# If mass bends space ,doesn't that imply that space has "substance" -- and if so , what is this "fabric of space". ?

Cosmo : I think both you and Neb beautifully describe the difference that should be made between the use of a coordinated spacetime arena ,and the substance of space itself .

### 5 Answers

- cosmoLv 74 weeks agoFavorite Answer
This is a really good question, in part because modern physics has no clear answer.

Technically, in General Relativity, the equations and their application do not require that space have any substance. What is "real" in General Relativity is the distance between spacetime events --- a specific thing happening at a specific time and place (like a firecracker going off). The ensemble of distances between spacetime events requires that the underlying manifold is not Euclidean, but is instead a Riemannian geometry with a non-flat metric, and in discussing this it is possible to interpolate between spacetime events and define the value of curvature at each point. People then attribute this to a curved "fabric of space".

But in the theory of General Relativity, it's not important that there be substance to that underlying geometry --- all that matters is that the dynamics of spacetime events can be predicted (for example, a spaceship falling into a black hole while a strobe light on its hull emits bursts of light that are quantifiable as spacetime events). And that can be done without granting any substance to the underlying geometry.

Now, in Quantum Field Theory, we know that space is not empty ---- the various fields of all the various particles occupy all of space, even when the fields are minimally excited. But that idea is remarkably incompatible with General Relativity, and the lack of a good theory of Quantum Gravity is something we don't yet understand, and so we don't really have an answer to your question. There is probably something about space that acts in such a way as to make the geometries of General Relativity work the way they do, but we don't know what that is.

- nebLv 74 weeks ago
Definitely a conceptual dilemma....

At face value, the solutions of Einstein’s field equations are the components of the metric tensor. The metric tensor defines how we make space and time measurements, and specifically as a mathematical representation, how we compute the inner product of vectors/covectors - how we compute angles and magnitudes in an invariant manner. The spacetime interval is just an example of this. This is pretty far abstracted from the idea of a substance ....

From the metric tensor, we can determine the dynamics of a system since the first order changes in the metric tensor are used to define geodesics. Second order changes in the metric tensor determine spacetime curvature. So, everything about gravity and spacetime have their source in the metric tensor which is determined by the constraints in the field equations.

One dilemma is that gravitational fields have energy. It’s hard to claim something that has energy as being ‘nothing’. Attempts have been made to characterize the energy solely from the metric tensor using a pseudo tensor (has a preferred coordinate system) but many are uncomfortable with that. We also have gravitational waves that are propagating changes in the metric that carry energy/momentum. Again, hard to characterize that as ‘nothing’.

Can we resolve that with tensor bosons - gravitons? Maybe, maybe not. But that would give us a field that we can hang our hat on that would exist in an uncurved spacetime ...

Last but not least, another dilemma - the idea of active general covariance. This implies that spacetime emerges as relational, defined by the relationships between the metric tensor and the things that generate gravity. Active spacetime transformations called diffeomorphisms acting on everything result in invariant relationships independent of what spacetime we chose. This is really Einstein’s field on fields.

So, take your pick.

- ANDYLv 54 weeks ago
Here, you mentioned three things. The first, mass bends space. Matter does not bend space. The gravitational force─one of the four fundamental forces of the universe─does. The second, space has substance. Space does have substance, as you call it. Astrophysicists say that 40 to 50% of the mass in the universe is in the intergalactic space. It contains rarefied plasma that connects galaxies. Third, the fabric of space. It is called space-time fabric. This was confirmed by the two LIGO in U.S.A. and VIRGO in Italy devices. Einstein had predicted the presence of gravitational waves a hundred years ago; and for 5 years now several waves were detected proving that space-time fabric does exist after all.

Do not forget that there is also something called Dark Matter which makes up five times the amount of baryonic matter (the universe we observe). Dark matter is still an enigma and only speculations are formulated.

- nineteenthlyLv 74 weeks ago
No. What it means is that a non-axiomatic, observable aspect of geometry turns out to be incorrect and our intuitions are based on experience on a relatively small scale. The properties of space are altered by the presence of mass. More specifically, parallel lines do meet before infinity and the closer one is to a given mass the closer that convergence is. There is no fabric of space because space merely describes distance and direction. Distance and direction don't have a fabric.

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