From: platt@watson.ibm.com (Daniel E. Platt)
Subject: Re: Axiom of Physics
Date: Wed, 26 Aug 1992 19:07:32 GMT
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: IBM T.J. Watson Research Center

In article <1992Aug26.174922.6115@pellns.alleg.edu>, frisinv@alleg.edu writes:
|> A friend and I have a small disagreement about the existance of an axiom  
|> of physics. She claims that all assumptions in physics are made from  
|> empirical evidence and therefore there are no axioms in physics. I  
|> maintain that the conservation of mass/energy is an axiom. Here is my  
|> argument: an axiom must be based on evidence. Euclid didn't just say  
|> parallel lines don't intersect, he saw evidence that they didn't and then  
|> stated the postulate. We have seen that energy and mass seem to be  
|> conserved. There is very strong evidence that they are conserved but (to  
|> my limited knowlege) there is no proof that they are conserved in all  
|> cases. Thererfore, conservation of mass/energy is an axiom of physics. Can  
|> anyone think of other axioms of physics?
|> -----
|> Vince

Axioms define properties of 'undefined terms.'  In a way, Axioms are
'definitions' of undefined terms in an operational sense.  In this sense,
you can start looking for axioms by looking for undefined terms.

In dynamics, distance is 'defined' from geometry.  Time is sort of defined,
but its actual measurement follows from dynamics, so should probably be put
in the class of undefined things.  Mass is undefined, and so is Force.
The first law goes a long way towards defining inertial frames and time.
The second law defines force and mass.  The third law imposes more
constraints on forces, and leads to conservation of momentum.  Conservation
of energy follows from integration of F=ma under special conditions (some
forces are not conservative).  In this sense, Newton's laws are axioms.

In electrodynamics, charge, electric fields, and magnetic fields are defined
in terms of Force.  Constraints on the behavior of the fields include the
definition (Lorentz force) and their equations of motion (Maxwell's
equations).  From this, extensions such as field momentum can be derived.
Conservation of energy and momentum thus gets extended in this context.

In thermodynamics, temperature and entropy are undefined.  Their definition
is obtained through the 2nd law (and 0'th law, though the 0'th law can be
shown to follow from the 2nd law, and the 2nd law is required to derive a
consistent measure).  Connections can be made to statistical mechanics of
these measurements, but in classical thermodynamics, these terms were
undefined.

As fields of study grew, more and more connections were made between
'undefined terms' and other elements of description, so that ideas such as
momentum and energy and entropy were seen to be more primitive in these
contexts.  This showed up in quantum mechanics and statistical mechanics, for
example.  Some 'laws,' such as Newton's laws, were seen to be inadequate to
describe objective reality.  The ideas were extended, and undefined terms had
better axioms applied; things that seemed to be derived were recognized to be
more fundamental, etc.

Bottom line: physics has some similarities to math, but you shouldn't try to
stretch things too far.  Its development is not really that organized or
systematic.  While it is possible to construct a fairly systematic
development of physics, it might not be a good idea to do that since really
fundamental shifts in physics seem to reflect changes in the ideas of what is
fundamental.  For example, the role of momentum and energy became more
important as a fundamental as thermodynamics, electricity and magnetism, and
as quantum mechanics developed; otherwise, they were thought of as following
from what had been taken as fundamental.


Dan