On 06-04-2022 08:18, Bruce Kellett wrote:
On Wed, Apr 6, 2022 at 10:14 AM smitra <smi...@zonnet.nl> wrote:
On 06-04-2022 01:14, Bruce Kellett wrote:
On Wed, Apr 6, 2022 at 9:03 AM smitra <smi...@zonnet.nl> wrote:
On 06-04-2022 00:21, Bruce Kellett wrote:
On Wed, Apr 6, 2022 at 1:13 AM smitra <smi...@zonnet.nl> wrote:
The conclusion that local hidden variables are rules out does
depend on
an argument about what would have happened had different
polarizer
setting been used than the ones that were actually used.
That is false. Where in the Aspect experiments is reference made
to
non-performed measurements?
It's in the argument that local hidden variable theories must
satisfy
Bell's inequalities.
You are stretching things quite a bit. All Aspect needed to do was
show that his measured results violated the inequalities. No
counterfactual reasoning involved. If you then want to argue that
Aspect's results extend to all possible such experiments, then of
course, not all those experiments have been done. But that does
not
impact Bell's theorem. Bell, himself, did not have to make any
measurements.
How does one conclude that a set of measurement results cannot be
explained by a local hidden variable theory if you don't invoke
counterfactual reasoning to the performed experiment?
That is a rather trivial appeal to counterfactual reasoning. Such an
appeal is not unique to Bell's theorem -- it applies to any theory
that is confronted with experiment. A theory will state that "if you
measure such-and-such, or perform such-and-such an operation, the
following will happen (or not happen)." That is the only type of
counterfactual involved in applying Bell's theorem to Aspect's results
to rule out a local HV account. Bell's theorem itself is independent
of any such counterfactual reasoning. He simply derives an inequality
that any local theory must satisfy. This may be cast in the form of
counterfactuals, if desired. But that is true of any theory. Bell does
not depend on counterfactual reasoning.
As I replied to Brent, this is obviously not true. There is no way you
can find a constraint on the correlations at one angle in terms of the
correlations at other angles, if not for making counterfactual
assumptions. And such assumptions are not valid in most interpretations
of QM.
To go further with analysis of Rubin's argument, he states: "Each
particle, even before its spin is measured by the analyzer, carries
with it information—“instruction sets,”—determining what its
response will be to the analyzer in every possible orientation." This
is a fatal assumption. It is ruled out by the Kochen-Specker theorem
which proves that no such complete set of instructions is possible.
This is where Rubib introduces counterfactuals -- if a complete set of
instructions for every angle is possible, then one can
(counterfactually) ask what would happen if the polarizers are at
auch-and-such an angle. But none of this is possible. And
counterfactuals do not arise. In any case, Bell did not argue in this
way.
I have yet to read the article by Rubin, he may well be completely wrong
with his argumentation.
Of course, Aspect could simply refer to Bell's theorem, but Bell's
theorem relies heavily
on counterfactual reasoning.
No, it does not. The claims by Rubin: "Bell's theorem depends
crucially on counterfactual reasoning....."; and "Bell's theorem is
avoided because the counterfactual reasoning which leads to it is not
required, and cannot be justified." are
just assertions. No textual evidence is provided that Bell ever used
counterfactual reasoning in any way. His proof is independent of
counterfactuals. Rubin gives a derivation of Bell inequalities that
does refer to non-performed experiments. But that appeal is not
necessary (and invalid); Bell himself did not reason in this way.
I explained that in detail to Brent. It's very clear if you consider any
particular Bell's inequality and see how the derivation works in detail.
The GHZ experiment is one of the simplest examples:
We have an entangled state:
|psi> = 1/sqrt(2) [|up, up, up> + |down, down, down>]
Alice, Bob and Charlie receive one spin and then choose to measure
either the x or y-component. Using:
sigma_x|up> = |down>
sigma_x|down> = |up>
sigma_y|up> = i |down>
sigma_y|down> = -i |up>
and with the notation: (A) (B) (C) |state> for tensor product of A, B,
and C so that A acts on the first
component of |state> and B on the second component, and C on the third
component, we see:
(sigma_x) (sigma_x) (sigma_x) |psi> = |psi>
So, of Alice, Bob and Charlie measure the x-components, then despite
their results being random, the
product of their results will always equal 1.
We also have:
(sigma_x) (sigma_y) (sigma_y) |psi> = -|psi>
So, if one person measures the x-component and the others measure the
y-component then the product of the
results will always equal minus 1.
Argument against local hidden variables: We assume that if the ith
person chooses to measure the X
component then the result will be Xi, while it will be Yi if the Y
component is chosen. This does not
depend on the choices made by the others.
For the cases where two people choose to measure the Y-component, we
then have the results:
(X1, Y2, Y3): product = -1
(Y1, X2, Y3): product = -1
(Y1. Y2, X3): product = -1
Taking the product of these results then yields:
-1 = Y1^2 Y2^2 Y3^2 X1 X2 X3 = X1 X2 X3
But as shown above, if all 3 measure the x-components and multiply their
results, the result will always
be equal to 1. This contradiction with local hidden variables clearly
follows from invoking counterfactual
measurement results.
Saibal
This is also why you can have
superderminisitic loopholes to the argument against local
deterministic
theories.
The superdeterministic argument stems from Bell's assumption of
statistical independence: the claim that the distribution of the
hidden variables does not depend on the future settings of either
polarizer. It is part of Bell's understanding of locality and
separability. He explicitly rules out superdeterminism as absurd.
Again, nothing to do with counterfactuals.
Yes, Superdeterminism can be invoked while avoiding the issue of the
setup having to be fixed, that's what Hossenfelder has recently shown.
But earlier 't Hooft did argue on the basis of not being allowed to
consider arbitrarily different settings than were actually used.
Saibal
Bruce
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