Re: [Phys-L] gravitational waves

[John Denker <jsd@av8n.com>]

On 04/10/2016 02:39 PM, Ludwik Kowalski wrote:

> I do not know how to explain this perpendicularity

> what is the gravitational
> analog of the vector E or vector B? Perhaps

Those are the right questions to be asking.  As I said before,
I can't teach you to leap tall buildings at a single bound.
I can however show you where the stairwell is, and we can
climb up step by step.  Learning proceeds from the known to
the unknown.  You cannot hope to explain gravitational waves
in any detail to students who don't have a decent understanding
of what waves are and what gravitation is.

1) A crucial first step is to understand gravitation and tidal
stress at the prosaic classical level;  see below for details.

2) Another sine-qua-non is to have a decent feel for special
relativity.

3) A crucial next step is to figure out how EM waves can be
transverse.

4) Another crucial step is figuring out that the interesting
part of the gravitational field is the tidal stress.  If you
focus on the plain old g field, you'll never make progress,
since we can make g go away by choosing a different frame
of reference.

At the next level of detail:

1)  It takes some work to understand the basics of gravitation.
Most textbooks screw this up royally.  You'd think that after
350 years people would have figured out how to explain this
properly, but evidently not.
  https://www.av8n.com/physics/weight.htm
  https://www.av8n.com/physics/tides.htm
  https://www.av8n.com/physics/gravity-perception.htm


2) The modern (post-1908) approach to special relativity
is discussed at:
  https://www.av8n.com/physics/spacetime-welcome.htm
Again, a lot of textbooks screw this up royally. There are
two ways of teaching SR; either one will get you through a
freshman physics course, but only one provides a suitable
foundation for GR. The other will have to be unlearned, at
great cost.


3) The easiest way to see the transverse EM field is to solve
for plane waves in otherwise-empty space (no sources, i.e.
no charges).  This is worked out in approximately every
textbook.

If you want to understand sources, things get a bit more
complicated.  Start with the Liénard-Wiechert potential
for a point charge.  The potential falls off like 1/r.
Loosely speaking, the field is the derivative of the
potential.  Less-loosely speaking, there are /two/
derivatives of interest:  
 *) The spatial derivative gives us a term that goes
  like 1/r^2, independent of time. This is the Coulomb
  law.
 *) The time derivative gives us a term that goes like
  ω/r.  That has the advantage that it falls off much
  more slowly, so in the far field it is the whole
  story.  On the other hand, it does not exist at DC.

Let's be clear:  The term that explains radiation is
absolutely not present in Coulomb's equation.

It takes some more work to figure out that the radiation
term is transverse while the Coulomb term is longitudinal.
  https://www.av8n.com/physics/lienard-wiechert.htm
Figuring this out is a lot easier if you know where to
look.  Trying to explain radiation in terms of Coulomb's 
law is like looking under the lamp-post, when the thing 
you are looking for is somewhere else.


4) Curvature is related to geodesic deviation, which we
experience as gravitation, more particularly as tidal
stress.

Far and away the best way to explain this is using masking
tape:
   https://www.av8n.com/physics/geodesics.htm

That is almost the only way I know of making sense of the
subject.  If you get to the point where you can construct
this model:
  https://www.av8n.com/physics/geodesics.htm#fig-darts
and understand what it means, that's a really important
step.  That's not all of GR, but it's a vantage point
from which you can see where GR wants to take you.

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

And a memo from the keen-grasp-of-the-obvious department:

If you are the least bit interested in understanding this
stuff, an outstanding reference is:

   Misner / Thorne / Wheeler
   _Gravitation_
   W.H. Freeman (1973)

It's a masterpiece.  It starts with a modern, no-nonsense 
discussion of special relativity, which is the best I've 
seen anywhere.  The Track-II stuff is more than you need,
but the Track-I stuff is quite readable, even poetic in
places.

The idea of separating Track I from Track II is clever
unto itself.  It supports the spiral approach to learning.
You can plan on reading the book more than once.  On each
subsequent reading, you can partake of more and more of the
Track-II stuff.  I wish more books were organized this way.