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?
Spacetime is a mathematical concept that combines the three dimensions of space and the dimension of time into a single entity. It is the fabric of the universe in which all objects and events exist. Elasticity, on the other hand, is the property of a material to deform and then return to its original shape when a force is applied. In the theory of relativity, spacetime is considered to have elastic properties, meaning it can be stretched and compressed by the presence of massive objects.
The concept of spacetime having elastic properties is based on the theory of general relativity proposed by Albert Einstein. This theory explains that the presence of massive objects, such as planets and stars, causes spacetime to bend and curve. This bending is similar to how a trampoline's surface bends when a heavy object is placed on it. This is considered evidence of spacetime's elastic properties.
If spacetime does indeed have elastic properties, it means that it is not a fixed and rigid structure, but rather a flexible and dynamic one. This has significant implications in the study of the universe, as it can affect the motion of objects in space and the way we perceive the passage of time. It also plays a crucial role in understanding the behavior of black holes and the expansion of the universe.
While we cannot directly observe the bending of spacetime, we can observe its effects on the motion of objects and the behavior of light. For example, the bending of light around massive objects, known as gravitational lensing, is considered evidence of spacetime's elastic properties. We can also indirectly observe these properties through the phenomena of time dilation and gravitational waves.
The theory of general relativity, which suggests the elastic properties of spacetime, has been extensively tested and verified through numerous experiments and observations. However, the concept of spacetime's elasticity is still a theoretical concept and is yet to be fully proven. Further research and experiments are needed to fully understand and confirm the extent of spacetime's elastic properties.