Horace Heffner wrote:
On Jan 26, 2006, at 5:21 AM, Stephen A. Lawrence wrote:
Right. I think that's similar to what I said.
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.
OK, I'm being sloppy, you're right, this is a bit different.
Mass of a system is the same in whatever
freefloat frame it is computed.
But none the less "invariance" means the same thing: It's the same in
any frame in which it's computed -- that means it's the same in any
Lorentz coordinates, which means it's a scalar on the manifold. Scalar
fields are "invariant", other things aren't.
First they needed to prove the 4-momentum of the _system_ of particles
was conserved. Once they had that, then they take the squared magnitude
of the momentum of the system of particles, and once again it works out
to something which is equal to the mass of the system in the center of
mass frame for the system. Right? I think?
The invariance of the 4- vector
interaction is an invariance of the products before and after an
interaction.
Um ... this sounds more like a statement of conservation than a
statement of invariance.
In the Taylor and Wheeler view mass is conserved in isolated systems,
while momenergy is not.
What?? Am I failing to understand you here? Do I know what you mean by
"momenergy"? Maybe not. I would guess it means 4-momentum.
But ... 4-momentum of an isolated system is not conserved?? No way!
Um ... Do we have an issue with the terms "invariant" and "conserved"?
As I understand it, the two terms are unrelated. "Invariant" means it
has the same value in all coordinate systems. The term "conserved"
means its value is independent of time. But you know that, right? That
can't be the point where we're disconnecting.
Horace, are you going to force me to buy Spacetime Physics? It's
supposed to be a very good book, but I've already got too many
relativity texts :-( Schutz says 4-momentum is conserved. I sure
_thought_ it was conserved.
If 4-momentum isn't conserved then all bets are off. If it is
conserved, then again, dotting it with the 4-velocity of an arbitrary
observer will give you a value which corresponds to the relativistic
mass of the system in that observer's rest frame, which to me means that
relativistic mass is just as much a first-class citizen as rest mass.
But I'm swimming against the tide here, I know.
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.
I'm no expert. I only learned one kind, and that not terribly well.
But every text I've seen on it only discusses events, and things that
happen at events, and whatever "reality" does between times is not part
of it. Similarly, the term "real" is hardly ever defined or used.
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.
Do you mean conservation of mass? All I was trying to clarify is what
is generally meant by the term "invariant".
My point, such as it was, was that saying rest mass is "invariant" means
less than it sounds like it means, and doesn't have much to do with how
"real" it is versus any other kind of mass.
Horace Heffner
