Setting the scene:
If I drop a stone into water, the stone will create a depression in the water that the surface tension of the water and gravity (so says the Wiki article: Dispersion (water waves)) will work to neutralise so that the water surface again becomes flat. This has the side effect of creating a disturbance in the "flatness" of the water surface that actually moves (away from its origin).
If I drop a stone in sand, which is also composed of particles, the depression largely remains when I remove the stone, and no traveling waves were created.
Back to the question:
Gravitational waves apparently travel through space, so in my primitive understanding of things, space (or spacetime?) must have a neutral "shape" that it is compelled to resume after being deformed. Is this true or am I misunderstanding?
If it's true, why doesn't spacetime behave like the sand in that it preserves deformations after the object that caused them has moved away?
Thank you for the replies! I think Cleonis' extended reply saying that gravitational waves are predicted to exist (or actually necessarily exist if I've understood correctly) and propagate in spacetime when assuming the Einstein equivalence principle is a satisfying answer if one is not to try to explain what the so-called "fabric of spacetime" is actually made of. I haven't done a textbook study of General Relativity though, so it's (yet) beyond me how one gets from the equivalence principle to gravitational waves. Maybe there's a non-mathematical way to explain this? (as hand-wavy as needed) [Update 2: See the 2nd reply by Cleonis]
I gather that the question of what the fabric of spacetime physically is is yet to be solved.
Cleonis and Ed999 inspired me to do some googling.
"spacetime as a fluid": This in particular leads to a Wiki article "Superfluid vacuum theory" in which the physical vacuum is assumed to be a superfluid (a fluid with zero viscosity) and consequences are then derived. It seems to be a fringe idea though.
"spacetime elasticity": This yielded two small technical papers. "What is the Stiffness of Spacetime?" (http://physics.princeton.edu/~mcdonald/examples/stiffness.pdf) and "The Elasticity of Quantum Spacetime Fabric" (http://www.bio21.bas.bg/conference/Conference_files/sa17/Cartas.pdf). The latter makes the intriguing claim that:
"The conclusion of all these is that the spacetime has to have a small-scale structure, which is granular. The “atoms” of the space time have to be subjects of a peculiar force. From the elastic point of view, there are good arguments for the Casimir force to qualify as the necessary force."
But the paper was too technical for me to make out if the author actually makes a convincing case for this.
Ed999 (in a new reply) gives an exposition of the idea of thinking of a gravitational wave as a compression wave in a fluid of spacetime "granules" expanding radially from a source so that the wavefront of the traveling disturbance forms an expanding spherical shell.
Two sections had me wondering, though.
Quoting from the reply:
"The strength of the wave is one-quarter at distance 2x, compared to distance x, simply because at distance 2x the expanding nature of the wave (i.e. its spherical expansion pattern) means that each unit of energy must displace four times as many of the granular units of spacetime"
"... the tensor pushes against the next adjacent unit, forcing it in the opposite direction; but, like a tiny spring, it also recoils after doing so, returning to a stationary state. Hence the deformation is temporary, i.e. elastic..."
Wouldn't the wavefront gradually lose its speed (even with elastic collisions between granules) when the kinetic energy transferred between the granules is spread out over an increasing amount of granules as time passes?
He ends his reply with:
"The overall implication of the math, both Newtonian and Einsteinian, is that waves of gravitation and electromagnetism obey the same physical laws, and for the same reasons: that both are a wave motion in a granular medium; a medium which responds to the ordinary, well-understood geometric principles associated with a spherical type of wave propagation based on vibration."
If we think of a traveling electromagnetic disturbance as also being a compression wave in a granular medium, I'm having some trouble imagining how a highly localized disturbance traveling in a straight line can arise such as when an atom emits a photon.
It makes some sense to me if I imagine the photon as being propagated as a single moving granule (or a group traveling in the same direction), but it seems then that the photon should change its traveling direction every time the carrier granule hits another granule at an odd angle, and just generally lose its speed as its kinetic energy gets spread out over an increasing number of granules through collisions along the way. Maybe this would correspond to an increasing wavelength of the photon over time?
This question from 2015 asks essentially the same thing as my post:
The answers to that are not restrained in their technicality as is the case here.