Re: [Phys-l] Relativisitic mass vs Invariant mass

[John Denker <jsd@av8n.com>]

Fayngold, Moses wrote:

>   I think anyone who really appreciates elegancy, would admit that 
> it is far more elegant to introduce the concept of relativistic
> mass 

Well, I think I appreciate elegance as much as the next guy,
and I don't admit any such thing.

> ... rather than go through indignities of 
> Eq. (1) and especially (3). 

As the proverb says, no matter what you are doing, you can always
do it wrong.  Equation (3) is the wrong way to do it -- so what?
Multiplying the rest mass by gamma is preposterous for massless
particles -- so what?  As John M. and others have pointed out,
the right way to do it is

   E^2 = (pc)^2 + (mc^2)^2.                            [A]

or, in the form I consider slightly preferable:

   E^2 - (pc)^2 = (mc^2)^2.                            [B]

Anecdote:  I use gamma so rarely that I barely remember the definition.
In contrast, I use the dot-product between 4-vectors all the time.
Equation [B] expresses the invariant gorm of the [energy,momentum]
4-vector.

I have never understood the seemingly idolatrous attachment to E=mc^2.
It looks simple to naive eyes, but alas it is too simple.  There's
a lot you can't do with it.

I posted the following puzzle a couple of years ago.
  http://www.av8n.com/physics/gravity-source.htm
So far nobody on the list has taken the bait.

I would be particularly impressed if somebody could solve this by
computing the mass (m) via "m=E/c^2" and then using that "m" in the
gravitational-force equation.

Let me know if you succeed.  Otherwise I will continue to believe
that "E=mc^2" is not the whole story.