From: *Brent Meeker* <meeke...@verizon.net <mailto:meeke...@verizon.net>>
On 7/9/2018 5:07 AM, Bruce Kellett wrote:
Where you are going wrong is in saying that they were in the right
branch at the start -- due to the properties of the singlet state.
This is misleading you, because you are not explaining how the
correlations arise at spacelike separations when the polarizer angles
are set at random. Sure, this is a property of the singlet state in
standard QM, because Alice's measurement collapses the state so that
only the correlated part is available to Bob. It is that part of the
explanation that is lacking in your account. You do not see any
non-locality, basically because you are assuming it with being aware
of what you are doing. Don't despair -- many other highly trained
physicists do exactly the same thing. But this does mean that you
have not explained anything -- you have simply assumed the result.
The individual measurements of Alice and Bob do influence each other,
or else no correlation could ever arise. This a logical consequence
of a correlation between two independent events. /Independent/ means
/no correlation/. Here we have spacelike separated events that do
show a correlation. Consequently, the assumption of locality is not
tenable, even though we appear to have only local interactions.
Whatever you say about branching or Everett is not going to alter the
basic logic of this situation.
This is where I see a different possible story. That all the branching
world lines of Alice and Bob exist in the same Hilbert space and that
only those that have consistent measurements can meet, those with
inconsistent measurements are the off diagonal terms of the density
matrix. This is still non-local because the Alice and Bob that can
meet have this element of coherent results which allows them to be in
the same "world"; this coherence came from measurements which were
space-like events. So are there Alice/Bob pairs that are
inconsistent. Sure, if they're measuring a singlet state there's (per
MWI) an Alice-up and a Bob-down that are consistent and there's also
an Alice-down and a Bob-up who are consistent. But that implies that
the other two pairings, Alice-up/Bob-up and Alice-down/Bob-down, exist
but are inconsistent. Bruce says they never exist, because the wf is
a single non-local object that doesn't allow those measurement events;
which I understand. But is it any different to say the incoherence of
wrong pairings just prevents them existing in the same world, i.e.
zeroes them out as part of the of diagonal terms? I'll have to see if
I can make the math work.
I thought it was clear that when you work back from the meeting pf Alice
and Bob, their lab books contain all possible measurement results --
there are no sets of measurements that Alice can make are not in one or
other of the 2^N 'Alice' log books. Similarly there is no set of
measurements that a Bob can make that is not in one of the 2^N 'Bob' log
books. So there is nothing off diagonal to be zeroed out -- even if that
concept makes any sense at all.
I wish you luck with trying to get the maths to work out on that
one..... Incompatible pairings of up/up or down/down for aligned
polarizers have zero probability in the wave function, so they do not occur.
Bruce
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