Question about Entanglement and SR

[LsT]

In the context of a photon entaglement experiment, let the observer be in the frame of reference of photon "a". Photon "a" starts its travel to Alice with a relative speed to her = C. If SR holds, photon "b" cannot be moved at all in the opposite direction, when "a" arrives at Alice. And vice versa from the frame of reference of photon "b". If this is the case, how is this interpreted?

 

[ShayanJ]

If this is the case

This is not the case!
Because there is nothing called "frame of reference of photon"! See here!

 

[craigi]

In the context of a photon entaglement experiment, let the observer be in the frame of reference of photon "a". Photon "a" starts its travel to Alice with a relative speed to her = C. If SR holds, photon "b" cannot be moved at all in the opposite direction, when "a" arrives at Alice. And vice versa from the frame of reference of photon "b". If this is the case, how is this interpreted?

As has already been mentioned, Lorentz contraction collapses everything to a plane as the relative velocity approaches the speed of light.

Try reformulating your question with near light speed particles and rest frames.

 

[LsT]

As has already been mentioned, Lorentz contraction collapses everything to a plane as the relative velocity approaches the speed of light.

If I can consider this the reality for the photon, there is nothing more to say. Because if a photon lives in a 2d univesrse with zero width at its direction, then entaglement is explained by SR, as I think of it.

 

[Nugatory]

If I can consider this the reality for the photon, there is nothing more to say. Because if a photon lives in a 2d universe with zero width at its direction, then entanglement is explained by SR, as I think of it.

Then how would you explain the similar experiments done with spin-entangled massive particles? These only move at speeds slower than the speed of light, yet non-local entanglement effects are still observed.

You are misunderstanding craigi's answer and the FAQ at that shyan pointed you towards. The conclusion that you should be drawing is not that the photon "lives in a 2d universe with zero width" in its direction of motion, it is that any model that doesn't start with the premise that the light signal is moving across a non-zero distance at the speed of light is guaranteed to give you meaningless answers.

 

[LsT]

Then how would you explain the similar experiments done with spin-entangled massive particles? These only move at speeds slower than the speed of light, yet non-local entanglement effects are still observed.

The correct thing to say was that just photon entaglement can be explained. I don't say I can do that for massive particles, but If they are massive I am curious about the answer in the lines of my first post question.

You are misunderstanding craigi's answer and the FAQ at that shyan pointed you towards. The conclusion that you should be drawing is not that the photon "lives in a 2d universe with zero width" in its direction of motion, it is that any model that doesn't start with the premise that the light signal is moving across a non-zero distance at the speed of light is guaranteed to give you meaningless answers.

Point to me a proof. Otherwise I canno't see why it is meaningless. For me it makes sense. Its in agreement with all experiments (?), so if it remains an option I can make it an assumption.

The fact that the rest frame of a photon does not make sense mathematically, can be considered the equivalent of a proof that each photon doesn't exist in its own relative spacetime as everything else?

 

[Nugatory]

The correct thing to say was that just photon entaglement can be explained. I don't say I can do that for massive particles, but If they are massive I am curious about the answer in the lines of my first post question.

Here's an experiment done with spin-entangled protons. (Reading it will also explain why we do these experiments with photons whenever possible - they are much easier to work with).

A pair of spin-entangled protons are generated. They move in opposite directions at a speed of about .6c (I picked that number so that I can do the rest of the calculations in my head... In fact the protons are moving a bit slower than that). The detectors are separated by roughly 2 meters, with the source in the middle.

In the rest frame of the lab, each proton takes about five nanoseconds to cover the distance between source and detector. Both protons arrive at their respective detectors at the same time, so it is clear that of the result at one detector can affect the result at the other, the influence must have traveled faster than light, which is to say it's non-local.

Viewed from a frame in which either proton is at rest, the other proton is moving towards its detector at a speed of $30c/34$ (google for "relativistic velocity addition" to see where this came from). Clearly both protons will eventually meet their respective detectors: the one that is at rest in the frame that we've chosen sees its detector moving towards it, and sees the other proton and its detector on a high-speed collision course.

Do note that the proton that is at rest in this frame will meet its detector before the other proton so certainly cannot be influenced by the result of the measurement at the other detector - but this is true for no matter which proton we consider to be at rest.

 

[craigi]

The correct thing to say was that just photon entaglement can be explained. I don't say I can do that for massive particles, but If they are massive I am curious about the answer in the lines of my first post question.

Your explanation doesn't work for any valid rest frame. Only for the invalid rest frame which is moving at c, relative to the entire universe. Try using it to explain the EPR experiment from the perspective of a stationary observer.

It also doesn't work for all photons, since photons in a medium don't travel at c (the speed of light in a vacuum).

What you're actually talking about is a general locality (and causality) abuguity in invalid rest-frames. This is just another way of saying that they're invalid.

 

[LsT]

Do note that the proton that is at rest in this frame will meet its detector before the other proton so certainly cannot be influenced by the result of the measurement at the other detector - but this is true for no matter which proton we consider to be at rest.

There I need some help understanding it, because the event of either proton reaching a detector is placed in the future light cone of the other (?). Is not that the definition of casuality violation between the frames? How is this interpreted?

Your explanation doesn't work for any valid rest frame. Only for the invalid rest frame which is moving at c, relative to the entire universe. Try using it to explain the EPR experiment from the perspective of a stationary observer.

It also doesn't work for all photons, since photons in a medium don't travel at c (the speed of light in a vacuum).

I agree with this. EPR uses massive particles AFAIK. Its just a stupid idea about photons at c that works intuitively (for me), and trying to see if it remains (or not) a possibility (and why).

 

[Nugatory]

There I need some help understanding it, because the event of either proton reaching a detector is placed in the future light cone of the other (?). Is not that the definition of casuality violation between the frames? How is this interpreted?

Both detection events are in the future light cone of the emission event, but neither detection event is in the future light cone of the other detection event. It's easiest to see this if you draw the three light cones in the lab frame, of course.

(This would be a good time to google for "relativity of simultaneity" if you are not familiar with that concept from special relativity).

 

[craigi]

j

I agree with this. EPR uses massive particles AFAIK. Its just a stupid idea about photons at c that works intuitively (for me), and trying to see if it remains (or not) a possibility (and why).

The simplest form of the EPR experiment uses light (massless), but could refer to the experiment using massive particles too.

Even if we consider the photon to have a rest frame, it's not sufficient to explain this case. We need to explain it for all observers and your explanation doesn't work for any valid observer.

There's another way in which it fails. Entangled photons don't need to travel in opposite directions. We can direct the photons to travel perpendicular to each other if we wish. In which case, even in the limit of the relative velocity of any rest frame approaching c, the the particles do not converge to a point on a plane.

I'd also check that you've fully grasped how light works in SR by asking yourself what speed would an observer measure the speed of light in each direcion, if they were to travel at 0.9999999c relative to the Earth.

 

[LsT]

@Nugatory

Of course you are right, that was a stupid thing to say about light cones, I now understand that they are independent from the frames.

So for conclusion you are saying to me that these 3 facts:
1. From rest frame a, when a reaches detector b has not reached yet
2. From rest frame b, when b reaches detector a has not reached yet
3. From rest frame of lab, both detectors "see" a particle at same time.
are just all about relativity of simultaneity, and no paradox at all?

If yes, please bare to answer also my next basic question so that I can clear things in my mind about this:

I suppose that there is a mechanism, which when detects a proton in detector a, places a barier just before detector b in a way that it closes the way of proton b (as seen from rest frame of proton a). This mechanism let's suppose it is a single object so it can tranfer the information instantly for the distance recuired (I am not sure if I can say this). Now what?

Even if we consider the photon to have a rest frame, it's not sufficient to explain this case. We need to explain it for all observers and your explanation doesn't work for any valid observer.

Help me a little more, because I am unable understand from what I know what is the difference of EPR experiment and entaglement experiment. If you talk about entaglement, I don't understand what is the difficullty from any valid observers frame.

There's another way in which it fails. Entangled photons don't ned to travel in opposite directions. We can direct the photons to travel perpendicular to each other if we wish. In which case, even in the limit of the relative velocity approaching c, the the particles do not converge to a point on a plane.

Hmm. You have a point of course. In fact your point holds in any case that Alice, emiter and Bob are not in the same line. I can only think two possible solutions to this now. The first one is that they converge to a point on a line, but that whould mean that dey would have only 1 dimensional polarization, which I suppose is not the case at all. The second solution I can think about, is that they still converge to a plane, that is perpendicular to the direction of their relative motion, but as we change thedirection of their relative motion for example though optical fibers, this plane continues to be perpendicular to that direction at all times, with the photon just changing a position in that plane if needed.

 

[Nugatory]

I suppose that there is a mechanism, which when detects a proton in detector a, places a barier just before detector b in a way that it closes the way of proton b (as seen from rest frame of proton a). This mechanism let's suppose it is a single object so it can transfer the information instantly for the distance required (I am not sure if I can say this). Now what?

That is not possible, as whatever is doing the transmission would have to move faster than the speed of light to cover the distance between the two detectors in the time between the two detections.

 

[LsT]

That is not possible, as whatever is doing the transmission would have to move faster than the speed of light to cover the distance between the two detectors in the time between the two detections.

I don't get this. Lets' suppose I hold a long pipe and I turn it with my hand in the "long" axis. Does not the "information" from my hand is transferred to the other end of the pipe faster than light?

 

[LsT]

The second solution I can think about, is that they still converge to a plane, that is perpendicular to the direction of their relative motion, but as we change thedirection of their relative motion for example though optical fibers, this plane continues to be perpendicular to that direction at all times, with the photon just changing a position in that plane if needed.

Forget also about this. That cannot be the case, because implies an opposing direction of the photons allways at detectors, which is not the case of course. So the one that remains is that the "plane universe" of each photon "follows" independently its direction by remaining perpendicular to it. But I admit, that does not makes sense to me also now.

 

[Nugatory]

I don't get this. Lets' suppose I hold a long pipe and I turn it with my hand in the "long" axis. Does not the "information" from my hand is transferred to the other end of the pipe faster than light?

It does not. We even have a FAQ for this: https://www.physicsforums.com/threads/can-i-send-a-signal-faster-than-light-by-pushing-a-rigid-rod.536289/

At this point, you might be best served by backing off from your efforts to understand entanglement in terms of relativity until you've solidified your understanding of special relativity. There's a reason why a standard undergraduate physics curriculum covers SR before QM.

 

[LsT]

It does not. we even have a FAQ for this: https://www.physicsforums.com/threads/can-i-send-a-signal-faster-than-light-by-pushing-a-rigid-rod.536289/

Sorry, my fault, get it now.