Re: [Phys-l] velocity-dependent mass (or not)

[John Denker <jsd@av8n.com>]

On 07/02/2009 04:37 AM, carmelo@pacific.net.sg wrote:

> > Did one author make a mistake? Does it matter whether it is a spring
> > balance or a two pan balance? Are both authors wrong by not bringing in
> > general relativity?
>
> It should be worthwhile to consider Wolfgang Rindler's recent  
> textbook, "Relativity: Special, General, and Cosmoslogical". (2006)
>
> In relativity there are good reasons for adopting the second  
> alternatives, though the first can be used as an occasional shortcut:  
> the 'real' location of any part of the energy is no longer a mere  
> convention, since energy (as mass) gravitates; that is, it contributes  
> measurably (in principle) to the curavture of spactetime at its  
> location. (Page 113)


All I can say is don't believe everything you read, in this forum
or in textbooks ... especially when highly selective snippets of
the text are being quoted.

On page 113, Rindler says "Particle physicists ... tend to discard
the notion of relativistic mass altogether.""

On page 156, "It comes as a surprise to most beginners in relativistic 
continuum mechanics that, as we transform away from the rest-frame, we 
do not find the expected relation ρ = γ 2(u)ρ0 between the mass density 
ρ0 in the rest-frame and that, ρ, in the general frame (one γ coming 
from mass increase and one from length contraction)."


To summarize:  We know that rest mass contributes as a source of the
gravitational field, and inetic energy contributes also, but the do *not* 
contribute in the same way.  Despite what you've been told in this thread, 
if you think you can calculate or explain the gravitational field of a 
fast-moving mass using only the so-called "relativistic mass" and pre-1908 
notions of time dilation and length contraction, it's not going to work ... 
it's not even a qualitative first-order approximation.  This should be 
obvious from the example
  http://www.av8n.com/physics/gravity-source.htm

More generally, we have multiple notions of "velocity dependent mass"
including
  mass = inertia = resistance to acceleration left/right, as in circular motion?
  mass = inertia = resistance to acceleration fore/aft, as in straight-line motion?
  mass = rest mass + kinetic energy divided by c^2?
  mass = source term for the gravitational field?

Now it turns out that in general, all four of these are numerically different.

I can understand why people might want to preserve the form of each of Newton's
equations ... but you can't always get what you want.  Redefining mass in N
different ways is a fool's errand.  It (arguably) makes *some* of the equations 
look simpler, but it makes the mass more complicated, so there is no net 
simplification.  In fact, it just makes things more complicated, because as 
previously discussed, many of the key equations e.g. 
  momentum = m d(x)/d(tau)
work just fine in terms of 4-vectors (and the invariant mass m), and are already 
as simple as they could possibly be.  Messing with m is a lose/lose proposition.