emh@bonnie.UUCP (Ed Hummel) (10/06/85)
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. 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. I would like to hear opinions about: What usage is more common? Are there good reasons for preferring one definition over the other? What exactly is the role of "inertia" in relativistic mechanics? ------------------- Ed Hummel
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (10/09/85)
> 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.
jheimann@BBNCC5.ARPA (10/09/85)
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emh@bonnie.UUCP (Ed Hummel) (10/14/85)
>> 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. >> 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. > They are mathematically equivalent. The question is about "semantics". >> 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. > I obviously was referring to usage in the context of relativistic mechanics. Particle and nuclear physicists as well as cosmologists and astronomers often use mass in situations were gamma is reasonably larger than one. Do any of them ever mean the traditional definition of gamma*(rest mass)? >> 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 If this is such a good reason then why did the founding fathers of relativity, (who were very aware of the invariance of the magnitude of the 4-momentum) insist upon using the mass=gamma*(rest mass) definition? >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. Take temperature, for example. It is a well defined concept. It is not an invariant. Why should there be a confusion regarding the definition of "mass"? >> 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. Defining inertia as "what mass measures" is obviously circular. Using the definition of inertia as "a property of matter such that a body at rest tends to remain at rest and a body in motion tends etc...." seems formal enough. Certainly physicists have an understanding of what is meant by inertia. I am asking for viewpoints about the role of inertia in relativistic mechanics. At one time Einstein thought the relativity of inertia was so important a notion that he listed it (in the form of Mach's principle) on equal footing with the principle of equivalence as a requirement for any good theory of gravitation. [Annalen der Physik 55,241(1918); Naturw. 8,1010(1920); and Annalen der Physik 69,436(1922)] >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. > > Doug Gwyn What do General Relativity and "unified field theories" tell us about the role of inertia? Tell me more. ---------------------------------------------------- I can give you a long list of Physics textbooks copyrighted in the last ten years which define mass as gamma*(rest mass). It seems to be the "official" definition of mass in the relativistic context. Ask a physicist why matter can't be accelerated beyond the speed of light? Most will tell you that mass increases with velocity and it becomes "infinite" at the speed of light, etc. Then why do particle physicists (and others) say mass to mean "rest mass". Is it just sloppy usage? I think not. Is it past time for a redefinition? -------------- Ed Hummel
sra@oddjob.UUCP (Scott R. Anderson) (10/14/85)
In article <581@bonnie.UUCP> emh@bonnie.UUCP (Ed Hummel) writes: > > 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. > 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". Given the first definition, this is *not* a redefinition of momentum, just of the term 'mass'. Momentum is the important quantity here, as it is the momentum which changes with the application of an external force. > Of course, the same goes for energy: > E=m*c**2 -> E=gamma*m*c**2. > I would like to hear opinions about: > What usage is more common? > Are there good reasons for preferring one definition over the other? It all depends on the situation in which it is being used. In the study of relativity, it is sometimes useful to consider the properties of a relativistic particle in your (rest) frame of reference. The noticeable property here is that the particle becomes more difficult to accelerate as its speed increases. In this case, it is useful to think of the 'mass' as gamma * (rest mass), because this fits in with our Newtonian idea that a more massive particle is harder to accelerate. This is therefore the way that relativity is usually taught, to base it in one's previous training in classical mechanics. However, particle physicists by necessity work with *two* frames of reference on a regular basis, the 'lab' frame and the 'center of momentum' frame. The latter is considerably easier to work with since the total momentum is zero, but it is necessary to work with the former because that is where the experiments take place. PP's are therefore constantly shifting back and forth between these two frames. It is therefore most useful to work with invariant quantities, in particular the four-momentum, (E, px, py, pz). The square of the rest mass is the 'length' of this four-vector, m^2 = E^2 - (px^2 + py^2 + pz^2) and is therefore also an invariant under the Lorentz transformation. One other thing to keep in mind is that, because c is an invariant, the energy E = gamma * m * c^2 is equivalent to the non-invariant mass "gamma * m". Why use two names for the same thing? Besides, if you use the right set of units, c = 1, there is no difference at all! :-). >Take temperature, for example. It is a well defined concept. It is >not an invariant. Temperature is essentially the total energy of a system; that is why 'temperatures' in the early universe are quoted in energy units such as TeV. Of course, this is in the CM system of the universe. Scott Anderson ihnp4!oddjob!kaos!sra
gjphw@iham1.UUCP (wyant) (10/14/85)
There certainly has been a shift in emphasis over the last ten years
concerning the use of mass and relativity. When I began graduate school (over
ten years ago), I recall that the standard treatment of mass used the
relativistic mass (gamma * rest mass). By the time I completed school, the
thinking had changed so that rest mass was in more common usage. This shift
is due, in part, to the increased prominence of high energy particle physics
and their way of dealing with concepts of nature.
Concepts change with time and fashion, and tend to follow the most
glamorous fields. Particle physics and its stalking of a unified field theory
(or grand unified field theories) is the glamor area of physics right now.
Like the lower class people imitating the upper class, a lot of physics has
adopted the mannerisms and formalisms of particle physics. While the energy-
momentum four-vector and the invariance of the rest mass were known to the
ancients (or at least the founding fathers of relativity (what, no mothers?)),
it was the relativity and not the invariants that were stressed.
Einstein claimed that his General Theory supported E. Mach's concept for
the origin of inertia (gravitational interaction between a body and the whole
universe), but there are differences between Mach's inertia and Einstein's
inertia. A recent experiment performed by someone at the National Bureau of
Standards seems to uphold Einstein's inertia as formulated in GR and not
support Mach's inertia. Oh well...
Patrick Wyant
AT&T Bell Laboratories (Naperville, IL)
*!ihwld!gjphw