What exactly is spacetime?

1. Aug 2, 2006

Ace Nova

I'm just wondering what is the nature of spacetime according to general relativity? Like what is the underlying geometry mean in laymans terms. What exactly is curved by the presence of gravity?

Any help would be appreciated.

2. Aug 3, 2006

Pythagorean

I don't have any relativity education (except what we lightly touched on in intro to modern physics, which wasn't much at all) but I will conjecture that I think Einstein's points was that space itself is what is curved, and this causes the phenomena we experience as gravity.

I think the whole point is that space is not just nothing, it actually has properties and interactions (such as how it interacts with time in GR).

I await the pros remarks though

3. Aug 3, 2006

turbo

What defines "empty" space? At a minimum, space is filled with the virtual particle pairs that define the Zero-Point Energy field, and that suffuse every bit of our Universe. This field contains the bulk of the mass-energy of our uiniverse, meaning that our visible universe is a very minor overdensity of matter vs antimatter in the whole scheme of things.

Your milage may vary. Not available in all universes.

4. Aug 3, 2006

5. Aug 3, 2006

Garth

We are familiar with living in a three dimensional space.
That is, we need to specify three coordinates to uniquely describe the position of a point in space.

Einstein pointed out that we cannot measure the position of an event except at a specific time, and that we cannot describe the time of an event except at a specific point in space. He therefore concluded we actually live in a four dimensional space-time. (Special Relativity)

The properties of this space-time are Minkowskian, which explains why the speed of light is invariant.

$$d\tau^2 = dt^2 - \frac{1}{c^2} [dx^2 + dy^2 + dz^2]$$ - the Minkowskian metric.

He further explained that this space-time manifold was curved by the presence of mass, strictly stress-energy-momentum, and this curvature was experienced as gravitation. This changes the coefficients in the metric.

Curvature of space-time is a subtle concept that has been much discussed here. In order to imagine it you have to embed it in a 5 dimensional space, however this is not necessary, 4 dimensional curvature can be intrinsically described by its internal geometry, the behaviour of parallel lines, the area and circumference of circles, the internal angles of a triangle, which may (flat space-time), or may not (space-time with curvature), be Euclidean.

If you slice space-time (foliate it) so a particular observer is at rest, you separate out what for them is space and time. Now in the presence of a gravitational field the space-like 3D hyper-surface will be described as curved, such as the curved funnel analogy, but it would be a misnomer to describe time as 'curved' (unless you are Salvador Dali!) instead the time component of space-time curvature is revealed as a time dilation.

Gravitational time dilation is observed when one clock at a particular depth in a gravitational field is observed by another clock at a different gravitational 'potential' depth. The lower clock is observed to run slow.

I hope this helps.

Garth

Last edited: Aug 3, 2006
6. Aug 3, 2006

Mickey

Einstein spent nearly a decade putting the theory together. If we could understand "exactly" what spacetime is in layman's terms, it's hard to imagine Einstein spending so much time on it.

However, for a glimpse at the geometry, it can be said that the notion of "speed" in ordinary terms is "slope" in spacetime geometrical terms. Light through a vacuum travels at a constant speed, so its path in spacetime geometry has a constant slope. Also, nothing can go faster than the speed of light, so no physical path can be plotted beyond that slope.

Last edited: Aug 3, 2006
7. Aug 3, 2006

MeJennifer

That is not exactly correct. Time dilation is the resut of the total curvature of both the space and time components.

8. Aug 3, 2006

Garth

You have not read my post accurately.

That is what I said:

Time dilation is an effect of the curvature of space-time - that is the static 4D manifold.

However, once a particular frame of reference is specified, say the observer's, this can be separated into a particular foliation of space and time.

The curvature of space manifests itself by the bending of light rays etc.

The time equivalent manifests itself as the observation of different rates of clocks at different gravitational 'potentials'; as well as between clocks moving relative to each other. An effect of the time dilation is to also add an equal component to light bending, which results in the total deflection being twice that calculated from a semi-relativistic Newtonian prediction.

Garth

Last edited: Aug 3, 2006
9. Aug 3, 2006

robphy

Some clarifications:

Since time-dilation appears in special relativity (which has a spacetime with no spacetime curvature), the presence of time-dilation does not imply that spacetime is curved.

10. Aug 3, 2006

MeJennifer

Observer perception of space is a function of both the space and time components of space-time.
And the same with time, observer perception of time is a function of both the space and time components of space-time.
If that is what you mean we are in agreement.

That is correct, relativistic time dilation and gravitational time dilation are two different things.

Last edited: Aug 3, 2006
11. Aug 3, 2006

baryon

Well Ace, here you go.

Imagine the universe as a two dimensional sheet of rubber that is stretched out evenly in all directions. Imagine that the celestial bodies are marbles sitting on the sheets. Each of the marbles will produce an indentation in the surface of the sheet where the marble sits. This indentation is analogous to a curve, it is a result of the rubber sheet curving under the weight of the marble. So in most places the sheet will be flat, but underneath each marble it will be curved.
Now any marble that is moved to the proximity of a heavier marble will be drawn toward the center of the heavier marble because of the curve. It will " roll toward" the heavier one. This is the phenomena known as gravity.
It has been experimntally proven that massive objects do exert gravitational forces on one another proportional to their individual masses. (i.e. The heavier marble is pulled by the lighter marble as well) However, if the two masses in question are more than a few hundred thousand kilograms different than the effect of the larger body on the smaller body will be the more apparent of the two.
Light tavels the simplest possible path, it doesn't want to fight the gravitational pull. It easily could but it won't. Therefore light, in the vicinity of a massive object will follow the curve as well. Imagine that you fire several small marbles(photons) along the surface of your sheet on a path tangent to a large marble. As the photonic marbles approach the more massive marble they begiin to curve. If you fired your photons at the right speed, they would be drawn to the massive object a tiny bit. This means that light also curves in the prescence of gravity. Of course if the massive object is not a neutron star (black hole) then the light, having sufficient escape velocity, will leave the vicinity of the massive objject and continue off into infinity on a straight line, That iis another principle of physics, that objects travel in straight lines unless some force causes them to curve again.
So if we didn't have gravity things would always be ramming into one another.

12. Aug 3, 2006

pervect

Staff Emeritus
Space is what you measure with a ruler. Time is what you measure with a clock.

The interesting thing about relativity is that events that seem to be 'at the same time' according to one observer do not necessarily occur 'at the same time' according to a different observer, one who is moving relative to the first observer.

Aside from this interesting distance, space-time is not much different that space + time. You measure spatial distances with a ruler and you measure time-intervals with a clock.

A few additional points: you need to know how to synchronize clocks to measure the time-distance between two points. This is done in special relativity via the Einstein convention (which takes advantage of the constancy of the speed of light).

Another more advanced point is that the metric is an important piece of mathematical machinery in GR, one that converts $\Delta$ coordinates into physical distances, the physical distances that you measure with rulers (and the time-intervals you measure with clocks). Conceptually, one imagines events in space-time labelled with a totally arbitrary choice of labels, chosen by human beings in some manner that's convenient.

The metric then allows one to calculate the measured distance between different events (a physical result) in space-time from their human-chosen coordinates.

Last edited: Aug 4, 2006
13. Aug 4, 2006

eep

I don't see how this analogy makes any sense because gravity is necessary for the marbles to cause the indentation in the first place.

14. Aug 4, 2006

Rach3

Why the arbitrary cutoff?

What does that mean?

The speed of light is a constant, in any locally intertial frame.

A neutron star is not a black hole.

15. Aug 4, 2006

star.torturer

thats what they are saying, its not a neutron star, its a black hole

16. Aug 4, 2006

Rach3

That's not what he said, look at the context.

17. Aug 4, 2006

baryon

My mistake

I meant to say, a COLLAPSED neutron star.:grumpy:

18. Aug 14, 2006

oldman

Exactly. Best way of defining something is to say what you can do with it. I still prefer my own operational definition: " Space is what you can swing a cat in" !

Spacetime, though, is more abstract. It is a coordinate space; something in the mind, represented by squiggles on paper or on a computer screen. But it is constructed from measurements of space with a ruler and time with a clock, just as you say. Similar to say, phase space.

Or, it's just something you can live in.

19. Aug 25, 2006