The discussion revolves around the concept of elasticity in spacetime, particularly whether it is meaningful to describe spacetime as having elastic properties in the context of general relativity and the effects of mass and energy on its structure. Participants explore various analogies and mathematical frameworks related to this idea.
Participants do not reach a consensus on the appropriateness of discussing elasticity in spacetime. Multiple competing views remain regarding the validity of the analogy and its implications in the context of general relativity.
Limitations include the potential misunderstanding of the "rubber sheet" analogy, the distinction between different geometrical frameworks, and the unresolved nature of how elasticity might relate to metric expansion.
No, it doesn't. In General Relativity, mass causes a "deformation" of space-time but the whole concept of a "fabric" of space or spacetime is a very unfortunate remnant of Einstein's having use that phrase before everything was well understood and it persists to this day in pop-sci presentations (but not in serious physics). We talk about "curved" space-time, for example, because we use Euclidean Geometry as our base whereas space-time is actually described by Riemann geometry (it's non-Euclidean) and things move in straight lines (called "geodesics") as defined by that geometry but they are curved when viewed from the point of view of Euclidean Geometry.Victor Escudero said:I would like to know if it has any sense to talk about the concept of elasticity of spacetime. So, if spacetime is like a clothing that can be deformed by a big mass or a big energy, does this “clothing” has some elasticity considering for example the deformation that makes a big star in the empty?
To nitpick: Pseudo-Riemannian geometry or, to be more specific, Lorentzian geometry.phinds said:space-time is actually described by Riemann geometry
Yeah, I did learn that from some time back and I probably should just say it correctly since a beginner isn't likely to care about the distinction and it's better to be correct. Thanks.Orodruin said:To nitpick: Pseudo-Riemannian geometry or, to be more specific, Lorentzian geometry.
The "rubber sheet" analogy is pretty flawed, so you can easily get misled. The basic equation of general relativity looks something like G=kT. In that equation, T is called the stress-energy tensor and actually contains the stress tensor from Hookes law and G is the curvature which seems like a geometric distortion similar to strain. So you might be tempted to think of k as being the stiffness and G the strain, but the units don't work out. Strain is dimensionless, but curvature has units of 1/m^2, so they are different things. Similarly, in Hooke's law the stiffness is measured in Pascals, but here it is Pascal/m^2Victor Escudero said:I would like to know if it has any sense to talk about the concept of elasticity of spacetime. So, if spacetime is like a clothing that can be deformed by a big mass or a big energy, does this “clothing” has some elasticity considering for example the deformation that makes a big star in the empty?
Victor Escudero said:I would like to know if it has any sense to talk about the concept of elasticity of spacetime.
What about elasticity in the sense of metric expansion of space? I'm thinking of the common balloon and ant on a rubber rope analogies.phinds said:No, it doesn't.
That is part of the G I mentioned abovestoomart said:What about elasticity in the sense of metric expansion of space?
Space doesn't stretch, the geometry just changes and things get farther apart. English doesn't do well describing this.stoomart said:What about elasticity in the sense of metric expansion of space?