The Nature of the Gravitational Field

[stevo247]

In Relativity: The Special and General Theory page 155, Einstein expressed this quality of spacetime as follows,

"Spacetime does not claim existence on its own but only as a structural quality of the [gravitational] field"

 

Am I correct to assume that empty space or a vacuum is essentially the qualities of the gravitational field?

 

I have trouble understanding the concept of time, without the idea of movement. Is there a motion that is associated with the gravitational field itself?

[swansont]

Space and spacetime aren't the same thing. Spacetime is the four-dimensional geometry we use to measure things.

[stevo247]

Space and spacetime aren't the same thing. Spacetime is the four-dimensional geometry we use to measure things.

 

Maybe I should just stay away from that concept until I get a handle on “space”.

 

Is space the gravitational field?

[insane_alien]

no, the gravitaional field exists in space. it isn't space itself.

[stevo247]

no, the gravitaional field exists in space. it isn't space itself.

 

Does space exist without a gravitational field?

 

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Einstein says that:

 

"There can be no space nor any part of space without gravitational potentials; for these confer upon space its metrical qualities, without which it cannot be imagined at all. The existence of the gravitational field is inseparably bound up with the existence of space."

 

http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html

 

Does the nature of space create the gravitational field?

[Realitycheck]

If the universe had no matter in it, then there would be no gravity, but then it would also be arguable that it wasn't a universe, either.

 

Matter creates the gravitational field.

[jedaisoul]

no, the gravitaional field exists in space. it isn't space itself.

Does space exist without a gravitational field? Einstein says that:

"There can be no space nor any part of space without gravitational potentials; for these confer upon space its metrical qualities, without which it cannot be imagined at all. The existence of the gravitational field is inseparably bound up with the existence of space."

I'm not sure whether insane_alien is expressing his own views, but what he says does not correspond to Einstein's view. You have correctly interpreted what Einstein said. He believed that space did not exist, and that the "place" in which objects exist and events occur is defined by the gravitational field. Without the gravitational field there is no space, no vacuum, not even nothing. There is nowhere.

 

Does the nature of space create the gravitational field?

See above...

[ajb]

The gravitational field from a modern point of view is a "geometric object*" on space-time. The gravitational degrees of freedom are the metric or the connection or vierbein and spin connection or some other set of variables like Ashtekar (or new) variables. All of which are really just useful ways of rewriting the metric**.

 

These all describe the local geometry of space-time. In fact, without these the space-time would have no geometry. So, I would say that gravity "is" the local geometry of space-time and not space-time itself.

 

 

*by this I mean it has a well defined transformation law under passive diffeomorphisms.

 

** we forget about torsion here for now.

[jedaisoul]

If the universe had no matter in it, then there would be no gravity, but then it would also be arguable that it wasn't a universe, either. Matter creates the gravitational field.

Not according to Einstein. In addition to the quote given in the OP, Einstein made his views quite clear in the original paper on General Relativity: "Thus according to the general theory of relativity, gravitation occupies an exceptional position... since the ten functions representing the gravitational field at the same time define the metric properties of the space measured". A Einstein "The Foundation of the Genrall Theory of Relativity", Annalen der Physic, 49, 1916. Furthermore, chapter 14 of that paper specifically dealt with "The Field Equations of Gravitation in the Absence of Matter". It is quite clear that Einstein saw the gravitational field as existing in the absence of matter, as he even derived the field equations for it!

[stevo247]

So space then, is a geometric construction based on the nature of the gravitational field. Einstein states that “the ten functions representing the gravitational field at the same time define the metric properties of the space measured”. These “functions”, I would have assumed, would be rooted in the properties of matter. Since Einstein used “field equations of gravitation in the absence of matter”, what exactly are the “ten functions of the gravitational field” based on?

[jedaisoul]

Since Einstein used “field equations of gravitation in the absence of matter”, what exactly are the “ten functions of the gravitational field” based on?

I hoped you would not ask that! You'd need to ask someone who understands general relativity better than I do. I focus on the conceptual meaning of the theory. When it comes to the mathematical functions, I'm out of my depth.

[ajb]

Look up the Einstein field equations on wiki for now.

 

You got more specific questions that I will try to answer them.

[stevo247]

The gravitational field from a modern point of view is a "geometric object*" on space-time. The gravitational degrees of freedom are the metric or the connection or vierbein and spin connection or some other set of variables like Ashtekar (or new) variables. All of which are really just useful ways of rewriting the metric**.

 

These all describe the local geometry of space-time. In fact' date=' without these the space-time would have no geometry. So, I would say that gravity "is" the local geometry of space-time and not space-time itself.[/quote']

 

 

What then is the nature of space-time itself, without the influence of gravity on a local geometry?

 

I have a few other questions. Please forgive my ignorance if any of my questions seem screamingly obvious. This stuff is all new to me and I’m just trying to get oriented.

 

1. Does energy have a gravitational force or is it only a property of matter?

 

2. Is empty space (no nothing) considered 3 dimensional?

 

3. Is energy considered 3 dimensional?

[timo]

What then is the nature of space-time itself, without the influence of gravity on a local geometry?

You can probably think of it as a background in which the physical objects (spacetime not being counted as a physical object for the sake of this argument) and processes are embedded. Like a piece of paper on which you draw a painting, except that the painting ususally doesn't influence the paper and that you usually view a picture at once, not line by line (<= time by time).

 

 

1. Does energy have a gravitational force or is it only a property of matter?

Energy is a property of matter and -strictly speaking- also of non-matter objects (e.g. electromagnetic waves are usually not considered matter). It is, however, a property that plays a role in the gravitational influence similarly to the role that mass plays in classical Newtonian gravity where twice a mass exerts twice a gravitational force on other objects. "Does energy have a gravitational force" does not seem like a correct statement; it seems akin to asking whether charges have an electromagnetic force.

 

2. Is empty space (no nothing) considered 3 dimensional?

In standard physics, there are three dimensions of space. However, there is no "the space" and "the time". Taking the piece of paper again: The piece is two-dimensional. Any line on the piece of paper is one-dimensional. There is, however, no "the line" as you can draw arbitrary lines on the piece of paper. You can decompose the piece of paper into sets of parallel 1D lines (ignoring that a piece of paper has finite size, here). Yet, there is not "the set of parallel 1D lines" since their orientation is still arbitrary.

Similarly, you can cast a non-curved (flat, no gravity) spacetime into a set of spaces (each representing a different time, then). While there's some restrictions that have no analogy with the piece of paper example, the main statement remains the same: There is no "the set of spaces", you have some arbitrariness in the definition.

 

3. Is energy considered 3 dimensional?

No.

[ajb]

What then is the nature of space-time itself, without the influence of gravity on a local geometry?

 

You should think of space-time as a "collection of events". By that I mean that if "something" happens it happens at a point in space-time. As each point p can be assigned a coordinate i.e a collection of numbers [MATH]x^{a}(p)[/MATH] with reference to a designated coordinate system every event can be assigned a coordinate. Space-time is thus a (smooth) 4-d (3 space + 1 time) manifold. Note so far we do not have a notion of lengths between point on the manifold.

 

Now, a metric should be thought of a way to define distances between near by points. From the metric you can build a geometry,.i.e you can give the manifold local curvature. How you do this is probably no so important right now.

 

So, you can not really talk about space-time with out gravity. Space-time is defined to be a manifold with a metric and the gravitation field is identified with the metric. By "no gravity" we mean that the metric is (locally) the same as on Minkowski space-time.

 

An analogue would be something like no electromagnetic field. What you really mean is that the field has a value of zero. Which is not quite the same as "no field".

 

I have a few other questions. Please forgive my ignorance if any of my questions seem screamingly obvious. This stuff is all new to me and I’m just trying to get oriented.

 

1. Does energy have a gravitational force or is it only a property of matter?

As Atheist says, energy is a property of "stuff".

 

Now, matter (fields are what I really mean) couple to gravity via there energy-momentum. So in a way you can say energy does have a gravitational force.

 

2. Is empty space (no nothing) considered 3 dimensional?

Yes, see my answer to your first comments.

 

3. Is energy considered 3 dimensional?

 

In short no.

[stevo247]

When the 3 dimensions of space and the 1 dimension of time are arranged in the coordinate system for the space-time grid, what is the nature of the space upon which the foundational grid is set up?

 

If the gravitational field and space are considered to be the same, and gravity is intimately involved with matter, does that imply that the original space-time grid is arranged on a space that possess relative states of matter, in motion?

[ajb]

When the 3 dimensions of space and the 1 dimension of time are arranged in the coordinate system for the space-time grid, what is the nature of the space upon which the foundational grid is set up?

 

I am not sure what you are asking here. Locally space-time "looks like" Minkowski space-time, i.e. it looks like [math]\mathbb{R}^{4}[/math]. It's "nature" is the same, a collection of events. Which is about the best answer you will get in the context of general relativity.

 

If the gravitational field and space are considered to be the same, and gravity is intimately involved with matter, does that imply that the original space-time grid is arranged on a space that possess relative states of matter, in motion?

 

The gravitational field is not to be identified with the underlying space-time. It should be considered as a field on the space-time, in particular the metric (or some other object essentially equivalent). You could say that the gravitation field is to be identified with the local geometry, but all that really means is what I have already said.

[swansont]

The space has a vacuum energy and properties such as electric permittivity and magnetic permeability. The metric for spacetime depends on the what the gravity looks like, though locally it will be flat.

[stevo247]

The gravitational field is not to be identified with the underlying space-time. It should be considered as a field on the space-time, in particular the metric (or some other object essentially equivalent). You could say that the gravitation field is to be identified with the local geometry

 

The space has a vacuum energy and properties such as electric permittivity and magnetic permeability. The metric for spacetime depends on the what the gravity looks like, though locally it will be flat.

 

These comments were especially helpful.

 

Thanks to all posters for hanging in there with me!

[pioneer]

If gravity can cause a change in space-time as defined by GR, and because SR can do the same thing using velocity, are the two related. For example, does relativistic mass generate gravity to create GR in motion? If this was true, does than mean one can convert energy into gravity. For example, we burn fuel based on EM chemicals for the propulsion energy to generate the rocket velocity to make the SR-GR gravity.

 

Another question I have about gravity is, since the space-time reference gets contracted and since the speed of light is constant, does the transmission of the gravity signal, take advantage of the contracted reference to reach distance objects apart from stationary reference? The affect that comes to mind is the idea of a black hole allowing the theoretical possibility of energy appearing elsewhere in the universe, sort of getting there without having to follow an energy beam we can track in stationary reference. Instead does the black hole see far distance like it is very close and moves the energy at the speed of light but using its own shrunken distance. So in our reference, it appears to just get there, without having to take the long space path indicative of our stationary reference? We see it appear, but the black holes sees an energy beam in motion reaching the final spot.

[ajb]

If gravity can cause a change in space-time as defined by GR, and because SR can do the same thing using velocity, are the two related. For example, does relativistic mass generate gravity to create GR in motion? If this was true, does than mean one can convert energy into gravity. For example, we burn fuel based on EM chemicals for the propulsion energy to generate the rocket velocity to make the SR-GR gravity.

 

Locally physics reduces to that of special relativity. This is the strong equivalence principle. This puts restrictions on how stuff can interact with gravity.

 

There are other weaker versions that say that locally space-time looks flat, which is just the statement that space-time is a manifold.

 

Really, you can think of special relativity as being contained within general relativity. The main differences are that in special relativity the metric is that of Minkowski and that we consider only linear automorphisms-> i.e. the Lorentz transformations as opposed to more general active diffeomorphisms.

 

 

Another question I have about gravity is, since the space-time reference gets contracted and since the speed of light is constant, does the transmission of the gravity signal, take advantage of the contracted reference to reach distance objects apart from stationary reference? The affect that comes to mind is the idea of a black hole allowing the theoretical possibility of energy appearing elsewhere in the universe, sort of getting there without having to follow an energy beam we can track in stationary reference. Instead does the black hole see far distance like it is very close and moves the energy at the speed of light but using its own shrunken distance. So in our reference, it appears to just get there, without having to take the long space path indicative of our stationary reference? We see it appear, but the black holes sees an energy beam in motion reaching the final spot.

 

Gravitational waves travel at c. Thus it is assumed that the gravitational interaction propagates at (or certainly at most) c.

[Farsight]

In Relativity: The Special and General Theory page 155, Einstein expressed this quality of spacetime as follows,

"Spacetime does not claim existence on its own but only as a structural quality of the [gravitational] field"

 

Am I correct to assume that empty space or a vacuum is essentially the qualities of the gravitational field?

No. Relativity: The Special and General Theory was written by Einstein in 1916. Here's an Einstein quote from 1920:

 

Mach’s idea finds its full development in the ether of the general theory of relativity. According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that ‘empty space’ in its physical relation is neither homogeneous nor isotropic....”

 

A "gravitational field" is a variation in the qualities of space. It's caused by matter/energy "conditioning" the surrounding space. Note that "curved spacetime" is an inadequate concept that describes what it does, not what it is.

 

I have trouble understanding the concept of time, without the idea of movement.

That's the correct approach. Time and motion are cofounded.

 

Is there a motion that is associated with the gravitational field itself?

No.

[Zephir]

The gravitational field is the direct consequence of Universe expansion. By relativity theory (the geometrodynamic theory in particular) every particle formed by gravitational waves (so called geon) should be forced to collapse into singularity. The expansion of Universe prohibits it.

 

By reciprocal (dual) way of quantum mechanic, every particle formed by probability wave should expand into infinity (this is steady state solution of Schrödinger equation for free particles, which isn't difficult to derive). The gravitational force prohibits such destiny, but the gravity can not be derived from quantum mechanics by any way and we can see, the same result can be achieved by omnidirectional collapse of universe.

 

If so, how the gravitational field appears, after then? We can imagine, the Universe collapses together with observable matter. But the matter is collapsing more slowly, being pre-collapsed and "more stiff" by such way. The subtle difference in space-time expansion near observable matter is the gravitational field.

 

 

We can observe the difference between matter and vacuum collapse speed by dilatation of iridium meter prototype, by weight loss of iridium meter prototype or by fading of standard supernovae candles with time (which has lead into finding of the acceleration of universe expansion), for example. So we can say, the omnidirectional Universe expansion is not just source of gravity, it's a source of "dark energy" as well. This is still a "classical physics" explanation. For explanation of Universe expansion as such we should consider more deeper theory.