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



On 02/25/2008 01:22 PM, Jacques Rutschmann wrote:
Thanks for your answers!
http://www.av8n.com/physics/gravity-source.htm is a great gedanken setup.

:-)

.....

But the temptations are so so strong:
1) Textbooks (introductory, SR and GR), in my experience, fail to warn against this.
2) Semi-classical quantum mechanics computations (while wrong in the
sense of a consistent theory) seem to be useful; by analogy trying to
do semi-classic computations in relativity is natural.
3) GR is complex, GR computations for actual experiments are scary
and the relation to measurements not easy...

That's all true.

To put it in perspective, I don't consider GR to be marked better or
worse than other advanced topics.
*) The correspondence principle still applies. That is, GR reproduces
the classical results in the appropriate limit (speed not too large,
acceleration not too large).
*) Semi-classical approximations are only _sometimes_ useful, for GR or
otherwise. Part of the trick is knowing when to use such approximations
and when not to. For instance, semi-classical approximations to QM
don't predict lasers, don't predict superconductivity, and don't resolve
the Gibbs "paradox".
*) On the other side of the same coin, there are some situations that
can be analyzed quantitatively by relatively simple (non-GR) methods,
yet reveal important facts about GR. For starters, consider the
notorious twins, one of whom goes on a trip while the other stays home.
http://www.av8n.com/physics/twins.htm
The key physics point is that one twin is /accelerated/ while the other
is not. This connects special relativity to acceleration, and acceleration
is connected to gravitation, so this puts us on a road that inevitably
leads to GR, if we pursue it far enough.


There are also classical models of spacetime curvature that convey
good information:
http://www.av8n.com/physics/geodesics.htm


Also there are useful analogies:
A) charge (scalar) --> source term for electrostatics
B) [charge, current] 4-vector --> source term for electromagnetism
C) mass (scalar) --> source term for Newtonian gravity
D) we shouldn't be too surprised to find nontrivial (non-scalar)
source terms as soon as we mix gravitation with relativity.
The scalar "relativistic mass" just ain't gonna do the job.

You can understand electromagnetism in terms of electrostatics plus
the geometry of spacetime, in simple cases:
http://www.av8n.com/physics/magnet-relativity.htm
and that tells you something about the issues involved.


Bottom line: GR is complicated and scary, but not infinitely scary.

======================
Tangential pedagogical remarks:

1) Typically the more-advanced theory tells you the limits of validity
of the less-advanced theory. For example, given the spacetime formula
E^2 - p^2 = m^2
then
a) That reduces to KE = .5 m v^2 to lowest order in v; and
b) It tells us how small v has to be, and tells us what the
next-order correction term must be.

The converse is not true; starting from .5 m v^2 it is not at all
clear what the limits of validity are, or what the more-general
expression is.

As an even simpler example, (G M m / r) will give you (m g h) in the
appropriate limit, but the latter won't give you the former.


2) This is hard on students, because they have to learn the less-advanced
theory before they can approach the more-advanced theory, which means
they often don't have a firm basis for understanding the limits of
validity of what they're learning. They don't know which parts will
have to be unlearned and which won't.

It's worth racking our brains to find ways to minimize the amount of
unlearning that will be needed, but there's only so far we can go.


3) This is why teachers need to know a lot more than is on the syllabus.
It takes a lot more than a high-school education to teach high-school
physics. Typically there are N different ways to present a less-advanced
topic, one of which dovetails with the more-advanced viewpoint, and N-1
that don't. It helps to know which is which!

This brings us back to relativistic mass, contracted rulers, and
dilated clocks. From the narrow perspective of special relativity,
such things are not technically "wrong" ... but they are in no way
better than the spacetime approach, and in some ways worse, in the
sense that they do not dovetail with a modern (post-1908) view of
the subject.

Remember, 2008 is the 100th anniversary of spacetime.
http://de.wikisource.org/wiki/Raum_und_Zeit_(Minkowski)

Truly an epochal document.