# Why don't entanglement and relativity of simultaneity contradict each other?

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Hey everyone, first post here :)

A while ago on another forum someone said that entanglement occurs in all reference frames (so is not subject to relativity of simultaneity).

How is this possible?

If two electrons are entangled and change spin (for example) how can these two events occur regardless of reference frame?

Thanks for clearing this out (and sorry that I don't put this in the relativity or quantum physics board but I couldn't choose between the two.

All of the best!

S.

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Entanglement means the nonlocality of quantum mechanics. But this does not contradict the theory of relativity, because this nonlocality cannot be used to transmit information.

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Posted (edited)
51 minutes ago, Freddy_das_boot said:

Hey everyone, first post here

A while ago on another forum someone said that entanglement occurs in all reference frames (so is not subject to relativity of simultaneity).

How is this possible?

If two electrons are entangled and change spin (for example) how can these two events occur regardless of reference frame?

Thanks for clearing this out (and sorry that I don't put this in the relativity or quantum physics board but I couldn't choose between the two.

All of the best!

S.

Modern and theoretical physics is just fine.

Let us take your example of two entangled electrons.

Call them A and B and the spins + and - for identification.

Now we do not need to know how they became entangled, just that they are entangled.

When you say they 'change spin' you need to be clear that they (the electrons) do not change spin by themselves.

Some agent causes a spin change of say electron A which is spin +.

Why do do think whatever event cause the spin change preserves entanglement ?

Can you offer an example of such a change ?

Here is an example of a change that does not.

Two electrons in the same orbital are entangled.

One electron is promoted to a free orbital with a spin change, leaving the other behind.

This change is the basis of what is known in spectroscopy as a triplet state, where the entanglement is broken and the left behind electron does not change spin.

Edited by studiot
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Posted (edited)
57 minutes ago, Freddy_das_boot said:

If two electrons are entangled and change spin (for example) how can these two events occur regardless of reference frame?

An electron doesn't change spin because the other has changed spin. There's no such thing as the electron changing its spin. It's more like the electron potentially being able to produce either + or - as a result of the measurement.

Pick one projection of spin; say z-projection for electron (1). Now measure its value. It can give either +1/2 or -1/2.

If it gives +1/2, and you measure the same projection of spin on the other, you know with absolute certainty it will produce -1/2. And vice versa. But you can't chose electron (1) to have any projection you want. This is key. If you could, you would be able to code a word in binary; say X=00101011010111 and have a person placed where electron (2) is, read the message and write down 11010100101000 (the opposite word). If you could do that, you would be able to send the word X. But you can't. You can only send random words, but those are not messages.

Also, the correlations are initial. When you prepare a singlet state $$\left|+\right\rangle \left|-\right\rangle -\left|-\right\rangle \left|+\right\rangle$$, all the correlations are initial. All the correlations are already there from the beginning. So nothing is sent instantly.

Edited by joigus
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Here we are talking about simultaneity. If we have, say, a pair of photons entangled in polarization, then determining the polarization of one photon will instantly determine the polarization of another photon. In any reference frame, the polarization of both photons will be determined simultaneously.

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26 minutes ago, SergUpstart said:

Here we are talking about simultaneity. If we have, say, a pair of photons entangled in polarization, then determining the polarization of one photon will instantly determine the polarization of another photon. In any reference frame, the polarization of both photons will be determined simultaneously.

But that wasn't the question, which was neither about determination of the particles nor about photons.

Yes simultaneity comes into it, but not in the way you suggest.

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1 hour ago, Freddy_das_boot said:

Hey everyone, first post here

A while ago on another forum someone said that entanglement occurs in all reference frames (so is not subject to relativity of simultaneity).

How is this possible?

If two electrons are entangled and change spin (for example) how can these two events occur regardless of reference frame?

The issue isn’t that they change spins - the spins are undetermined until measured. And in entanglement, once you measure one particle, you know the spin of the other. It’s one event.

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If I put each member of a pair of gloves in boxes, and mail them to opposite sides of the earth, I should not be surprised that by looking inside one box I can determine (in the sense of know) the handedness of the glove in the other.   Nothing is being determined,  in any sense of causal action or superluminal data transfer,  it's just a matter of our knowledge at that moment.   It's more as if the way I open the one box will be a method that gives me handedness,  and sort of brings that property into reality.   Once I know one member of the pair is left-hand then I instantly know the other is right-hand.   If this is wrong or simplistic, someone LMK.

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1 hour ago, swansont said:

The issue isn’t that they change spins - the spins are undetermined until measured. And in entanglement, once you measure one particle, you know the spin of the other. It’s one event.

But if, in an orbital there are two electrons, you know that they have opposite spins, you just don't know which is which until you 'measure'.

Freddy seems to think that if one spin is changed (and this can happen), then the other must also change.

This is not necessarily the case.

One electron only need have its spin changed, but it then has to leave the orbital.
This, of course, results in disentanglement.

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4 hours ago, TheVat said:

If I put each member of a pair of gloves in boxes, and mail them to opposite sides of the earth, I should not be surprised that by looking inside one box I can determine (in the sense of know) the handedness of the glove in the other.   Nothing is being determined,  in any sense of causal action or superluminal data transfer,  it's just a matter of our knowledge at that moment.   It's more as if the way I open the one box will be a method that gives me handedness,  and sort of brings that property into reality.   Once I know one member of the pair is left-hand then I instantly know the other is right-hand.   If this is wrong or simplistic, someone LMK.

In QM, the fact is that the glove itself in the box does not know what it should be, left or right, until one of the boxes is opened.

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12 hours ago, swansont said:

. It’s one event.

You can formulate it this way. But only then it is necessary to add that this event occurs at once in two places separated by a distance.

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On 7/31/2021 at 10:48 PM, joigus said:

There's no such thing as the electron changing its spin.

Just to correct myself. There are cases in which you can say an electron changes its spin, of course. But not for spin-entangled states. For example, you put an ion in an ion trap and subject it to a magnetic field. The ion will flip its spin. The devilish property of a maximally-entangled state is that you cannot say its spin has any particular value whatsoever.

On 7/31/2021 at 11:49 PM, TheVat said:

If I put each member of a pair of gloves in boxes, and mail them to opposite sides of the earth, I should not be surprised that by looking inside one box I can determine (in the sense of know) the handedness of the glove in the other. [...]

Yes, it's very much like that; they're initial correlations. The tricky part is that correlations are quantum. All hell breaks loose when correlations are quantum and you want to think about the gloves as actually possessing all these properties at a given time.

Quantum mechanics embeds a different (non-classical) kind of logic when you express it in terms of properties you can measure. 'Quantum gloves' need to be able to occupy states that are neither right-handed, nor left-handed (superpositions); neither black nor white, etc.

And we need to be able to measure several properties of the gloves. If we want to have properly quantum gloves and display all the 'trickery' of quantum entanglement, we would need:

1) Several measurable properties. Take three observables, say: handedness (H), colour (C), and material (M).

2) Measurements of any one of these properties (observables) completely mess up measurements of the other; and you can't measure (H,C), or (C,M), (H,M), at the same time. (Incompatible observables.)

3) (For simplicity) the observables have a discrete dichotomic spectrum (possible values when measured):

• H {left-handed, right-handed}
• C {black, white}
• M {natural, synthetic}

4) When the gloves are in a definite state of handedness, the H-incompatible properties C and M are maximally scrambled, or 'blurry': Equally likely to be black or white; equally likely to be natural or synthetic. The gloves simply don't have those C, M properties when H is well defined!

If they had, it's not difficult to prove that, for many series of repeated experiments on a given glove:

Probability(left-handed & white)+P(black & synthetic) greater or equal than Probability(left-handed & synthetic)

This is called Bell's inequality, and it's just a consequence of the properties H, C, and M actually having a value. Quantum probabilities violate this inequality for certain choices of observables.

But wait a minute. Didn't we say that properties H (handedness) and C (colour) are incompatible? How can I even make sense of Probability(left-handed & white)? I'm not supposed to be able to measure handedness and colour at the same time! (for the same glove).

Yes, but the whole basis of this combined-probability setup is based on the assumption that when I measure, eg, H for one glove and the result is 'left-handed', I know with certainty that, were an experiment to be performed at the other glove's location, it would produce the result 'right-handed' with total certainty. And sure enough, it does, when I do so. So I'm counting 'left-handed' outputs for the other glove as 'right-handed' outputs for this glove. This is very important to keep in mind.

So the gloves would have to be kinda schizoid.

But the whole thing is local. In order to see that, let's go back to a pair of electrons. We take electrons from separate parts of the world, completely uncorrelated. We bring them together and have them interact. They reach a maximally entangled state called the singlet. This only happens because they've been proximal and interacting (local!!!). Now (and not before) they display perfect anti-correlation. If I perform my experiment on them when they're still next to each other, they display all the craziness that I've just described.

Now the state decays (splits apart). I perform the same sequence of measurements. The perfect anti-correlation is still there. It hasn't changed. So it didn't come from me doing anything on one of the electrons and the other 'sensing' what I did. It came from the initial interaction that produced the anti-correlations.

Murray Gell-Mann was very frustrated that people, decades after Bell, Clauser, Shimony, and all that saga, still called this 'non-locality'.

Just as an indirect evidence of how much confusion this term 'non-local' has caused in physics, here's a quotation:

Quote

By locality I mean something like the Atiyah-Segal axioms for Riemannian cobordisms

(taken from a scientific forum.)

Ooooooo-kay.

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2 hours ago, joigus said:

Just to correct myself. There are cases in which you can say an electron changes its spin, of course. But not for spin-entangled states. For example, you put an ion in an ion trap and subject it to a magnetic field. The ion will flip its spin. The devilish property of a maximally-entangled state is that you cannot say its spin has any particular value whatsoever.

You can change the spin, or with photons change the polarization. With the latter you just send it through a half-wave plate. All this does is change the correlated states. If the initial entanglement was up/down (or H/V for photons) then you've made the correlation to be the same state. If you measure a spin to be up, you know the other is up.

These actions do not inherently break the entanglement

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3 hours ago, swansont said:

You can change the spin, or with photons change the polarization. With the latter you just send it through a half-wave plate. All this does is change the correlated states. If the initial entanglement was up/down (or H/V for photons) then you've made the correlation to be the same state. If you measure a spin to be up, you know the other is up.

These actions do not inherently break the entanglement

Thanks. I hadn't thought about that particular setup. It makes sense. If I understand you correctly, you've kept the correlation, while making it a perfect up-up correlation instead of an up-down correlation. There is no reason for the state to break the entanglement.

The point I was trying to make was a disclaimer. I said something that could have been interpreted as 'flipping spins is never possible':

On 7/31/2021 at 10:48 PM, joigus said:

There's no such thing as the electron changing its spin.

And that's not what I wanted to say. What I wanted to say is that, for an entangled state, measuring one particle's spin does not flip the other particle's spin. But flipping spins is possible in general acting locally on one particle (magnetic fields for charged particles, polarisers for photons, etc.)

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1 hour ago, joigus said:

Thanks. I hadn't thought about that particular setup. It makes sense. If I understand you correctly, you've kept the correlation, while making it a perfect up-up correlation instead of an up-down correlation. There is no reason for the state to break the entanglement.

We read up on entanglement in our journal club probably 5 or 6 years ago, and I recall from one paper where there were different polarization state combinations possible, but one in particular was desired*, and you could do a unitary transformation in the QM analysis to get from one to another. In an experiment this would be a half-wave plate in one of the photon paths. I'm much more attuned to optics/lasers techniques than spin, so that's what stuck.

*this is an educated guess rather than a clear recollection, but having cross-polarizations mean you can combine or split them using a polarizing beamsplitter, which might have been what they were after

Quote

The point I was trying to make was a disclaimer. I said something that could have been interpreted as 'flipping spins is never possible':

And that's not what I wanted to say. What I wanted to say is that, for an entangled state, measuring one particle's spin does not flip the other particle's spin. But flipping spins is possible in general acting locally on one particle (magnetic fields for charged particles, polarisers for photons, etc.)

Right. And it's a common misconception (and repeated in pop-sci articles) that you are wiggling one particle and seeing the other instantly wiggle in response, and that's decidedly NOT happening.

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