Re: Speed and mass


Tom Roberts wrote:
David.Paterson@xxxxxxxx wrote:
Over in a different science discussion forum:
http://www2b.abc.net.au/science/k2/stn/
http://www2b.abc.net.au/science/k2/stn/newposts/2309/topic2309840.shtm
there is a long term disagreement over whether the increase of mass
with speed is a real or virtual effect.

This argument is primarily a difference in the usage of words.


I'd like to know if this
disagreement is a real one, or whether it's just a different
interpretation of the same mathematical equations. The two views are:
A) Mass increases with speed and this increase is given by the equation
m=m_0/sqrt(1-v^2/c^2).

Most physicists today, when they say "mass" without qualifier, mean the
invariant mass of an object. So we say the mass of an electron is 511
keV/c^2, and do not need to specify any speed for which it is valid,
because this is invariant. This choice for the use of the word "mass" is
primarily motivated by connection to its original meaning of "amount of
stuff", which _clearly_ must be invariant for a given object (looking at
an object from a different reference frame cannot possibly change the
object itself).

And even this motivating meaning is soon found to be outmoded, because
the invariant mass of a *system* of particles is not (surprise!) the
sum of the invariant masses of the particles in the system. That is,
the invariant mass of a system does not necessarily represent the
amount of "stuff" present, which we intuit to be additive. The
invariant mass of two colliding electrons, for example, is frequently
seen to be several thousand times larger than 2 x 511 keV/c^2.

The anachronism "relativistic mass" to which the OP refers is also
motivated by a classical meaning of mass: the m that appears in F=ma.
To account for the fact that "a" drops lower than proportion with F
would indicate, a rise in "m" was suggested, but that is purely based
on trying to make the old physics connect with the new.

It's in fact interesting, and many physicists have worried about this
over the last century, that there is no persistent concept for what
mass *is* anymore, other than an operational definition by virtue of
invariance.


For a massive object this is the same as its rest mass, which you
notated as m_0 above (most physicists notate it simply as m). Your m
above is normally called "relativistic mass"; it is really an
anachronism, and it does not appear explicitly in any modern theory of
physics; the invariant mass appears in many places in every modern
theory of physics.



.

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