Re: [Phys-l] Invariant mass and relativist mass...

[John Denker <jsd@av8n.com>]

On 02/26/2008 05:06 PM, LaMontagne, Bob wrote:
> I am still having a problem understanding why the gamma factor would
> be applied to the mass 

That's a good question.  I sympathize.

> at the introductory level. 

Or at any other level.

> If students are at
> the F=ma level, then the "m" that gives the reistance to acceleration
> is really m0/(1-v^2/c^2)^(3/2), as I had noted in another posting.

We certainly agree about the presence of a gamma^3 factor.
But why attach it to the mass?  It would be better to attach 
it to the acceleration, or leave it unattached.  Gamma is 
basically d(t)/d(tau) ... and the 3-acceleration is where all 
the t factors are.

> The gamma factor is actually not the factor that gives the increased
> resistance to acceleration - so why use it?

I don't use it!  (Not for that purpose, anyway.)

Factors of gamma are needed when converting from a 4-velocity
to a 3-velocity, because the former is defined in terms of
d/d(tau) while the latter is conventionally defined in terms
of d/d(t).

It's got nothing to do with mass, inertia, or momentum.  It's
all about projecting from one reference frame to another.  
The rule is:  relativity is just the geometry and trigonometry
of spacetime.

The gamma^3 factor is worked out in some detail, from a modern
(post-1908) spacetime point of view, at
  http://www.av8n.com/physics/spacetime-acceleration.htm

The factor of gamma^3 is derived without ever mentioning mass.
It's got nothing to do with mass.