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Re: [Phys-l] Teaching Special Relativity




On Jul 3, 2009, at 12:55 PM, John Mallinckrodt wrote:

I don't think or claim that it is a pedagogical disaster to say that
it might seem "as if" the mass of the object were increasing with
velocity. But I do think that it approaches pedagogical malpractice
not to point out in something like the same breath that it should not
be taken seriously because it leads to all sorts of other problems.
Furthermore, it seems to me to be a simple and appropriate matter to
go on to point out that the more appropriate way to view the result
is either

1. that the classical formula for momentum is simply wrong although
it obviously works very well at low speeds

and/or

2. as John Denker has pointed out, that we are simply using the wrong
velocity, that the correct velocity measures distance traveled in the
frame of the observer per unit time interval in the frame of the
object (i.e., the spatial component of the "proper velocity.")

I'd also take this opportunity to say that, just as I firmly believe
that mass should be viewed as a property of an object, I also agree
with John Denker that the length of an object should be, and is
certainly more elegantly viewed as a property of the object (and
further that the time interval between causally connected events and
the distance between acausally connected events should be viewed as
properties of the relationship between the events.) Nevertheless,
unlike the case with mass, it seems to me that it is easy to
operationally define a frame-dependent "length of a moving
object" (and frame dependent times and distances between events) and
that there is not, in these cases, such grave downsides to doing so.
Moreover, I maintain that considerable enlightenment accrues to those
who follow that path carefully, work through several of the apparent
paradoxes, come to see that relativity is beautifully self-
consistent, and eventually graduate to a more elegant worldview based
on the geometry of spacetime and invariant quantities.

John Mallinckrodt
Cal Poly Pomona

On Jul 3, 2009, at 8:29 AM, Richard Tarara wrote:


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

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.


OK--then help me out here, for my gen-ed students and in fact
myself. Low velocity momentum is mass x velocity. We know the
velocity of a an object is limited by 'c'. The momentum of a fast
object increases faster than the velocity. Is there really any
'conceptual' way to view this other than that the mass has
effectively increased. Saying just that the momentum increases non-
linearly may be the most 'correct' thing to say, but not very
satisfying. I know JD will say use time-space diagrams and maybe
that is best for science, especially physics students, but I don't
have the time and I doubt the ability of my gen-ed students to go
this route.

BTW: I once upon a time used Eugene Hecht's gen-ed text "Physics
in Perspective" where he clearly talks about mass being velocity
dependent but in his Calculus level text he does not take that same
approach. That, IMO, is probably a wise approach overall.

This begs for another question. What is more important, for non- physics majors, "more elegant worldview" or "understanding of everyday phenomena" ?

Ludwik


- - - - - - - - - - - - - -
Ludwik Kowalski, a retired physics teacher and an amateur journalist. Updated links to publications and reviews are at:

http://csam.montclair.edu/~kowalski/cf/ http://csam.montclair.edu/~kowalski/my_opeds.html http://csam.montclair.edu/~kowalski/revcom.html

Also an ESSAY ON ECONOMICS at: http://csam.montclair.edu/~kowalski/economy/essay9.html