On 20-04-2018 02:58, Bruce Kellett wrote:
From: SMITRA <[email protected]>
One can a priori rule out any non-local effects using the fact that
the dynamics as described by the Schrödinger equation is local.
That is false. The dynamics in the Schrödinger equation are given by
the Hamiltonian. And there is absolutely no reason why the Hamiltonian
should describe only local dynamics. It is easy to construct non-local
Hamiltonians.
No, this is not's not false, because we know that the Hamiltonian does
in fact only include local interactions and there are good theoretical
reasons why this should be the case.
So, in any theory where there is no collapse and everything follows
from only the Schrödinger equation, there cannot be non-local
effects other than due to common cause effects. Then suppose that in
an example where things are simplified to allow for Alice and Bob
thought experiments to be discussed without having to rigorously
show how Alice, Bob and the experimental apparatus used are to be
extracted from the wavefunction one does see non-local effects, then
it follows that these non-local effects are artifacts of these
simplifications.
That does not follow at all. You forget that in addition to the
possibility of non-local dynamics, the wave-function for many-particle
systems is defined in configuration space, and things that are local
in configuration space can easily be non-local in ordinary 3d space.
And we live in 3D space, so have to live with non-local effects.
Common cause explanations do not work for space-like separations.
As long as the dynamics is local and unitary, you won't get any
non-local effects other than via common cause effects. That "we live in
a 3d space" is only true in an effective sense, in principle everything
lives in a Hilbert space.
Now, in standard quantum mechanics one does routinely make such
simplifying assumptions, this allows for QM to be useful as a
practical theory, but we then also know that strictly speaking, it's
not how Nature really works.
How do you know how Nature really works? We observe correlations in
Bell-type measurements. These indicate non-local effects in the world.
Going to another world does not actually help you, because we are
stuck in 3D reality.
To prove that one cannot get rid of non-local effects (i.e. explain that
in terms of common cause effects), you can't just show that non-local
effects remain present in an effective theory where one pretends that
the effective world observers find themselves in, is fundamental.
Saibal
Bruce
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