Is it possible to extend Newtonian gravity to include energy as well as mass?

[trees and plants]

Hello there.My question is:can Newtonian gravity be generalised to include not only bodies with mass but energy also?Thank you.Can my thread be moved to classical physics?

 

[Ibix]

Um... bodies in Newtonian physics do typically have energy, and Newtonian physics works as is. What generalisation do you think is needed?

 

[trees and plants]

Um... bodies in Newtonian physics do typically have energy, and Newtonian physics works as is. What generalisation do you think is needed?

You mean kinetic energy?Sorry for my thread and question perhaps it should be deleted.

 

[Ibix]

Kinetic energy, heat, chemical potential, all sorts. They don't affect gravity in Newtonian physics but they are present.

 

[trees and plants]

Does gravity pull electromagnetic radiation like light?Did general relativity involve light as a case for this?I somewhere read that Newtonian gravity also predicts the bending of light from gravity.

 

[Ibix]

Does gravity pull electromagnetic radiation like light?

You already know that it does, from how you phrased your question here.

I somewhere read that Newtonian gravity also predicts the bending of light from gravity.

Where did you read this? It's possible to kinda sort of put light into a model of Newtonian gravity, but the obvious way to do it gives the wrong answer for the deflection angle and some approaches say it won't be deflected at all. Fundamentally, Newtonian gravity is a low-speed weak field approximation to general relativity and is invalid for fast moving objects, of which light is an excellent example.

 

[PeterDonis]

Can my thread be moved to classical physics?

Not if you're going to ask questions like this:

Does gravity pull electromagnetic radiation like light?

That isn't a question about classical physics, it's a question about physics, period, and should be answered using our best current theories of physics, which in this case would be GR.

 

[trees and plants]

You already know that it does, from how you phrased your question here.

Where did you read this? It's possible to kinda sort of put light into a model of Newtonian gravity, but the obvious way to do it gives the wrong answer for the deflection angle and some approaches say it won't be deflected at all. Fundamentally, Newtonian gravity is a low-speed weak field approximation to general relativity and is invalid for fast moving objects, of which light is an excellent example.

What about other kinds of electromagnetic radiation like gamma rays, radio waves, microwaves or other types of radiation like gravitational radiation, beta radiation or sounds?Are they pulled by the gravity of a body like the sun or a star?Are there other physical objects like radiation without mass that are energies?Are they pulled by gravity?

 

[Ibix]

Everything is affected by gravity. Anything that isn't would violate the equivalence principle and there is exactly zero evidence of such a violation.

 

[trees and plants]

My other questions are off thread:Is spacetime only a mathematical construct or is it something physical?Because it is in four dimensions we can not know because we do not perceive it in real life?Some people I think say that general relativity imply that the current universe we perceive is a shadow of the real is this wrong?Is curvature of spacetime a consequence of the unification of space and time, because without time passing we would not know how spacetime is curved?Sorry if I made wrong questions.

 

[PeterDonis]

Is spacetime only a mathematical construct or is it something physical?

It's something physical--at least, that's the standard interpretation of GR.

Because it is in four dimensions we can not know because we do not perceive it in real life?

We do perceive four dimensions in real life: three dimensions of space and one of time. There is a difference between them since we can move in arbitrary directions in space, but we can only move into the future in time. The mathematical model of relativity reflects this difference since spacelike and timelike curves are treated differently.

Some people I think say that general relativity imply that the current universe we perceive is a shadow of the real is this wrong?

You would need to give specific references that make such claims before we could answer this question.

Is curvature of spacetime a consequence of the unification of space and time

I'm not sure this question makes sense.

without time passing we would not know how spacetime is curved?

It is true that detecting spacetime curvature requires measurements to be made that include the dimension of time. However, "without time passing" makes no sense since we cannot avoid time passing.

 

[Ibix]

Some people I think say that general relativity imply that the current universe we perceive is a shadow of the real is this wrong?

The universe we perceive is a 3d subspace of the 4d whole, following GR's notions of spacetime.

Is curvature of spacetime a consequence of the unification of space and time

Well, you couldn't have curvature of spacetime without spacetime. But you can have flat spacetime.

 

[PeterDonis]

The universe we perceive is a 3d subspace of the 4d whole

This depends on what you mean by "the universe we perceive". What we perceive directly is our past light cone, which is not a 3d spacelike hypersurface. What we construct from our perceptions is a mathematical model of a 4d spacetime, which can be "sliced" into 3d spacelike hypersurfaces one of which we label "now". So it can be said that we construct a 3d subspace (but that's not all we construct), but I don't think that's the same as perceiving it.

 

[Vanadium 50]

What is this thread about? It seems to be meandering all over the place.

Can Newtonian gravity be generalised to include not only bodies with mass but energy also?

Has a simple answer: "No, because then it would be something other than Newtonian gravity." If you then want to change this to something kinda-sorta-like-Newtonian gravity, you need to explain to us what you mean by kinda-sorta-like-Newtonian gravity and why GR doesn't "count".

If you instead want to know what GR is, that is probably too big a bite for one thread.

 

[Ibix]

I don't think that's the same as perceiving it.

Well, the past light cone is a 3d surface, isn't it? $S^2\times R$? It's not spacelike, indeed, but that's why I said "subspace" and avoided words like "slice", which I'd agree fit a spacelike "now" better.

 

[PeterDonis]

Well, the past light cone is a 3d surface, isn't it? $S^2\times R$? It's not spacelike, indeed, but that's why I said "subspace" and avoided words like "slice", which I'd agree fit a spacelike "now" better.

$S^2\times R$ is not a "3d surface" in the usual sense of that term--that would be $R^3$. It is a topological 3-manifold, but it is "missing a point" (the apex point of the cone, which is the event "here and now").

 

[trees and plants]

What is this thread about? It seems to be meandering all over the place.
Has a simple answer: "No, because then it would be something other than Newtonian gravity." If you then want to change this to something kinda-sorta-like-Newtonian gravity, you need to explain to us what you mean by kinda-sorta-like-Newtonian gravity and why GR doesn't "count".

If you instead want to know what GR is, that is probably too big a bite for one thread.

I think general relativity is the answer as the next generalisation to Newtonian gravity.I try to learn general relativity,trying to learn about light cones, world lines, solutions of the einstein field equations, but I think the introduction has pretty much taken a big part of my interest and although I want to read about de Sitter spacetime or other spacetimes I find it difficult to not consider these topics on general relativity as of less interest compared with the introduction of general relativity.

 

[Ibix]

the apex point of the cone, which is the event "here and now"

Ah, yes. Had forgotten that bit.

 

[PAllen]

$S^2\times R$ is not a "3d surface" in the usual sense of that term--that would be $R^3$. It is a topological 3-manifold, but it is "missing a point" (the apex point of the cone, which is the event "here and now").

Well, you could add that point - it makes sense to do so for a directly experienced notion of now. Then, I believe the topology does become R³.

 

[PeterDonis]

you could add that point - it makes sense to do so for a directly experienced notion of now.

I'm not sure I would say we experience all the events on our past light cones, from which we are receiving light signals here and now, as "now". We construct a "now" from that information, but I don't think we directly experience that information as "now", except at very short distances (roughly speaking, where the light travel time is less than the characteristic time for our brains to process information--something like 10 milliseconds).

Then, I believe the topology does become R³.

Adding the apex point would make the topology $R^3$, yes, but it would induce a discontinuity in the tangent vectors to the manifold at the apex point.

 

[PeterDonis]

I think general relativity is the answer as the next generalisation to Newtonian gravity.I try to learn general relativity,trying to learn about light cones, world lines, solutions of the einstein field equations, but I think the introduction has pretty much taken a big part of my interest and although I want to read about de Sitter spacetime or other spacetimes I find it difficult to not consider these topics on general relativity as of less interest compared with the introduction of general relativity.

It's good that you want to learn about GR, but one PF thread is not going to accomplish that. You will need to spend some time working through textbooks--I would recommend Sean Carroll's online lecture notes as a starting point:

https://arxiv.org/abs/gr-qc/9712019

You can ask particular questions in new threads about things you have difficulty understanding; but "I want to learn about GR" is much too broad and general as a topic for a PF thread.

 

[haushofer]

An intuitive answer: the Newtonian limit can be considered as a c-->oo limit of GR. On dimensional grounds this explains why time derivatives, going as 1/c, and energy terms, going as 1/c^2, are contracted away.

A similar question to your OP would be: can Newtonian gravity be extended such that the gravitational potential becomes time-dependent (i.e. the partial derivative w.r.t. t becomes non-zero)?

 

[PeterDonis]

the Newtonian limit can be considered as a c-->oo limit of GR. On dimensional grounds this explains why time derivatives, going as 1/c, and energy terms, going as 1/c^2, are contracted away.

Not all time derivatives. Velocities have to be small compared to $c$, so terms in velocities that are in GR but not in Newtonian gravity go away. But not all time derivatives are like that. See below.

can Newtonian gravity be extended such that the gravitational potential becomes time-dependent (i.e. the partial derivative w.r.t. t becomes non-zero)?

This already happens in Newtonian gravity for non-static systems, i.e., systems where mass is in motion. The GR terms in $v / c$ induced by such motions vanish in the Newtonian approximation; but the time derivatives of the direct Newtonian potential terms due to the moving masses don't.

 

[haushofer]

Not all time derivatives. Velocities have to be small compared to $c$, so terms in velocities that are in GR but not in Newtonian gravity go away. But not all time derivatives are like that. See below.
This already happens in Newtonian gravity for non-static systems, i.e., systems where mass is in motion. The GR terms in $v / c$ induced by such motions vanish in the Newtonian approximation; but the time derivatives of the direct Newtonian potential terms due to the moving masses don't.

Yes, I should be more clear. Of course, a time-dependent mass density makes the potential time dependent. I meant that it's impossible (AFAIK) to extend the Poisson equation with a time derivative of the potential.

 

[PeterDonis]

I meant that it's impossible (AFAIK) to extend the Poisson equation with a time derivative of the potential.

Yes, agreed.