On Sat, Oct 5, 2019 at 1:10 AM Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 3 Oct 2019, at 13:31, Bruce Kellett <bhkellet...@gmail.com> wrote:
>
> And there is no FTL action -- that would be a local hidden variable causal
> explanation, and Bell rules that out.
>
>
> This I do not understand, unless you bring t’Hooft super-determinism. In a
> unique universe, the violation of BI requires that when Alice do a
> measurement she influences and change the “map of the accessible reality”
> of Bob. They still cannot do signalling, but, with or without hidden
> variables, Alice does restrict instantaneously the state available Bob.
> Withe MW, as long as the light has not entangle Bob, Bob can make a
> measurement entangling him so other Alice of the multiverse. Everyone will
> agree with what the singlet state predicts, and no FTL signalling, nor
> influence has to occur.
>
You contradict yourself, Bruno. You say "when Alice do a measurement she
influences and changes the 'map of accessible reality' of Bob". Then you
say "Everyone will agree...no influence has to occur."
I think your complete failure to understand the non-local entangled state
-- the fact that the wave function itself is non-local -- is at the root of
all your misunderstandings, and leads you into these contradictory
positions. Let us start again. Consider the entangled singlet state that we
have been talking about:
|psi> = (|+>|-> - |->|+>)/sqrt(2).
This refers to two spacetime locations; let us call them (t1,x1) and
(t2,x2), where the x1 and x2 stand for 3-vectors. The spacetime interval
between these particles or events when measured, is s^2 = (t1-t2)^2 -
(x1-x2)^2. When s^2 > 0, the separation is time-like, and when s^2 < 0, the
separation is space-like (in the (+,-,-,-) metric that I am using. When
Alice makes her measurement, she gets, say, 'up'. According to the above
non-separable wave function, that means that Bob gets only the ket |->, in
the basis of Alice's measurement. Similarly if Alice gets 'down', Bob must
measure the |+> ket, in Alice's basis. By rotating these kets into his
local measurement basis, Bob gets 'up' or 'down' with the required
probabilities.
This is a what your statement "when Alice do a measurement she influences
and changes the 'map of accessible reality' of Bob" means. And I agree with
this. So (this all assumes, without loss of generality, a frame in which
Alice's measurement is first) Alice's measurement does inevitably affect
the state that Bob can measure. The question then is, how does this effect
come about? What is the mechanism? You appear to be only able to think of
some FTL influence. But that cannot work. There are a lot of problems with
such an idea. Apart from violations of special relativity, it would involve
the exchange of some particle or tachyon that conveys Alice's result and
polarizer orientation to Bob *before* he makes his measurement. Dynamics
for that might be conceivable, but there is a problem in deciding whether
it is a particle or an FTL tachyon that must be exchanged. Notice that when
this information has to be sent out from Alice's measurement, Bob still has
not made his measurement, and there is no way at the spacetime point
(t1,x1) to know when Bob will make his measurement. It could be at either
space-like or time-like separation, s^2 > 0 or s^2 < 0, and there is no way
of knowing, so there can be no suitable dynamics that will send a particle
or a tachyon appropriate to the situation (because the situation is unknown
at the relevant time).
There is an additional dynamical problem in understanding how this particle
or tachyon conveying Alice's information is actually going to affect Bob's
state when it arrives there. If the correct statistics are to come out at
the end, it would seem that this intermediate particle must suppress that
part of Bob's state that is inconsistent with Alice's result. I leave the
design of such dynamics to you -- it is beyond me to even begin to imagine
it. On top of this, there is the problem that in some other frame, Bob's
measurement is first, so his measurement must affect the joint state in a
symmetrical way!!!!!
I think this goes beyond impossibility to the point of absurdity.
So what are we left with? I think we can rule out FTL interaction, or even
sub-light speed interactions for time-like separations, because there are
too many contradictory requirements on such a particle exchange of
information. But the influence must occur, because the final correlations
can only be explained in that way. (Attempts to explain the correlations
away by MWI, or further interactions when the light cones overlap, have all
failed. Mainly because there are no relevant interactions at the point of
overlap of the future light cones from the separated measurements.)
We are left with a non-local influence, or interaction. Where by non-local,
I mean precisely that -- an action on two separated spacetime points
*without* there being any local causal contact between them, by exchange of
particles or tachyons or whatever. If there were such an exchange,
impossible as it seems, that would be a *local* explanation, because
interactions via particle exchanges are the paradigm of locality.
I know that this is contrary to all our instincts -- we believe that there
is no "spooky action at a distance". And I know that your rejection of such
action at a distance is why you have always called references to
'non-local' effects, FTL exchanges. I hope it is clear that I absolutely
reject that interpretation, and do not think that any dynamical theory of
such FTL exchanges could ever be made to work.
Non-locality is exactly what it says -- a non-local influence or
interaction between two points separated in space and time, whether by a
space-like or a time-like interval -- call it "spooky action at a distance"
if you must. But there is nothing spooky about it --no other rational
explanation of the situation is available.
Your further point about an infinity of different possible 'worlds' for
Alice and Bob coming from the rotational invariance of the singlet state is
just a smoke screen, having nothing to do with any rational explanation of
what is going on.
Bruce
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