From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 11 Aug 2018, at 02:29, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 9 Aug 2018, at 14:03, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
The original Alice and Bob are those in the same branch of the wave
function all the way along. There are no unmatched Alices or Bobs.
In each branch, I agree. But to get the reasoning right, and treat
the case of the violation of Bell’s inequality, we need to take into
account the unmatched Alice and Bob who exist “transworldly” if I
can say. They belong to different branches, and can never meet
again. That is important to make the FTL eventually into an
illusion, still keeping the violation of the Bell’s inequality.
It is fairly clear that you are not talking about quantum mechanics
here, but rather about some weird theory of your own. There is no
infinity of Alices and Bobs who exist before any measurement is made.
Do you agree that there is an infinity of Alice in the case of aIu> +
bId> when a^2 is irrational? I really don’t see how you interpret the
singlet state in the non-collapse QM.
No, I don't agree that there are any infinities of anything in the case
of irrational coefficients (or of any other coefficients, for that
matter). What on earth are you talking about? The Born rule gives a
probability interpretation to the square of the coefficients in the
expansion the wave function. That is all that the coefficients in the
expansion are -- complex coefficients that when squared give
probabilities. You don't have to have the appropriate relative numbers
of branches to get the probabilities -- that is just naĩve branch
counting, which has long been known not to work. Besides, how do you
ever get a complex number of branches?
If you are basing your notion of a pre-exisiting infinity of Alices on
such an idea, then you are simply wrong. No such interpretation of the
wave function is even close to being correct. Just think of
probabilities as propensities rather than as relative numbers of branches.
They do not "belong to different branches" because they do not exist,
and have never existed. This notion seems to be important to your
idea, and I can assure you that you are wrong about this.
How could that be possible? You suppress the infinities of Alice and
Bob only because you know in advance what is the direction in which
Alice will make her measurement. What if she changes her mind?
That is not the case either. I do not suppress any infinities because no
such infinities exist. They are only in your mind because you have
strange notions about the origin of probabilities in quantum mechanics.
Alice makes a measurement along a particular axis. She can change her
mind an infinite number of times before she makes that measurement, but
in the end she makes only one measurement in one direction. That is the
only direction and measurement that exists or matters.
If you think you can justify this, then I ask you to write out the
full quantum mechanical treatment, in Everett's relative state
formulation, that establishes that this infinity of pre-measurement
people is a feature of the actual theory, and not just a figment of
your imagination.
Perhaps, after the combinators. If I do that I will use the GHZ state,
to avoid the use of probability. But in my opinion, Price computations
gives the right hint to proceed, and in the simple case we see what
happens.
No, Price is wrong. He collapses the wave function in a non-local
manner, even though he doesn't seem to realize it. Let me try again. The
state is
|psi>= (|u>|d> - |d>|u>).
Let Alice interact with particle 1 at one end:
|Alice>|psi> = |Alice>|u>|d> - |Alice>|d>|u>
Alice interacts only with particle 1 (locally), so |Alice>|u>|d> -->
|Alice sees u>|u>|d>, and similarly for the other component.
Now Bob interacts with a different state. He does not see |psi> as
above, but rather
|Alice sees u>|u>|d>|Bob> - |Alice sees d>|d>}u>|Bob>
The, if Bob measures along the same axis, he gets down for Alice's up,
or up for Alice's down. If he measures at some different angle, he gets
the appropriate rotated results. But Bob NEVER sees the original
unaltered rotationally symmetric singlet state: Alice's measurement
(assuming Alice measures first in some frame) collapses the state
non-locally to affect the state that Bob sees. Since the original state
is non-separable, the fact that Alice has interacted with it changes the
whole state.
This is the calculation as Price and Tipler give it, and this
calculation is clearly non-local. Going to the GHZ state will not change
anything. What you have to do is show how to re-interpret this
calculation so that Bob sees the original singlet AFTER Alice has
measured her particle. I insist that the original non-separability of
the state makes any such demonstration impossible. And even if it were
possible, it would not reproduce the known quantum correlations; the
non-separability and the above non-local reduction of the state is an
essential part of quantum mechanics.
The strange things with QM is that he phase space is real, and it is
the place where the wave evolves purely locally. That explains already
the locality, and the appearance of non-locality in all branches.
That is meaningless gibberish which explains nothing.
Then yes, I extracted something close to Everett from arithmetic
alone. With mechanism, it becomes a zero universe theory, but is still
a many-histories theory. An history is always an infinity of
computations that I am unable to distinguish.
You haven't extracted anything like the Schrödinger equation from
arithmetic alone. Don't make unjustifiable exalted claims.
Bruce
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