home *** CD-ROM | disk | FTP | other *** search
- Path: sparky!uunet!ogicse!das-news.harvard.edu!husc-news.harvard.edu!husc8!mcirvin
- From: mcirvin@husc8.harvard.edu (Mcirvin)
- Newsgroups: sci.physics
- Subject: Re: Converting the masses
- Message-ID: <mcirvin.712113680@husc8>
- Date: 26 Jul 92 01:21:20 GMT
- Article-I.D.: husc8.mcirvin.712113680
- References: <9868@sun13.scri.fsu.edu> <1992Jul22.193837.18095@sfu.ca> <131163@lll-winken.LLNL.GOV> <1992Jul25.194550.1970@smsc.sony.com>
- Lines: 115
- Nntp-Posting-Host: husc8.harvard.edu
-
- markc@smsc.sony.com (Mark Corscadden) writes:
-
- >No! Here's a statement of my position that relativistic mass can't be
- >dispensed with when dealing with the mass of macroscopic objects (looking
- >again to spare helpless straw men from beatings):
-
- > 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.
-
- In order to spare straw personnel further injury, let me state that
- the relativistic mass is obtained in this manner not from F = ma,
- but from F = dp/dt and p = mv. I'm sure you know this, though.
- This has no real bearing on the rest of your statements, except
- for the additional caveat that to get the rest mass this way,
- you have to define quantities in the object's rest frame.
-
- [a bit deleted]
- > Yet you can't make this
- > notion of mass work in *full generality* without using
- > the notion of relativistic mass. More precisely, if
- > you reject relativistic mass then the amount of mass
- > you have on hand is subjective and completely dependent
- > upon how you think the objects on hand should be viewed.
-
- This is quite true. Mass is no longer a substance you have in various
- amounts; you can only define it for a system, having first drawn a
- boundary around the system, so to speak. This seems to be the
- primary thing that bothers you and Leigh, and it's made most
- apparent in the situation with the cannonballs in the box.
-
- I don't think that this is that much of a problem, though. Consider
- an analogous situation with three-dimensional vectors. Suppose you
- have a complicated system with a lot of particles flying around.
- The particles are peculiar in that they are constrained to fly at
- a constant speed: the magnitudes of their momenta are always
- constant, and this magnitude depends in a simple way on the type
- of particle. You would agree with me (since you like the use of
- mass to mean rest mass in particle physics) that this magnitude would
- be more worthy of a special name than, say, the x-component of
- momentum. Let us borrow a word from R. P. Feynman and call it
- "wakalixes."
-
- Now look at the whole collection of flying particles. How
- much wakalixes is there? You'll get much more if you add
- up the magnitudes of individual momenta than if you find the magnitude
- of the momentum of the whole system. For a situation in which the
- boundaries of the system under consideration are unclear, the magnitude
- of the momentum is ill-defined. The x-component of momentum, on the
- other hand, can be treated as a local density that adds quite nicely,
- and the dependence on the boundaries of the system is very simple.
-
- This doesn't mean that we have to take the word "wakalixes" and
- suddenly apply it to the x-component of momentum when we deal
- with macroscopic objects. The wakalixes as defined previously is
- quite permanent as long as we don't let momentum flow into or
- out of the system, and, furthermore, it's rotationally invariant,
- which the x-component is not.
-
- Even in the real world, of course, we don't seem to have much
- trouble dealing with the magnitude of a macroscopic system's
- momentum, even though the system may consist of Avogadro's number
- of moving parts. It's dependent on how you group objects together
- into systems, but it's a useful quantity, and more significant than
- any one component taken alone.
-
- Now, this is, of course, a terribly unfair parable, not because
- of the ridiculous nature of the assumptions, but because I haven't
- taken into account the fact that in our everyday lives we are almost
- always dealing with reference frames very, very close to each other.
- The real analogy would be with a world like the one described above
- in which, in addition, momenta usually pointed in the x direction with
- a maximum deviation of a thousandth of a degree.
-
- However, special relativity was formulated to deal with situations
- far from the everyday norm, and in my imaginary world the equivalent
- theory would deal with how things look like when things go in radical
- and strange directions far from the x-axis. If the full theory possesses
- rotational symmetry, when teaching it to students you shouldn't give
- them the idea that the symmetry goes away in the macroscopic limit.
-
- I must also repeat Leigh's reminder that this argument is about
- words and pedagogy, not physics. I'm increasingly of the idea that
- we should at least mention both definitions to students, so that
- they know what various people are talking about, but work
- primarily in terms of mass = rest mass. To understand how the two
- definitions differ is to understand a lot about special relativity.
- It's okay to add lots of details as long as you make them as
- coherent and consistent as possible: more data makes it easier
- to detect a pattern.
-
- As for the cannonball situation, I don't see any trouble as long as
- the experimenter is properly acquainted with special relativity.
- Measure the rest masses of all the parts of the system by the
- usual procedure (being sure to put yourself in the rest frame of
- each flying object first); then find the total 4-momentum of the
- system, since you know the relative speeds (after all, you needed
- to catch up with the flying cannonballs to do the measurements!),
- then use the fact that the mass of the whole system is the invariant
- length of this 4-vector. It sounds quite indirect, but it can be
- found without using the idea of relativistic mass. You might say
- that the relativistic mass is one component of the 4-momentum, but
- I didn't have to think of it that way.
-
- (Also, remember that you have to be careful when tugging on the
- sealed box to measure the mass initially: how the box accelerates
- is not necessarily how the system of box plus cannonballs accelerates,
- unless you measure average acceleration over a large enough time that
- the cannonballs can bounce around many times! This simple-seeming
- operational definition can have pitfalls of its own.)
-
- --
- Matt McIrvin mcirvin@husc.harvard.edu
-