Re: [Phys-L] gravitational waves

[John Denker <jsd@av8n.com>]

On 04/02/2016 08:29 PM, Ludwik Kowalski wrote:

> 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.

> the two "pistons," in my model, are surrounded by a vacuum, where a
> variable gravitational field is established, due to the mass of the
> "oscillating piston S."

The word picture is too vague.

I tell students, whenever possible, draw the diagram.  I've seen
too many students try to figure out stuff in their heads, in 
situations where world-famous experts would have drawn the diagram.

The canonical Gedankenexperiment for launching gravitational waves
is a mechanical oscillator, i.e. two masses on a spring, oscillating
180 degrees out of phase so that the center of mass is stationary.
Meanwhile the canonical detector is two beads sliding on a stick.

                                      |
         M  ↕                         O
         s                            |
         s                            |
         s                            |
         s                            |
         M  ↕                         O
                                      |

The transmitter has a mass distribution with a changing quadrupole 
moment.  This is analogous to an electromagnetic transmitter that
has a charge distribution with a changing dipole moment.  The
beads are what's important;  the stick is just there so we can
define what we mean by "distance" without going crazy.

Transmitter plan B is to have two masses on a stick and spin it,
with the plane of rotation in the plane of the paper.  Again
there is a changing quadrupole moment.   This is analogous to 
an EM spinning dipole.

         →                            |
         M                            O
         |                            |
         |                            |
         |                            |
         |                            |
         M                            O
         ←                            |

Of course you can spin the receiver also.  If you spin it at just
the right rate, you get a synchronous receiver with enhanced
sensitivity.

Some decent animations of how the gravitational wave affects a
bunch of free particles can be found here:
  https://en.wikipedia.org/wiki/Gravitational_wave#Effects_of_passing

In words: you're expecting a time-dependent tidal stress.  If you
try to construct something simpler, you're just fooling yourself.
It's like trying to make a wave out of the Coulomb interaction.
You might be able to make something happen in the near-field region,
but it doesn't propagate properly.  It's not a wave.  In the far
field, it simply does not exist.