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Re: [Phys-L] gravitational waves



I am giving up.

Is the model I invented, to explain gravitational waves in terms of Newton's laws, really worthless?

I hope someone will comment on what John wrote.

Following his advice, I was trying to explain something new in terms of what is already known, thinking about typical high school students.

Ludwik Kowalski
====================================

On Apr 9, 2016, at 2:39 AM, John Denker wrote:

On 04/08/2016 08:35 PM, Ludwik Kowalski wrote:

The distance x, (between the two disk-like pistons in my model),
changes because the the source disk is oscillating. The gravitational
wave intensity, the amplitude of g(t), at any given x, is inversely
proportional to the x^2,

Suppose the source disk oscillates through a distance k.
I claim the amplitude of g-field oscillations scales like
k/x^3 (not 1/x^2). You can obtain that result via dimensional
analysis, or via a Taylor series : k (d/dx) (1/x^2).

For such a wave, the energy per unit volume in the wave should
scale like amplitude squared, in analogy to EM waves, sound
waves, et cetera. So that scales like k^2/x^6. The power
per unit area is c k^2/x^6, with the same x-dependence.

Now calculate the total energy crossing an imaginary sphere
of radius x (centered on the source). That is c k^2/x^4.
Alas, that is not a constant. So the wave, if it propagates
at all, does not conserve energy.

There is no way of fixing this problem without ultra-drastic
changes to the model.

Getting the scaling law wrong by 4 factors of x corresponds
to getting the received power wrong by 48 orders of magnitude
in typical astrophysical situations.

avoiding general relativity [...] is desirable

Forgetting about GR is one thing. Forgetting about conservation
of energy is something else. It's tantamount to forgetting about
physics entirely.

I have to ask, what are we trying to do here, and why?
Are we doing physics, or is there some other objective?

*) Gravitational waves have rather little direct practical value
to most students. With a gravitational wave plus a dollar you
can buy something at the dollar store (unless they charge tax).

*) Maybe gravitational waves can serve as a cross-check on what
we know about gravitation and about waves. Well, the model
based on the oscillating disk is known to give the wrong answer
for electromagnetic waves (assuming the disk is charged). I
don't see any value in taking a known-wrong argument and
extending it into a new area.

*) Perhaps one lesson that really can be learned is that GR is
hard. It took Einstein many years to figure out gravitational
waves, contradicting himself at least twice, even after the
fundamental GR equations were known. Arguing by analogy to
other types of waves doesn't suffice. GR is significantly
harder than EM, so even if you repaired the disk model to get
the right answer for EM waves you /still/ wouldn't necessarily
have a good handle on gravitational waves.

*) Another lesson that can be learned is:

-- Show the work.
-- Check the work.
-- Show the checks.

IMHO that ought to be posted on the wall of every classroom,
from first grade on up.

For example: If you invent a new type of wave, check that
it conserves energy.

-- Show the work.
-- Check the work.
-- Show the checks.

Showing the checks should be part of the grade on every exam.

BTW this is one of the many poisonous things about multiple-
guess tests: They do not encourage or even permit the students
to show the work or show the checks.

==================================

Also: In the spirit of taking things one pedagogical step at
a time, and in the spirit of comparing one technique to another,
I added a section that calculates geodesics using only simple
18th-century classical physics, starting with the Lagrangian
for a free particle, which is almost as simple as anything
could possibly be.
https://www.av8n.com/physics/geodesics.htm#sec-geodesic-classical

A later section solves the same problem again, using some
19th-century mathematics such as Christoffel symbols.
https://www.av8n.com/physics/geodesics.htm#sec-geodesic-fancy

Furthermore, if you want something even simpler, you can
calculate geodesics in /flat/ space. In polar coordinates
it's not quite trivial. This is mentioned (but not worked
out) at
https://www.av8n.com/physics/geodesics.htm#sec-flat-polar

Also, as previously mentioned, the masking-tape model works
at any level from 5th grade on up.
https://www.av8n.com/physics/geodesics.htm#sec-spacetime

So there are some pieces of the puzzle that can be worked out
correctly, without requiring a super-huge investment.
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