Re: [Phys-L] Decoherence and gravitation

[John Denker <jsd@av8n.com>]

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

> a student of mine asked last week why gravitational interaction does
> not cause decoherence of a quantum state.

Here's what I would have said:

There are several regimes to consider:  

 a) If you think of the gravitational field as arising from a
  fixed potential, then motion in the potential is reversible ...
  mechanically and also thermodynamically reversible.  It doesn't 
  change the entropy.  The quantum state might become a tangled 
  mess, but technically it's still a single quantum state.

 b) If you consider the possibility of gravitational waves, you come
  to a different conclusion.  If the object can emit or absorb
  gravitational wave, it will decohere.  This is what Tony Leggett
  called the "watched pot" effect.

  Here's an analogy.  It suggests an experiment you could probably
  do in high school, although I've never actually tried it.  In
  any case, it works as a Gedankenexperiment.  Set up a trough 
  of optically-active liquid, perhaps sugar water.  Stick in two 
  linear polarizers with the same orientation, and adjust the
  concentration and the geometry so that no light gets through,
  because the plane of polarization gets rotated 90 degrees.

  Then add a third polarizer, halfway between the other two, all
  with the same polarization.  Lots of light gets through!  It
  is remarkable that adding something that seems like it can
  only absorb light allows more light to get through.  If you
  add yet more polarizers, yet more light gets through, nearly
  as much as would get through N polarizers in the absence of
  the optically active medium.

  The polarizer is an example of a measuring device.  Repeated
  measurement ("watching the pot") prevents the state vector
  from exhibiting its natural time dependence;  the vector gets
  locked into a state determined by the measuring device.

  An interaction with the graviton field will lock the particle
  into a state determined by the matter/field coupling.

 c) In typical situations gravitational decoherence is utterly 
  negligible, because long before that happens, the state
  vector will be locked in a basis determined by the coupling
  to the /electromagnetic/ field, which is a much stronger
  coupling.


In Feynman volume III there is a magnificent discussion of the
ammonia maser.  One thing he forgets to mention is that the
analysis applies to almost *no* molecules bigger than ammonia.
A dextrose molecule or an alanine molecule couples more strongly
to the EM field, and locks up via the watched pot effect.  That's
why you can buy L-alanine and D-alanine, even though arguing by
analogy to ammonia would lead you to imagine that the ground
state is the gerade combination of the L- and D- states, and
that the various forms would rapidly interconvert.  Even if
you imagine that the rotation in state space is super-slow,
you have to wonder why it got stuck in a state of definite
dipole moment, rather than some random point on the surface
of the SU(2) sphere.

It locks up in a state of definite dipole moment, because that's
what couples to the EM field.  You wind up with a /dressed state/
consisting of a molecule and a bunch of EM field that it has to
drag around.  If you need help imagining a dressed state, consider
this:  The effective mass of a submarine is bigger than you might
think, because when the submarine is in motion there is kinetic 
energy in the water, since you have to move the water out of the
way.  By the same token, the tunneling between the alanine D- 
and L- basis states is strongly disrupted, because you have to
rearrange the field.

Given that something as small as an alanine molecule is locked
up, you can be sure that any micron-sized particle will be
locked up ... unless super-heroic measures are taken to decouple
it from the EM field.