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

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of John
> Denker
> Sent: Wednesday, September 30, 2015 4:36 PM
> To: Phys-L@Phys-L.org
> Subject: Re: [Phys-L] foundations of physics: Galilean relativity, including KE
>
> On 09/30/2015 12:48 PM, Jeffrey Schnick wrote:
> > Can we agree that the total internal energy of a system is the mass of
> > that system?
>
> I agree with the intended meaning, I agree with the physics idea ... but the
> terminology is tricky.

That's a good way of putting it.  Thanks for going with the intended meaning.  By /system/ I mean what the engineers call a control mass rather than a control volume; a collection of entities rather than a closed region of the universe.

My thinking is that for any system A, in any inertial reference frame, there is a system B having a three-momentum that is the negative of that of system A.  So, for system C, consisting of both A and B, in that inertial reference frame, the total energy of system C is the mass of system C and it is the internal energy of system A + the internal energy of system B + the kinetic energy associated with the motion of the center of mass of system A + the kinetic energy associated with the motion of the center of mass of system B + the potential energy associated with any interactions that might be taking place between systems A and B.  In other words all the energy of system A contributes to the mass of system C, hence, all the energy of system A is mass.  The kinetic energy associated with the motion of the center of mass of system A makes no contribution to the mass of system A so it is not energy of system A, rather, it is energy of system C.

I don't think it is important to identify and specify systems B or C any more than one has to specify which oxygen molecules in the atmosphere are going to combine with the carbon atoms in the oil when one states that the thermal energy resulting from the burning of the oil was not contained in the oil itself but is rather the energy of the fuel plus oxygen system.




> It might be safer to say the /rest energy/ is equal to the mass of the system,
> in the appropriate units.
> That's pretty much a direct translation of Einstein's equation into words.
>
> 	E_0 = m c^2
>
> I suggest calling the LHS the /rest energy/ because thermodynamics books
> have various definitions of "internal energy" that you probably wouldn't be
> very happy with.
>
> Also I suggest writing Einstein's equation with a subscript zero on the E, to
> remind people it's just one piece of the energy.
>
> The idea of /rest/ energy refers to the CM of the system being at rest.  If you
> have a spinning flywheel, or thermal phonons in a solid, the KE of the
> excitations /relative to the CM/ is part of the system's rest energy and
> contributes to the mass of the system.
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