The discussion centers around gravitational waves, specifically their properties related to the superposition principle, their nature as transverse or longitudinal waves, and the implications of their non-linear interactions as described by Einstein's equations. Participants explore theoretical aspects, potential applications, and personal reflections on the topic.
There is no consensus on the applicability of the superposition principle to gravitational waves, with participants presenting competing views on its validity under different conditions and contexts.
Participants acknowledge the complexity of Einstein's equations and the challenges in applying linear approximations, particularly in high-energy scenarios or near strong gravitational fields.
This discussion may be of interest to those studying gravitational physics, wave mechanics, or anyone curious about the implications of gravitational wave research and its theoretical underpinnings.
In general: No. The Einstein eqns. are highly non-linear. Only in certain cases, where you can neglect the self-interactions, does the superposition principle hold. That's why we need simulations to calculate events like colliding black holes.iramos2488 said:So, do gravitational waves abide by the superposition principle/property?
haushofer said:In general: No. The Einstein eqns. are highly non-linear. Only in certain cases, where you can neglect the self-interactions, does the superposition principle hold. That's why we need simulations to calculate events like colliding black holes.
haushofer said:In general: No. The Einstein eqns. are highly non-linear. Only in certain cases, where you can neglect the self-interactions, does the superposition principle hold. That's why we need simulations to calculate events like colliding black holes.
Yes, but that's because self-interactions are then neglible, as you know. ;)bcrowell said:They're transverse. They approximately obey the principle of superposition at low amplitudes -- and the amplitudes we're talking about detecting here on Earth in real experiments are extremely low.
That's true for the near field, but by the time the waves get to us they are so low in amplitude that the linearized approximation is essentially perfect.
iramos2488 said:So I heard the news today about gravity waves being confirmed. I really like learning about all the different types of waves and would like to expand my knowledge on gravitational waves. So, do gravitational waves abide by the superposition principle/property? Does anyone suggest a website or somewhere I can learn more about gravity waves.
The fact that Einstein's field equation is nonlinear is well-known. This implies that if you have two exact solutions, there is almost never any way to linearly superimpose them.
Recent [as of the time of the writing of the book] research has clarified the singularity structure of most colliding plane wave space-times. These have been found to have a surprisingly rich variation.
bcrowell said:They're transverse. They approximately obey the principle of superposition at low amplitudes -- and the amplitudes we're talking about detecting here on Earth in real experiments are extremely low.
Einsteins eqs were well beyond the spectrum of my calc based physics courses. I remember when we learned about gravity, you know the eq something like FsubG=GMm/r^2 and was not satisfied with the explanation for gravity. (Not the equations and their effectiveness at calculating force of gravity; but just what gravity was in general. I visualize in my head and sadly after that lecture the picture in my head was pretty blank.) I theorized gravity being in the form a wave such as light and sound but now I know. I figured it would be iffy to assume G-waves acted and interacted the same as light, seeing as light and sound waves are very different. I was especially interested in superposition because there was bound to be some interference after the black holes clashed and... I guess I continue digging. Thanks so much.haushofer said:In general: No. The Einstein eqns. are highly non-linear. Only in certain cases, where you can neglect the self-interactions, does the superposition principle hold. That's why we need simulations to calculate events like colliding black holes.