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

["Alfredo Louro" <louro.alfredo@gmail.com>]

On Wed, Feb 27, 2008 at 11:53 AM, Rick Tarara <rtarara@saintmarys.edu> wrote:
> OK--here is my question about starting with momentum and force = delta-p/delta-t.
>
>  When asked something like:  "What is the necessary average force needed to stop a 1000 kg car from a speed of 30 m/s in 10 seconds?" aren't you forced to return to p = mv?  Once there, introducing the relativistic observations that the momentum of a given object (an electron for example) is not linear in velocity since both the velocity and momentum can be measured experimentally, isn't there a very strong temptation to look at something going on with the mass?  That is, if one almost always pulls momentum apart into mass and velocity at low speeds, why not at high speeds?

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