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Re: [Phys-l] Relativity Question about spring



Philosophical remark: As a rule, I say authors should be
allowed to define whatever notation and terminology they
like, so long as they use it consistently ... and warn
people if the terminology is deceptive and/or unduly
unconventional.


On 05/08/2007 09:30 AM, William Maddox wrote:

If m is taken as a
measure of inertia and inertia depends on more than rest mass, then you have new mass = m = mo + ½ kx2/c2.

Well, you *could* do that ... but why would you want to?
It practically begs to be misunderstood.

AFAICT, in this field there has always been (until now???)
universal agreement that
a) m0 denotes rest mass, and
b) rest mass already includes the ½ kx^2 spring energy

Even people who disagree about other things (such as whether
rest mass is "THE" mass) agree about items (a) and (b).

Rest mass is a central, fundamental idea in special relativity,
and if you go around re-defining it you are going to break all
sorts of things. So unless you are prepared to re-invent all
of special relativity -- re-expressing all the results in non-
standard terminology -- you probably don't want to introduce
a non-standard meaning for m0 and/or rest mass.

If you want to express the difference between the uncompressed
energy and the compressed energy, there are much, much more
conventional ways of expressing it. For example, you could
write
E(x) = E(relaxed) + ½ kx^2
and call it "the" energy as a function of x ... and I don't
think anybody would complain.

Does anyone know if current technology allows a mass change that small to be measured?

For steel springs, not at present.

OTOH as I said before, the mass deficit associated with the
binding energy of nuclear reactions and suchlike is directly
and routinely observable. It's the same sort of thing:
the laws of relativity don't distinguish one type of potential
energy from another.

The mass deficit associated with /chemical/ binding energy
is (so far as I know) presently out of reach ... but only
barely so, and I would be impressed but not surprised to
hear of such a measurement.