On Fri, 26 Nov 2010 10:53:41 -0800, hanson wrote:

"PD" wrote:
"hanson" wrote: snip.
Paul "PD" snip

"hanson" wrote:
PD, kindly clarify, delineate, describe, IOW, do teach,
IYOW, what mass is, fundamentally, so that neutrino
oscillations can be explained without you resorting to
abstract terms, such as "flavor" like you did below.
TIA, hanson
snip

Pau wrote:
OK.
Mass has had its meaning refined, especially over the
last 100 years or so.
What it means now is the frame-independent quantity
of a physical system (where a physical system is a
collection of physical things, possibly interacting with
each other) that can be calculated from measured
energy and measured momentum:
(mass) = sqrt ((Sum (energies))^2 - (Sum (momentum))^2).
The fact that it is invariant regardless of inertial reference
frame is what makes it interesting.
For a closed physical system -- one where no net interaction
crosses the boundary -- the fact that the mass is also conserved
is also what makes it interesting. This conservation means that
it will have the same value in a closed system, no matter what
happens INSIDE the system. Conserved quantities always
point to some fundamental law of symmetry in nature.

There is the tendency to ask,
"But what IS it, other than a quantity?"
This is a misplaced question, because some quantities are
interesting in their own right in physics, because they exhibit
frame-independence and conservation. They don't have to have
another "explanation" other than these circumstances.

What we also know is that mass is not what we once thought
it was, though it is close. For example, we once thought mass
was a measure of "the amount of stuff". This rule doesn't work,
though, because mass isn't additive -- you can't get the mass
of a system by adding the masses of the parts of the system.
We once thought that mass was a measure of the *inertia* of
an object, where that is the ratio of the force applied to the
acceleration observed. That rule doesn't work either though,
because there is a velocity-dependent factor missing in that
relationship (which just happened to be close to 1 for most of
the everyday examples we looked at). Since these previous
qualitative descriptions have fallen short, we now just talk
about it as a quantity with the observed frame-independence
and conservation behaviors -- which is about the same as what
we do with a number of other properties like electric charge.

hanson wrote:
THANK YOU, Paul. Let me fine-comb thru it for a while & then
tell you how it came across to me and what I perceived you
have meant to tell me, from my pov. I appreciated it, Paul.
I'll be back. hanson


Paul wrote:
snip


I think this will be helpful for me in understanding concept, but I
stumbled over this:

(mass) = sqrt ((Sum (energies))^2 - (Sum (momentum))^2).

It seems to need factors of 'c' for consistency in conventional units:

(mass) = sqrt ((Sum (energies))^2 - (Sum (momentum * c))^2) / c.