Re: [Phys-l] Invariant mass and relativist mass...

[Hugh Haskell <hhaskell@mindspring.com>]

At 11:55 AM -0500 2/26/08, Rick Tarara wrote:

> First--I'd like to hear from _anybody_ teaching HS or general education
> physics who approaches special relativity from JD's point of view (4D
> geometry).  How does it work?

For years I taught from the invariant mass POV, although I didn't use 
4-vectors, since the students I taught were not yet literate in 
trigonometry, so I limited myself to one-dimensional physics for the 
most part. I found that it created fewer problems to consider mass as 
an invariant. After all, we consider charge as an invariant and no 
one has any problems with that. And I had already spent some time 
emphasizing that mass and charge were properties of matter that has 
no definitions beyond the operational ones that related them to how 
they reacted to certain forces. I think that this approach worked 
with my students, although I did not undertake any formal research to 
verify this.

> Second--the paradoxes are the 'fun' part of this material--at least for the
> students named above.

I agree with this. The paradoxes emphasized the differences that 
exist between newtonian and relativistic physics. In fact I started 
my introduction to relativity with a paradox related to simultaneity, 
and how, in order to keep things that we see as important in 
describing nature invariant, we had to abandon the ideas of absolute 
time and space and also simultaneity. It was a struggle for the 
students, but they ultimately came to understand that the process was 
not that much different from the Galilean approach, once they 
understood the significance of the postulate about the speed of light 
being the same in all inertial reference frames.

> Third--the primary point one is usually making with these students is that
> the phenomenon of high speed motion deviates from the Newtonian model that
> they've been working on and thus requires a different model.

Right, and the difference arises from the speed of light postulate, 
which, although it wasn't Einstein's approach, makes the explanation 
of the Michelson-Morely experiment straightforward. I also argued 
non-mathematically, that the appearance of the speed of light in the 
standard statement of Maxwell's Equations makes the light postulate 
pretty logical, since it doesn't make much sense to have a universal 
constant that will be different for different inertial observers.

>  What they will
> immediately 'demand' is proof that indeed the 'phenomenon' exist.
> Experiments with atomic clocks and the lifetime of muons are offered as
> direct verification of problems with clocks while the twin paradox is the
> seminal example of the ultimate consequences of 'time dilation'.  One can
> then turn to particle accelerator work (was a PSSC film on this as well as
> the muons) that measures velocity and momentum of particles moving very
> fast.  The experiments clearly show that momentum rises must faster than
> velocity at high velocity.  For the student group in question--comparing
> this to their ideas of momentum  (p = mv) the conclusion _has_ to be that
> mass has increases.  So I am totally unconvinced that the approach which is
> best for a Modern Physics Course for physics majors is the approach one
> should take (or even can take) with HS and non-science students.  3-D
> geometry is a mystery to most and a 1/R^2 dependency is as difficult to
> fathom as Jackson's E&M was to most of us.

I didn't find my students "demanding" experimental verification of 
the counterintuitive results of relativity, but I pressed such 
verifications on them anyway, to attempt to further instill the idea 
that they need to demand such verifications for any idea, but 
especially for scientific ideas. Hopefully, by the time they got to 
college, they were prepared to ask the hard questions about meaning 
and verification of their professors. I suspect that the science 
professors mostly welcomed such questions and some of the non-science 
professors were less than enthusiastic about such questions.

Hugh
--

************************************************************
Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

Hard work often pays off after time. But Laziness always pays off now.

			February tagline on 2007 Demotivator's Calendar