Astner
The Ghost Who Walks
Originally posted by Magnon
That is the old convention in SR but not the modern usage, as I said in my post.
I'll denote the rest mass m₀ for clarity.
What you said was "speed doesn't increase mass," which is wrong. Your argument was that in the expression E² = p²c² + m₀²c⁴, m₀ does refer to the rest mass (and is therefore not relative), implying that this expression is not a function of relativistic mass. The problem is that p = mv = m₀γv.
And from the above expression if follows that m = m₀γ, and since γ is a function of v, so is m.
Originally posted by Magnon
These days the term [B]mass, with the symbol m, simply refers to invariant mass. This quantity can be conveniently measured in the rest frame of the particle as its "rest mass", but the same mass (apart from a conversion constant) is obtained in any inertial frame by calculating the four-length i.e. the Minkowski norm of the particle's four-momentum vector. Thus, the mass is invariant by definition.[/b]
"If you define the mass as the rest mass then it's velocity-invariant." Yeah. But it's disingenuous and misleading, because the actual mass does increase.
Granted, a particle's relativistic mass is rarely talked about (normally it's addressed it in terms of energy), but a particle's mass does increase with its velocity. It's clear from the expression above that it has to. How you decide to interpret this increase in mass doesn't really matter, there is and increase, and saying that there isn't is wrong.
Originally posted by Magnon
The frame-dependent quantity is simply the [B]energy, i.e. the quantity E on the left-hand-side of the eqn in my previous post. There's not much value in introducing synonyms for this quantity; however, when the energy is expressed in mass units the term "relativistic mass" can be used for it. It's then important to include the word "relativistic" so that the reader doesn't confuse it with mass m (which is an invariant).[/B]
Are you trying to pass off your claim "speed doesn't increase mass," as "speed doesn't increase rest mass?" Because that's like saying "movement doesn't affect my position" to then clarify "position" refers to your "starting position."