Gravitational waves: how should we imagine them?

This post is not a post. It’s just a reminder for myself to look into gravitational waves at some point in time. We know how electromagnetic waves travel through space: they do so because of the mechanism described in Maxwell’s equation: a changing magnetic field causes a changing electric field, and a changing magnetic field causes a (changing) electric field, as illustrated below.

So… Electromagnetism is one phenomenon only, but we do analyze the E and B fields as separate things, as the equations below illustrate:

B is co-defined with E, and then all of the dynamics work themselves out through the ∂E/∂t and ∂E/∂t functions. Now, when talking gravity, we only have positive ‘charges’, referred to as masses, always attracting each other, but that doesn’t matter all that much: Coulomb’s and Newton’s Law have the same mathematical structure (as shown below), except for the minus sign, and so there must be some equivalent to the electromagnetic wave, explaining gravitational waves , using the same mathematical concepts, as a propagation of a force on a ‘unit charge’ (so that’s a unit mass in this case) using the very same concepts, i.e. the concepts of a field – two separate fields, I should say, just like E and B  – and of its flux and circulation. 

So we’d have an E_G and a B_G field, so to speak, or a G_E and a G_B field, and formulas for the flux and circulation of both, resembling Maxwell’s equations. In fact, they’d be the same, more or less. It’s a powerful idea, and I am sure the idea has been fully developed elsewhere. In fact, I quickly googled a few things, but it seems that the whole area is a pretty new area of research, both theoretically as well as experimentally—to my surprise!

Hmm… Interesting idea, but I’ll need to do a lot more analysis to be able to grind through this… One day, I will… The first thing I need to do, obviously, is to thoroughly study how these equations for E and B above can be derived from Maxwell’s equations. I’ll need some time for that, and then I can see if it’s consistent with Einstein’s special and general theories of relativity.

I’ll update you on progress. 🙂

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