[Phys-l] frame dependence +- lattice dynamics etc.

[John Denker <jsd@av8n.com>]

On 11/29/2006 01:54 PM, Bob Sciamanda wrote:

> Query: Is a universe governed by a frame-dependent physics impossible a 
> priori?

Absolutely not impossible.
It's not even uncommon.

Consider the electrons in a solid.  Band structure and all that.
Slightly N-doped silicon, so the electrons of interest are few,
and tend to rest at the bottom of the band.

Near the bottom of the band, the electron kinetic energy is well
described by 0.5 meff v^2, where meff is the "effective mass".

This looks a lot like ordinary classical physics, except that
 -- the effective mass is different in different directions.
 -- the effective mass becomes a function of speed, if the
  speed gets too big.
 -- there can be transitions into other bands
 -- et cetera.

As for "our" universe:  there is a long tradition of devising
"lattice gauge theories" and "cellular automaton theories" of
the universe.  It is easier than you might have guessed to
make the underlying lattice not affect the dynamics to first
order.  Of course if you look closely enough, eventually you
will see something weird.

FWIW Feynman uses this trick to /derive/ the Schrödinger equation:
he does the discrete lattice first ... and then takes the limit
of an ultra-fine-grained lattice to produce the continuum result
i.e. the usual Schrödinger equation.

So it is a provably never-ending cat-and-mouse game:  experiments
rule out coarse-grained lattices, but theorists can always propose
a finer-grained lattice, and then the experimentalists must go
back to the drawing board.......