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

[John Denker <jsd@av8n.com>]

On 10/01/2015 02:43 PM, Jeffrey Schnick wrote:
> 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?       [1]

Yes.

>   It
> suggests that the amount of mass in a region of space depends on how
> you visualize it.           [2]

Let me suggest a less alarming way of saying the same thing:  The
mass of any system, subsystem, or parcel depends on where you draw
the boundaries thereof.             [3]

    (You don't even need boundaries, if you have some other way 
    of identifying what's included and what's not, but let's 
    stick with the language of boundaries for now.)

Proposition [3] has got nothing to do with subjective "visualization".
Once the boundaries are drawn, everybody agrees how much mass there
is within each parcel.  This proposition seems completely prosaic, 
completely unsurprising.

Proposition [1] is not so prosaic, because the masses don't add up
the way your high-school chemistry teacher said they should.  We
can summarize this by saying things like:
  -- mass is not additive
  -- mass is not an extensive quantity

> This seems more profound than a lack of conservation of mass.

An excellent point!  Non-extensive is different from non-conserved.

By way of contrast:  Let's consider heat flow in a region where 
some heat is being produced, perhaps by a tiny radioactive seed.
The heat is still extensive.  It can be described by a continuity
equation /with a source term/.  (This stands in contrast to a
conserved quantity, where source/sink terms are absent from the
continuity equation.)

* Some things are extensive but not conserved, e.g. heat as discussed above.

* Some things are neither extensive nor conserved, e.g. mass.

* Lots of things conserved and also (to a good approximation) extensive.

* Some things are conserved but not extensive, e.g. the energy of a 
 not-too-large crystal.  If you cleave it into tiny pieces you increase
 the surface area.  There is energy per unit area due to broken and/or 
 reconstructed bonds.