On Saturday, April 9, 2016 12:21 PM, Ludwik Kowalski asked:
"Is the model I invented, to explain gravitational waves in terms of
Newton's laws, really worthless? "
I don't think it's worthless, but instead helpful for beginning students to
understand (and old retired physicists like me to remember) the basic
differences between wavelike behavior and simple time-dependent behavior.
It made me search through my introductory physics books to review the basic
properties of waves. The general consensus was that waves have three
characteristics:
1) Some type of disturbance is propagated at a FINITE speed.
2) The disturbance carries energy with it which, therefore, also propagates
at a finite speed.
3) If the wave disturbance requires a medium to propagate in, "particles" of
the medium only undergo short range motion as the wave disturbance passes.
The same particles do not travel with the wave over long distances.
For Ludwik's large piston (M)/small piston (m) model, separated by a large
distance x, with the large piston oscillating about equilibrium with small
amplitude k, and Newtonian gravity, I get the same time dependent
perturbation in the g field at the small piston that John Denker computed
with amplitude 2kGM/x^3 assuming k << x. So using Newtonian gravity, there
is a time dependent oscillation in the g field at m. However, this time
dependent oscillation does not have wave characteristics (1) and (2) above.
Instead, the calculation I did for the perturbation amplitude assumed the
disturbance was instantly felt by the small piston. So the speed of
propagation was infinite. This is my understanding of how Newtonian gravity
works unlike general relativity.
My guess is that gravitational waves do not need a medium to propagate in,
so Characteristic 3 above is mute for Ludwik's model. However, perhaps one
of the more knowledgeable members of this list could state this with more
certainty one way of the other.
Don
Dr. Donald Polvani
Adjunct Faculty, Physics, Retired
Anne Arundel Community College
Arnold, MD 21012