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Given two entangled particles A and B barely separated by a very tiny small distance such as the communication delay between both observers Alice and Bob willing to measure the state of A and B respectively is almost null, assuming the classical communication channel between Alice and Bob is reliable and the synchronization between Alice and Bob is perfect (using an atomic clock for instance), that is if Alice measures particle A, Bob will do the same for B INSTANTLY, I really wonder what would be the outcome of this experience ?

user-x220
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    Leaving aside that perfect synchronisation is not experimentally possible and that according to relativity simultaneity is reference frame dependant and so cannot have any effect on the outcome of events, the reason EPR originally raised questions was because quantum entanglement simply does not care about the ordering of the measurements, including measurements that had a space like separation. Why do you think your set up is any different? – By Symmetry May 11 '18 at 11:19
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    Given an EPR pair, measuring one particle's state will determine the state of the other. If you say that entanglement does not care about the order of the measurements, that is before the measurement both particles are in superposition state, however at any given moment in time, the state of the first particle is different from the state of the second's (either before, during or even after the measurement). – user-x220 May 11 '18 at 11:30
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    Otherwise, it could happen that both particles might have the same state just before we proceed to measure them and if we have a perfect synchronized and reliable communication channel, we would notice that both particles have the same state. I hope I have cleared enough the confusion that I am having on this particular point. – user-x220 May 11 '18 at 11:30
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    As @BySymmetry pointed out, your setup is just EPR itself. There is nothing special here. Having a distance between A and B, whatever small it is, implies that notions such as before, during, or after measurement are ill-defined because there is no absolute order and no well-defined simultaneity for spacelike separated events in spacetime. – Stéphane Rollandin May 11 '18 at 12:07
  • Just for a moment, if you imagine that the entangled particles are determinated in their states from the beginning of their entanglement, would it change something in the outcome of the experiment? Since for example in the pair production of two photons the result of the experiments show a statistical dependence, that the orientation of the electric field component is orthogonal to each over, why not suppose that their state is determinated in the phase of the creation of the photon pair? – HolgerFiedler May 13 '18 at 08:02
  • @HolgerFiedler this can't be the case because if say both decided which state to pick beforehand such as both particles are in perfect synchrony (when one is up the other is down). However what if we change our mind and decide to measure the horizontal state instead of the vertical state. How would the second particle guess that we picked this measurement (horizontal) and not the first one (vertical). How could the second particle adjust its polarization suddenly so that we won't be able to trick it into spinning either up or down while it has to spin left or right? – user-x220 May 14 '18 at 19:55
  • There are no such hidden variables (See Bell's Inequality). – user-x220 May 14 '18 at 20:02
  • user-x220 with your thought about the direction of polarization you touched the main point. Producing a pair of photons we are not able to control the direction of the polarization, we only able to design the process so that the polarizations of two particles are orthogonal on each over, the orientation by itself is randomly distributed around 360°. Now using a polarizer to find the orientation of the particles we do not get a signal in 50% of our measurements (with the best designed polarizer (for the right wavelength)). – HolgerFiedler May 15 '18 at 04:07
  • Let the polarizer is orientated to the vertical (0°). Getting a signal (the photon goes through the device), we will know that the photon has had an orientation from -45° to 45° and from 135° to 225°. Not getting a signal we are allowed to say, that the photon has an orientation in the opposite to the above mentioned angles. To count this not measured photon we are able only after getting the information from the second measurement device, that a photon in their setup was measured. In reality simply the number of measured incidents is compared. – HolgerFiedler May 15 '18 at 04:15
  • The question that is fundamental stays the same: “Just for a moment, if you imagine that the entangled particles are determinated in their states from the beginning of their entanglement, would it change something in the outcome of the experiment? ”. Compare it with my explanation of the measuring process above and the explanations you get usual. – HolgerFiedler May 15 '18 at 04:17

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