# Is the deformation of spacetime, elastic deformation or plastic deformation? [closed]

Is the deformation of spacetime, elastic deformation or plastic deformation?

• What do you mean by "elastic" or "plastic" here? Spacetime is not an ordinary object where it would be clear what those words mean - without further elaboration, it's unclear what you're asking. Commented Jul 29, 2016 at 10:43
• Relativistic spacetime is a strange beast. Intuitively, I would say elastic most of the time, and could be plastic and singular at times, when a black holes forms, which irreversibly stretches and torn spacetime forever. The analogy of spacetime with a kind of fluid or solid isn't new and is even pursued in research today.
– Cham
Commented Jul 17, 2017 at 0:29

I would argue that it is an elastic deformation because when a mass moves from place to place the "deformation" to spacetime does not persist.

@peterh made an interesting point when bring up the energy loss due to gravitational waves in a many-body system (like the Sun+Earth). But for a single body in space moving at a fixed velocity, say a rogue star without a solar system, it will not radiate gravitational waves (see below). But this star will still locally deform spacetime and that deformation will not persist after the star passes.

According to Wikipedia:Gravitational wave sources,

In general terms, gravitational waves are radiated by objects whose motion involves acceleration, provided that the motion is not perfectly spherically symmetric (like an expanding or contracting sphere) or rotationally symmetric (like a spinning disk or sphere). A simple example of this principle is a spinning dumbbell.

• A spacetime with a single body passing makes no physical sense. Moreover, just change the coordinate system to be centered on that body, and now you have a static spacetime. It's a bad example to draw any physical conclusion on the ill defined elasticity of spacetime. The answer is that anything that happens in spacetime, follows the laws of physics, affects the spacetime and viceversa, and you have to solve the nonlinear general relativity (GR) equations (or the unknown quantum gravity equations). For non-quantum gravity any nontrivial dynamics will produce GWs, and changes happen. Commented Jul 29, 2016 at 5:14
• @BobBee Good point. My point was to consider a system with negligible gravitational waves. Simplified systems are often very helpful to building intuition. I agree that in theory any nontrivial dynamics will produce gravitational waves but in practice the radiated energy could be too small to matter. I also agree that "elasticity" of spacetime seems a bit ill defined but it doesn't seem an unreasonable analogy. I would be very interested to see your comment expanded into an answer. Commented Jul 29, 2016 at 5:28
• It is not a good analogy. It implies that if spacetime expands, i.e. is stretched, it will tend to contract after. But that's not true, except in oscillation i.e., wave, conditions. A spacetime will contract with positive curvature and expand with negative curvature, and that means it is determined by the energy (etc) density, plus nonlinearities. In cosmology, for instance, the expanding universe keeps expanding, no elasticity. And your negligible grav radiation - 3 solar masses out of 60 is not negligible. Elasticity is a bad intuition for spacetime. Use real physics. Commented Jul 29, 2016 at 5:58
• @BobBee are you saying that a rubber sheet model for visualizing spacetime is never appropriate? If so, maybe explaining that would be very constructive. Commented Jul 29, 2016 at 12:39
• Elasticity or whatever plastic deformation means implies some way in which the spacetime reacts (i.e., evolves, changes) after having some initial change. That is the essence of the dynamics of spacetime (with or without matter), which is complex and best visualized as various different graphics of the spacetime itself -ideally but impossibly the 4 dimensions depicted, or usually 2 or 3. That will give you space-time, i.e., space evolving over time. Or 2 or 3 spatial dimensions in a movie, you can visualize the space sections changing. But you then can then miss the space-time co-relations. Commented Aug 1, 2016 at 6:25

Lets begin with a very basic of elastic deformation in continuum mechanics, where people starts with defining the "deformation" of field as $u^{\alpha}(x)\equiv \bar{x}^{\alpha}-x^{\alpha}$. Which is in fact indicates how each point in a solid moves under a deformation.

The deformation contributes to the thermodynamic functionals like free energy, entropy etc. To the lowest order, the thermodynamical functionals will be quadratic in the scalars constructed from the derivatives of the deformation field. The extremisation of the relevant functional (entropy, free energy ....) allows one to determine the equations which govern the elastic deformations.

The analogue of elastic deformations in the case of spacetime manifold will be the transform as $x^{a}(x)\rightarrow \bar{x}^{a} =x^{\alpha}+v^{a}(x)$. If we accept the general coordinate transformation as elastic deformation of spacetime then one can derive the consistency of elastic condition deformation provided that Einstein field equations are satisfied! In this respect we can say that spacetime behaves like a solid, which can undergo elastic deformation.

For a complete derivation please check this paper Gravity as elasticity of spacetime

• The paper seems to be your own theory, published in some journal that I'm not familiar with. You derive Einstein Field Equations (EFE)by requiring the extremization of an action that you called entropy, and THAT it should lead to EFE. You defined a diffeomorphism the hard way, and got EFE. It is known that EFE can be gotten from extremizing the GR action, yours is related. You got no new physics, no new understanding. Calling a general coordinate transformation elasticity means nothing. This question, and the answers, are devoid of new physics. If you disagree cite some papers that used it. Commented Jul 29, 2016 at 4:57
• I agree with @BobBee, calling a coordinate transformation an elastic deformation is non-sensical since a change of coordinates is unphysical by the very foundation of general relativity. (By the way, Bob, if you think questions or answers are wrong or useless, you should downvote them, especially if they are so highly upvoted as the things at this question) Commented Jul 29, 2016 at 10:48
• @CuriousMind Actually I wanted to explain why it made little sense, and that the answers also didn't make sense. I am surprised that they got so many up votes. The question is sort of silly, but could just be a naive one. The answers are much much worse, it tells people that that concept makes sense. Commented Jul 29, 2016 at 23:38
• @CuriousMind kI flagged the question as not related to physics, not mainstream, no physics and etc. but it was denied by your reviewer. Commented Aug 2, 2016 at 3:37

Extending @LasersMatter : I would also vote for a nearly perfectly elasticity.

A little bit of the energy is lost due to gravitational waves. Thus, the process can't be reversible perfectly. We can say, the gravitational waves radiated away have an entropy.

It is very little in nearly all settings: for example, the spacetime deformation of the Earth-Sun system loses only around 200W due to them. In the black hole merge which was found recently by the LIGO, around 3 Solar mass was lost from the 60 Solar masses of the black holes.

• I hadn't thought about gravitational waves. Neat idea. Commented Jul 28, 2016 at 18:16
• Even then, when the energy is radiated away, spacetime is restored -> perfectly elastic. Commented Jul 28, 2016 at 21:13
• @JRiverside If I clash a rubber ball to a stone wall, they heat, and radiate away energy. It is an irreversible process. If we would have a closed gravitationally interacting many-particle system, it would go into a thermodynamical equillibrium with the GWs in it around. Commented Jul 28, 2016 at 21:15
• Interesting point! Should the gravitational wave radiation be regarded as 'heat' then, or is it more comparable with an electron oscillating, radiating away the energy? The last case is in principle reversible, right? Commented Jul 28, 2016 at 22:20
• @JRiverside Yes. Even the QM properties of the hyphotetised gravitons are quite similar for the photons (for example, $E=h\nu$). Now the problem is that no closed gravitationally interacting system is known (which would be closed on a level that even the GWs remain in the system). The irreversibility of the process is caused by the entropy. Commented Jul 29, 2016 at 0:32

Your question makes no sense if, as theoreticians almost universally believe nowadays, spacetime does not exist and has to be "retired":

https://www.youtube.com/watch?v=U47kyV4TMnE Nima Arkani-Hamed (06:11): "Almost all of us believe that space-time doesn't really exist, space-time is doomed and has to be replaced by some more primitive building blocks."

https://www.edge.org/response-detail/26563 Nobel Laureate David Gross observed, "Everyone in string theory is convinced...that spacetime is doomed. But we don't know what it's replaced by."

What scientific idea is ready for retirement? Steve Giddings: "Spacetime. Physics has always been regarded as playing out on an underlying stage of space and time. Special relativity joined these into spacetime... [...] The apparent need to retire classical spacetime as a fundamental concept is profound..."

New Scientist: "Rethinking Einstein: The end of space-time [...] The stumbling block lies with their conflicting views of space and time. As seen by quantum theory, space and time are a static backdrop against which particles move. In Einstein's theories, by contrast, not only are space and time inextricably linked, but the resulting space-time is moulded by the bodies within it. [...] Something has to give in this tussle between general relativity and quantum mechanics, and the smart money says that it's relativity that will be the loser."

• You should ask a question based around this viewpoint, imo
– user108787
Commented Jul 28, 2016 at 20:45
• This just says that quantum gravity thinks spacetime is a classical approximation. Ask a specific question or answer a specific one on quantum gravity. The rest above is generalities on what we need to think about in quantum gravity. It's not a viewpoint, physics doesn't do viewpoints, that's what politics does. Ask or answer something on quantum gravity. Commented Jul 29, 2016 at 5:17
• Regardless of what the question is actually trying to ask, this doesn't answer it, it's just quotes from people saying that quantum gravity should maybe do away with the idea of spacetime. I have flagged this answer as not an answer for deletion. Commented Jul 29, 2016 at 10:50