Re: Thermodynamics

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

At 09:41 AM 8/30/01 -0400, Hugh Haskell wrote:

> > "There is no reason to expect that an object will have any one particular
> > acceleration given a certain force.  When the acceleration of the object is
> > measured, however, we find that it obeys a law of the form a = F/m."
> I would say that this would be true only if one has definitions of
> both force and mass that do not involve acceleration in any way.

I agree that we don't want to rely on circular definitions.

> I don't think any exist.

I disagree.

> In fact, we use the above relationship to identify forces.

I mostly disagree.

There do exist meaningful operational non-circular ways to define mass and
force and the other things that need to be defined.  The following is one
way (not the only way) to proceed:
  -- Define an arbitrary standard force using a spring scale.  Choose a
"standard" spring and extend it a "standard" amount.  If you want twice as
much force, put two such standards in parallel.  If you want half as much
force, construct a secondary standard such that two of them together equal
one standard force.  Observe operationally that the forces obey the laws of
vector addition.
 -- Similarly define an arbitrary standard mass in terms of some
artifact.  If you want twice as much mass, harness two such standards
together.  Observe operationally that such masses obey the laws of scalar
addition.  Technically speaking it is a semi-group, because negative masses
are not available.

> ... NSL is a statement about how nature works ...
> it is probably not too far off,
> as long as we remain firmly in the arena of large objects, to treat
> it as a way to define force (as long as we can all agree on what
> "mass" is).

Again, it is certainly not necessary (and usually not advantageous) to
define force in terms of mass times acceleration.  Force is related to
momentum, and momentum is a first-class conserved quantity (in quantum
mechanics as well as classical mechanics).  There is no good reason
(conceptually or operationally) for saying that mass is more fundamental
than force, or vice versa.

Everything in physics is related to everything else, in the sense that we
have N unknowns connected by a whole lot more than N equations.  If you
know N-1 of these quantities, you can in general calculate the Nth
one.  Indeed you can probably calculate it in many different ways.  The
point, once again: there is no good theoretical or metaphysical basis for
choosing any particular subset of the N variables and declaring them to be
more fundamental than the others.

You can, if you wish, choose your own personal set of "fundamental"
variables and calculate everything in terms thereof, but
 a) you will probably want to change your mind from time to time, choosing
a different set of "fundamental" variables, depending on the problem at
hand; and
 b) you certainly must respect the right of other folks to choose differently.