I just wanted to ask what is spacetime.

GR claims that mass curves, or bends, spacetime. If this is true, does that mean that spacetime is composed of something? If it isn't, how do you curve, or bend, "nothingness". What does the spacetime curvature in Einstein's GR equations physically represent?

Hi Tom,

Many great minds have thought about that question, that actually turns out to be more philosophic than scientific in nature. I think the most common viewpoint is that spacetime is "the thing that holds matter and energy and where those two can move in".

Now that I come to think of it, I've nowhere ever read a definition of spacetime which is different than R⁴ with a metric defined on it. But then again, I did not read many books on GR, only on SR. Perhaps James or somebody has something to add to this ?

Bye!

Crisp

Crisp,

I basically asked the questions I asked to resolve a contradiction I keep seeing on these forums.

Relativists will say that aether doesn't exist, and that electromagnetic waves don't need a medium to travel, but then claim that mass curves spacetime. It seems to me that if spacetime really does curve, then it has to be some kind of substance, like an aether or medium, since you obviously can't curve nothingness.

Tom

Originally posted by Prosoothus
I just wanted to ask what is spacetime.

GR claims that mass curves, or bends, spacetime. If this is true, does that mean that spacetime is composed of something? If it isn't, how do you curve, or bend, "nothingness". What does the spacetime curvature in Einstein's GR equations physically represent?

If you read anything on the search quantum gravity, you'll often see the quantization of the gravitational field mentioned, or in other words, spacetime itself. This field does not rely on matter for it's existence, and GR can consistently describe empty universes. This leads some to conclude that GR is an aether theory, and that spacetime is made of some kind of substance. To add to the confusion, Einstein himself made some comments that might lead one to believe that the aether is indeed restored in GR. But this is misleading.

John Baez writes this on the subject:

"What Einstein really meant was that the aether which had been overthrown by str (and thus was incompatible with gtr, which incorporates str) involved a a specific ``preferred frame of reference'' in the classical field theory, whereas the field equation of gtr involves no ``prior geometry'' (such as the euclidean geometry of ``space'' which has assumed by Maxwell and his contemporaries), much less any ``preferred frame''. Nonetheless, gtr does not quite say there is ``nothing'' in ``empty space''; in general there will be gravitational waves running about, and these carry (very tiny) amounts of energy, which gravitate. So in this sense, a very different kind of ``aether'' in the very weak sense of there being ``something there'' in a vacuum (namely nonlocalizable gravitational field energy, metric properties of ``space'' in a 3+1 decomposition, etc.), could be said to enter into gtr.

The general idea seems to be that the gravitational field is fundemental (and thus not made of anything else), though no one has been able to unify all physical forces in terms of one single field.

I think that spacetime IS 'nothingness' as Prosoothus puts it. And I think it can still be curved. I dont think something (or nothing!!!) has to have mass to be curved. For example light does not have mass, it is simply a disturbance of an EM field but it can be curved. Would u say that an EM field is nothingness?

I guess it depends on what ur definition of nothingness is but one thing is certain, spacetime is curved by mass!

Hi Tom,

You are convincing me more and more to do a thourough investigation into GR every day. Good.

"It seems to me that if spacetime really does curve, then it has to be some kind of substance, like an aether or medium, since you obviously can't curve nothingness."

You can also put it in another way: nothing curves, but the objects in spacetime (stars, planets) act like if it were curved. You see, the whole point of geodesics (paths in spacetime) is exactly that objects "naturally tend to minimize" their energy. I suppose you can put it to words in some other way. The underlying maths (and mind you, that is general relativity, a bunch of differential geometry, not some cheap words) will stay the same.

Bye!

Crisp

Beercules,

The general idea seems to be that the gravitational field is fundemental (and thus not made of anything else), though no one has been able to unify all physical forces in terms of one single field.

Gravitational fields can't be fundamental since they come in different strengths. For example, since the gravitational attraction caused by a blackhole is much greater than the gravitational field caused by the Earth, the space a hundred miles away from the blackhole has to be somehow "different" than the space a hundred miles away from the Earth. Einstein claimed that the difference is the actual curvature of spacetime. If this is the case, you can't have "nothingness" curved in two different ways, much less one.

Tom

Originally posted by Prosoothus
Gravitational fields can't be fundamental since they come in different strengths.
That's just silly. All forces come in different strengths based on distance.

Einstein claimed that the difference is the actual curvature of spacetime. If this is the case, you can't have "nothingness" curved in two different ways, much less one.
Curved space is a term. It doesn't mean space is actually curved. It just means that objects within that area act as if it is.

John Connellan,

I think that spacetime IS 'nothingness' as Prosoothus puts it. And I think it can still be curved. I dont think something (or nothing!!!) has to have mass to be curved. For example light does not have mass, it is simply a disturbance of an EM field but it can be curved. Would u say that an EM field is nothingness?

Please explain how "nothingness" can curve.

Einstein's field equations can't represent any properties of "nothingness", since "nothingness", by definition, has no properties.

As for light, it is a physical entity (whether you consider it a particle or wave) so it has properties. Because light has properties, like location, it is possible for those properties to change.

I guess it depends on what ur definition of nothingness....

By nothingness I mean that there isn't any mass, energy, or any fields. Now whether there is no space, I haven't decided yet. :)

Originally posted by Prosoothus
By nothingness I mean that there isn't any mass, energy, or any fields. Now whether there is no space, I haven't decided yet. :) There is never nothingness. Gravity is always present.

Persol,

That's just silly. All forces come in different strengths based on distance.

If forces come in dfferent strengths, wouldn't that mean that the forces are "composed" of something? You can't have force of different strengths that is composed of nothing, can you?

Curved space is a term. It doesn't mean space is actually curved. It just means that objects within that area act as if it is.

Are you saying that a gravitational field is not curved space, but is rather composed of a substance, or an exchange of particles? If so, it appears that your concept of gravity is different than Einstein's.

Persol,

There is never nothingness. Gravity is always present.

What is gravity?

Originally posted by Prosoothus
Beercules,

Gravitational fields can't be fundamental since they come in different strengths. For example, since the gravitational attraction caused by a blackhole is much greater than the gravitational field caused by the Earth, the space a hundred miles away from the blackhole has to be somehow "different" than the space a hundred miles away from the Earth.

The problem here is that the gravitational field of GR, which literally is spacetime, is often confused with Newton's gravitational field(s). Recall that in Newton's theory of gravitation, there is a mysterious force field between massive bodies, with the strength of the force falling off the further away one gets from the body. In GR, this mysterious "force" is given a geometric explanation in the form of spacetime curvature. However, the field that defines spacetime is (unfortunately) also called the gravitational field.

This field however, is not dependent on mass for it's existence. You can have a gravitational field where spacetime is flat, and hence there is no gravity. In that case, the choice of words to name the field of spacetime seems poor, but at any rate it only matters that the 2 fields are not the same. Curvature of a more fundemental field is Newton's gravitational field(s).

Einstein claimed that the difference is the actual curvature of spacetime. If this is the case, you can't have "nothingness" curved in two different ways, much less one.

As I said, it doesn't help much to call space nothingness, when it's really just the structural quality of the gravitational field. The more curvature in a given region, the more mass you have.

In the general relativistic picture of gravity, it is common to talk about the "curvature of spacetime". The thing people are missing in this thread is that when physicists say things like "mass curves spacetime" they are talking in the context of a particular theory.

You can't see curved spacetime, or detect curvature directly in any way. All you can see is the effects on objects and events. So, the question of whether spacetime "really" curves, or whether saying it is curved is just a convenient picture which leads to correct explanations of the behaviour of objects and events is more one of philosophy than physics. Physics does not attempt to answer philosophical questions such as whether space is really curved. Physics aims for correct descriptions of events.

So, the fact that GR says spacetime is curved says absolutely nothing about whether space has "substance" or not. Saying space is curved near object z might just as well be shorthand for saying "object x behaves in manner y in the gravitational environment associated with object z".

When it comes to the "ether" concept, you need to be specific about what you mean. General relativity absolutely rules out the existence of the kind of "ether" which physicists talked about prior to Einstein - i.e. a substance which carries light waves and which constitutes an absolute state of rest. This, as it happens, is almost always the ether which people who don't believe in relativity subconsciously mean when they use that word.

Well put James R.

The term 'curved space-time' make people tend to imagine intutively & incorrectly about an invisible curvature in space-time construct rather than an effect.