Re: philosophy and the vacuum

[John Denker <jsd@MONMOUTH.COM>]

At 11:22 AM 9/11/00 -0500, Joel Rauber wrote:

> This means that the standard for the meter will be different depending on
> which vacuum you use as a reference.  Which implies a logical problem in
> the definition.  Unless we agree on which vacuum to use, and then are we
> using the same one that the SI guru's intend?

You asked about philosophy:  It is philosophically important to keep in
mind that physics is a natural science.  It is not an exact science like,
say, arithmetic.

By way of analogy:  In the lab, we never find that F equals ma
exactly.  But we believe that F equals ma to an excellent approximation, in
the appropriate limits (e.g. the nonrelativistic limit).  We believe that
we can make _controlled_ approximations;  in the case of F = ma we believe
that we can place useful bounds on the magnitude of all unmeasured forces
(air resistance, stray electromagnetic fields, et cetera).

The same philosophy and the same sort of procedures apply to the
speed-of-light experiment, which is more properly called the
meter-stick-calibration experiment.  Your calibration will never be
_exactly_ the same as my calibration.  But we believe that (if we do it
right) we can greatly reduce the magnitude of junk effects (stray gas in
the cell, waveguide effects due to the walls of the cell, et cetera) and
then place tight bounds on the magnitude of any remaining junk
effects.  The "SI gurus" intended an idealization, namely extrapolation to
the limit where the junk effects are negligible.

In practice it is not particularly hard to carry out this correction /
extrapolation process so such a high degree that labs around the world can
calibrate their meter sticks to an amazing degree of consistency.

You asked in particular about the effects of the walls.  So stop
philosophizing and do the calculation yourself.
 -- Suppose the experiment involves a chamber that is 1 meter on a side.
 -- Suppose you fabricated the chamber using 0.1 mm tolerances -- not hard.
 -- Suppose the experiment involves ordinary optical frequencies.
 -- Plug this into the waveguide equation, to calculate how the
propagation speed depends on chamber size.
 -- Then calculate the ratio of the uncorrected laboratory speed (1m
chamber) to the ideal speed (infinite chamber).  Hint:  This is a small
number.  I  expect you'll get something like one part in 10^13.  Note that
this is _not_ a source of uncertainty or inconsistency, because everybody
agrees on how to make this correction / extrapolation.
 -- Finally, calculate the actual uncertainty / inconsistency introduced
by the fabrication tolerances.  Hint:  This is a verrrry small number.  I
expect you'll get something like one part in 10^17.

If the actual uncertainty is large enough to cause you trouble in practice,
please explain what you are doing that requires such high accuracy!