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

On Saturday, October 3, 2015 2:14 PM, John Denker <jsd@av8n.com> wrote:




On 10/03/2015 08:50 AM, Moses Fayngold wrote:

It is important to note that condition of being at rest in the
system's CM is not enough to determine its rest energy.

Actually it's not important.  Being at rest relative to the
CM(*) is /more/ than enough.
This statement is 1) Not supported by any argument and 2) Generally wrong. My specific example showed the two cases of stationary e and p in an e-p pair, but at different separations, and the rest energies of the system in these two cases are accordingly different. These clear examples have not been refuted.   

If the parts of the system interact with one another, then the
distance between them is very important.

No, it's not important.  Re-arranging the energy and momentum
/within/ the system has no effect on the [energy,momentum]
4-vector of the system as a whole, and therefore no effect
on the mass.  The proof of this is about three lines long.
1) Assert that [E,p] is conserved.
2) Assert that the dot product is a Lorentz invariant.
3) Therefore system mass is constant (for any closed system)
 >and Lorentz invariant.
All this by itself is absolutely correct, but wrongly addressed. It relates to one closed system, whereas in my example we have two different systems, [E1, p1] and [E2, p2]. One of them [E1, 0] is a pair of stationary e and p at large separation, and the other [E2, 0] is prepared from the first one by making e and p approach each other infinitely slow, absorbing the released energy and transferring it to outside of the system (this is what I called the "adiabatic contraction"). The resulting system, albeit containing the same particles, is physically different from the initial one, with E2<<E1. 

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.

The field energy is part of the system energy.
True, but it only confirms what I had said. 

By bringing them close together while still keeping them at rest
(call this process "adiabatic contraction") we can make their net EM
field negligible.

That process requires transferring energy across the boundary
of the system,
Yes!
or storing energy in some as-yet-unmentioned
part of the system.  
This is NOT what I meant by "adiabatic process".
Either way, looking at the pair does not
account for all of the /system/ energy.
Just looking - does not, but measuring the system with known physical properties does. 

To repeat:  In /any/ frame (not just the rest frame) you can
calculate -p•u, where p is the 4-momentum and u is the 4-velocity
of the center of mass(*) of the system.  I claim that -p•u is the
rest energy of the system.  In the rest frame this is obvious,
since we know the components of u in that frame.  If you choose
some other frame -- or no frame at all -- it may be less obvious,
but it is no less true:  -p•u is the rest energy.
I am happy to agree with this concluding statement.

Moses Fayngold,NJIT
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