Tom Mattson said:
What--exactly--is wrong with pmb's post? I know that he's not adhering to the preferred convention of defining mass as the norm of the 4-momentum. But that's all it is: a convention. Conventions aren't "proven wrong". They are simply adopted or rejected based on their usefulness or lack thereof.
dw knows, as
fact, that nothing is wrong with my post. However I'd
love to see him directly answer your question. If dw does post a direct response (rather than simply repeat his claim again) please let me know. Thanks.
Reflector - Since I don't know you all that well and don't know if you're familiar with this whole debate thing on the term
mass in relativity let me explain. This is one of those things that people in the relativity community have debated for many decades. That there topic is hotly debated can be seen in the physics literature such as
Physics today,
The American Journal of Physics (other physics journals, referances given upon request,
Concepts in Mass in Contemporary Physics and Philosophy etc. The plain fact of the matter, Reflector, is that the concept is still used and to understand much of the physics literature on several points, you must know this fact.
One case that comes to mind is a book a friend of mine just sent me to read during my convalescence. The author is the author of one of the most widely used GR texts that exists today and that is used to teach GR. The name of this new (Pub. 2003) is
Gravity: From the Ground Up, by Bernard Schutz, Cambridge University Press (2003). On pages 187 he lists what he calls
...the most important consequences of special relativity. They are
(1) Nothing can travel faster than light.
(2) Light cannot be made to stand still.
(3) Clocks run slower when thery move.
(4) The length of an object contracts along the direction of its motion.
(5) There is no universal definitioin of time and simultaneity.
(6)
The mass of an object increases with its speed.
(7) Energy is equivalent to mass.
(8) Photons have zero rest mass.
(9) The Doppler redshift formula changes slightly.
Most of my relativity texts speak of mass in this way in some place or another in the text. And that includes texts published on or after 1994, of which there are 9. 3 of them use the concept throughoput the text. Some (Like Schutz's GR text) will say what I say, i.e. that inertial mass (aka relativistic mass) depends on speed while rest mass (an invariant) does not. The others don't use the concept at all, of which there are 4. I have 8 relativity texts published before 1994 and of them 2 do not use the mass = inertial mass (aka relativistic mass) definition.
For a complete discourse on the concept of mass in relativity please go to
www.geocities.com/physics_world and click on the link labeled
On the concept of mass in relativity.
Tom -
m0 = Proper mass/invariant mass/rest mass is not
defined as the magnitude of 4-momentum
P. It is a
related to 4-momentum, as you indicated, through,
(m_{0}c)^2 = \bold g(\bold P, \bold P) = \bold P \bullet \bold P
where
g is the metric tensor. If you try to define proper mass in that way then you'd have a circular definition. Proper mass is an
implicitly defined such that the quantity
m0 P where
P is 4-momentum, is a conserved quantity (for free particles which interact only through contact forces). For a precise definition see Eq. (37) in the paper I mentioned to Reflector above (I use mu for proper mass in that article since I think that's the best letter for it since I think proper quantities should be greek letters, like tau for proper time etc).
Pete
