On Jan 26, 2006, at 5:21 AM, Stephen A. Lawrence wrote:
Horace Heffner wrote:
On Jan 25, 2006, at 6:22 AM, Stephen A. Lawrence wrote:
Thank you for the summary. I had one comment (really just one,
this time!)
Horace Heffner wrote:
Mass in the conventional spacetime metric is considered invariant.
There's a semantic problem here. "An invariant" is a well-
defined mathematical concept. However, it's just that -- a
mathematical concept. Saying "this is an _invariant_" doesn't
mean it's some simple physical property which always has the
same value.
Wheeler and Taylor say the mass of any isolated system is
invariant. In other words:
m^2 = E^2 + p^2
in one frame then
m^2 = (E')^2 - (p')^2
in another for that isolated subsystem.
Right. I think that's similar to what I said. I was talking about
a single body, but it's the same thing, really. If we put the
whole system in a box, then the squared magnitude of the 4-momentum
of the box is
m^2 * gamma^2 * (v^2 - 1)
which is, rearranging terms,
(m^2 * gamma^2 * v^2) - (m^2 * gamma^2)
or in more familiar terms,
p^2 - E^2
But it also is equal to -m^2, since the gamma^2 and the (v^2-1)
terms cancel.
Either way it's a mathematical invariant.
And the inner product of the 4-velocity of an observer with the 4-
momentum of an isolated system is _another_ invariant, and it gives
the relativistic mass of the system, which is more often referred
to as the energy these days.
Taylor and Wheeler are careful to distinguish that the mass of
identical types of individual particles having the same (rest) mass
is a concept completely separate from the principle that mass of an
isolated system is invariant. Mass of a system is the same in
whatever freefloat frame it is computed. The invariance of the 4-
vector interaction is an invariance of the products before and after
an interaction.
In the Taylor and Wheeler view mass is conserved in isolated
systems, while momenergy is not.
Problem is, no subsystem of mass is isolated. Stuff comes in and
out of the vacuum constantly. A significant portion of the
magnetic field of the proton comes from strange quark pairs
popping in and out of the vacuum, for example. Acceleration
affects how things pop in and out of the vacuum and how long they
stick around.
It's easy to forget that relativity theory says _nothing_ about
what is "real" and what is not.
Who's relativity? Certainly not mine! You make it sound like
there is only one version! 8^)
Oh, I just meant the kind that Einstein worked on. It consists of
a mathematical model, and a bunch of points of contact with
reality, which are called "events". That theory can predict what
measurements can be made by particular observers at particular
"events" but what goes on between "events" is open to speculation,
and the question of "why" anything happens is also left open.
You make it sound like there is only one of those. There is plenty
of controversy about relativity, both SR and GR. That's my point.
There is not single view though I assume there is common agreement
about how to calculate most things until the quantum realm is
reached. I only had the audacity to mention "mine" because that
proves the existence of at least two points of view.
With all that said, when someone refers to the "invariant mass"
they mean the rest mass.
Not Wheeler and Taylor.
Really? Not everybody uses the term at all. But if they use it,
_and_ they use it to refer to something else, that's a surprise.
Try googling "invariant/mass" -- it's on an awful lot of websites
and as far as I can tell it's used to mean the mass of an object in
its own rest frame.
Yes. Still, I have good reason to doubt the invariance of mass but
can not go into it now.
Horace Heffner
