't.

Your view has been discussed here many a time, and the decision is: it is not good for this site. Obviously the objective here is primarily for readers to gain knowledge and enjoyment. It is not intended for original research. There are other places for that, and many of those do not have moderators as PF does. And I completely agree. And in fact the moderators are responsible for keeping this place sane!

Honestly, no one is trying to discourage you from having novel ideas. But when a novice skips what would be covered in introductory textbooks, it hardly makes much sense to debate that. Einstein was at the cutting edge of physics at the time of his early work, attacking some very perplexing problems of that time. And supplying answers.

Believe me, there are much more complex entanglement scenarios than what we are discussing. Read more about the basics, and increase your grasp of the subject. You will not be wasting your time.