Justification for the quantum equilibrium hypothesis

[Kanwarpreet Grewal]

Hi,

I have been reading a few papers on Bohmian mechanics( or the de
Broglie-Bohm pilot wave
theory). Overall the theory looks very promising and inspiring.

However I have not come to terms with the "quantum equilibrium
hyphothesis".

I read Durr et al's paper "Quantum equilibrium and the Origin of
Absolute Uncertainty" but
I am not really convinced about the "quantum equilibrium hypothesis".

What is the status of this hypothesis and its justification? Any
pointers to recent papers/ideas
will be appreciated.

regards
kanwar

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[Igor Khavkine]

Kanwarpreet Grewal wrote:
> Hi,
>
> I have been reading a few papers on Bohmian mechanics( or the de
> Broglie-Bohm pilot wave
> theory). Overall the theory looks very promising and inspiring.
>
> However I have not come to terms with the "quantum equilibrium
> hyphothesis".

Despite having been around for a long time, Bohmian mechanics is far
from a mainstream education. You'll greatly increase your chances of
getting an answer if you explain what the "quantum equilibrium
hypothesis" actually is.

Igor

[Ilja Schmelzer]

"Kanwarpreet Grewal" <kanwar@cadence.com> schrieb
> I read Durr et al's paper "Quantum equilibrium and the Origin of
> Absolute Uncertainty" but
> I am not really convinced about the "quantum equilibrium hypothesis".
>
> What is the status of this hypothesis and its justification?

Justification 1 is very simple and clear: If there is quantum equilibrium
given in the initial conditions, then it always holds. And if it holds,
the predictions of BM are indistinguishable from QM predictions.
Above claims are precise and simple theorems.

A more complicate justification is related with the mathematical
apparatus also known as decoherence. We consider some
part of a physical system and, using the global wave function,
try to construct some effective wave function relevant for the
considered part of the universe.

This partial wave function is unable to handle anything
correctly, but allows to describe, nonetheless, some
restricted subset of all possible measurements correctly.
(Some information about correlations between the state
of the part and the remaining universe is lost.)

Now, for this effective wave function we can also obtain
some quantum equilibrium, given that we have enough
uncontrolled interaction with the surroundings so that
decoherence works. I have not checked how detailed
this has been worked out, but the basic idea is nice
enough. It is also pure math only. And the result is
also agreement between predictions of BM and QM.
The advantage of this variant is that we need no longer
the additional assumption about the initial state of the
universe being in quantum equilibrium. The state of the
universe may be a delta-like state, and the quantum
equilibrium we obtain only via construction of the
effective wave function for parts of the universe.

Ilja

[msleifer]

I was not aware that decoherence could be used to justify the
equilibrium hypothesis. It doesn't seem likely to me, but if there are
some papers on the topic then perhaps you can provide some references.

You might also like to check out the papers of Anthony Valentini at
www.arXiv.org. He believes that quantum equilibrium is the same sort
of thing as equilibrium in classical statistical mechanics. If I were
a Bohmian then I think this would be my preferred position.