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Re: [Phys-l] Teaching Special Relativity



Rick wrote:


----- Original Message -----
From: "John Mallinckrodt" <ajm@csupomona.edu>

The same cannot be said for "relativistic mass increase," which has
no observational basis. What we observe is that objects moving at
high speed have more momentum than that predicted by Newtonian
mechanics. There are two possible responses to this fact: 1) let the
mass of an object increase with velocity or 2) alter the dependence
of momentum on mass and velocity.

In either case the correction is exceedingly simple and noticeable
only at high velocities. The first response, however, leaves one
with myriad difficult if not unresolvable questions: How does one
actually measure the mass of a rapidly moving object? Where does
the extra "stuff" come from? What about gravitational effects?

The second response sidesteps all of those problems. Why on
Earth would anyone not choose it?

John Mallinckrodt
Cal Poly Pomona

But who chooses it when momentum is introduced?

Who chooses mass to depend on velocity when it is introduced. Something's obviously got to give. Why not let it be the thing that makes the most sense?

I can't think of any text that I've seen that doesn't define momentum as mv.

Really? These days I think relatively few of 'em do ... at least when they finally get around to correcting themselves in "Chapter 32." But by the same token, I can't think of any that suggest that mass might depend on velocity when the concept of mass is first introduced in "Chapter 5." Used to be that they changed their mind about THAT in "Chapter 32." Now most of 'em leave well enough alone.

This is what the intro student (indeed myself) comes to special relativity with. The magnetic field example (again I must say that I've calculated and set the fields for
bending high speed protons using 'relativistic mass' and been quite successful in getting the beam to the target) presents us with a measured velocity but a momentum that has increased non-linearly with that velocity.

Of course. That's what momentum does. And I'll bet that I can set the fields pretty accurately too using the simple fact that the required field is directly proportional to the momentum.

Again, I'm not saying that we should teach relativistic mass to physics majors, but really, how are our gen-ed students, with the hard won idea that momentum is mass x velocity (actually work to convince them that they instinctually have a great feel for this) supposed to deal with the observations. I'm quite willing to use some 'weasel' words--the result is as though the mass has increased--but that is, in my mind, the quickest and easiest way to present the effect of very high velocities in light of the student's knowledge, background, and the level of detail (or lack thereof) that is possible within the framework of the course and the students.

If you say so, but the students are going to have to let go of some "hard won" idea one way or the other. I personally find it pedagogically distasteful to make them give up the idea that the mass of an object is a "property" of the object.

John Mallinckrodt
Cal Poly Pomona