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Alice entangles a pair of particles and sends one of the pair - particle B - towards Bob, keeping the other one - particle A - trapped within some sort of containment device. Alice is on Earth and Bob is several light minutes away, say on Mars. Alice and Bob each have two apparatus for measuring spin, one (device X) measures in direction [itex]\vec{x}[/itex] and the other - device Y - measures spin in direction [itex]\vec{y}[/itex] which is perpendicular to [itex]\vec{x}[/itex]. These directions are specified relative to the CMBR reference frame, so that Alice's and Bob's X measuring apparatuses always remain aligned with one another, as do their Y apparatuses.
When the other particle reaches Bob he traps it within a containment device.
Say Alice and Bob have worked out at what time (T) particle B will arrive at Bob and have arranged to take it in turns, at two second intervals, measuring the spin of their particle. So Bob measures the spin at T+1, Alice at T+2, Bob at T+3, Alice at T+4 and so on. Alice and Bob decide independently of one another which of their two apparatuses to use for each measurement. So Alice may use X, X, Y, X and Y at times T+2, T+4, T+6, T+8 and T+10, and Bob will likely follow a different pattern.
I have two questions:
1. Do the particles remain entangled throughout this process? If not, what causes them to become disentangled?
2. If so, does that then mean that whenever one of them measures using a different device from that which their partner used immediately prior (eg if Alice uses her X device at time T+k when Bob has just used his Y device at T+k-1), they instantly change the state of their partner's particle, and hence the probability distribution for their partner's next measurement?*
thank you
* My understanding is that, if Bob measures using Y at T+k-1 and gets an 'up' result and then measures using Y again at T+k+1 then:
- if Alice measured using device Y at T+k, Bob has a 100% chance of getting an 'up' result at T+k+1
- if Alice measured using device X at T+k, Bob has a 50% chance of getting an 'up' result at T+k+1
When the other particle reaches Bob he traps it within a containment device.
Say Alice and Bob have worked out at what time (T) particle B will arrive at Bob and have arranged to take it in turns, at two second intervals, measuring the spin of their particle. So Bob measures the spin at T+1, Alice at T+2, Bob at T+3, Alice at T+4 and so on. Alice and Bob decide independently of one another which of their two apparatuses to use for each measurement. So Alice may use X, X, Y, X and Y at times T+2, T+4, T+6, T+8 and T+10, and Bob will likely follow a different pattern.
I have two questions:
1. Do the particles remain entangled throughout this process? If not, what causes them to become disentangled?
2. If so, does that then mean that whenever one of them measures using a different device from that which their partner used immediately prior (eg if Alice uses her X device at time T+k when Bob has just used his Y device at T+k-1), they instantly change the state of their partner's particle, and hence the probability distribution for their partner's next measurement?*
thank you
* My understanding is that, if Bob measures using Y at T+k-1 and gets an 'up' result and then measures using Y again at T+k+1 then:
- if Alice measured using device Y at T+k, Bob has a 100% chance of getting an 'up' result at T+k+1
- if Alice measured using device X at T+k, Bob has a 50% chance of getting an 'up' result at T+k+1