🚀 go-pugleaf

In article <1992Jul25.194550.1970@smsc.sony.com> markc@smsc.sony.com (Mark Corscadden) writes:

> 	It's perfectly reasonable to talk about the mass of a
> 	macroscopic object.  The inertial mass of the object
> 	can be operationally defined in terms of the force
> 	that has to be applied to the object to produce a given
> 	rate of acceleration.  Methods exist which allow you to
> 	measure the mass of an object, so defined, with great
> 	precision.

This is true: in Newtonian mechanics, the acceleration of an object is
proportional to the force applied on it, and the constant of
proportionality is its mass.  That is,
		\vec{F} = m \vec{a}.  				    (1)
Sorry about the TeX notation, but it really is necessary for the point
I wish to make, which is that this is a vectorial equation: the 
acceleration really is proportional to the force, because it is in the
same direction.

This is a Newtonian equation, however, and it is not valid for a
relativistic object, no matter how "m" is defined.  For a relativistic
body, the force and the acceleration are *not* proportional.  The
acceleration is not in the same direction as the force.  In other
words: there is no such thing as an inertial mass in relativistic
physics, so there is no point in trying to define "mass" so as to
preserve this Newtonian concept.  (Note that the "m" in Eq. (1) is
numerically equal to the "rest mass" and to the "relativistic mass";
for a nonrelativistic system, the two are equal.)

As I said earlier, this fact was known even before Einstein; folks
used to talk about two different "inertial masses," one for forces
parallel to an object's velocity, and one for forces perpendicular to
it.  They gave up this particular silliness rather quickly, though,
and just decided that Eq. (1) did not apply to relativistic systems.


--
Matthew Austern              I dreamt I was being followed by a roving band of
(510) 644-2618               of young Republicans, all wearing the same suit,
matt@physics.berkeley.edu    taunting me and shouting, "Politically correct
austern@theorm.lbl.gov       multiculturist scum!"... They were going to make
austern@lbl.bitnet	     me kiss Jesse Helms's picture when I woke up.