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Re: [Phys-L] foundations of physics: Galilean relativity, including KE

Are you saying that if I have one box B containing the two photons in your example and I subdivide B into two parts which I call box G and H such that one of the photons is in G and the other is in H, then, at any one instant in time, there is no mass in box G and there is no mass in box H but there is mass 2q in box B?

This seems more profound than a lack of conservation of mass. It suggests that the amount of mass in a region of space depends on how you visualize it.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of John
Denker
Sent: Thursday, October 01, 2015 2:09 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] foundations of physics: Galilean relativity, including KE

On 10/01/2015 09:40 AM, Jeffrey Schnick wrote:

I have been thinking in terms of a control mass system [...] Your
example is expressed in terms of a control volume system

I suppose that's true, but I don't think it changes the physics at all. It seems
to me, you can define "+" to mean adding particles or adding volumes, and it
doesn't matter in this context, because as soon as you write

system G "+" system H = system B

then you can have a situation where G and H are each massless, but B is not.
I realize that everybody had "conservation of mass"
drilled into their heads in high-school chemistry, but Mother Nature has
other ideas.

It's a simple calculation. Just add the components. Given two photons G and
H that we group together to make B, the four-momenta
are:

G = [q, +q, 0, 0]@lab
H = [q, −q, 0, 0]@lab
B = [2q, 0, 0, 0]@lab

Then calculate the mass. For diagram and details, see
https://www.av8n.com/physics/spacetime-welcome.htm#sec-invariance-
conservation

[scenario snipped]

You thought this left 0 mass inside the box because the only thing in
the box was a photon and it has zero mass.

Yes, I thought exactly that, and still think that. If the only thing in the box is
the one running-wave photon, then I know the [energy,momentum] 4-
vector and I can calculate the mass.
I still think it's zero. It's an easy calculation.

What you didn't notice was that amount q of system mass was still
inside the box.

Where's That From? It seems to rely on some intuitive notion of "system
mass" that I don't know how to calculate. Given the choice between that
and the plain old mass that I do know how to calculate, I'm gonna stick with
the latter. It is easy to keep track of the energy and momentum, because
they are conserved quantities ... and then it is easy to use them to calculate
the mass. I doubt there is a 4-vector anywhere that corresponds to "an
amount q" of mass inside the box. We have only two photons to play with,
and it's pretty much a binary choice as to whether you group them together
or don't.
https://www.av8n.com/physics/spacetime-welcome.htm#sec-invariance-
conservation


The locality of the conservation of anything is best expressed
(perhaps can only be expressed) in terms of a control volume system so
I want to go there.

If we exclude continuous fields and consider only discrete particles, as we've
been doing here, I reckon the conservation law can be expressed either way
(control mass or control
volume). Conservation becomes a statement about continuity
of world lines. For diagrams and discussion, see:
https://www.av8n.com/physics/conservation-continuity.htm

Conservation of charge corresponds to continuity of electric current, which
corresponds to continuity of the world line for an abstract quantum of charge
(not to be confused with any particular charge- carrying particle).

Note that electric current is *not* a conserved quantity.
We have conservation of charge, but /continuity/ of current.

In the introductory course, the particle-based formulation is easier to
formalize. After all, F=ma is a particle-based concept.
The control-volume formulation is easier to /visualize/ ... but to quantify it in
a useful way, in a way that students can connect to other stuff they know, is
a bit of an uphill slog. I suggest starting with the special case of electric
charge, where we have well-behaved ammeters to measure the current,
and generalizing from there.

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