Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site brl-tgr.ARPA Path: utzoo!watmath!clyde!bonnie!akgua!whuxlm!harpo!decvax!ucbvax!ucdavis!lll-crg!seismo!brl-tgr!gwyn From: gwyn@brl-tgr.ARPA (Doug Gwyn ) Newsgroups: net.physics Subject: Re: Definition of mass in relativistic mechanics Message-ID: <1997@brl-tgr.ARPA> Date: Tue, 8-Oct-85 20:04:54 EDT Article-I.D.: brl-tgr.1997 Posted: Tue Oct 8 20:04:54 1985 Date-Received: Sat, 12-Oct-85 19:20:35 EDT References: <576@bonnie.UUCP> Organization: Ballistic Research Lab Lines: 52 > I have a question about semantics. The concept of mass in > relativity is substantially different from the Newtonian view. Yet, for > convenience, the word has been kept. Most texts (even recent ones) > and all the early papers use the result (definition): > > mass = gamma * (rest mass). > > This is consistent with keeping the Newtonian formula for momentum. Right. > Most of the professional physicists that I know, do not use the > word "mass" according to the above definition, but use it to mean "rest > mass". The preferred usage seems to be to redefine momentum: > > momentum = gamma * mass * velocity. > > Where mass is understood to be "rest mass". Of course, the same goes > for energy: > E=m*c**2 -> E=gamma*m*c**2. Of course this is physically equivalent to the other approach. > I would like to hear opinions about: > What usage is more common? Both. Most considerations of "mass" occur in cases where there is no difference in numerical value, since the matter is (nearly) stationary. > Are there good reasons for preferring one definition over the other? Yes. Rest mass is invariant with respect to motion, whereas gamma-mass is dependent on the state of motion (coordinate system). Momentum and energy together form a 4-vector, which has a (generalized) invariant meaning independent of coordinate system. So rest mass, momentum, and energy all name physically meaningful characteristics whereas gamma-mass refers to something with an inherent dependence on convention (or, on "the observer"). Physics largely consists of looking for invariant relationships among properties independent of any observer. Gamma-mass is not a useful property for this endeavor. Any attempt to express gamma-mass in an invariant manner leads to just using rest mass anyway. > What exactly is the role of "inertia" in relativistic mechanics? I don't think "inertia" has a formal technical meaning. It could be taken to be just what "mass" measures, which doesn't get one anywhere. An "inertial frame" is a set of space-time coordinates in which the "law of inertia" (Newton's first law) appears to hold; laws of physics look somewhat simpler in such coordinate systems. Attempting to generalize physical laws to hold in (nearly) arbitrary coordinate systems leads into the realm of general relativity and unified field theory.