Re: [Phys-L] gravitational waves

[John Denker <jsd@av8n.com>]

All analogies are imperfect.  That's why we call them analogies
rather than copies or instances.

It helps to know in what ways the analogy is faithful to reality,
and in what ways not.  Consider the blank space in the following
chart:

	*	**	***	****
	x	xx	xxx	xxxx
	+	++		++++
	o	oo	ooo	oooo
	v	vv	vvv	vvvv

Here the rows are faithful as to shape, while the columns are
faithful as to number.  In this way we can communicate the idea
of "three plus signs" even if it is expressed directly.

This analogy is itself imperfect, insofar as "three plus signs"
could have been expressed directly.  However, you can extrapolate
to physics, where a great many ideas cannot be so easily expressed,
and instead must be built up via a series of approximations and hints.

Still the point is that it is important to know in what ways
each analogy is faithful to reality, or not.

On 04/17/2016 09:03 PM, William Katzman wrote:

> We do use the trampoline model of the universe to explain
> gravitational waves.  It is flawed - as the mathematics don’t work
> well, but it does provide several apt analogies - including the
> analogy that it actually can stretch - like space.

I'm not convinced.

It seems to me that the trampoline model qualitatively represents
some sort of field that mediates an interaction between the
particles.  This field is a real physical thing with its own 
dynamics.  So far so good.

However, things go downhill rapidly after that.

*) Consider a region that is locally cylindrical, like
the bottom of a long shallow trough.  There is "curvature"
in the high-school sense, i.e. extrinsic curvature, but no
intrinsic curvature, no Gaussian curvature.  The paths of
free particles are not straight and do not even behave the
same as one another.  However, the geodesics remain straight,
i.e. there is no geodesic deviation.

Therefore it seems that the trapoline model has conceptual
problems (not just math that "doesn't work well").  It seems
there are multiple problems at the most fundamental, qualitative,
conceptual level:

 *) In the trampoline model, free particle trajectories don't 
   follow geodesics.  In the real world, they do.
 *) The aforementioned "stretch" is not an "apt" analogy. 
  -- In the trampoline model, the crucial idea is the deflection
   in the /off-universe/ direction, i.e. the deflection into
   the embedding dimension.  The aforementioned "stretch" is a
   second-order effect.  It can be made arbitrarily small by 
   suitable engineering, and the model still works.
  -- In contrast, in the real world, there is no need for an
   embedding dimension.  Everything happens /within/ the universe.
   The stretch is pretty much the whole story.
 *) The model doesn't represent the polarization correctly.
 *) It is a model of space, and it's not the least bit obvious
  how to generalize it to spacetime.
  -- In particular, AFAICT the model predicts zero gravitational
   redshift.
  -- In contrast, general relativity predicts a redshift.
   Forsooth, special relativity gets this more-or-less right
   (hint: traveling twins).
 *) The model can represent repulsion just as easily as
  attraction, which is yet another sign that whatever is
  being exhibited is not really gravitation.
 *) The model depends on an "ether" that carries the disturbances.
  Special relativity takes a dim view of such things.

Overall, I'm not convinced this model is particularly apt.
Better models are available.  If I wanted to learn (or teach)
about gravitation, I wouldn't start with this.