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

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of Moses
Fayngold
Sent: Saturday, October 03, 2015 11:50 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] foundations of physics: Galilean relativity

On Thursday, October 1, 2015 1:04 PM, Jeffrey Schnick
<JSchnick@Anselm.Edu> wrote (quoted in italics):



 "...  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..."

  It is important to note that condition of being at rest in the system's CM is
not enough to determine its rest energy. If the parts of the system interact
with one another, then the distance between them is very important. An
electron (positron) energy can be considered as stored in its EM field. The
field energy of e-p pair is much greater when the members of the pair are
widely separated than when brought to rest close together.  An electron and
positron both at rest in their CM frame will have net energy close to E=2mc^2
only when they are far away from each other. By bringing them close
together while still keeping them at rest (call this process "adiabatic
contraction") we can make their net EM field negligible. It will be the electric
field of a dipole d=qs with vanishing separation s . The initial energy of the
system is pumped out of the box in such process. Now, if they annihilate, the
rest energy of the resulting photon pair will be E<< 2mc^2. It may be a pair of
IR photons instead of the gamma-photons.  As we know, generally the parts
of the system do not need to be at rest for the system to have rest energy.
Neither of the photons in the previous example is at rest, but their system
has rest energy and non-zero rest mass. "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."
  The CM of the system cannot be fixed (stationary) in the field of gravity. As
Jeffrey says quite correctly, it is accelerating towards the center of the planet
before annihilation, but then it cannot be at rest relative to the planet.

By at rest here, I meant having zero velocity at time 0.

And
this fall must continue after the annihilation as well! And it is precisely the
gravitational deflection that takes care of the continuity of the process, so we
cannot say that the CM will remain "essentially fixed" if it was initially falling.
  "Two years later, the center of mass is still at the initial position of the
electron-positron pair." If we track the trajectories of both photons, we will
see that two years later their CM is far away from its initial position.

Good point. Thanks. I picked too long a time. I estimate that for a planet like Mercury, after 10 seconds, the positronium would fall about about 185 meters below the drop point whereas the center of mass of the two-photon system would fall about .6 meters. I don't know how to do the calculation using general relativity so I used double a classical estimate. After 2 years it will have dropped on the order of the radius of the planet.

  "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". This is a very good
argument, and I agree with it 100%! But the drawn conclusion below does
not make sense to me:
"These two contributions to the total mass of the system are not the masses
of the photons, they cannot be, the photons are massless."
This again raises the question: If each photon is really "massless", where the
non-zero rest mass of their composite system comes from? From their
individual energies Ei? So it is legal to write M=(2Ei)/c^2, but illegal to
write M=2mi with mi=Ei/c^2 (the photon's relativistic mass)? None of the
known "explanations" why it is illegal sounds reasonable. The frequently
exploited word "modern" is not a physical explanation. Not everything
modern is good.


Is it really illegal, or is it just a different model with slightly different terminology?


"...the system mass at the location of the photon is not the mass of any
particle, the photon is massless."
So the system does have mass at the location of each photon, after all?
Again, I agree with this 100%. But if it is not the mass of any particle, then
mass of what is it?

I think of it as mass of the two-photon system. So, for the case of two non-interacting massive particles, each having the same mass, moving away from each other, as viewed in the center of mass frame of the system, the mass of the system is greater than the sum of the masses of the particles. I think of the mass of one of the particles as being the norm of the four momentum of that particle. The time-like component E of the four momentum of one of the particles is its mass m plus the kinetic energy K associated with the particle's motion through space. The mass is an inherent property of the particle but since one can change the kinetic energy of the particle just by changing one's reference frame, that seems to have more to do with the interplay between space and the particle so it is not an inherent characteristic of the particle. The mass of the system of two particles is the norm of the four momentum of the total system. Since we are viewing it in the rest frame of the system, this is just (2E,0,0,0) so the norm is 2E which is the sum of the rest masses of the particles plus the sum of the kinetic energies associated with the motion of the particles through space.

Moses Fayngold,NJIT

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