Exploring Quantum Entanglement & Special Relativity

[Degeneration]

Hi all! I had a question about conflict between quantum mechanics and special relativity. Before i start, let me ask you to keep the math down to a minimum. I'm currently a high school student, so I would greatly appreciate it if you could try not to use any math beyond simple calculus. I also don't know much about these two except the common laymans point of view.

Okay, so regarding quantum entanglement and special relativity, does there have to be a conflict? I am going to use this space time diagram which I borrowed from someone else.

http://i209.photobucket.com/albums/bb185/BobC_03/Entanglement3.jpg"

This is spacetime diagram for anyone who doesn't know, and if you have any questions, please ask me. Two photons are entangled in two different coordinate systems (red and blue). The red guy detects the photon at point A to spinning up, so the other entangled part must be spinning down, which is detected at point B. Both of these are detected in the interval of t"2. In the blue guys reference system, he detects the photon at point B to be having down spin. The problem is in the fact that at that time interval, the blue guy detects the photon at point C also, meaning that the photon is spinning up at both point C and point A. However, this cannot be possible seeing as how its spin was first measured at point A, and according to the quantum interpretation, nothing can be known until it is measured.

Is there any situation where there does not necessarily have to be a conflict between QM and SR? Maybe removing effects of time dilation and length contraction?

Thanks

 

[lbrits]

I'm going to go against your wishes and say that QM and SR disagree before entanglement (the QM you're thinking of, that is). This is essentially due to the fact that the Lorentz group's parameters are not compact (an angle goes between 0 and 2 pi, whereas a boost parameter goes from 0 to infinity). This in turn leads to the requirement that SR requires infinitely many degrees of freedom, and quantum field theory results.

Ignoring this little caveat, the usual answer to your question is that no information is transmitted faster than light. For instance, if I shine a laser at the moon and wiggle my hand back and forth, the spot on the moon moves faster than the speed of light. However, SR is not violated.

 

[RandallB]

keep the math down to a minimum. I'm a high school student, Thanks

To keep it simple the conflict your looking at has nothing to do with change referance frame as in SR twins etc. All the QM EPR spin or Polarization pardox issues can be shown in a singlw frame of refrance with observations taken at distances. What SR gives is that no light or information can span that distance FTL.
The problem is "wierid action at a distance" is seen in EPR -Bell experamental only FTL information exchange can solve the issue.

 

[Degeneration]

Ignoring this little caveat, the usual answer to your question is that no information is transmitted faster than light. For instance, if I shine a laser at the moon and wiggle my hand back and forth, the spot on the moon moves faster than the speed of light. However, SR is not violated.

with entanglement though, there really isn't any significant information transmitted is there? all you get is the spin, velocity and polarization, but what can you do with that? and its not really transmitting it because youre just measuring it

To keep it simple the conflict your looking at has nothing to do with change referance frame as in SR twins etc. All the QM EPR spin or Polarization pardox issues can be shown in a singlw frame of refrance with observations taken at distances. What SR gives is that no light or information can span that distance FTL.
The problem is "wierid action at a distance" is seen in EPR -Bell experamental only FTL information exchange can solve the issue.

Right but again there isn't any significant information transmitted. Would it be correct to say that the problem lies in the fact that we acquaint our measurements with light, and therefore have to deal with length contraction and time dilation?

 

[Parlyne]

There is no violation of relativity here. No information is transmitted faster than light because, when a photon is detected, it cannot be known a priori that the photon is one of an entangled pair. Without this foreknowledge, it cannot be said that you know instantaneously the state of the spacially separated photon. You can only make the contingent claim that if the photon you detected was part of an entangled pair that the other photon in the pair will be in the commensurate state.

 

[Haelfix]

In relativistic quantum mechanics, this is actually more of an axiom than anything else.

Two local gauge invariant operators at spatially removed (lightlike) locations must commute. So for instance you cannot have an experiment with an electron on Alpha Centauri giving you information instantenously about something happening on earth.
(This actually goes through in curved spacetimes as well)

Relaxing this condition absolutely destroys the quantum theory and makes it nonsensical, so it makes excellent sense to believe in it.

 

[Phrak]

In relativistic quantum mechanics, this is actually more of an axiom than anything else.

Two local gauge invariant operators at spatially removed (lightlike) locations must commute. So for instance you cannot have an experiment with an electron on Alpha Centauri giving you information instantenously about something happening on earth.
(This actually goes through in curved spacetimes as well)

Relaxing this condition absolutely destroys the quantum theory and makes it nonsensical, so it makes excellent sense to believe in it.

I have no idea what that means. But if Alice over on Alpha Centauri, agrees to measure the |+> component of one half of a spin-singlet prepared pair of electrons, where at the same time, according to Earth Bob's inerital frame, Bob also measures |+> of the other electron, Bob will know instantaniously what Alice measures.

 

[Haelfix]

Thats fine, but note that no 'information' has been passed between the two. Bob has no idea what Alice wants to tell him with this information, nor can he figure out whether he just made a random measurement or not.

This is a called the 'no communication theorem'. You cannot use entangled systems to transmit information ftl.

 

[Degeneration]

is that the only conflict between SR and QM? then there really isn't one is there? because the EPR paradox is kind of useless since they were wrong in their assumptions

 

[dkv]

I have question. Suppose if two entangled particles are sent to two different people A and B living on different edges of the planet...
They have an agreement ... If the spin up is measured the person will shoot himself and his body will be sent to the person alive.
Suppose A measures spin down then he instantaneously knows that B is dead and he can start preparing for the funeral... even before B is dead. The knowledge is useful since it saves the time for the funeral. Can we call this knowledge a kind of information?

 

[Parlyne]

I have no idea what that means. But if Alice over on Alpha Centauri, agrees to measure the |+> component of one half of a spin-singlet prepared pair of electrons, where at the same time, according to Earth Bob's inerital frame, Bob also measures |+> of the other electron, Bob will know instantaniously what Alice measures.

This only works if Bob somehow knows a priori that the electron he measures is entanged. There is no measurement he can do with the single electron that will tell him this. The only way to know is to look at correlations with Alice's electron, which will require information to be sent classically.

I have question. Suppose if two entangled particles are sent to two different people A and B living on different edges of the planet...
They have an agreement ... If the spin up is measured the person will shoot himself and his body will be sent to the person alive.
Suppose A measures spin down then he instantaneously knows that B is dead and he can start preparing for the funeral... even before B is dead. The knowledge is useful since it saves the time for the funeral. Can we call this knowledge a kind of information?

The same problem applies here. This situation requires foreknowledge that the particle is entangled.

 

[Phrak]

This only works if Bob somehow knows a priori that the electron he measures is entanged. There is no measurement he can do with the single electron that will tell him this. The only way to know is to look at correlations with Alice's electron, which will require information to be sent classically.

All particles are entangled. But this is about a specific entanglement.

 

[jtbell]

if Alice over on Alpha Centauri, agrees to measure the |+> component of one half of a spin-singlet prepared pair of electrons, where at the same time, according to Earth Bob's inerital frame, Bob also measures |+> of the other electron, Bob will know instantaniously what Alice measures.

But Alice cannot control whether she gets |+> or |-> for a particular electron. So she cannot use this mechanism to send a message to Bob. If she happens to get a |+> (and therefore Bob must have gotten a |->), that's not going to do her much good if she really wanted Bob to get a |+>. :uhh:

 

[dkv]

Any discussion based on prior knowledge of entanglement entangles the macroscopic observers... In my example the A and B are entangled using entangled particles...
If A is alive B must be in dead state ... and if B is alive then A must be dead.
Is this true ?

 

[Degeneration]

Any discussion based on prior knowledge of entanglement entangles the macroscopic observers... In my example the A and B are entangled using entangled particles...
If A is alive B must be in dead state ... and if B is alive then A must be dead.
Is this true ?

but the particle is already entangled so its not really any information transmitted since youre basing this off of something that's already set down (in this case the spin)

 

[dkv]

Thats ok. But can we say that entangled particles entangles the Observers also.

 

[Degeneration]

not really. In the sense that one is dead while the other is alive I guess your right, but entanglement implies complete reliance on each other. A cannot do something without oppositely affecting B. The only way the only way the observers are entangled is through their reliance on the entanglement of the particles. Really all people are entangled because were all made from the same energy but that's a different concept because in that matter were entangled with everything.

 

[RandallB]

Right but again there isn't any significant information transmitted. Would it be correct to say that the problem lies in the fact that we acquaint our measurements with light, and therefore have to deal with length contraction and time dilation?

What does “significant information” information have to do with it?
There is sufficient information being conveyed that we can measure "weird action at a distance" that can only be explained by some form of “entanglement” which may or may not involve FTL information transfer.
EPR-Bell is NOT a conflict with SR other than SR claims that FTL be part of the solution.
Entanglement and the QM as a self declared “complete theory” claims a complete solution to to the EPR-Bell paradox. The real conflict with that claim is not SR, but the Einstein and others claim that the QM claim to a complete solution is incomplete based on Local Realism.

You specifically requested replies be at a simple high school level in your OP. But your follow ups are based on misunderstanding things beyond that level just as your OP diagram is pointless relative to this topic.
You will not understand what you’re asking let alone the replies you’re getting on this topic until you know and understand the differences between things like:

What are limits of the QM “complete” theory: i.e. uncertainty HUP?
What is required by Local Realism and how does it fail to solve EPR-Bell.
What does entanglement mean and how does it solve EPR-Bell.

You cannot understand the conflict between LHV’s and the QM Entanglement solution without understanding at least those things and the LHV idea is not something unique to SR.

Pick key words from the above to search for other threads in this forum and you will find plenty of comments and links – you just need to find the one at your level that will help you move your understanding along.

 

[Degeneration]

I really couldn't find anything on QM complete theory. I don't think I even know what that is. As for the other two questions, (I understand this is exactly what you said) but does local realism not complement EPR? Dont they both go against entanglement?

 

[RandallB]

I really couldn't find anything on QM complete theory. I don't think I even know what that is. As for the other two questions, (I understand this is exactly what you said) but does local realism not complement EPR? Dont they both go against ?

The thread https://www.physicsforums.com/showthread.php?t=219649
is a good one to start at. Dr Al posted some links in post #13.
Just remember some things may be too advanced till you understand more.

“EPR” is based on “Local Realism”.

"Entanglement" is an attempt to visualize the QM solution but strictly speaking as it tries to explain what is happening between Origination and Detection it is not really a direct part of QM.

Part of what makes QM complete is in how it only deals with direct observation as in how things are at ORIGINATION and what is measured at DETECTION, without concern for what happens in-between.
That ties in with the limits of what make the QM view complete by using “uncertainty” and “HUP”

In contrast Local Realism cannot stand not knowing what is happening between Origination and Detection while QM takes as a given we will never know with certainty. That alone means these two will always be in conflict.

“quoted” items make better search terms and are all things you need to understand.

Good Luck