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Re: [Phys-L] gravitational waves -- Ludwik's Lecture Map



Introducing GW--Ludwik's Hypothetical Lecture Plan.

(a) Review the F=m*a and Newton's Law o Universal Gravitation.

(b) Draw the x-axis and place two circles on it, labeled S (for Sun) and P (for planet. The larger circle S is at the origin; the much smaller circle P is on the right side of the axis. The star S is much more massive than the planet P.

(c) Ask the Question: "what would happen to the force, F, with which S acts on P , when something is causing the Sun to oscillate back and forth along the x axis? The planet would also oscillate along the x-axis. This kind of action over distance would be attributed to invisible gravitational waves.

(d) Explain (later in the course) that GW would be visible if small particles, like dust, were floating in space around the planet.

(e) Tell students that sound waves are also invisible.

(f) Also introduce the idea that waves are carriers of energy (work is done on the star when it is jerked).

(g) It is useful to say that the recently discovered GW were not due to oscillations of our Sun; they are believed to be due to another kind gravitational disturbance taking place outside our galaxy (a collision of neutron stars or black holes).

h) Please comment on the above. Please post another lecture plan.

Thank you in advance,

Ludwik. P.S. (i) People who try to explain GW, for example journalists, usually refer to A. Einstein, and to his Theory of General Relativity. Why do they do this, addressing general public?

Ludwik

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




On Apr 1, 2016, at 8:58 PM, Ludwik Kowalski wrote:

Thank you John. I wish my brain were able to benefit from your penetrating description. And I hope that a qualitative explanation of recently discovered GW, based on elementary physics, will soon be published (here or elsewhere else) by someone.

Ludwik, born in 1931.

On Apr 1, 2016, at 7:20 PM, John Denker wrote:

On 04/01/2016 03:01 PM, Ludwik Kowalski wrote:

I am thinking about recently discovered gravitational waves,
originating outside of our planetary system. Can they be explained by
classical Newtonian mechanics only?

Classical, yes; Newtonian not so much.

Here's the concept map:

Electrostatics Electrodynamics electromagnetic waves
(Coulomb) (Maxwell) (Larmor)

Static gravitation Dynamic Gravitation gravitational waves
(Newton) (Einstein)


My point is, the interesting analogy moves vertically from
electromagnetic waves to gravitational waves (not starting
from static Newtonian gravity).

Let's be clear: You cannot figure out electromagnetic radiation
starting with electrostatics. I've seen plenty of textbooks that
claim to do this, but it's pure nonsense. In the Liénard-Wiechert
potentials, the term you need to explain radiation /does not show up/
in the electrostatic formulas. This is spelled out at
https://www.av8n.com/physics/lienard-wiechert.htm
especially
https://www.av8n.com/physics/lienard-wiechert.htm#sec-fields

By the same token, you cannot figure out gravitational waves
starting from just Newtonian gravitation.

On a more constructive note: It is an amusing exercise to derive
the Larmor formula for the total radiated power using little more
than scaling arguments. You can then obtain the gravitational
wave formula in the same way. I really like scaling arguments.

Suppose we have an oscillating electric dipole. The radiated
power cannot depend on the dipole moment itself; otherwise a
static dipole would radiate, which would not make sense physically.
Similarly the power cannot depend on the time derivative of the
dipole moment, because two charges moving past each other in
uniform straight-line motion cannot possibly radiate. Neither
one radiates by itself, so (by superposition) they cannot radiate
together ... yet this configuration has a time-varying dipole
moment. So the lowest term that makes sense is the /second/
time derivative of the dipole moment.

Step 2: The radiated power must depend on the /square/ of
that, for any number of reasons including symmetry with respect
to flipping the definition of positive versus negative charge.
Also we know that the fields are proportional to the dipole
moment, and the energy goes like the square of the field.

Step 3: We need a factor of 1/ε0 out front, to get something
with dimensions of energy (as opposed to field strength). Then
we need a factor of 1/c^3 to make the dimensions come out right.

Step 4: If you want the received power per unit area at some
distance r from the source, divide by 1/r^2. Also at this point
you need to worry about polarization and other directional
effects, but let's not worry about that.

Conceptually, that's all there is to it. There are some factors
of π running around, but let's not worry about that. We have
a perfectly reasonable /feel/ for what's going on.

-----------

We can replay the whole story for gravitational waves.

You can't have a mass dipole, so the lowest-order thing we
need to worry about is the quadrupole moment. (If you want
to get fancy, it's the /reduced/ quadrupole moment, but let's
not worry about that.)

It can't be the quadrupole moment, or the first time derivative,
or even the second time derivative thereof, because otherwise
two masses moving past each other in uniform straight-line
motion would radiate, and we know that's not going to happen.
So the object of interest is the /third/ time derivative of
the reduced quadrupole moment.

Step 2: The radiated gravitational-wave power must depend
on the /square/ of that, for any number of reasons including
time-reversal symmetry. Also we should be very unsurprised
to find that the energy goes like the square of the field
strength.

Step 3: We need a factor of capital G out front, to get
something with units of energy (as opposed to field strength).
Then we need a factor of 1/c^5 to make the dimensions come out
right.

Step 4: If you want the received power per unit area at some
distance r from the source, divide by 1/r^2. Also at this
point you need to worry about polarization and other directional
effects, but let's not worry about that.

Conceptually, that's all there is to it. There are some factors
of 2 running around, but let's not worry about that. We have
a perfectly reasonable /feel/ for what's going on.

Note that G is small, 1/c^5 is small, and ω^6 is small for
typical events involving massive objects. So we are not
surprised to hear that the gravitational waves are weak.


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

Did I mention that I really like scaling arguments?

IMHO scaling laws are simpler and more age-appropriate than
most of what gets taught in typical introductory physics
courses. Simple ... yet reeeeally powerful. They have been
central to modern physics since Day One (1638).

They remain a big deal at all levels, from the simplest level
on up. I get 118 hits from
https://www.google.com/search?q=scaling+site:nobelprize.org


Of course it's not magic. Scaling won't solve the problem by
itself. You need to have some intuition about how the universe
is put together, some feel for what's important and what's not.
Still, the point remains that intuition + scaling laws will get
you a lot farther than either one separately.
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