# An apparent contradiction combining entanglement and relativity [closed]

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. According 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.

## closed as unclear what you're asking by AccidentalFourierTransform, WillO, G. Smith, Jon Custer, ZeroTheHeroSep 11 at 21:25

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• Hi, welcome to SE Physics. Your question is very unclear in the post; I'd recommend that you cut off the unnecessary parts and separate sentences into separate paragraphs to make it easier to read and understand. – F16Falcon Sep 10 at 1:33
• Possible duplicate of Does entanglement not immediately contradict the theory of special relativity? – AccidentalFourierTransform Sep 10 at 2:00
• If you want to have any hope that people will read and understand this question, you need to start by specifying exactly the entangled state you have in mind, rather than listing a bunch of correlations and expecting the reader to work out whether there is in fact any entangled state that produces those particular correlations. You might also want to consider not naming your observables A and B after you've already named your particles A and B. – WillO Sep 10 at 3:43
• Thanks for the comments. This exact post was posted in Physics Forum 2 weeks ago with many responses see: physicsforums.com/threads/entanglement-relativity.976564 I will be happy to clarify any unclear issue. i.s. – Ronit Ve Israel Shapira Sep 10 at 4:38
• "the measuring device state" is the actual physical position of the measuring device. For example if we measure a photon, we will use a polarizer which in our example will have a vertical or horizontal state. see 1 "If for example, we measure a photon with a polarizer in State A, we may get a measuring state of either 1 or 2". – Ronit Ve Israel Shapira Sep 10 at 7:08

There are a lot of misconceptions about quantum mechanics to unpack in this question. Here are as many as I have time to address:

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.

You're missing part of the statement - for a particular choice of measurement basis, measurements of spin on a spin-1/2 particle can have 2 possible values. This has nothing to do with them being elementary particles, by the way - silver atoms (as used in the Stern-Gerlach experiment) are also spin-1/2 and also have two values for spin. In general, a spin-$$s$$ particle will have $$2s+1$$ possible post-measurement states. (So the photon, being a spin-1 particle, should have 3, but since it's massless the longitudinal polarization state is forbidden, leaving only the two transverse polarization states.)

So if you were to measure the spin of an electron, you could measure it as up or down along the $$x$$-axis, up or down along the $$y$$-axis, or up or down along any other axis. The probability of measuring up or down is determined by the wavefunction of the electron prior to measurement. Likewise, you could measure the photon polarization in many different bases, including:

• Horizontal/vertical,
• Diagonal/opposite diagonal,
• Left circular/right circular,

and so on. Each choice of basis has a different set of measurement probabilities for each basis state.

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.

The measuring device state isn't particularly relevant here, so it will be ignored. What is relevant is the choice of basis for each measurement.

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).

That's not really how correlation works. To see why, here's an example: two electrons are entangled such that, when one is measured along the $$x$$-axis to be spin-up, the other, if measured along the $$x$$-axis, will also be spin-up. Likewise, if one is measured along the $$x$$-axis to be spin-down, then the other, if measured along the $$x$$-axis, will also be spin-down. That part you got right. The issue is in what happens when you choose a different measurement basis: if one electron is measured along the $$x$$-axis and is spin-up, and the other is measured along the $$\mathbf{y}$$-axis, then that particle will have a 50% chance of being measured as spin-up and a 50% chance of being measured as spin-down (which is normal for a particle that is known to be spin-up along the $$x$$-axis).

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.

There are three cases here: either the measurements are spacelike separated (distance > light travel time), timelike separated (distance < light travel time), or lightlike separated (distance = light travel time).

If the measurements are spacelike separated, then which measurement is the "first" is entirely dependent on reference frame. There is no objective way of determining which one was "first" without leaving the inertial reference frames you've set up. (The important question is: from which reference frame are you looking at the clocks?)

If the measurements are timelike or lightlike separated, then one of the measurements is unambiguously "first", in every reference frame. There exists no reference frame that will see the other measurement first.

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.

Sure, but this is just a restatement of the no-communication theorem - the fact that you can't use entanglement to transfer information faster than light.

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.

No, you definitely can't say this. Neither particle is affected by the measurement of the other. If you were to make this assumption, you would arrive at a contradiction with special relativity, but the assumption you make here is false. For proof of this, see the delayed choice quantum eraser experiments.

Since your example is based on this false assumption, the same response applies to it.

• "Since your example is based on this false assumption". "delayed choice quantum eraser experiments" does not "prove" that "Neither particle is affected by the measurement of the other" - special relativity is already built in to this experiment and all others like experiments of past changing. Since this post is named "An apparent contradiction combining entanglement and relativity" I would not consider this as a "proof". How could a measurement of particle B at time 3 affect the state of particle A that was measured at time 1 and was already recorded (in the same room) and transmitted? – Ronit Ve Israel Shapira Sep 12 at 9:42
• "Sure, but this is just a restatement of the - the fact that you can't use entanglement to transfer information faster than light". How does "no-communication theorem" fits here? we do not deal with information transferring faster than light, and "no-communication theorem" forbids such a transfer in any speed. The bottom line is this: Do you see any way that particle A measurement at time 1 hour was affected in any way by the measurement of particle B at time 3 hour even though the state of particle A (1 or 2) was already recorded 2 hours earlier and the process takes place in a room? – Ronit Ve Israel Shapira Sep 12 at 9:57
• “Neither particle is affected by the measurement of the other” see Nick Herbert quantumtantra.com/bell2.html “ In this situation, a non-local reality means that what happens at Miss A's SPOT detector--whether this particular photon registers as "1" or "0"--cannot depend on causes in Anaheim alone but must somehow depend also on the setting of Mr B's distant detector in Baltimore”. So how can you talk about a particle that is not affected by the measurement of the of the other? – Ronit Ve Israel Shapira yesterday