Exploring the Phenomenon of Momentum Entanglement: Experiments and Applications

In summary, momentum entanglement can occur between two particles and can be maintained even if one particle is accelerated, although most interactions that accelerate the particle will break the entanglement. The effect of gravitational acceleration on momentum entanglement is still an open question. It is possible to boost the momentum of a particle without breaking entanglement, as demonstrated by the precession of spin in a magnetic field. However, this does not cause a related change in the momentum of the other entangled particle.
  • #1
Ostrados
65
9
I rarely hear about momentum entanglement, do you know any experiments/applications for momentum entanglement?

If we do momentum entanglement on 2 particles, and then we accelerate one of the particles, will the other particle slow down to obey conservation of momentum? or entanglement will be destroyed?
 
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  • #2
Ostrados said:
If we do momentum entanglement on 2 particles, and then we accelerate one of the particles, will the other particle slow down to obey conservation of momentum? or entanglement will be destroyed?
No. Whatever interaction is involved in accelerating the particle will also break the entanglement.
 
  • #3
Nugatory said:
No. Whatever interaction is involved in accelerating the particle will also break the entanglement.

What about gravitational acceleration? it will not involve direct interaction with the particle.
 
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  • #4
Nugatory said:
Whatever interaction is involved in accelerating the particle will also break the entanglement.

A very minor quibble, O Nugatory One, and I am probably going to put my foot in my mouth before finishing... :smile:

If that interaction has the effect of being an irreversible measurement, then of course you are correct. However, there are transforms that don't have that effect. And those do not break entanglement.

Frequency entangled photons (essentially momentum entangled) can move through fiber, changing their direction. They can even have their frequency modified (boosted for example) without breaking their entanglement. As long as no information is gained about their momentum.

I assume similar transforms could occur with electrons.
 
  • #5
Ostrados said:
What about gravitational acceleration?

This is an open question. Quantum gravity would imply that there might be an effect (however small). Otherwise, it should not.
 
  • #6
DrChinese said:
If that interaction has the effect of being an irreversible measurement, then of course you are correct. However, there are transforms that don't have that effect. And those do not break entanglement.
Indeed there are... But I am having trouble imagining one that would could be said to "accelerate the particle" in the sense that the OP is thinking about (that is, we know that the result of a momentum measurement after the interaction will be different than before) without breaking the entanglement. That may be a failure of imagination on my part.

In any case OP's line of thought, that we can "slow down" the other particle seems completely illegitimate. "Slow down" implies that the other particle had some (counterfactual) velocity that we've reduced by our interaction with the first particle.
 
  • #7
Nugatory said:
I am having trouble imagining one that would could be said to "accelerate the particle" in the sense that the OP is thinking about (that is, we know that the result of a momentum measurement after the interaction will be different than before) without breaking the entanglement.

You should be able to boost the momentum of a particle without breaking entanglement. We can precess spins with a magnetic field without breaking their entanglement and it's basically the same idea I think.

It's actually an interesting exercise to figure out why the boosting/precessing doesn't necessarily measure the momentum or spin, despite momentum conservation / angular momentum conservation requiring that some external system be pushed in the opposite direction.
 
  • #9
So let's say we used 2 electrons, and the speed of the 2nd electron was boosted without breaking the entanglement (which as I understood from the comments is possible), what will happen to the 1st electron? will it slow down?
 
  • #10
Ostrados said:
So let's say we used 2 electrons, and the speed of the 2nd electron was boosted without breaking the entanglement (which as I understood from the comments is possible), what will happen to the 1st electron? will it slow down?

Definitely not. Under no scenario that has been discussed above - which is the exception and not the rule - will doing something to A's momentum cause a related change in B's momentum. The question above is only whether there can be alterations to A's momentum that do NOT break the momentum entanglement with B.
 
  • #11
DrChinese said:
Definitely not. Under no scenario that has been discussed above - which is the exception and not the rule - will doing something to A's momentum cause a related change in B's momentum. The question above is only whether there can be alterations to A's momentum that do NOT break the momentum entanglement with B.

But my question was about momentum entanglement
 
  • #12
Ostrados said:
But my question was about momentum entanglement

And the answer is: accelerating A does not decelerate B in any related manner. It would normally break the entanglement with B (as Nugatory said), but there are occasions which it might not. Gravity would not break entanglement, unless it is a quantum force.
 
  • #13
DrChinese said:
And the answer is: accelerating A does not decelerate B in any related manner. It would normally break the entanglement with B (as Nugatory said), but there are occasions which it might not. Gravity would not break entanglement, unless it is a quantum force.
What about conservation of momentum why it will not hold (in case entanglement was not broken)?
 
  • #14
There is conservation of momentum. Entangled A+B is a constant prior to any acceleration X acting on A. After including X, you have (A+X) +B. Conservation holds.
 
  • #15
DrChinese said:
There is conservation of momentum. Entangled A+B is a constant prior to any acceleration X acting on A. After including X, you have (A+X) +B. Conservation holds.
Ok. So what you are saying in other words is that any added momentum for one of the particles will add to the total momentum of the entanglement system and momentum will be conserved with this new value.

So if we have pA+pB= p and we added x momentum to A then that is equivelent to saying pA+pB = p+x

Its interesting that we can manipulate the total entanglement state without breaking the entanglement.
 
  • #16
Ostrados said:
Its interesting that we can manipulate the total entanglement state without breaking the entanglement.

Yes, and again there are caveats around that. I don't know of any good experimental references for that for particles with mass - only for light. But I believe the theory is the same.
 

1. What is momentum entanglement?

Momentum entanglement is a quantum phenomenon in which particles that are separated in space can still be connected in a way that their momenta are correlated. This means that a change in the momentum of one particle will result in an immediate and opposite change in the momentum of the other particle, regardless of the distance between them.

2. How is momentum entanglement different from other types of entanglement?

Momentum entanglement is a specific type of quantum entanglement that involves the momenta of particles. It is different from other types of entanglement, such as spin entanglement, which involves the spin properties of particles. Momentum entanglement is also unique in that it can occur between particles that are separated by large distances.

3. What are some applications of momentum entanglement?

Momentum entanglement has potential applications in quantum information processing, quantum communication, and quantum sensing. For example, it could be used to create secure quantum communication networks or to improve the precision of sensors by using entangled particles as probes.

4. How is momentum entanglement studied in experiments?

In experiments, momentum entanglement can be created by entangling the momenta of particles through interactions or measurements. These entangled particles can then be separated and their momenta can be measured to confirm their correlation. Other experimental techniques involve manipulating the wave functions of particles to create entanglement.

5. What challenges are scientists facing in exploring momentum entanglement?

One of the main challenges in exploring momentum entanglement is the fragility of entangled states. These states can easily be disrupted by interactions with the environment, making it difficult to maintain entanglement over long distances or periods of time. Additionally, creating entanglement between particles with high momenta differences can be technically challenging. Further research and advances in technology are needed to overcome these challenges and fully understand the potential of momentum entanglement.

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