| Chronology | Current Month | Current Thread | Current Date |
| [Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
Thank you again, John D.
As you say, teachers should build knowledge on the basis of what is already known to students. That is what I tried to do yesterday, thinking about typical students (as they were in my classes, when I retired).
How would I modify this plan today? My two hypothetical spheres (S and P) would be replaced by two hypothetical pistons, also of very different masses, (M>>>m). The S piston, in my model, creates a beam of gravitational waves traveling along the x axis; the P piston is part of the detector, measuring the beam intensity.
By the way, I believe you that explaining gravitational waves in terms of Newtonian g field is likely to give wrong answers to some quantitative questions.
But I am not asking such questions, I am trying to explain gravitational waves qualitatively, to people like educated laymen, first year college students, etc.
Ludwik
===================================
On Apr 2, 2016, at 9:56 PM, John Denker wrote:
On 04/02/2016 10:57 AM, Ludwik Kowalski wrote:
(a) Review the F=m*a and Newton's Law o Universal Gravitation.
On a separate page ("B"), review Coulomb's law of electrostatics.
(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.
On page B, draw the X-axis and two positive charges, S and 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.
On page B, wiggle the charge S back and forth along the axis
Any effect on P is *not* due to electromagnetic waves.
There might be some near-field effects, but there is *no*
propagating radiation in that direction.
This should be obvious for numerous reasons, including
the fact that EM radiation is transverse.
Conclude that this line of reasoning is fatally flawed.
It gets the wrong answer for EM waves. Extending it to
gravitational waves makes things worse, not better.
As I said in the previous message, you cannot explain EM
radiation in terms of Coulomb's law. I am aware that lots
of introductory physics texts claim to do this, but it's
nonsense. It gives the wrong dependence on angle, the wrong
dependence on distance, grossly wrong notions of polarization,
et cetera. The term you need to explain the propagating
radiation /does not appear/ in the electrostatic equation.
This is worked out in detail at:
https://www.av8n.com/physics/lienard-wiechert.htm
especially
https://www.av8n.com/physics/lienard-wiechert.htm#sec-fields
If you have never been able to understand the Iʼitoi diagrams
such as
https://www.av8n.com/physics/lienard-wiechert.htm#fig-iitoi-bogus
I say good for you, that shows you're paying attention.
The diagrams are bogus.
By the same token, trying to explain gravitational waves
in terms of Newtonian g fields is absolutely guaranteed
to get the wrong answer. It's wrong several times over.
This includes the bogus animation at
http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
====
As a separate matter, if the sun is wigging back and forth,
there must be a treeeemendous amount of momentum flowing into
and out of the system. You can't just ignore that momentum
when calculating the gravitational radiation, for the same
reason that you can't ignore the current when calculating
the EM radiation.
================================
(a) Review [...] Newton's Law o Universal Gravitation.
Be careful with that, because a great deal of what is said
about gravitation in introductory physics textbooks is
incomprehensible and/or wrong.
In particular, as is so often the case, there are two quite
different concepts masquerading under the same name.
I define
*) the /framative/ gravity g, and
*) the /barogenic/ gravity δg
Everybody starts out by learning about the framative g. It
has direct practical importance. However, alas, it has very
little fundamental significance. If all you have is a uniform
g field, you can make it go away by choosing a different frame
of reference, in accordance with Einstein's principle of
equivalence. There is nothing "universal" about this g.
The only reason we can detect or even define g is because
the local g on the other side of the earth is opposite to
our g. The laboratory frame is attached to the earth, and is
connected to all the rest of the earth, so our local g is
definitely not the only thing that matters to us.
That brings us to the barogenic δg. It tells us how much
the local g differs from the center-of-earth g. A change of
reference frame would change all the g vectors, but it would
not change the difference.
*) the framative g is completely frame-dependent
*) the barogenic δg is completely frame-independent
It's called barogenic because it depends on the mass.
Consider the Taylor series for the gravitational potential:
φ = φ|0 + ∇φ|0 Δx + ∇∇φ|0 Δx^2
baseline g field tidal
potential stress
We can make the baseline potential go away, by choice of
gauge. We can make the g field go away by choice of reference
frame. So if we're looking for fundamental physics, we need
to look at the tidal stress.
I mention this because:
oscillate along the x-axis.[...]
GW would be visible if small
particles, like dust, were floating in space around the planet.
It is unhelpful to talk about the "axis". It's too vague
and too abstract.
In particular, if the axis is constructed by marking some of the
dust particles, the dust does not move relative to the "axis"!
Each dust particle reports that it is in free fall the whole time,
oblivious to the passage of the wave.
This is not a trivial problem. People were confused about this
for 40 years. Einstein predicted gravitational waves, then changed
his mind and argued vehemently that they did not exist, and then
changed his mind again. Nobody trusted any of his arguments in
either direction. If he couldn't figure it out, don't expect your
students to figure it out.
The issue was finally settled by some guy named Richard Feynman.
Here is an improved version of the argument: Consider two beads
that are free to slide on a stick:
-----O----------O-----
This is a real solid mechanical stick, not an abstract axis.
When the gravitational wave comes along, the worldlines of
the beads are affected. They move relative to one another.
The atoms in the stick are subject to the same stress, but
they don't move relative to one another because the atoms
have a definite size determined by the laws of atomic physics.
So the stick gives us a robust notion of distance that the
dust cloud did not. The beads slide relative to the stick.
If we add a tiny bit of friction, some heat is produced,
providing indisputable evidence of the passage of the wave.
Let's be clear: the gravitational wave produces tidal stress
in the stick, but very little strain.
Also: Tidal stress causes /geodesic deviation/. That is,
two free-particle worldlines that started out parallel wind
up non-parallel when acted upon by the tidal stress. To first
order, the amount of deviation is proportional to the distance
between the two worldlines. If you have only one bead, or only
one planet, or N things all in the same place, you cannot even
define what you mean by geodesic deviation.
Let's be clear: The analogy between Coulomb's law and gravity
is imperfect, because in electrostatics the E field has plenty
of physical significance, whereas the analogous g field has
little if any fundamental significance. We can make g go away
(locally) by choosing a different reference frame. Do not try
to explain gravitational waves in terms of g. Thinking in terms
of tidal stress is part of the price of admission.
============
Suggestion: There is a pedagogical proverb that says learning
proceeds from the known to the unknown. In that spirit, it pays
to have a solid understanding of what gravitation is, before
trying to figure out gravitational waves.
Here are some possibly-useful resources that avoid some of the
worst misconceptions:
https://www.av8n.com/physics/weight.htm
https://www.av8n.com/physics/geodesics.htm
_______________________________________________
Forum for Physics Educators
Phys-l@www.phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@www.phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l