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Suppose a pair of entangled particles having opposite up/down spins are produced on Earth.

These two particles are then separated, one remaining on Earth, and the entangled pair being brought by colonists to Alpha Centauri.

When the colonists have successfully settled in Alpha Centauri, they perform an explicit measurement of the spin of their entangled particle, by passing it through an inhomogeneous magnetic field (Stern Gerlach measurement).

This measurement in Alpha Centauri fundamentally changes the yet unmeasured particle pair left on Earth. Its spin has now changed from being indeterminate to being decidedly up or down, even before we measure it.

Could there be a Bell test that can be performed here on Earth, by once more entangling this yet unmeasured particle on earth with another particle, then performing a Bell test to measure their super correlation?

A particle with already pre-determined spin (due to previous measurement of its entangled pair) cannot exhibit telepathic Bell correlation anymore, when given random test environments. Only particle pairs with true un-determined spins can spontaneously collude their spin states to exhibit this super correlation phenomena given random Bell test conditions.

In other words, could there be a Bell test on Earth that tests whether the far away entangled pair in Alpha Centauri had been "opened" or not?

Norbert Schuch
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James
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  • Have you tried constructing an explicit example? – WillO Nov 27 '22 at 15:43
  • @WillO the scenario in the question seems as explicit as I can make it. A explicit Bell test procedure can follow https://www.nature.com/articles/nature15759 . The results should show whether there is super-correlation or not between the secondarily entangled particles. I'd like to understand why this particular experimental setup will or will not work, without appealing immediately to higher categorical reasoning like information travel limit is the speed of light, therefore it is not possible. – James Nov 27 '22 at 15:47

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No -- otherwise, faster-than-light communication would be possible, which is not possible within quantum mechanics.

As an alternative perspective, note that the description the people on earth have of the particle on earth did not change due to the measurement, so any subsequent test to be run on it will return the same outcomes, whether it has been measured or not.

Norbert Schuch
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  • The Earth particle twin would behave differently when subjected to a Bell-type super-correlation test, after the measurement of its Alpha Centauri particle twin has been performed, would it not? – James Nov 27 '22 at 15:27
  • No. ___________ – Norbert Schuch Nov 27 '22 at 15:35
  • Could there be a Bell test that can be performed here on Earth, by once more entangling this yet unmeasured particle on earth with another particle, then performing a Bell test to measure their super correlation? A particle with already pre-determined spin (due to previous measurement of its entangled pair) cannot exhibit telepathic Bell correlation anymore, when given random test environments. Only particle pairs with true un-determined spins can spontaneously collude their spin states to exhibit this super correlation phenomena given random Bell test conditions? – James Nov 27 '22 at 15:38
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    @NorbertSchuch 's second paragraph is all you need. (His first paragraph is also all you need, but his second is better because it works even if you don't know that FTL communication is impossible.) But you'd have discovered this on your own if you'd tried calculating a few examples, which is really the only way to understand this stuff. (Which remains true for many other values of "this stuff", incidentally.) – WillO Nov 27 '22 at 15:48
  • @WillO the spin of the Earth particle twin is no longer indeterminate after its twin particle spin in Alpha Centauri has been measured, would you agree? Its spin is now decidedly up or down, even before we measure it. – James Nov 27 '22 at 15:54
  • @James: No, it is not decidedly up or down. It could be anything at all, depending on what measurement was made. [Incidentally, I have no idea what "indeterminate" means here. The spin state of an unentangled particle is what it is. The spin state of an entangled pair of particles is what it is. There is no such thing as an indeterminate state. Are you using "indeterminate" to mean "unknown to the experimenter"?] – WillO Nov 27 '22 at 16:52
  • @WillO thank you. Let's suppose the particle spin measured in Alpha Centauri is |UP>. Then the spin of the Earth twin particle must therefore be |DOWN>, since the measurement made on one of the twin has collapsed the superposition states of the |UP> and |DOWN> states of the unmeasured Earth twin particle as well, would you agree with this? – James Nov 27 '22 at 16:58
  • @WillO in the Bloch sphere representation, making the {UP> measurement on the Alpha Centauri particle twin immediately causes the 3D vector of the Earth particle spin Bloch sphere representation to instantly orient its direction along the pure |DOWN> axis, giving a 100% probability of measuring this particle's spin as being |DOWN>. Is this statement accurate? – James Nov 27 '22 at 17:09