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Re: [Phys-L] gravitational waves

Thank you for comments, John.

1) I did not introduce the term "faithful," and I do not want to discuss its numerous meanings.

2) Why do I resist replacing the M by the Q? Because electromagnetic waves are transverse while gravitational waves are longitudinal, at least in my mind.

3) What was the purpose of sharing my simple model on this forum? I wanted to demonstrate that one can describe gravitational waves to students who are not familiar with general relativity.

4) Replying to me privately, one teacher wrote: "I haven't looked carefully at your model, but for your intended audience I would say that anything that comes remotely close is better than nothing." Do we all agree with this?

5) My model does not predict "the wrong dependence of GW intensity on x." Wrong with respect to what? Do the experimental data exist?

6) The last question applies to three other "wrong" predictions:

" the wrong dependence of GW intensity on angle.
-- the wrong dependence of GW intensity on frequency.
-- the wrong speed of propagation of the GW."


7) John wrote: "In previous message I asked what is the objective. I renew the
question. What is this model /supposed/ to predict and/or explain?"

Part of the answer is in point 3 above. I am not trying to predict or explain anything specific. I am describing my own interpretation of the term "gravitational waves." How can a retired teacher resist an opportunity to share what he knows and what he thinks.

Best regards to all,

Ludwik Kowalski, Ph.D. (see Wikipedia)?

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


On Apr 10, 2016, at 12:00 PM, John Denker wrote:

All analogies are imperfect, even the most useful ones. That's why
we call them analogies rather than copies. Analogies should not be
overvalued nor undervalued. The imperfections must be taken into
account when deciding which analogies are appropriate in this-or-that
situation.

As a separate matter: It is ambiguous and highly confusing to ask
whether a model is "quantitative" or "exact". The ratio K = 22/7
is famous for being a decent rational approximation to π. It serves
as a /model/ for π. Obviously K has an exact value, so the model
is "exact" unto itself; however, it is not an exactly faithful
representation of π.

Like all models, K = 22/7 is in some ways faithful and in some ways
not. For example, if you are estimating the amount of dough needed
to make a 12" pizza, K is plenty good enough. OTOH tan(1240 K) is
not particularly close to tan(1240 π).

On 04/10/2016 07:34 AM, Ludwik Kowalski wrote:
Let me be quantitative.

1) I am treating the source disk (the source of the field at x=0) as
it were a point particle of mass M. The detector is at the distance x
from the source. Therefore the field intensity, g, at any given
distance from the source‚ is given by Newton's law:

g=G*M/x^2, where G is the universal gravitational constant.

2) The distance x is time dependent, due to some unspecified process.
That is why g is also time dependent.

3) Te frequency of longitudinal gravitational waves (in my gedanken
setup) is the same as the frequency at which the x is changing.

4) What is wrong with this classical reasoning?

What's wrong is the implicit claim that it is a faithful model of
gravitational radiation. The model is "quantitative" unto itself,
but it does not serve the purpose for which it was constructed,
because it is not faithful to the physics of real gravitational
waves. It is unfaithful to a spectacular degree. It predicts:
-- the wrong dependence of GW intensity on x.
-- the wrong dependence of GW intensity on angle.
-- the wrong dependence of GW intensity on frequency.
-- the wrong speed of propagation of the GW.

In previous message I asked what is the objective. I renew the
question. What is this model /supposed/ to predict and/or explain?
In what ways are we /supposed/ to be better off with the model
than without? You tell me.

You could start out by saying a gravitational wave is a wave
and it's gravitational. That's not much, but at least it's
not wrong. You don't need a mechanical model for that.

Now if you want to add additional details, what details do you
consider important? You tell me.

If you're going to construct a mechanical model, construct one
that gets the desired details right. It doesn't have to get
everything right, but it ought to get /something/ right.

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

Again I renew the suggestion to replace the mass M by a charge
Q and replace Newton's universal gravitation law by Coulomb's
electrostatic law. Then every word of the "classical reasoning"
given above still applies. The disk model is exact unto itself,
but alas it is not a faithful model of the real physics of
electromagnetic waves. It is spectacularly unfaithful.

The electrical version has the advantage that the true physics
is simpler and more widely known.

If the "classical reasoning" cannot get the "quantitative"
answer in this simpler situation, why would you want to
extrapolate it to a more complicated situation?

Arguing by analogy is risky at best, but even so, one generally
takes a correct law and extends it into unknown territory. I
don't see the point of taking something that is known to be
wildly wrong and extrapolating it into new territory.

Again I emphasize the importance of checking the work. A line
of "classical reasoning" that gets the wrong answer in simple
easy-to-check situations is obviously invalid.

Bottom line: The disk model is "quantitative" unto itself, but
it is not a faithful model of what it's supposed to represent.
Just because you can build a model doesn't mean it is faithful
to reality.
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