General relativity does not seem to address gravity

[LostConjugate]

So as I learn general relativity I am finding that it does not appear to address gravity in any way. The entire subject addresses the fact that gravity is different in all places. And this is a result of different shaped massive objects and your distance from the object.

Since most large objects are round it means gravity is both different at distances and from side to side, which is where the term "curved space" comes from, however there is no magic happening here, it is the round object which is curved and it is easier mathematically to address space as being curved since it works under transformations to another reference frame.

The question of why an object in a gravitational field appears to be in a non-inertial frame does not seem to be answered, just accepted.

 

[Passionflower]

So as I learn general relativity I am finding that it does not appear to address gravity in any way.

How far have you been in learning it? Keep learning until you know enough about general relativity to understand it does address gravity.

The entire subject addresses the fact that gravity is different in all places. And this is a result of different shaped massive objects and your distance from the object.

Since most large objects are round it means gravity is both different at distances and from side to side, which is where the term "curved space" comes from, however there is no magic happening here, it is the round object which is curved and it is easier mathematically to address space as being curved since it works under transformations to another reference frame.

It seems to me that your current level of understanding is seriously flawed. What books do you use to learn general relativity?

The question of why an object in a gravitational field appears to be in a non-inertial frame does not seem to be answered, just accepted.

You have to be more specific. For instance a free falling object in a gravitational field is in a (local) inertial frame. A stationary object in a gravitational field is in a non-inertial frame but not because of gravity but because it is accelerating "against" gravity.

 

[LostConjugate]

You have to be more specific. For instance a free falling object in a gravitational field is in a (local) inertial frame. A stationary object in a gravitational field is in a non-inertial frame but not because of gravity but because it is accelerating "against" gravity.

A stationary object.

and that is exactly my question, a stationary object on the surface of the Earth appears to be in a non-inertial frame, however in real non-inertial frames such as a stationary object in an accelerating elevator this can only go on for so long as eventually the object would approach the speed c. This follows because, and it goes without saying, the definition of a non-inertial frame is a non zero second time derivative of space.

I am reading these papers http://preposterousuniverse.com/grnotes/
and following Leonard Susskind's course on youtube.

I am not sure it is a flawed way of looking at it, for example imagine a flat planet that extends to infinity, then you would not have a curved space, but only a stretched space. The curvature depends on the object, this is because each particle of energy in the object is responsible for the gravitational field, therefore it looks curved if the object is curved.

 

[JesseM]

and that is exactly my question, a stationary object on the surface of the Earth appears to be in a non-inertial frame, however in real non-inertial frames such as a stationary object in an accelerating elevator this can only go on for so long as eventually the object would approach the speed c.

In SR you can accelerate with constant proper acceleration (constant acceleration as measured by onboard accelerometers, which also implies a constant G-force is experienced) without ever reaching c, the key is that your coordinate acceleration in any inertial frame is constantly decreasing, the two types of acceleration are not the same (proper acceleration at any given instant corresponds to coordinate acceleration in the inertial frame where your velocity is zero at that instant). See http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html for more info.

This follows because, and it goes without saying, the definition of a non-inertial frame is a non zero second time derivative of space.

"second time derivative" relative to what coordinate system? An inertial one? That seems like a somewhat circular definition, I think it'd be better to define a non-inertial frame as one where the laws of physics take a different form than they do in the set of inertial frames in SR that satisfy the two postulates of SR. Also, can we presume you're familiar with the equivalence principle?

I am not sure it is a flawed way of looking at it, for example imagine a flat planet that extends to infinity, then you would not have a curved space, but only a stretched space. The curvature depends on the object, this is because each particle of energy in the object is responsible for the gravitational field, therefore it looks curved if the object is curved.

What do you mean by "looks curved"? General relativity defines curvature in terms of the metric which tells you the proper time along different worldlines in spacetime, it isn't based on visual appearances.

 

[espen180]

It appears to me that you are relating the curvature of space-time with the curvature of the objects distorting it. This is a misconception. The curvature in GR is given by the Riemann tensor, which is more complicated than you are suggesting.

 

[LostConjugate]

In SR you can accelerate with constant proper acceleration (constant acceleration as measured by onboard accelerometers, which also implies a constant G-force is experienced) without ever reaching c, the key is that your coordinate acceleration in any inertial frame is constantly decreasing, the two types of acceleration are not the same (proper acceleration at any given instant corresponds to coordinate acceleration in the inertial frame where your velocity is zero at that instant). See http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html for more info.

Ok I guess I can see that, but you do approach c relative to the initial inertial frame. Then you kind of linger in the continuous area between c and less than c?

"second time derivative" relative to what coordinate system? An inertial one? That seems like a somewhat circular definition, I think it'd be better to define a non-inertial frame as one where the laws of physics take a different form than they do in the set of inertial frames in SR that satisfy the two postulates of SR. Also, can we presume you're familiar with the equivalence principle?

I mean't relative to some inertial frame, this is the way it is explain usually, the way space becomes hyperbolic from the view of some inertial frame. The equivalence principle just says the motion of an object in a gravitational field is equivalent to an object in a non-inetrial frame right? The only obstruction is that these field permeate from objects of different shapes and distances, so are different everywhere.

What do you mean by "looks curved"? General relativity defines curvature in terms of the metric which tells you the proper time along different worldlines in spacetime, it isn't based on visual appearances.

I mean't looks curved on paper, mathematically.

It appears to me that you are relating the curvature of space-time with the curvature of the objects distorting it. This is a misconception. The curvature in GR is given by the Riemann tensor, which is more complicated than you are suggesting.

I don't think the Riemann tensor is more complicated... It is exactly what I am saying, the space "looks" curved on paper because the massive object is round or some complex shape. For example what is the Riemann tensor for a gravitational field that is constant everywhere, very simple.

 

[George Jones]

I don't think the Riemann tensor is more complicated... It is exactly what I am saying, the space "looks" curved on paper because the massive object is round or some complex shape. For example what is the Riemann tensor for a gravitational field that is constant everywhere, very simple.

What about the curvature tensor of a vacuum?

 

[Ikoro]

i have studied general relativity and i have also reached the same conclusion it does not really tell us what gravity really is. It tells us that gravity can be due to geometry of space but it fails to define what space is. So relativity only opens one doorway to gravity by relating it to geometry which is logically sound but fails to define how something you can't see or touch(space) can have physical properties. So in that sense the theory breaks down. It is like saying the sun gives us energy but not defining how the energy is produced by the sun.

 

[espen180]

i have studied general relativity and i have also reached the same conclusion it does not really tell us what gravity really is. It tells us that gravity can be due to geometry of space but it fails to define what space is. So relativity only opens one doorway to gravity by relating it to geometry which is logically sound but fails to define how something you can't see or touch(space) can have physical properties. So in that sense the theory breaks down. It is like saying the sun gives us energy but not defining how the energy is produced by the sun.

Even if GR did explain how space can exhibit physical properties, that explanation would be founded on another set of unexplained axioms. I view the spacetime in GR as nothing more than a mathematical construct used to express the theory. The concept of a wavefunction in QM is in the same boat. I feel that questions like "What is gravity really?" falls outside the domain of science. At least, that's how I view it.

 

[JesseM]

Ok I guess I can see that, but you do approach c relative to the initial inertial frame.

Well, you only "approach" it in the limit as coordinate time in the initial inertial frame goes to infinity, at any finite time your velocity in the initial inertial frame is some finite amount less than c.

The equivalence principle just says the motion of an object in a gravitational field is equivalent to an object in a non-inetrial frame right?

You can describe it in terms of an "equivalence" between being at rest in a gravitational field and accelerating in flat spacetime, but the more common way of describing it is that saying the local observations of an observer in free-fall in a gravitational field (i.e., no non-gravitational forces acting on him) are equivalent to those of an inertial observer in flat spacetime (but only if the free-falling observer confines his observations to events in a small local region of spacetime around him...the equivalence only becomes precise in the limit as the size of this small local region approaches zero).

I don't think the Riemann tensor is more complicated... It is exactly what I am saying, the space "looks" curved on paper because the massive object is round or some complex shape.

But you understand the curvature tensor describes the curvature of space[/i]time[/i], not just of space, right? And that it describes it by giving a way to integrate ds^2 along any arbitrary worldline, which for a timelike worldline gives you the proper time? For example, objects following geodesics don't follow worldlines with the shortest spatial length, they follow worldlines with the greatest proper time (relative to other 'nearby' worldlines)

 

[LostConjugate]

But you understand the curvature tensor describes the curvature of space[/i]time[/i], not just of space, right? And that it describes it by giving a way to integrate ds^2 along any arbitrary worldline, which for a timelike worldline gives you the proper time? For example, objects following geodesics don't follow worldlines with the shortest spatial length, they follow worldlines with the greatest proper time (relative to other 'nearby' worldlines)

Yes I think I do understand all this, not perfectly but generally.

Let me re-phrase my question.

What does GR have to say about gravity that is constant everywhere?

I feel it has nothing to say, since it only addresses the consequences of gravity being slightly different everywhere which doesn't address GRAVITY itself.

 

[espen180]

If you can find a situation where that is the case, GR will give you the metric for that spacetime.

In Newtonian gravity, an infinite sheet of constant mass distribution causes a uniform gravitational field. I don't know if GR will predict otherwise. The reason is that in GR, gravity couples to energy as well as mass. Since the gravitational field has energy, gravity is itself a source of gravity.

 

[jcsd]

Yes I think I do understand all this, not perfectly but generally.

Let me re-phrase my question.

What does GR have to say about gravity that is constant everywhere?

I feel it has nothing to say, since it only addresses the consequences of gravity being slightly different everywhere which doesn't address GRAVITY itself.

Minkowski space describes constant gravity.

Whilst Newtonian gravity takes a different approach to describing gravity, in both GR and NG a constant gravitational field is equivalent to a suitable non-inertial frame in a space where there is no gravity.

That's really just an illustrartion of the motivations behind general relativity.

 

[jcsd]

If you can find a situation where that is the case, GR will give you the metric for that spacetime.

In Newtonian gravity, an infinite sheet of constant mass distribution causes a uniform gravitational field. I don't know if GR will predict otherwise. The reason is that in GR, gravity couples to energy as well as mass. Since the gravitational field has energy, gravity is itself a source of gravity.

It requires an infinite flat plate to create that kind of gravitational field.

If the gravitational field is constant in time as well as space then it is by definition static so we needn't worry about the gravitational waves.

 

[espen180]

It requires an infinite flat plate to create that kind of gravitational field.

If the gravitational field is constant in time as well as space then it is by definition static so we needn't worry about the gravitational waves.

Waves weren't my concern. Since gravity couples to itself, the field at one point is not equal to the superposition of the fields of the two masses like in Newtonian gravity, since the field energy density must be taken into account. (Am I misunderstanding?)

Since the fact that an infinite sheet has a constant gravity in NG is a result of the face that fields can be linearily added, and since in GR this is not the case, i wonder how the situation changes.

 

[LostConjugate]

I am trying to do away with the talk of gravitational waves and curved space, and just focus on why gravity is like a non-inertial frame.

Because energy warps space to me just means we found an elegant way of expressing it mathematically, it does not give any insight.

I understand how GR is very useful to NASA and very important, I just wonder if I am missing any great insights into the gravitational field or are they just not there.

 

[Passionflower]

In Newtonian gravity, an infinite sheet of constant mass distribution causes a uniform gravitational field. I don't know if GR will predict otherwise.

Such solutions only work in GR if we allow for negative mass. See for instance the Taub plane-symmetric static vacuum spacetime.

 

[jcsd]

Waves weren't my concern. Since gravity couples to itself, the field at one point is not equal to the superposition of the fields of the two masses like in Newtonian gravity, since the field energy density must be taken into account. (Am I misunderstanding?)

Since the fact that an infinite sheet has a constant gravity in NG is a result of the face that fields can be linearily added, and since in GR this is not the case, i wonder how the situation changes.

I think I spake a buit too hastily there, but on the other hand we should be able to see what kind of symmetries there are from the specificaion that the field is constant in some sense.

 

[Daverz]

I don't think the Riemann tensor is more complicated... It is exactly what I am saying, the space "looks" curved on paper because the massive object is round or some complex shape.

Interesting. I'm curious to see how this worked out.

 

[Troponin]

i have studied general relativity and i have also reached the same conclusion it does not really tell us what gravity really is. It tells us that gravity can be due to geometry of space but it fails to define what space is. So relativity only opens one doorway to gravity by relating it to geometry which is logically sound but fails to define how something you can't see or touch(space) can have physical properties. So in that sense the theory breaks down. It is like saying the sun gives us energy but not defining how the energy is produced by the sun.

It's the opposite of this.
GR says that geometry of space is due to gravity, not that gravity is due to the geometry.

If it were symmetric then geometry would create gravity as well, but GR (I believe) doesn't include this. It only allows for gravity to create geometry.

 

[JesseM]

What does GR have to say about gravity that is constant everywhere?

Well, a "uniform gravitational field" would just be understood as what is experienced in a non-inertial frame in flat SR spacetime, similar to the fictitious forces that appear in non-inertial frames in Newtonian mechanics (like the 'centrifugal force' and the 'coriolis force' in a rotating frame). See the remarks on "uniform pseudo-gravitational fields" on this page from the twin paradox FAQ.