# Entangled particles and relativity

## Main Question or Discussion Point

What happens when you take two entangled particles and put one on a spaceship that moves close to the speed of light? Now you measure one of the two particles. The state of the other should become decided at the exact moment you do the measurement. But there is no absolute simultaneity if you are dealing with two different reference frames. So relative to which reference frame is the process instantaneous?
And what happens if you send one of the particles into the future using a spaceship that returns to earth after a while? Does a measurement on one of them still affect the other instantaneously?

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Waiting on an answer for this too.

I don't even know enough to know if it's nonsensical reasoning.

"
Thinking of the instantaneous correlation between "anti-correlated" particles I thought of the distance between them.

Since any moment between the anti-correlated particles is perfectly correlated, I assume the distance (specifically length in this case) between them is perfectly orthogonal to the temporal/time dimension. If that's true the distance between the particles could be called a proper length (plane of simultaneity).

I guess my question is it possible to spoil this correlation between "entangled" particles. If so how?"
<- for example like the OP asks.

Speculation like this kind of misses the point.

Non-locality applies to the time dimension too.

Bill_K
Now you measure one of the two particles. The state of the other should become decided at the exact moment you do the measurement.
The state of the other particle is decided, but there is nothing that says WHEN it is decided. Simultaneity is not involved. Just that, after you have observed both particles, their states will match. In some frames you observed A first. In other frames you observed B first. Doesn't matter.

In the Many Worlds interpretation, the states of the two particles have matched ever since they interacted. There's one world in which A=up, B=down, and another world in which A=down, B=up. All that happens later when you do your measurement is you find out which world you're living in. You don't have to believe the Many Worlds interpretation if you prefer another, but in other interpretations the results are the same - AS IF the MWI was valid.

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The state of the other particle is decided, but there is nothing that says WHEN it is decided. Simultaneity is not involved. Just that, after you have observed both particles, their states will match. In some frames you observed A first. In other frames you observed B first. Doesn't matter.
good post Bill, Isn't the state decided at time of measurement? because:

photon B is unaffected by whatever happens to photon A after measurement/detection.

photon B matches (oppositely) only the state of photon A at the time of measurement (?)

however, not sure what the time lag, if any, would be in "transmission of the spin" across differing frames of references

mfb
Mentor
- It does not matter in which order you measure the photons
- The measurements can be space-like separated (no classical communication possible, no unique time-ordering of the measurements) or time-like separated (one measurement is done before the other)
- The photons do not even have to exist at the same time

Any time-ordering is irrelevant. The result is the same in all experiments: If you look at both results together, you see correlation, if you look at a single detection it appears completely random.

- It does not matter in which order you measure the photons
- The measurements can be space-like separated (no classical communication possible, no unique time-ordering of the measurements) or time-like separated (one measurement is done before the other)
- The photons do not even have to exist at the same time

Any time-ordering is irrelevant. The result is the same in all experiments: If you look at both results together, you see correlation, if you look at a single detection it appears completely random.
agreed mfb, well said

perhaps there are two things/elements to this:

1. the decision about the spin (..which i guess is made at the time of measurement)
because
once photon A (or B) has been measured...the decision is made....

2. "transmission of that decision" to photon B...which I agree...can be delayed (...photons don't have to exist at same time....space/time separation is allowed)

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You don't have to believe the Many Worlds interpretation if you prefer another, but in other interpretations the results are the same - AS IF the MWI was valid.
You don't have to believe in God, but whatever happens, the results are the same AS IF God has decided that it should happen in this way, AS IF the [religion of your choice] would be true.

What happens when you take two entangled particles and put one on a spaceship that moves close to the speed of light? Now you measure one of the two particles. The state of the other should become decided at the exact moment you do the measurement. But there is no absolute simultaneity if you are dealing with two different reference frames. So relative to which reference frame is the process instantaneous?
There are two possibilities to answer such questions:

1.) You give up realism. Once you cannot distinguish by observation, if A or not A is true, it means that nor A nor not A is true. You have to give up the search for truth about reality, at least for causal explanations of the correlations we observe in our life.

2.) You have to accept that some correlations - namely the correlations which violate Bell inequalities - require a causal explanation which violates Einstein causality. Or A -> B, or B-> A, in a situation where as A->B, as B->A violates Einstein causality. It is also a situation where we have no method to distinguish which of the two possible explanations - A -> B, or B-> A - is the correct one. But, once there is no other possibility for explanation (the third classical explanation by a common cause C->A, C->B is excluded because in this case Bell's inequalities cannot be violated), you accept this nonetheless as a proof that or A -> B, or B-> A is true, and, therefore, Einstein causality is false.

In this case, there is an unknown, hidden preferred frame. There is, in fact, a nice candidate for this frame, without any serious competitor - it is the frame of the CMBR radiation. There is no proof for this identity, but this is the simplest hypothesis.

mfb
Mentor
You don't have to believe in God, but whatever happens, the results are the same AS IF God has decided that it should happen in this way, AS IF the [religion of your choice] would be true.
The difference is that MWI needs a single equation (or maybe a set of equations) to describe the dynamics of past, present and future, where religion needs a big list of every single interaction* of god and cannot predict any future interactions (unless the predictions are identical with scientific predictions).

*that is a feature of collapse interpretations, too :D

1.) You give up realism. Once you cannot distinguish by observation, if A or not A is true, it means that nor A nor not A is true.
Or A is true in one branch and notA is not true in another branch.

What happens when you take two entangled particles and put one on a spaceship that moves close to the speed of light? Now you measure one of the two particles. The state of the other should become decided at the exact moment you do the measurement. But there is no absolute simultaneity if you are dealing with two different reference frames. So relative to which reference frame is the process instantaneous?
And what happens if you send one of the particles into the future using a spaceship that returns to earth after a while? Does a measurement on one of them still affect the other instantaneously?
It's not necessarily true that there's no absolute simultanetiy when dealing with two different reference frames, because it's always the case that there's some larger, more encompassing, reference frame including both, or that both can refer to a common reference frame.

There's no demonstrably physical sense in which a measurement on one particle affects another particle simultaneously or instantaneously. These sorts of notions arise from ignorant popularizations of the qm formalism, perhaps related to misunderstandings of what, exactly, 'wavefunction collapse', etc., refers to. The principles and conclusions of SR regarding reference frames moving relative to each other have nothing to do with this.

The states of entangled particles are only related in a logically deducible way when the filters measuring (proper) time correlated particles are aligned. When this is the case, then, upon the registration of a qualitative result at one detector, one can, 'instantaneously', deduce the result at the other detector.

There's no demonstrably physical sense in which a measurement on one particle affects another particle simultaneously or instantaneously. These sorts of notions arise from ignorant popularizations of the qm formalism, perhaps related to misunderstandings of what, exactly, 'wavefunction collapse', etc., refers to. The principles and conclusions of SR regarding reference frames moving relative to each other have nothing to do with this.

The states of entangled particles are only related in a logically deducible way when the filters measuring (proper) time correlated particles are aligned. When this is the case, then, upon the registration of a qualitative result at one detector, one can, 'instantaneously', deduce the result at the other detector.
Sorry, but the violation of Bell's inequality is a demonstrably physical effect. You can ignore it, give up realism, but this is not a good idea. Giving up realism means you can as well ignore a working FTL phone and continue to believe in relativity.

And the theory that the correlations are somehow connected with true time seems unreasonable.

The difference is that MWI needs a single equation (or maybe a set of equations) to describe the dynamics of past, present and future, where religion needs a big list of every single interaction* of god and cannot predict any future interactions (unless the predictions are identical with scientific predictions).
Sorry, but I cannot identify nor the point where MWI needs the Schrödinger equation (anyway, once the wave is nonezero in a given point of configuration space, the configuration exists, and to derive the Born rule in MWI has not been successful(, nor the point where religions need a big list of interactions - a single sentence is sufficient: God moves in mysterious ways.

Or A is true in one branch and notA is not true in another branch.
Yep. It is this failure to predict anything which prevents me from accepting MWI as a realistic interpretation.

mfb
Mentor
I cannot use "God moves in mysterious ways" to predict a measurement result, or to describe the state of the universe in the past.

and to derive the Born rule in MWI has not been successful
I think that approach is good. And even if you don't like an infinite universe: You can do consistent science in MWI where the Born rule appears naturally in the interpretation of physical results. Not as probability (MWI is deterministic), but as method to do science.

Yep. It is this failure to predict anything which prevents me from accepting MWI as a realistic interpretation.
Predicting amplitude ratios (which can be correct in every branch with a large amplitude) is not enough? What else do you want?

I cannot use "God moves in mysterious ways" to predict a measurement result, or to describe the state of the universe in the past.
I also cannot use the wave function for this purpose without the Born rule, but the Born rule requires probabilities, which is something which makes no sense if all imaginable configurations exist.

I think that approach is good. And even if you don't like an infinite universe: You can do consistent science in MWI where the Born rule appears naturally in the interpretation of physical results. Not as probability (MWI is deterministic), but as method to do science.
As well, I can do consistent astrology in MWI - and the universes where astrology gives correct predictions will also have extremely small but nonzero amplitudes, thus, are also part of existing branches. I have been unable to identify a point in that paper where probability is somehow derived, as far as I was able to understand the experimenters already use standard QM by assigning α and β as in QM, instead of using some improbable but nonetheless imaginable version of astrology for this purpose. So, it looks like a variant of circular reasoning to me.

Predicting amplitude ratios (which can be correct in every branch with a large amplitude) is not enough? What else do you want?
What means correct? In MWI everything is possible, and I see no way how amplitudes can obtain some importance. They are simply function values, have therefore no influence on the underlying configurations. If you tell me that there exists a function which has the value of 0.08055820958490 + 48594383i for my actual state, why should I have to care about this? (Even if I actually am a local branch of this function, I would not see a reason to care.)

mfb
Mentor
I also cannot use the wave function for this purpose without the Born rule, but the Born rule requires probabilities, which is something which makes no sense if all imaginable configurations exist.
This looks like circular reasoning to me. You use probabilistic interpretations to justify the existence of probabilities (with the Born rule), and use that existence to say that all interpretations have to be probabilistic.
As well, I can do consistent astrology in MWI - and the universes where astrology gives correct predictions will also have extremely small but nonzero amplitudes, thus, are also part of existing branches.
I don't understand the first "also". Right, they are existing.
Probabilistic interpretations give a tiny probability that astrology becomes an accepted science in the future, just by chance. Is that better than getting astrology in worlds with a tiny norm?
"Consistent" here means that the dominant branches (in terms of the norm) will reject astrology. Which is fine, as astrology is wrong.

I have been unable to identify a point in that paper where probability is somehow derived, as far as I was able to understand the experimenters already use standard QM by assigning α and β as in QM, instead of using some improbable but nonetheless imaginable version of astrology for this purpose. So, it looks like a variant of circular reasoning to me.
The zero norm of worlds with different probability is the important point.

If you tell me that there exists a function which has the value of 0.08055820958490 + 48594383i for my actual state, why should I have to care about this? (Even if I actually am a local branch of this function, I would not see a reason to care.)
If you tell me that I exist with probability 1, why should I care?

If I tell you that the measurement apparatus will show "1" with amplitude 0.8*(our amplitude) and "0" with amplitude 0.6*(our amplitude), you cannot test this with a single experiment - that is the same in all interpretations. But you can decide to run that experiment 1000 times, and call it a success in branches where a fraction of roughly 0.8^2 gives "1" and the others give "0". Most amplitude squared will go into those branches - if my prediction is right, you'll see a success in the dominant part of the norm of our branch. If the apparatus shows much more "0", branches where the experiment fails will have the dominant part of the norm, and you can reject my hypothesis in all of them.

This looks like circular reasoning to me. You use probabilistic interpretations to justify the existence of probabilities (with the Born rule), and use that existence to say that all interpretations have to be probabilistic.
????? If something exists, it makes no sense to tell me it exists with some probability < 1. Or it exists (that means with probability 1), point, or it is not clear if it exists or not.

There may be a lot of different hypotheses about probabilties, the Born rule is one of them. But they all require that it makes sense to talk about probabilities at all. Something has to be uncertain, for some reason, or (in the Bayesian variant) unknown. But in MWI everything is certain - all imaginable configurations exist. (Except possibly for some subset of codimension 2 of the zeros of the wave function.)

I don't understand the first "also". Right, they are existing.
Those with higher probabilities according to the Born rule are existing too. But I don't understand their difference. Above exist all the time. What justifies to assign a higher probability to one of them? Frequencies don't make sense once they all exist all the time. Bayesian expectations too - once they all exist all the time, there is no uncertainty.

Probabilistic interpretations give a tiny probability that astrology becomes an accepted science in the future, just by chance. Is that better than getting astrology in worlds with a tiny norm?
Yes, because it makes sense. Having a tiny norm is meaningless, as meaningless as having a small imaginary part.

"Consistent" here means that the dominant branches (in terms of the norm) will reject astrology. Which is fine, as astrology is wrong.
But how do you conclude that branches with large norms are "dominant"? They exist in the same sense as those with a tiny norm. May be those with tiny norm are dominant?

(They are in a large majority, so, from a democratic point of view they should be dominant, SCNR.)

That the Born rule is itself consistent is without question. The question is what is the connection between MWI and the Born rule. There is none.

The zero norm of worlds with different probability is the important point.
I don't understand why this could be important. For a general wave function, the configurations where the amplitude is really zero have measure zero in the configuration space, because it is a subset of codimension 2. So everything exists, every configuration is part of some branch with nonzero norm (independent of the definition of the branches).

Ok, you can consider some limits, as that of an infinitely large universe. In this case, no wonder that one can find some sequences with a zero norm in the limit. But what does this tell us? Nothing. We have, last but not least, a single real wave function, and not sequences with limits.

If you tell me that I exist with probability 1, why should I care?
Who has told you that you should? The probabilistic interpretation tells you something about the future you don't know yet. MWI doesn't.

If I tell you that the measurement apparatus will show "1" with amplitude 0.8*(our amplitude) and "0" with amplitude 0.6*(our amplitude), you cannot test this with a single experiment - that is the same in all interpretations. But you can decide to run that experiment 1000 times, and call it a success in branches where a fraction of roughly 0.8^2 gives "1" and the others give "0".
Yes, in interpretations with probability interpretation. But there is none in MWI which makes sense.

There exists, of course, a branch where all these experiments have been done and give 1 roughly 0.8^2 times the number of the experiments. There exist other branches where this happens only 0.1^2 times. The last has a tiny norm, but so what?

Most amplitude squared will go into those branches - if my prediction is right, you'll see a success in the dominant part of the norm of our branch.
Sorry, but "most" and "go" do not make sense, once all configurations exist all the time. The wave function changes, but who cares? The undefined subdivision of the whole wave function into branches may change, but who cares?

If the apparatus shows much more "0", branches where the experiment fails will have the dominant part of the norm, and you can reject my hypothesis in all of them.
This hypothesis makes sense in a universe where we have probabilities. In MWI we do not have such things, every imaginable world exists.

mfb
Mentor
????? If something exists, it makes no sense to tell me it exists with some probability < 1. Or it exists (that means with probability 1), point, or it is not clear if it exists or not.

There may be a lot of different hypotheses about probabilties, the Born rule is one of them. But they all require that it makes sense to talk about probabilities at all. Something has to be uncertain, for some reason, or (in the Bayesian variant) unknown. But in MWI everything is certain - all imaginable configurations exist. (Except possibly for some subset of codimension 2 of the zeros of the wave function.)
Right. Therefore, if you require that an interpretation reproduces the Born rule, you require that the interpretation is probabilistic.

Those with higher probabilities according to the Born rule are existing too. But I don't understand their difference. Above exist all the time. What justifies to assign a higher probability to one of them? Frequencies don't make sense once they all exist all the time. Bayesian expectations too - once they all exist all the time, there is no uncertainty.
There are no probabilities.

Yes, because it makes sense. Having a tiny norm is meaningless, as meaningless as having a small imaginary part.
I don't see the fundamental difference between small probability and small norm. They are different, of course, but where is the problem?

But how do you conclude that branches with large norms are "dominant"? They exist in the same sense as those with a tiny norm. May be those with tiny norm are dominant?
No, I define "dominant" based on the norm.

That the Born rule is itself consistent is without question. The question is what is the connection between MWI and the Born rule. There is none.
Squared amplitudes are relevant both in MWI and in probabilistic interpretations. That is the connection.

Ok, you can consider some limits, as that of an infinitely large universe. In this case, no wonder that one can find some sequences with a zero norm in the limit. But what does this tell us? Nothing. We have, last but not least, a single real wave function, and not sequences with limits.
Well, you have the same state (same observable universe) in different locations, and they are indistinguishable. Instead of "this is there", you can talk about the whole distribution at once, where that limit is exact. The norm of all deviations from that is exactly 0, which corresponds to 0 probability (not "impossible"!) in probabilistic interpretations.

Who has told you that you should?
I don't know, you started that.
The probabilistic interpretation tells you something about the future you don't know yet. MWI doesn't.
The probabilistic interpretations just tell me what could happen. MWI can tell you what will happen.

If I tell you that the measurement apparatus will show "1" with amplitude 0.8*(our amplitude) and "0" with amplitude 0.6*(our amplitude), you cannot test this with a single experiment - that is the same in all interpretations. But you can decide to run that experiment 1000 times, and call it a success in branches where a fraction of roughly 0.8^2 gives "1" and the others give "0".
Yes, in interpretations with probability interpretation. But there is none in MWI which makes sense.
None of what?

There exists, of course, a branch where all these experiments have been done and give 1 roughly 0.8^2 times the number of the experiments. There exist other branches where this happens only 0.1^2 times. The last has a tiny norm, but so what?
Exactly, so what? I can determine the laws of physics in branches with a summed norm (1-epsilon) where epsilon can be made arbitrary small (0 in the limit of an infinite series of measurements). That is fine.

Sorry, but "most" and "go" do not make sense, once all configurations exist all the time. The wave function changes, but who cares? The undefined subdivision of the whole wave function into branches may change, but who cares?
"go" as time-evolution of the branch we are in currently - the norm is conserved by unitary evolution, so all future branches together will have the same sum of their norms. If you split 1 apple and give 0.6 to A and 0.4 to B, 0.6 apples "go to" A.

If the apparatus shows much more "0", branches where the experiment fails will have the dominant part of the norm, and you can reject my hypothesis in all of them.
This hypothesis makes sense in a universe where we have probabilities. In MWI we do not have such things, every imaginable world exists.
The second phrase is right, but the first does not follow.
"more" as in "with a larger amplitude".

Hmm, I think we are a bit off-topic.