Re: [Phys-l] momentum first and relativistic mass

[Rick Tarara <rtarara@saintmarys.edu>]

Let me try and make my point clearer.  What I'm suggesting is not denying or 
ignoring the 4-space/Minkowski/Denker approach, but rather trying to justify 
an introductory approach that deals with slow clocks, compressed lengths, 
and increased mass BECAUSE as 3-dimensional beings living in linear time 
(unlike the wormhole aliens of DS-9 ;-) our experiences--or at least our 
extrapolations to what we think we would experience tend to fit those ideas. 
Thus, a first pass through SR with slow clocks etc. seems more reasonable to 
me than immediately jumping into a more mathematical approach.

Rick

----- Original Message ----- 
From: "Alfredo Louro" <louro.alfredo@gmail.com>
> Four-momentum is m dr / d tau, where tau is the proper time, and dr is
> a displacement in space time [dt, dx, dy, dz]. Thus the time component
> is gamma m, and each of the spatial components is gamma m v_{x,y,z}.
> The gamma doesn't appear because the mass is variable, but because
> ordinary time is not invariant. You can also define a four-force as
> dp/d tau.
>
> I think a good approach is to think that nature doesn't know about
> different reference frames. So we expect any natural laws that arise
> to refer to invariant quantities. There is an invariant mass.
>
> Another thing worth considering is that while you can recover the
> familiar newtonian mechanics in the limit v << c, you can't really
> extrapolate in the other direction.
>
> Alfredo