Zeno's paradox

To communicate information you still have to have something transmitted classically iirc which is limited by the speed of light. Kinda tricky to understand, I'm not sure on all the details, but I think of it like this: You couldn't know that your counterpart on the other side of the entangled whatever actually tried to communicate information till receiving a classical signal.
 
Entangled particles communicate instantaneously, no matter how far apart they are, even if they are on opposite sides of the universe. However, it's not really "communication" in the first place. The entangled particles are more like a single particle that's in two places at once, which means that if you measure one and find it is in a certain state, the other will instantaneously be in that state too.

I know this because I happen to share an office with a quantum physicist and I just asked him.
 
Iirc the reason why you can't use quantum entanglement for FTL communication is cryptography. Imagine Alice and Bob are far away from each other, but both own one of a pair of entangled particles. Alice wants to send a message to Bob, so she changes the state of her particle in some way. This has to be done by letting her particle interact in some way with at least one other quantum.

Alice can't completely influence how those two quantums interacted. But this is a vital information for Bob to decode her message - remember: Bob's particle takes the same state as Alice's twin version of it, but without knowing what interaction caused this state, he can't find out what her "input" was. So Alice has to pass information about how the interaction happened to Bob, but obviously, she has to do this the classical way, because else they'd run into the same problem again.

So what's the matter with quantum entanglement communication? It gives you the perfect encryption method. The quantum which interacted with Alice's particle holds all information about how her information was encrypted - it's the encryption key. Without having this key, there's no way to decrypt the information again.


I apologize for errors and imprecision, quantum mechanics is something that's already hard to put into words when it's fresh in your head, so I hope a physicist can set any eventual errors straight later. But it should give you the principle idea why there's no FTL communication.
 
Entangled particles communicate instantaneously, no matter how far apart they are, even if they are on opposite sides of the universe. However, it's not really "communication" in the first place. The entangled particles are more like a single particle that's in two places at once, which means that if you measure one and find it is in a certain state, the other will instantaneously be in that state too.

I know this because I happen to share an office with a quantum physicist and I just asked him.

Wouldn't this be impossible to determine, by definition?
 
Iirc the reason why you can't use quantum entanglement for FTL communication is cryptography. Imagine Alice and Bob are far away from each other, but both own one of a pair of entangled particles. Alice wants to send a message to Bob, so she changes the state of her particle in some way. This has to be done by letting her particle interact in some way with at least one other quantum.

Alice can't completely influence how those two quantums interacted. But this is a vital information for Bob to decode her message - remember: Bob's particle takes the same state as Alice's twin version of it, but without knowing what interaction caused this state, he can't find out what her "input" was. So Alice has to pass information about how the interaction happened to Bob, but obviously, she has to do this the classical way, because else they'd run into the same problem again.

So what's the matter with quantum entanglement communication? It gives you the perfect encryption method. The quantum which interacted with Alice's particle holds all information about how her information was encrypted - it's the encryption key. Without having this key, there's no way to decrypt the information again.


I apologize for errors and imprecision, quantum mechanics is something that's already hard to put into words when it's fresh in your head, so I hope a physicist can set any eventual errors straight later. But it should give you the principle idea why there's no FTL communication.

Oh, ok. Thank you for the key analogy, I've heard most of this before but didn't appreciate that limitation.
 
Wouldn't this be impossible to determine, by definition?

No. Have experimenters A and B watch over an entangled quantum particle, with its first location at A and its second location at B, which should be reasonably far apart. Then have experimenter A manipulate the particle at a fixed time, and experimenter B document when he observes the activity. If experimenter B observes it at the same time A manipulated it, then that means the change in the particle happened without regard to the distance separating itself.

Of course, that's only theoretical. I don't know how that holds up practically.

Alice can't completely influence how those two quantums interacted. But this is a vital information for Bob to decode her message - remember: Bob's particle takes the same state as Alice's twin version of it, but without knowing what interaction caused this state, he can't find out what her "input" was. So Alice has to pass information about how the interaction happened to Bob, but obviously, she has to do this the classical way, because else they'd run into the same problem again.

I don't see how this prevents some sort of Morse code-like transmission.
 
That would be my initial thought too, but it doesn't work, because entanglement requires superposition. This basically means that the particle in question has indeterminate states: it exists in many (inconsistent) states at once, or perhaps in none of them, depending on your viewpoint. As soon as you look at it, that resolves the indeterminacy, and it no longer has superposition.

But because entanglement requires superposition, this effectively means that as soon as you look at the particle, it is no longer entangled. This is the fundamental reason why you can't use entanglement for faster-than-light transfer of information. Alice and Bob may each have one of a pair of entangled particles, but Bob can't watch his particle to see if its state changes, because if he does so, they will no longer be entangled.
 
No. Have experimenters A and B watch over an entangled quantum particle, with its first location at A and its second location at B, which should be reasonably far apart. Then have experimenter A manipulate the particle at a fixed time, and experimenter B document when he observes the activity. If experimenter B observes it at the same time A manipulated it, then that means the change in the particle happened without regard to the distance separating itself.

Of course, that's only theoretical. I don't know how that holds up practically.

When discussing quantum mechanics, I tend to question the concept (and application) of "fixed time". Certainly I would wonder how you would know, beyond reasonable doubt, that it was instantaneous.

And this not even taking into account Plotinus' most recent explanation.
 
I don't see how this prevents some sort of Morse code-like transmission.
This is what I was trying to cover when I said "Alice doesn't know how she changed her particle's state".

The state of her particle is indeterminate, thus she cannot find out what exactly happened, and she cannot measure it because it destroys the superposition that's necessary for the entanglement in the first place (as Plotinus already said). For reasons I can't really explain, the information about what happened is saved into the other quantum it "reacted" with, therefore this particle can be used to decrypt Bob's twin of the other particle.

When discussing quantum mechanics, I tend to question the concept (and application) of "fixed time". Certainly I would wonder how you would know, beyond reasonable doubt, that it was instantaneous.
As far as I know, quantum mechanics usually assume fixed time. Physics has found no way to reconcile quantum mechanics and general relativity yet (in fact, this is the great question for modern theoretical physicists), so the implications of general relativity like relative time are not taken into account for quantum mechanics.
 
The best way to show, that no faster-than-light communication is possible with entanglement is to consider just one particle of an entangled pair. According to quantum mechanics, the behavior of this single particle is indistinguishable from an unentangeled singe particle in a similar state. The result of a measurement is totally random in both cases. So one cannot even decide whether a given particle is entangled with anything else or not. So if I have one particle of an entangled pair it does not matter what someone does with the other particle, I always get random results.

It is only when each of the particles is measured and these results are compared strange correlations can be noticed that should not be there according to non-quantum physics. But to compare the results there has to be an exchange of classical information which cannot happen faster than light.

So to get any use out of quantum communication there has to be a channel that is limited by the speed of light.

How these correlations actually occur is a question that has not really been solved yet.

It is kind of funny, that the discussion went from a Zeno paradox to quantum mechanics, as the latter sort of revives a Zeno paradox with the quantum Zeno effect.
 
To go back to the OP:
With the caveat that I've been corrupted by reading about Quantum Gravity by Lee Smolin:

I'm under the impression that reality is not actually composed of 'material' that is infinitely divisible. This means that Zeno's paradox is untrue because it's based upon an untrue premise, that we can continually divide the amount of space which each animal is moving. If you chop up space finely enough, the turtle is in 'space A' until it is in 'space B', and if you click forward units of time even more slowly, the turtle is not actually moving.
 
How frequently must it be observed to have measureable and/or statistically significant results?

I would say the observation would have to happen with a higher frequency than the linewidth of the decay. "Watching" that fast is not so easy, though, because you have to (state-selectively) scatter photons somehow. So you need to have another transition, which is faster than the one you want to prohibit.
 
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