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





-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of John
Denker
Sent: Wednesday, September 30, 2015 7:09 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] foundations of physics: Galilean relativity, including KE

CUT

hence, all the energy of system A is mass.

Here I should have said, both the internal energy of A and the energy associated with the motion of the center of mass of A are mass (they both contribute to the mass of C). I should have phrased it that way because the energy associated with the motion of the center of mass of A is not energy of A but rather energy of C. I do not think this would have changed your response.


Does not follow!

Here's an industrial-strength counterexample, where *none* of the energy
of system A is mass:
http://www.av8n.com/physics/spacetime-welcome.htm#sec-invariance-conservation

As mentioned earlier, I have been thinking in terms of a control mass system (a set of particles or a set of particles and fields). Your example is expressed in terms of a control volume system (a close region of the universe--the inside of the box). In the control mass system, the two photons are the system, the mass of the system never changes, and for the example you give, the position of the center of mass of the system never changes. 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. I have been thinking about essentially the same example, one discussed earlier in this thread, a control mass system originally consisting of an electron and a positron, each of which is at rest in the systems center of mass frame, as viewed in that center of mass frame. The particles annihilate, the system becomes a pair of photons traveling along one and the same line in opposite directions. If we define a control volume system to be the interior of an imaginary sphere then, if the center of mass of the system is not at the center of the sphere than one photon gets out before the other and by your way of thinking the mass inside the sphere changes from 2q to zero the instant that photon escapes. If we are to discuss local conservation of mass then it isn't sufficient to say that the two-photon system has mass, we need to say where it is.

Suppose the electron-positron system were at the surface of a planet with no atmosphere (and initially at rest relative to the planet). Consider the separation between the two particles to be negligible. With no annihilation the pair falls with the acceleration due to gravity of the planets. If they annihilate while still at rest relative to the planet, and the photons shoot out horizontally, assuming a small planet, the gravitational deflection of the light is miniscule and the center of mass of the system of two particles remains essentially fixed. Two years later, the center of mass is still at the initial position of the electron-positron pair. This tells me the mass of the system of two photons is not at the center of mass of the system. In fact it tells me that it is, for the vast majority of the two-year time interval, the mass is very far from there. Suppose that two years after the annihilation event, they each hit a rock. Each of the two rocks has always been at rest relative in the only frame in this discussion. In each case the photon is absorbed by an atom in the rock--an electron in that atom gets knocked up to a higher atomic energy level. Considering the rocks to be so massive that upon acquiring the momentum of the photon, the velocity of the rock is negligible, the mass of each rock increases by q (where q is the energy associated with the motion of each photon). This tells me that half the mass of the system of two photons is at the location of one of the photons and the other half is at the location of the other photon. These two contributions to the total mass of the system are not the masses of the photons, they cannot be, the photons are massless.

Your example suggests one more way of figuring out where the mass is. While both photons are in the box, we agree that the mass of the two photon system is inside the box. We need to narrow it down some more. Instead of a box, I want to go with a long skinny right circular cylinder with end caps. I'll call it a tube. I'm going to start with the electron-positron pair at rest at the center of the tube. They annihilate and the photons travel along the axis of symmetry of the tube. Right up to the last instant before they go through the end caps, the mass of the control volume system, the interior of the tube, is 2q. Just after they go through, the mass is 0. Consider an ever so slightly longer tube within which the original tube is centered. Just after the photons of the control mass system consisting of the two photons passes through the endcaps of the shorter tube, the mass of the system is outside the shorter tube control volume system but it is inside the longer tube control volume system. In other words, it is right where the photons are. Again, the system mass at the location of the photon is not the mass of any particle, the photon is massless.

In your example that started with a pair of photons in a box, even though you are focusing your attention on a specific closed region of the universe, the control mass system of two photons still exists whether or not either photon is in the box. In your example, when one photon left the box, you correctly stated that it carried zero mass with it because it has zero mass. What you failed to realize is that amount q of system mass slipped out of the box with it. You thought this left 0 mass inside the box because the only thing in the box was a photon and it has zero mass. What you didn't notice was that amount q of system mass was still inside the box. When amount q of system mass left the box along with the first massless photon to leave the box, the amount of mass inside the box decreased by q and the decrease occurred right there where the system mass passed through the boundary between inside the box and outside the box. This means the conservation was local.

Objection: Mass moving at the speed of light!?

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