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- 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.

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.