Re: [Phys-L] Decoherence and gravitational time dilation

[John Denker <jsd@av8n.com>]

On 10/26/2015 01:31 PM, Savinainen Antti wrote:

> I just became aware of an interesting paper discussing how quantum
> decoherence could be due to gravitational time delay: 
> <http://arxiv.org/abs/1311.1095

I cannot make sense of that paper.

It concerns a particle, perhaps a micron-sized particle, with 
a nonzero temperature T.  The immediate question arises, how is 
this temperature established?  Generally, Plan A is to hold the 
particle in contact with a heat bath at some given temperature,
but no, this particle is isolated from its environment.  OK,
Plan B is (loosely speaking) to have each half of the particle
serve as a heat bath for the other half.  For lack of anything 
better, I have to assume that's what's going on here.

The particle starts out in a coherent quantum state, and the
paper calculates the decoherence time, which depends on the
temperature.

But wait a minute!  If the initial state is coherent, it's not
thermal ... and if it's thermal, it's not coherent.  So the
entire premise of the paper is self-contradictory.  I give
up.  If anybody knows how to make sense of this, please let
me know.

  (For the next level of detail, see below.)

> The paper was published in Nature Physics so it should have some credibility.

Sorry, that's not how it works.  Journals do not offer 
a money-back guarantee of correctness.  That applies to
Macmillan (publisher of Nature), to Reader's Digest, to
the New York Times, and all the rest.  Do you remember
the front-page articles about weapons of mass destruction
by Judith Miller?

Appeal to authority is very, very weak evidence.
  https://www.av8n.com/physics/authority.htm
  https://www.av8n.com/physics/ex-cathedra.htm

===============

If you want to follow my thought process in more detail, think
about the density matrix.  A typical pure-state density matrix 
is something like this:

        [ 9/13	6/13 ]     [ 0.692	0.462 ]
  ρ  =  [     	     ]  =  [      	      ]
        [ 6/13	4/13 ]     [ 0.462	0.308 ]

  Note that ρ^2 = ρ, which is the hallmark of zero entropy.

Meanwhile, the corresponding thermal mixture would be

        [ 9/13	  0  ]     [ 0.692	  0   ]
  ρ  =  [     	     ]  =  [      	      ]
        [   0 	4/13 ]     [   0  	0.308 ]

  Note that ρ^2 ≠ ρ.

Generally speaking, the process of decoherence consists of
washing out the correlations, i.e. washing out the off-diagonal 
elements of the density matrix.


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As a tangentially-unrelated issue:  The whole notion of "time
dilation" is 100 years out of date.  It's not the smart way to 
think about what's going on.  It is a magnet for misconceptions.
It's a conceptual disaster, with clocks that can't be trusted,
rulers that can't be trusted, N incompatible notions of velocity-
dependent mass, et cetera.  You can avoid the misconceptions if 
you're very very careful, but you can get the right answer more 
easily and more intuitively using the modern approach:  proper 
time, proper length, 4-vectors, spacetime, and (in the presence 
of gravity) curvature.

In case you were wondering, spacetime is curved quite a bit
/in the time direction/.  This explains how clocks can get out
of sync, even though each clock is keeping time with perfect
accuracy.  Here is a model that makes this understandable at
the grade-school level:
  https://www.av8n.com/physics/geodesics.htm#fig-darts