## What is space-time "made out of"?

A thread in another forum about the definition of "nothing" got me thinking. I know matter is composed of molecules, which are composed of atoms, which are composed of electrons, neutrons and protons, which are composed of quarks, etc ...

But what about space-time itself? Since in General Relativity space-time is said to be curved, it must exist as a thing in some way. If mass or matter is thought of as "clumps" in space time, and matter is composed of clumps of atoms and so forth, does "empty" space, i.e. space with no rocks, gas or dust clouds, etc .. just a vacuum, contain sub-atomic particles as well, just perhaps not as bunched together?

And I also understand that in our universe matter is neither created nor destroyed, only rearranged. Was all the matter in the universe created in the Big Bang, or was it already there, and the Big Bang merely changed its form?
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 Originally posted by scott does "empty" space, i.e. space with no rocks, gas or dust clouds, etc .. just a vacuum, contain sub-atomic particles as well, just perhaps not as bunched together?
Some simplified answers to your questions: empty vacuum has been shown to not really be "empty", but instead to be a sea of quantum enery fluctuations. That is, tiny energy-anti-energy "bubbles" appear randomly, but only last for a specific period of time imposed by uncertainty principles. As to what the actual "fabric" of spacetime is -- who knows!

 And I also understand that in our universe matter is neither created nor destroyed, only rearranged. Was all the matter in the universe created in the Big Bang, or was it already there, and the Big Bang merely changed its form?
Very good question, to which no one has a clear answer (and if they claim to, they're lying!). In fact, to further complicate matters, the notion of "before" the Big Bang is not well-founded (unless you subscribe to cyclic bang/crunch theories, or other bizzare brane-world ones).
 Blog Entries: 1 Recognitions: Gold Member http://www.physicsforums.com/archive/topic/5732-1.html this topic has been discused on PF before, have a look at this link.

## What is space-time "made out of"?

Sugar and spice and everything nice?
 Recognitions: Gold Member Science Advisor Staff Emeritus The terms "space-time" and "gravitational field" are basically interchangeable. If it weren't for mass, there would not really be any space-time. But I guess that doesn't really help answer the question. [g)] - Warren

 But what about space-time itself? Since in General Relativity space-time is said to be curved, it must exist as a thing in some way.
Spacetime is not made out of anything.

In General Relativity a region of spacetime may or may not be curved. Its curved only when there are tidal forces present. A region in which there is a uniform gravitational field the spacetime is flat.

 Originally posted by chroot The terms "space-time" and "gravitational field" are basically interchangeable.
In an inertial frame of referance in flat spacetime there is still spacetime. However there is no gravitational field in that case so the terms are not synonymous

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 Originally posted by pmb_phy In an inertial frame of referance in flat spacetime there is still spacetime. However there is no gravitational field in that case so the terms are not synonymous
It's semantics. Some authors would say that in the absence of mass, space and time are "separate," and thus space-time does not really exist. Some authors (Wald, etc.) have made the point that "space-time" and "gravitational field" are synonymous -- I'm not the first person to say it. Whether or not it's a useful thing to say, however, is certainly up for debate.

- Warren

 Originally posted by pmb_phy Spacetime is not made out of anything. In General Relativity a region of spacetime may or may not be curved. Its curved only when there are tidal forces present. A region in which there is a uniform gravitational field the spacetime is flat.
This isn't true. Tidal forces are strictly determined by a non-zero Weyl tensor. The Ricci tensor can exist for constant curvature (where the Weyl tensor is zero). After all, that's the basis of the cosmological principle: vanishing Weyl tensor (no tidal forces, no gravitationally preferred direction -- and thus isotropy).

 Originally posted by chroot It's semantics. Some authors would say that in the absence of mass, space and time are "separate," and thus space-time does not really exist. Some authors (Wald, etc.) have made the point that "space-time" and "gravitational field" are synonymous -- I'm not the first person to say it. Whether or not it's a useful thing to say, however, is certainly up for debate. - Warren
Do you have a referance for where Wald said that? I'd like to see the context in which he said it so I can understand exactly what he meant.

Thanks

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 Originally posted by pmb_phy Do you have a referance for where Wald said that? I'd like to see the context in which he said it so I can understand exactly what he meant. Thanks
I'll try to find the passage when I get home tonight -- I don't have the book with me here at work. It might have actually been in Foster and Nightingale's "Short Course on General Relativity." I'll try to find it.

- Warren
 So are you saying then, that massive objects which exist create a field between them, a gravitational field, and this field can be flat or curved depending on the mass of the objects? Is the gravitational field anything like an electrical field or a magnetic field? Is the gravitational field at all analagous to the fields (forces)which attract electrons to nuclei and which keep protons and neurtrons together? So space-time is just this gravitational field?

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 Originally posted by scott So are you saying then, that massive objects which exist create a field between them, a gravitational field, and this field can be flat or curved depending on the mass of the objects?
Yes. Mass curves spacetime, and curved spacetime makes masses move. According to the general theory of relativity, gravitation -- the attraction of two masses to each other -- is the result of those objects moving through curved spacetime.
 Is the gravitational field anything like an electrical field or a magnetic field?
In some respects it is, but in other it is not. Gravity is like E&M in that forces fall with the square of the distance. It is unlike E&M in that the forces are "ficticious." It is also unlike E&M in that (so far, anyway) no one has been able to determine a suitable gauge group for gravity. E&M, on the other hand, has just about the simplest possible gauge group.
 Is the gravitational field at all analagous to the fields (forces)which attract electrons to nuclei and which keep protons and neurtrons together?
Not really, no. There are very, very many differences between gravity and the other three forces.
 So space-time is just this gravitational field?
In a sense -- but don't snarled up in the definition of the words.

- Warren

 Originally posted by chroot The terms "space-time" and "gravitational field" are basically interchangeable.
i would say spacetime is a manifold, and the gravitational field is the metric on that manifold.

in other words, i do not think they are quite interchangable

 Originally posted by chroot If it weren't for mass, there would not really be any space-time.
oh? so what is the meaning of vacuum solutions to Einstein's equation which are not Minkowski space? these can have nontrivial gravitational fields. you can have gravitation even in the absense of all matter.

and of course, see my above objection: spacetime is not the same as metric. Einstein's equations cannot even be formulated in the absence of a spacetime.

 Originally posted by lethe i would say spacetime is a manifold, ...
There is a manifold which is the mathematical representation of spacetime if that is what you mean?
 ...and the gravitational field is the metric on that manifold.
Now that I agree with! [:)]

 Originally posted by pmb_phy There is a manifold which is the mathematical representation of spacetime if that is what you mean?
well, i don't really like arguing semantics, so i will just say that all these things are words that we use to represent elements of our models. these elements of our models are mathematical structures, like the manifold.

an implicit assumption in science is that we expect our models to accurately describe the real world. the more starry-eyed among us begin to not distinguish the model from the real thing, and then we freely abuse the language and say things like:

"spacetime is a manifold"
 I find it interesting--and baffling--that the gravitational force and the electrostatic force can be so empirically similar and yet give rise to such completely different theory. Why do we not explain electrostatic attraction by saying that the presense of a *charge* warps space-time? Why do we not use the fact that gravitational fields are conservative to develop a scalar potential, formulate gauges, obtain Maxwell-esque equations, etc.? How is it that photons come tantalizingly close to having mass--they are affected by grav fields, they have a non-zero momentum and can impart some of it to massive objects--but have no charge-like properties? To put my question another way (reminiscent of Jackson's Chapter 0), grav and e-static potentials can both be written as some function of r times r^$$\epsilon$$, where $$\epsilon$$ is some number. Why is it that, in both cases, the 'some function' is just the number one, and the epsilon is (confirmed to a very high degree of precision) exactly negative one? Just wondering. P

 Originally posted by rocketcity I find it interesting--and baffling--that the gravitational force and the electrostatic force can be so empirically similar and yet give rise to such completely different theory.
the fact that in the static limit, the gravitational and electric force both obey the inverse square law is not at all surprising. it has nothing to do with similarities between the two forces.

any long range isotropic force must obey an inverse square law. this is because we live in 3 spatial dimensions. there is no choice about it.

but put the objects in motion, introduce dipoles, and you will see that the way the forces act are actually very different, when you are not looking at a static isotropic problem.

 Why do we not explain electrostatic attraction by saying that the presense of a *charge* warps space-time? Why do we not use the fact that gravitational fields are conservative to develop a scalar potential, formulate gauges, obtain Maxwell-esque equations, etc.?
because there is no equivalence principle for electric forces.

if you put a piece of charged styrofoam and a piece of neutral metal in an electric field next to each other, they will follow different paths. and we therefore cannot attribute their paths to curvature of spacetime.

however, if you put two objects next to each other, any two objects, made of anything at all, in a gravitational field, then they will follow the same path. does not matter how much charge, mass, or spin they have.

 How is it that photons come tantalizingly close to having mass--they are affected by grav fields, they have a non-zero momentum and can impart some of it to massive objects--but have no charge-like properties?
photons have no charge because if they did, they would not be a long range force, it would only act on subatomic scales, and we would not be able to see them.

in other words, photons have no charge because we can see them!

they don't have to have no charge. in fact, there are other bosons that are a lot like photons, except that they do have charge. they are the gluons. we can't see them because they do have charge, and so only act on short distances.

we got pretty lucky that photons have no charge.

 To put my question another way (reminiscent of Jackson's Chapter 0), grav and e-static potentials can both be written as some function of r times r^$$\epsilon$$, where $$\epsilon$$ is some number. Why is it that, in both cases, the 'some function' is just the number one, and the epsilon is (confirmed to a very high degree of precision) exactly negative one?
see above. in 3 dimensions, any long range isotropic force must have inverse square law.