# I Entanglement + relativity

#### snuz2001

Summary
An apparent contradiction when combining entanglement with relativity.
1. An elementary particle like a photon or electron can be measured in 2 possible states - spin up or down in electron, vertical or horizontal in photons. We'll call those states state 1 or 2, and the measuring device state A or B.

If for example, we measure a photon with a polarizer in State A, we may get a measuring state of either 1 or 2.

2. if a particle is fully entangled to another particle, then the results of the measurements will be correlated: if particle A will be measured in state A and the result is 1, then if particle B will be measured in state A the result will always be 1, an if particle B will be measured at state B, the result will always be 2. (we'll neglect the situations when the results are opposite).

3. The distinction between which of the particles is the first one to be measured is made by synchronized clocks next to the particles. If for example particle A was measured at time 2 and particle B at 5, then Particle A is the first and B is the second.

4. Thus in the previous example, At time 1 we have no knowledge at what state we'll find the particles, at time 3 we know the state of particle A, (1 or 2) and if we know the measuring states of both measuring devices in both sides, at time 4 we know already the state 1 or 2 of the measuring of particle B, and the measuring of particle B itself will always confirm our knowledge.

5. We can say then that the measuring of the first particle was not affected by the measurement of the second and the result could be either 1 or 2, and that the second particle was affected by the measuring of the first. Once measured, the measuring result is final, can be recorded and transmitted.

6. Suppose a space ship carries a particle that is entangled to a particle on earth.

7. At time 0 in both the earth and the ship the ship passes earth in a relativistic speed so that factor Gama equals 10.

8. The ship measures its particle at time 2 hours ship time in measuring state A, and earth measures it's particle at time 3 hours earth time in state A. once a measurement was done, its transmitted by radio.

9. since the systems, Ship and earth, are symmetrical - each passes each other at the same speed - we can conclude that the measurement at 2 in the ship was the first and thus was not affected by the measurement on Earth at 3.

10. from (2) we can say that the measuring results in both earth and ship be either 1 or 2 in both.

11. at time 1 hour in the ship, it passes a planet which its clock is synchronized with earth's clock. the time in the planet - 10 hours. (relativistic time dilation).

12. Acording to the Planet, the measurement on earth occurred 7 hours earlier at 3 and was transmitted already, and the measurement result - 1 or 2 - will reach the planet in 3 hours.

13. In the ship they decide to change the measuring state to B.

14. Because the measuring in the ship is the first (9) it is not affected from the measuring on earth (5) and the result could be either 1 or 2.

15. Thus we got the situation that the measuring states is B in the ship and A on earth, and the results are either 1 or 2, in contradiction to (2):

"2. if a particle is fully entangled to another particle, then the results of the measurements will be correlated: if particle A will be measured in state A and the result is 1, then if particle B will be measured in state A the result will always be 1, an if particle B will be measured at state B, the result will always be 2".

16. We also got the situation that the measurement on earth at 3 was affected by a measurement that is done 7 hours in the future..

I.S.

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#### Demystifier

2018 Award
Is that a question or a statement?

#### msumm21

Summary: An apparent contradiction when combining entanglement with relativity.

2. if a particle is fully entangled to another particle, then the results of the measurements will be correlated: if particle A will be measured in state A and the result is 1, then if particle B will be measured in state A the result will always be 1, an if particle B will be measured at state B, the result will always be 2. (we'll neglect the situations when the results are opposite).
I haven't read further, but if you are saying here that both particles will have a 1 measurement result if "A" is measured, but that both particles will have a 2 measurement result if instead "B" is measured on the 2nd particle, then this is not a valid quantum state and indeed would violate relativity. (By changing the measurement choice A or B on the second particle you could send a FTL message to someone holding the first particle.) Quantum entangled states don't have this property.

#### PeterDonis

Mentor
since the systems, Ship and earth, are symmetrical - each passes each other at the same speed - we can conclude that the measurement at 2 in the ship was the first
No, you can't, because the measurement events as you've defined them are spacelike separated, so they do not have an invariant time ordering. You show this yourself later on when you figure out that in the Earth frame the measurement at 3 on Earth is first.

Thus we got the situation that the measuring states is B in the ship and A on earth, and the results are either 1 or 2, in contradiction to (2)
No, you don't get a contradiction, because you are not using the actual quantum predictions for this experiment, but instead your own incorrect mental model of what you think is going on.

Because the measurements are spacelike separated, they have no invariant ordering, as above. That means it is not correct to think of either measurement as "affecting" the other. The only thing you can say is that the measurements will be correlated according to the entangled state. So the correct quantum prediction is that, if the Earth measurement is the A measurement and the ship's measurement is the B measurement, then the results will be opposite. You cannot say that either result "affects" the other because you cannot say which one occurs first. But the correlation between them does not depend on which one is first. It only depends on the entangled state that was prepared.

#### DrChinese

Gold Member
As stated already: the ordering makes no identifiable difference to the observed outcomes in any scenario. When you later compare the results of the separated measurements, you will see a pattern that follows the quantum mechanical prediction.

#### snuz2001

1. "Is that a question or a statement?" both, can you find anything wrong in what I'm saying, I'll really want to know.

2. "I haven't read further, but if you are saying here that both particles will have a 1 measurement result if "A" is measured, but that both particles will have a 2 measurement result if instead "B" is measured on the 2nd particle, then this is not a valid quantum state and indeed would violate relativity. (By changing the measurement choice A or B on the second particle you could send a FTL message to someone holding the first particle.) Quantum entangled states don't have this property."

no, this is not what I'm saying.

3. "No, you can't, because the measurement events as you've defined them are spacelike separated, so they do not have an invariant time ordering. You show this yourself later on when you figure out that in the Earth frame the measurement at 3 on Earth is first."

How about if the ship moves at a slow speed relative to earth, say 10 km/h. then everything is as before, even if the measurements take place when the distance between the 2 bodies is 20 and 30 kilometers, no?

So at what speed between 10 km/h and c they do not have an invariant time ordering?

4. "You cannot say that either result "affects" the other because you cannot say which one occurs first. But the correlation between them does not depend on which one is first. It only depends on the entangled state that was prepared".

Let's say that the measurements happened at a 1 km distance (a very modest distance for a typical Bell experiment).

Don't we get a clear distinction here between the "first" who measured at time 2 hours and the second who measured at time 3 hours?

and if you do not agree - about a distance of 1 meter?

So at what distance between 1 meter and million light years we lose the notion of firs and second and "It only depends on the entangled state that was prepared"?

5. "As stated already: the ordering makes no identifiable difference to the observed outcomes in any scenario. When you later compare the results of the separated measurements, you will see a pattern that follows the quantum mechanical prediction".

well, if the ordering makes no difference, then why can't one in any way tell in advance the measurement result - 1 or 2 - of the first particle before the measurement, and can tell the result of the second particle if he knows the result of the measurement of the first particle, and the measuring devices state - A or B?

#### PeterDonis

Mentor
Let's say that the measurements happened at a 1 km distance (a very modest distance for a typical Bell experiment).

Don't we get a clear distinction here between the "first" who measured at time 2 hours and the second who measured at time 3 hours?
Yes, but in that case your reasoning breaks down because your reasoning was assuming that in the ship frame the ship measurement occurs first. If the measurements are only 1 km apart and happen at 2 hours and 3 hours in the Earth frame, then their ordering is the same in the ship frame--the Earth measurement occurs first in both frames. (The times in the ship frame will be very slightly different because the ship will be moving very slowly relative to Earth in order to cover 1 km in the Earth frame in 1 hour.)

if the ordering makes no difference, then why can't one in any way tell in advance the measurement result - 1 or 2 - of the first particle before the measurement, and can tell the result of the second particle if he knows the result of the measurement of the first particle, and the measuring devices state - A or B?
The ordering makes no difference to the correlation between the results or to the probabilities for results of each measurement. That doesn't mean the people making the measurements can't know the correlations.

If the measurements are spacelike separated, the person on the ship cannot know the result of the Earth measurement before he makes his own. He can only learn about the result of the Earth measurement from information traveling from that measurement on Earth to him, and that information can't travel faster than light (a radio message or something like that). Similarly, in this case the measurement on the ship occurs first in the ship frame, but the person on Earth cannot know the result of the ship measurement before he makes his own, since he can only find out about it from information traveling from the ship measurement at the speed of light.

So when you say "tell in advance", you are not talking about anyone being able to tell in advance the result of their own measurement before they make it. You are talking about each person being able to tell the result of the other measurement after he makes his own. But that's just because he knows the two measurement results are correlated.

In the case where the measurements are not spacelike separated (as in the case where they are 1 km apart and occur 1 hour apart in the Earth frame), the person making the second measurement can know the result of the first before he makes his own, and therefore knows in advance what result he will get; but there's also no need for any influence to travel faster than light between the measurements to enforce the correlations.

#### DrChinese

Gold Member
So at what distance between 1 meter and million light years we lose the notion of first and second and "It only depends on the entangled state that was prepared"?
Imagine these 3 entangled scenarios:

1. Alice measures before Bob.
2. Bob measures before Alice.
3. We cannot determine who measures first because it varies by reference frame.

The predictions of QM are the same for all 3 scenarios. Information gained from any measurement is essentially redundant vis a vis the other measurement. There is no specific distinction that identifies the first measurement or the second measurement.

#### snuz2001

I would like to quote the last response since I believe it goes down to the bottom of my argument.

1. Alice measures before Bob.
2. Bob measures before Alice.
3. We cannot determine who measures first because it varies by reference frame.

The predictions of QM are the same for all 3 scenarios. Information gained from any measurement is essentially redundant vis a vis the other measurement. There is no specific distinction that identifies the first measurement or the second.

Let’s look at 1:

If Alice measures before Bob - Is there any way Bob’s measurement could affect Alice’s measurement?

I believe the answer must be negative. The result of Alice’s measurement was recorded and transmitted before Bob’s measurement.

Was Bob’s measurement affected by Alice’s measurement? I believe the answer must be positive. Bob knows in advance what will be the result of his measurement just by listening to the radio and learning of Alice’s measurement’s result and her measuring device state, A or B (polarizer in case we are dealing with photons).

Note also that Bob can choose the result of his measurement in advance by selecting the state of his device. In case of photons, he can choose to measure the photon in a horizontal or vertical polarizer to achieve the desired result.

So far agreed?

#### PeroK

Homework Helper
Gold Member
2018 Award
I would like to quote the last response since I believe it goes down to the bottom of my argument.

1. Alice measures before Bob.
2. Bob measures before Alice.
3. We cannot determine who measures first because it varies by reference frame.

The predictions of QM are the same for all 3 scenarios. Information gained from any measurement is essentially redundant vis a vis the other measurement. There is no specific distinction that identifies the first measurement or the second.

Let’s look at 1:

If Alice measures before Bob - Is there any way Bob’s measurement could affect Alice’s measurement?

I believe the answer must be negative. The result of Alice’s measurement was recorded and transmitted before Bob’s measurement.

Was Bob’s measurement affected by Alice’s measurement? I believe the answer must be positive. Bob knows in advance what will be the result of his measurement just by listening to the radio and learning of Alice’s measurement’s result and her measuring device state, A or B (polarizer in case we are dealing with photons).

Note also that Bob can choose the result of his measurement in advance by selecting the state of his device. In case of photons, he can choose to measure the photon in a horizontal or vertical polarizer to achieve the desired result.

So far agreed?
No. Bob cannot achieve a desired result. He may know in advance what a measurement will return, but only because the system has already been measured.

In principle this is not much different from a classical conservation scenario. An object explodes into two parts. By measuring the momentum of one part, you automatically know the momentum of the other part (equal and opposite, by conservation of momentum). But, there is no communication between the parts after separation.

The difference in QM is not entanglement, per se, but that the particles, entangled or otherwise, do not have well defined dynamic properties before measurement.

You need to digest that before considering the implications of entanglement.

#### snuz2001

Not sure what is it that you saying. Was Alice’s measurement affected by Bob’s measurement if she measured an hour earlier? Her measurement was recorded and transmitted, so how could Bob’s measurement affect her’s?

And do you say that Bob’s measurement was not affected by Alice’s?

#### PeroK

Homework Helper
Gold Member
2018 Award
Not sure what is it that you saying. Was Alice’s measurement affected by Bob’s measurement if she measured an hour earlier? Her measurement was recorded and transmitted, so how could Bob’s measurement affect her’s?

And do you say that Bob’s measurement was not affected by Alice’s?
They were two measurements on the same system of two particles.

You cannot view them as separate measurements on separate particles.

I would say neither affected the other; in the same sense as the classical example I gave.

PS looking for a classical cause/effect relationship is hopeless in QM. That's the wrong way to look at the problem.

#### snuz2001

I am not looking for anything, just ask simple questions:

1. Was Alice’s measurement affected by Bob’s measurement an hour later?

2. Was Bob’s Measurement affected by Alice’s measurement an hour earlier?

#### PeroK

Homework Helper
Gold Member
2018 Award
I am not looking for anything, just ask simple questions:

1. Was Alice’s measurement affected by Bob’s measurement an hour later?

2. Was Bob’s Measurement affected by Alice’s measurement an hour earlier?

If a pair of shoes is separated and sent in opposite directions: one to Alice and one to Bob.

Alice measures her shoe and gets left or right. Bob measures his shoe and gets left or right. In all cases the two measurements are opposite.

1) does Alice's measurement affect Bob's.

2) Does Bob's measuremention affect Alice's?

3) Does it matter in what order the measurements take place?

#### snuz2001

1. No.

2. No.

3. No.

Questions:

How is this applied to our discussion?

Could Alice in your example get a different shoe or only left (the shoe that was sent to her).

Could Bob?

Since as you mentioned earlier, in the quantum case the particles have no defined state until they’ve been measured.

Could Alice’s or Bob’s measurements affect each other in the shoes example?

#### PeroK

Homework Helper
Gold Member
2018 Award
1. No.

2. No.

3. No.

Questions:

How is this applied to our discussion?

Could Alice in your example get a different shoe or only left (the shoe that was sent to her).

Could Bob?

Since as you mentioned earlier, in the quantum case the particles have no defined state until they’ve been measured.

Could Alice’s or Bob’s measurements affect each other in the shoes example?
That example is classical entanglement, where the shoes are determined at separation. Quantum entanglementions is subtler, as both possibilities exist after physical separation. But, to try to fit nature's decision making into a cause and effect model involving two separate particles cannot be the answer. In fact,like much of QM, there is no theoretical mechanism to describe how nature does what she does.

Hence the "shut up and calculate" mantra.

#### snuz2001

Classical entanglement is fundamentally different from quantum, no?

1. Was Alice’s measurement affected by Bob’s measurement an hour later?

2. Was Bob’s Measurement affected by Alice’s measurement an hour earlier?

Homework Helper
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2018 Award
Yes.

1) No.

2) No.

#### PeterDonis

Mentor
at what distance between 1 meter and million light years we lose the notion of firs and second and "It only depends on the entangled state that was prepared"?
Never. It always depends only on the entangled state that is prepared. The only reason people focus on the spacelike separated case is that that's the one that show that it's impossible for the correlations to be enforced by some ordinary process that people find intuitively plausible.

#### snuz2001

I believe that Bob’s measurement’s result was affected by Alice’s - otherwise how could he predict his measurement result in advance? Why wouldn’t it be random and can have 2 outcomes like Alice?

Never mind. So we both agree that Alice’s result are not affected by Bob’s measurement an hour later?

#### snuz2001

PeterDonis, do you agree with me that it does not matter how fast the ship travels and how far it is, if it measured an hour earlier than earth it’s measurement would not be affected by the measurement on earth?

#### N88

The difference in QM is not entanglement, per se, but that the particles, entangled or otherwise, do not have well defined dynamic properties before measurement.
I'd like to clarify this wording, please. I suspect I'm hung up on the word "well-defined."

The particles, even if entangled "do not have well-defined dynamic properties before measurement."

It seems to me that particles entangled in pairs, taken separately, have deterministic properties that will yield results [results USUALLY not known to us before we test them] with certainty.

HOWEVER, if we know Alice's result for a test in the direction a [a unit-vector] on particle p1, and Bob is about to test the corresponding particle p1' in the same direction a: then we can predict Bob's result, say +1, with certainty.

So it seems to me: we can define this particular property of p1' for Bob: p1' has the definite well-defined property that it will deliver the result +1 if you test it in the same direction as Alice tested p1.

Further, IF Alice had tested in direction b THEN we could have given Bob a similar definite property.

So should we more accurately say something like this?

"Entangled particles have definite* deterministic properties that dynamically determine their response to every test --- like the classical dynamics of spin-torque-precession --- but, in general, such properties are hidden* (and thus not well-defined) because we can reveal just one of these dynamic properties via an appropriate test."

* Definite, hidden until a test reveals one of them --- well-defined --- but we can't define the rest of them.

Then, regarding the OP: relativity precludes these independent spacelike-separated results being causally-dependent; for they are not linked by spooky-actions at a distance; etc.

So Einstein was right ontologically, and Bohr was right epistemologically!

Thanks

#### snuz2001

1. Was Alice’s measurement affected by Bob’s measurement an hour later?

2. Was Bob’s Measurement affected by Alice’s measurement an hour earlier?

#### DrChinese

Gold Member
I'd like to clarify this wording, please. I suspect I'm hung up on the word "well-defined."

The particles, even if entangled "do not have well-defined dynamic properties before measurement."

It seems to me that particles entangled in pairs, taken separately, have deterministic properties that will yield results [results USUALLY not known to us before we test them] with certainty.

HOWEVER, if we know Alice's result for a test in the direction a [a unit-vector] on particle p1, and Bob is about to test the corresponding particle p1' in the same direction a: then we can predict Bob's result, say +1, with certainty.

So it seems to me: we can define this particular property of p1' for Bob: p1' has the definite well-defined property that it will deliver the result +1 if you test it in the same direction as Alice tested p1.

Further, IF Alice had tested in direction b THEN we could have given Bob a similar definite property.

So should we more accurately say something like this?

"Entangled particles have definite* deterministic properties that dynamically determine their response to every test --- like the classical dynamics of spin-torque-precession --- but, in general, such properties are hidden* (and thus not well-defined) because we can reveal just one of these dynamic properties via an appropriate test."

* Definite, hidden until a test reveals one of them --- well-defined --- but we can't define the rest of them.
Your argument is the same as the original EPR paradox (1935). Bell's Theorem (1964) shows us that does not work. The argument seems fine as long as Alice and Bob measure in the same direction. But it falls apart at most other angle settings (for example 60 degrees). Unfortunately, it takes a bit of math and analysis to understand why.

If you are not familiar with Bell (and I am pretty sure you know it): read up a bit... my own website is not a bad place to start: Bell's Theorem: An Overview with Lotsa Links

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