On 11-04-2022 14:02, Bruce Kellett wrote:
On Mon, Apr 11, 2022 at 5:35 PM smitra <smi...@zonnet.nl> wrote:
But why not simply analyze what the evolution according to the
Schrödinger equation would lead to? Obviously all that's going to
happen
is that the measurements o the spins will cause the entanglement to
spread further. we started with two entangled spins and now we end
up
with the entire Bob and Alice sectors becoming part of this
entanglement.
The trouble with this is that the entanglement spreads only at the
speed of light or less. If faster than that, then it is npn-local.
Alice and Bob make their separate measurements at spacelike
separations. So if the entanglement resulting from Alice's measurement
affects Bob's measurement, that that is FTL or non-local.
If the polarizer are parallel then if Alice finds spin up
there is only a "Bob finds down" in her sector. That's clearly what
the
local time evolution according the the Schrödinger equation
predicts.
|Alice>[|up,down> - |down, up>] ---> |(Alice sees with up) ,down> -
|Alice sees down, up>]
It's a local interaction because Alice interacts only with her spin,
not
with Bob's spin.
Your equation is revealing. Since Alice and Bob are spacelike
separated, Alice's measurement cannot locally affect Bob's. But in
your equation you have reduced
|Alice>[|up,down> - |down, up>] to two parts. where
|Alice sees up ,down> drops the |up> part of the wave function that
Bob sees.
Similarly
|Alice sees down, up> drops the |down> part of the wave function that
Bob sees.
Since in the local case, Bob's measurement is independent of Alice's,
he must see |up> and |down> with equal probability (in different
branches). By dropping the entangled part of the wave function after
Alice's measurement, you rule out the possibility that Bob can get
|up> or |down> with equal probability after Alice's measurement (as he
certainly can before her measurement). What is it about Alice's
measurement that changes the probabilities for Bob's result? At
spacelike separation, this can only be a non-local influence.
Here you go wrong.
I did not write Bob's state in here, let's do that now
|Alice, Bob>[|up,down> - |down, up>] ---> |Bob>|(Alice sees up) ,down> -
|Alice sees down, up>]
And now Bob is going to measure his spin:
|Bob>|(Alice sees with up) ,down> - |Alice sees down, up>] --->
||(Alice sees up) ,Bob sees down> - |Alice sees down, Bob sees up>
So, both Bob and Alice interact only with their own spins. There is no
issue whatsoever with getting the correct pairings.
Saibal
Bruce
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