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Re: Is mass really frame-independent?



Savinainen Antti wrote:

My question is: is m (invariant mass) frame-independent also if
non-inertial reference frames are considered? I would tend to think
so but I can't justify it; special relativity starts with the
postulates explicitly dealing with inertial frames. Would then all
the linked notions (like energy-momentum four-vector) share this
crucial restriction?

OTOH special relativity can deal with accelerating systems, at least
in some situations: e.g. the twin paradox can be understood
completely in terms of special relativity as shown by former Phys-L
postings (also by John D. in <http://www.av8n.com/physics/twins.htm>)

The main question is:

> My question is: is m (invariant mass) frame-independent also if
> non-inertial reference frames are considered?

That is quite a penetrating question, and probably needs to be
answered on several levels.

The outline of the argument goes something like this:
a) Let us _hypothesize_ that m is independent of acceleration.
b) There is no experimental or theoretical evidence in conflict
with this hypothesis.
c) Therefore, for the time being at least, the hypothesis is
strongly favored because of its simplicity. This is an
Occam's razor argument.

At the next level of detail: It is easy to say that it is
"conventional and convenient" to assume or hypothesize that
m is independent of acceleration, or even to *define* m
such that it is independent of acceleration ... but that
is a long way from being a proof. At the very least, we
need to show that independence is _consistent_ with all
the other assumptions/hypotheses/definitions that are
floating around.

> special relativity can deal with accelerating systems,....
> http://www.av8n.com/physics/twins.htm

(In particular, that twins.htm page advocates using inertial
reference frames that are instantaneously comoving with the
accelerated frame. This solves all sorts of problems with
accelerated frames, not just in SR, but also in more prosaic
situations such as merry-go-rounds and rapidly maneuvering
aircraft.)

That's an important part of the argument. Suppose we choose
to define our notion of m-in-an-accelerated-frame to be whatever
m would be measured in an instantaneously comoving freely-
falling frame. Then if you believe special relativity, you
have a guarantee that m is consistent (indeed invariant) for
all observers, accelerated or not.

So we have a definition of m that is conventional, convenient
and consistent.

I don't think any stronger conclusion is possible. For example
we have seen the velocity-dependent "relativistic mass". I
don't think it is possible to prove this wrong; I just say
it is unconventional and IMHO inconvenient. Similarly it must
be possible to cook up some sort of acceleration-dependent
mass; I just can't imagine why anyone would want to.