Re: single-particle universe

["John S. Denker" <jsd@MONMOUTH.COM>]

At 08:06 PM 4/14/01 -0400, Robert B Zannelli wrote:

> According to Mach's principal, inertia is the result of the interaction of
> the accelerated object and the rest of the Universe.

I'm not convinced that Mach's principle is necessary or even helpful.

My argument is in several parts:
  1) If you wish to consider a model universe that does not contain
electromagnetism, I'm not interested.  That model is too artificial.
  2) If you include electromagnetism, you have to be careful because it
automatically contains an infinite number of EM modes.
     2a) If you consider the EM excitations to be particles (i.e.
photons), then the game is over immediately.  There is no such thing as a
one-particle universe.
     2b) If you don't count the EM excitations as particles then it *is*
possible to have a universe with a single particle.  And in this universe
it makes perfect sense to talk about the mass and the acceleration of this
single particle.  The motion of the EM waves tells us enough about the
structure of spacetime that we can detect the acceleration of the particle
when a wave scatters off it.

The conclusion seems inescapable:  If there is any such thing as a single
particle, in a realistic universe, it is perfectly well behaved.

If it helps, you can view this as the limit of a regular universe with a
modest number of sparsely distributed, weakly-interacting particles.

To say the same thing in slightly different words:
   x) There is no absolute reference for position coordinates.
  x') There is no absolute reference for velocity.  It's all relative.
 x'') The EM field *does* provide an absolute reference for
acceleration.  We know what the ground state of the EM field looks like
(zero-temperature equilibrium).  But if you accelerate past such a state,
in the accelerated frame it does not look like the ground state.  It will
have nonzero temperature, including thermal photons.

I agree that in a universe with only a single particle nothing very
interesting happens, but I fail to see how it disturbs the epistemological
foundations of physics.