Gravitational Wave Modeling: A Thought Experiment

[Jim Lundquist]

I am thoroughly confused regarding the modeling and graphic depictions of gravitational wave propagation. These waves must propagate in three dimensions, not in the planar rubber sheet example that is often shown or the ripples on a pond example. Even the recently publicized example of the collision of neutron stars, shows the stars rotating about an axis that we can call the y-axis in a plane that we can call the (x, z) plane. The subsequent collision propagates a wave in that (x, z) plane. I understand that one can argue that the stars approached each other in that plane, but the gravity of that system is still manifested in three dimensions. For sake of argument, let’s just say that the “hand of God” placed these two stars in empty space and motionless relative to each other, and I am an invisible observer observing from an arbitrary (x, z) plane, what would determine the plane of rotation?

Thought experiment: If there were simultaneous collisions of 6 pairs of neutron stars (2 pairs on each axis of a symmetrical grid composed of x, y and z axes) and all of equal mass and all pairs equidistant from each other along each axis, what would be the effect on space at point (0, 0, 0) on that grid? Could this be how quantum particles are formed…by the constructive interference of gravitational waves?

 

[phyzguy]

A couple of comments:

(1) Orbiting masses don't just radiate gravitational waves in the plane of the orbit, they radiate them in all directions, although the polarization changes depending on the viewing angle with respect to the orbital plane.

(2) If you place two stars in empty space motionless with respect to each other, they will not orbit, they will just fall together. However, this is a very unlikely event. Real stars have some angular momentum. The objects we are seeing in the recent gravitational wave announcements are in bound orbits, and have been orbiting each other for a long time.

 

[Ibix]

Gravitational waves propagate in all directions from a pair of in-spiralling masses, although not equally powerful in all directions. But actually illustrating this kind of thing is difficult. So they do something like choose the slice of space in the ecliptic plane and plot the wave amplitude as height.

The plane of rotation is just the plane defined by the initial velocity vectors of the stars.

 

[Ibix]

Thanks for your replies, but what about the thought experiment I posted?

The gravitational waves at the centre of your cube would depend on the relative orientations of the neutron star pairs, the size of the cube, and the phases of the neutron star orbits. Probably you will need access to fairly hefty computer resources to get any detailed answer.

Also, there is no quantum theory of gravity yet (or rather, there are many partial ones, but we've no idea if any of them are right), and we do not have a quantum description of a gravitational wave so far as I am aware. Certainly not a universally agreed upon one. Any description you do get will be purely classical.

[Moderator's note: Edited to remove reference to deleted speculative post.]

 

[berkeman]

Thread closed for Moderation...

Edit: Thread reopened.

 

[PeterDonis]

Could this be how quantum particles are formed…by the constructive interference of gravitational waves?

If, as you say, you are "thoroughly confused" by what our current theories say, you should not be proposing new theories, which is what this is. Please refer to the PF rules on personal speculations. This particular suggestion is off topic for this thread, and further posts about it will be deleted and will receive a warning. Please note that I have also deleted some posts in this thread that discussed this speculation.

 

[PeterDonis]

These waves must propagate in three dimensions, not in the planar rubber sheet example that is often shown or the ripples on a pond example.

This is true, but since humans have difficulty in visualizing four dimensional spacetime (three dimensions of space plus one of time), we have to adopt simplified models to help us understand what is going on.

For sake of argument, let’s just say that the “hand of God” placed these two stars in empty space and motionless relative to each other

You can't assume that, because in General Relativity, mass (or more generally stress-energy) can't just appear from nowhere. That violates the Einstein Field Equation.

Please note that this is not just a general statement about conservation of energy. It is a stronger statement: in GR you cannot even construct a consistent model in which stress-energy is not conserved. So if you find yourself imagining thought experiments where objects just appear out of nowhere, you can't model them at all in GR, which means you can't use GR to answer questions about them. And since GR is our best current theory of gravity, that basically means such thought experiments are simply out of bounds; there's no point in proposing them since there's no way to consistently analyze them.

what would determine the plane of rotation?

The general answer is, random chance. Some random combination of events gave the system that eventually formed that pair of neutron stars angular momentum in some plane. There is no law of physics that says it has to be a particular plane, but for any specific isolated system it is highly likely that there will be angular momentum present, and if it is, it has to be in some plane. There is no such thing as an isolated system with "three dimensional" angular momentum; any system with angular momentum picks out a particular plane in space.

If there were simultaneous collisions of 6 pairs of neutron stars (2 pairs on each axis of a symmetrical grid composed of x, y and z axes) and all of equal mass and all pairs equidistant from each other along each axis, what would be the effect on space at point (0, 0, 0) on that grid?

First, the effect is on spacetime, not "space". Simplified models of gravitational waves, used to analyze experiments like LIGO, assume that the gravitational waves passing Earth from distant sources are transverse plane waves. That is what allows a particular system of coordinates to be constructed (they are called "transverse traceless" coordinates) in which we can view the effect of the gravitational wave passing as stretching and squeezing "space", and that's it. But your thought experiment clearly does not satisfy the assumptions of such a model, so you can't view the effects in that case as affecting just "space". You have to look at the full-blown 4-dimensional spacetime curvature model.

Second, I don't know that there is any exact solution for the situation you are describing; it would have to be modeled numerically, as
@Ibix suggested. I would not hazard a guess as to the qualitative results that such a numerical model would give.