Re: Test2 SPF

Hi Rich and Guys.
I think this is a three cent article :-).

On Oct 9, 12:15 am, "Rich L." <ralivings...@xxxxxxxxxxxxx> wrote:
My two cents on this issue:

I consider math to be a tool with which we construct models of the
real world. Mathematics is an incredibly rich subject, with
mathematics that describe things that most likely don't exist (e.g. 57
dimensional spaces, spaces with a -1, -1, 1, 1 metric, etc.). Doing
math without testing it against reality is just as bad as trying to do
physics without math. I've always worked hard to relate the
mathematics to the physics, although the more advanced I've gotten in
physics the more difficult this has been.

I recall two clear experiences that confirmed for me the importance of
maintaining contact between the math and the physics. In one case an
undergraduate Electromagnetism professor was calculating the
scattering of light by a free charge. Because of an algebraic error
he came up with an expression that gave the polarization of the
scattered light as being in line with the poynting vector of the
incident wave, rather than perpendicular to it. Even when I pointed
out this unphysical result the professor maintained that I was wrong.
He had lost the connection between the math and the physics.

Another case was a classical mechanics class teaching variational
calculus. The simple problem of the shortest path between two points
on a sphere was being calculated. At one point an approximation was
made. If you related that approximation back to the original problem,
you were approximating the sphere to be a circular cylinder. While in
fact this approximation still gives a valid result (if the two points
are not too far away on the sphere), it should give one pause to
wonder exactly what problem was actually solved.

In the case of the Lorentz transformations, there is great difficulty
relating our ordinary experience with the implications of the Lorentz
transform. The discussion cited earlier I think is a very good
example. It is difficult enough to get our minds around length
contractions and time dilations. When you deal with a series of
boosts in different directions, and rotating frames, our physical
intuition fails us. The mathematics then is essential to appreciating
the more subtle implications of the physical theory. In this case it
yields an understanding of the Larmour precession and gyromagnetic
ratio of the electron. The mathematics is not nonsense in this case,
but it is very difficult to relate to the physical effects it
predicts. Part of the problem is jargon, and part is that there is
rarely an attempt to show the physical significance of the
mathematical ideas.

The problem is that mathematicians (and mathematical physicists) tend
to get wrapped up in the math and loose touch with the physics, like
my electromagnetism professor. On the other hand a physicist that
cannot work with the math, or worse is ignorant of the mathematical
theory, is likely to make equally absurd predictions. What is really
needed is a cultural (and educational) emphasis on always making the
connection between the two. This is what I see lacking in modern
physics. Of course the real difficulty is that the connection is
difficult to make. I have been working at it, off and on, for 30
years now, with not very spectacular results. What really bothers me
is that so many practicing physicists seem to have given up even
making the attempt. I've lost count of all the books on general
relativity I've read that start out with theorems about vectors,
covectors, formal definitions of metrics and 1forms, 2forms, etc.
etc. This mathematical theory is clearly all good stuff, but what is
missing is how to relate it to the physics. I got so frustrated with
this sort of thing during my first try at graduate school in the
1970's that I ended up dropping out. Based on the text books I've
seen since then I don't think the situation has changed that much. I
suspect that it would be much better if modern physics (I'm thinking
primarily of quantum mechanics and general relativity) would be taught
with alternating physical and mathematical arguments, so the student
could gradually develop a physical understanding about how all these
mathematical objects relate to the real world.
Rich L.

Of course I agree.
I compare using math and physics to walking,
with one foot being math and the other physics.
Walking from A to B, using one leg is hopping,
you'll look a bit funny on the way to a grocery
store, and it's a definite liability in an ass-kickin'
contest, if you have only one leg.

In this article, (see the sample using Hi & Lois),
http://physics.trak4.com/MST_UFT.pdf
I tried to inject an ancedotal connection to relate
power to the metric. Did I succeed?

If so, I can suggest your 60 Watt light bulb is
emitting quantized power in the form of photons
and then generalize that power "W_00" is quantized.

The meaning of quantizing W_00 means the differential
d(W_00) =0 , since NO continous function of power is
possible, however power can vary incrementally so we
can use /\W_00 , (/\ is the finite increment Delta).

The next problem is the equation, /\g_00 = - /\W_00,
that requires the quantization of the metric g_00.
(that's why the article ends with a comma).

Sometimes producing (defining) a question is as
important as a solution.
For example, do we need a new calculus basing GR
entirely on increments, and dismiss the continuum?

I'm tending to think that way, especially in view of the
Quantum Theory, but with conditions.
For example consider velocity, dx/dt, it's quantized
only for light c=1=dx/dt locally.
So then the conditions of quantization (the use of the
increment) needs to be reasoned out logically.
Regards
Ken S. Tucker
.

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