Model for Gravity -- What mechanism distorts space in the real case?

[talanum52]

Homework Statement:: Model for Gravity
Relevant Equations:: Rg -Rg = G/(8pi*c^4)T

The rubber table model for gravity can't quite translate to reality. One sees that a ball placed on the table distorts it, but this is due to it being in a uniform gravity field. Just what mechanism distorts space in the real case? General Relativity doesn't provide a mechanism.

 

[Chestermiller]

It is space-time that is distorted, not just space.

 

[malawi_glenn]

General Relativity doesn't provide a mechanism.

Define "mechanism"

 

[talanum52]

Define "mechanism"

An animated picture of how mass distorts spacetime.

 

[Ibix]

An animated picture of how mass distorts spacetime.

I wouldn't really call that a mechanism, but @A.T.'s animation is one of the better efforts:

The "rubber sheet" model visualises the curvature of Schwarzschild spatial planes. Neglecting that entirely is part of the approximation that gives you Newtonian gravity - it only matters if you're travelling near the speed of light or near a black hole. The important part is better visualised above.

 

[AboveSky]

Define "mechanism"

A trick explaining some physics we don't have access to in terms our homo sapiens day to day experience so that it would make sense to our poor brains, like someone secretly bending space-time with his hands, or a magician's trick creating an invisible supranatural thread between two entangled particles.

I'm absolutely not laughing at OP, of course. I'm just describing the hope of many people when they learn some popular science that at some point, all could be described in terms of object they already understand (a marble pulled by someone, colliding with another marble, a sheet being deformed, this kind of things). To this regards, images use in popular science (or sometimes objects name in real science, like "curvature") are both helping to start understanding things and very misleading, to the point people end deceived and convinced that science doesn't understand anything.

 

[FactChecker]

An animated picture of how mass distorts spacetime.

IMHO, this is a poor definition of "mechanism".
GR provides a theory that has successfully explained many observed phenomena. To me, that seems like a "mechanism"?
From Einstein's Theory of Gravitation: "General relativity predicted many phenomena years before they were observed, including black holes, gravitational waves, gravitational lensing, the expansion of the universe, and the different rates clocks run in a gravitational field." (emphasis theirs)

 

[Dale]

An animated picture of how mass distorts spacetime.

There are certainly such animations for GR, but this is not a mechanism scientifically speaking. Scientifically a mechanism is a mathematical framework where you can input a measurable description of a scenario, solve the math, and produce a predicted measurable outcome.

For general relativity the mechanism is the Einstein field equations.

 

[A.T.]

An animated picture of how mass distorts spacetime.

Check out the illustrations here:
https://www.physics.ucla.edu/demowe..._and_general_relativity/curved_spacetime.html

And in the links I posted here:
https://www.physicsforums.com/threa...ng-gravitation-geodesics.1050005/post-6855831

 

[talanum52]

I see an animated picture with general distances as a possible analogue to a mathematical equation.

 

[malawi_glenn]

You are asking for an analogy?

 

[Dale]

I see an animated picture with general distances as a possible analogue to a mathematical equation.

An analogue or an analogy is not a mechanism. At best an analogy is a teaching aid.

The mechanism for GR is clear and well established: the Einstein field equations.

 

[Ibix]

I see an animated picture with general distances as a possible analogue to a mathematical equation.

The problem with pictures of spacetime is that there's always a path of zero length between any two events, which makes it really hard to draw in Euclidean space. Diagrams that are honest representations of various spacetimes can be drawn, but some knowledge is needed to interpret them.

 

[jbriggs444]

See Feynman respond to the same question about something more pedestrian: magnetism.

 

[PeterDonis]

there's always a path of zero length between any two events

Between any two events? I think that's too strong.

It's also more than is actually required. Just the presence of any zero length paths between distinct points is enough to show the difficulty in trying to draw a diagram of Minkowski spacetime on a Euclidean sheet of paper.

 

[Ibix]

Between any two events?

For a path of any type (timelike, spacelike, null, a mixture) you can connect two nearby events on it by at most two null segments, so you can connect one end of the path to the other by iterating this to produce a series of null line segments. I can't think of a circumstance where that construction fails if the path exists, or where there can be two events in the same spacetime that can't be connected by some path.

Just the presence of any zero length paths between distinct points is enough to show the difficulty in trying to draw a diagram of Minkowski spacetime on a Euclidean sheet of paper.

Indeed.

 

[PeterDonis]

null segments

Ah, ok. But these segments, though they can be continuous, will not form a single smooth curve. (In fact in the general case I don't think they will even form a single differentiable curve; differentiability will fail at each corner, and you can't "round off the corners" without violating the null requirement.)

 

[Ibix]

But these segments, though they can be continuous, will not form a single smooth curve.

Sure. I only said such a path existed, not that it was smooth.

If we're restricting ourselves to smooth null curves then every event is connected to some distinct events by a smooth curve of length zero, and I can't see how you could represent that in an intuitively understandable way.

 

[PeterDonis]

If we're restricting ourselves to smooth null curves then every event is connected to some distinct events by a smooth curve of length zero, and I can't see how you could represent that in an intuitively understandable way.

Sure we can: you're just describing the light cone of the given event.

 

[Ibix]

Sure we can: you're just describing the light cone of the given event.

Yes - but the request in #10 was a diagram showing "general distances", which I took to mean intervals. Minkowski diagrams (et al) are honest representations of spacetimes, but they don't represent intervals accurately and I can't see how they can do.

If we take the request to just mean "I want a diagram", even Minkowski diagrams need a bit of knowledge to interpret. Considering spacetimes with curvature just makes the diagrams more abstract.

 

[PeterDonis]

the request in #10 was a diagram showing "general distances", which I took to mean intervals.

Yes, I would take it that way too. But the interval between events is an invariant, and it is not the case that the interval between a given event and any other event is null. You can of course concoct a "path" between, say, two timelike separated events that is composed of null segments, but I don't think you would claim that that means the interval between those two timelike separated events is not timelike, but null. That's why I said that I think your original statement was too strong. Just the presence of null intervals, i.e., that each event has a light cone, is enough.

Minkowski diagrams (et al) are honest representations of spacetimes, but they don't represent intervals accurately and I can't see how they can do.

Yes, I agree; it's impossible to accurately represent Minkowski intervals on a Euclidean sheet of paper. And I would say that the simplest way to see why is to note that Minkowski intervals along light cones are null--zero "distance" between two distinct points. That, right there, is sufficient to make an accurate diagram on Euclidean paper impossible.

 

[FactChecker]

To me, the term "mechanism" implies some cause/effect explanation. I don't know if there is such a thing. The geometry of GR spacetime just is the way the Einstein field equations are. It might be some other geometry, but then the same question could be asked about that geometry, with equally mysterious answers.

 

[Dale]

To me, the term "mechanism" implies some cause/effect explanation.

Well, if you insist on that then Maxwell’s equations are not a mechanism either.

I don't know if there is such a thing.

I think the ADM formalism is what you are looking for in GR. It would be like Jefimenko’s equations in EM in this sense.

 

[FactChecker]

Well, if you insist on that then Maxwell’s equations are not a mechanism either.

Yes. Exactly. I think that is the point I was trying to make. Some things just are a certain way. They don't really require or admit an explanation. Their mathematics and physics just work out beautifully. Why is the Universe the way it is? We may never know.

I think the ADM formalism is what you are looking for in GR. It would be like Jefimenko’s equations in EM in this sense.

Very possibly. That is beyond me.

 

[talanum52]

The general relativity equation just shows an equalness between curved spacetime and the stress energy tensor, not a mechanism how the curvature arises when mass moves into a new position or new mass gets produced. It does not describe this process.

 

[Ibix]

It does not describe this process.

Of course it describes it. How do you think the gravitational wave signatures LIGO detects get analysed to determine what produced them?

 

[Dale]

The general relativity equation just shows an equalness between curved spacetime and the stress energy tensor, not a mechanism how the curvature arises when mass moves into a new position or new mass gets produced. It does not describe this process.

That is the mechanism and the description of the process. An animation is not.

 

[talanum52]

For this to be the mechanism for explaining how new mass distorts space, one has to substitute for the stress-energy tensor a step function (Cu(x)). Then the formula tells nothing about what happens at x = 0 or how the curvature evolves if one zoom in on zero.

 

[Ibix]

For this to be the mechanism for explaining how new mass distorts space, one has to substitute for the stress-energy tensor a step function (Cu(x)). Then the formula tells nothing about what happens at x = 0 or how the curvature evolves if one zoom in on zero.

Oh, this is a disguised "what if the Sun vanished" question. GR makes a very strong statement that it is not possible to have a stress energy tensor that violates local conservation of energy like your proposed one does.

 

[Dale]

For this to be the mechanism for explaining how new mass distorts space, one has to substitute for the stress-energy tensor a step function (Cu(x)).

The GR mechanism explicitly excludes such scenarios. According to the mechanism such scenarios are not possible, so they do not need to be explained.

not a mechanism how the curvature arises when mass moves into a new position or new mass gets produced.

It definitely does describe the first process: how curvature arises when mass moves to a new position. As I said above, the EFE is the mechanism.

 

[Ibix]

To expand slightly on the last two posts, the Einstein Field Equations are $G^{\mu\nu}=8\pi T^{\mu\nu}$. Having a step function for $T^{\mu\nu}$ means that $\nabla_\mu T^{\mu\nu}\neq 0$, which obviously means $\nabla_\mu G^{\mu\nu}\neq 0$. But that last is false - $\nabla_\mu G^{\mu\nu}=0$ is the Bianchi identity, a geometrical fact about manifolds a bit like all triangle interior angles adding to zero.

If we ever saw a star pop into existence out of nowhere then GR would be falsified.

 

[vanhees71]

Between any two events? I think that's too strong.

It's also more than is actually required. Just the presence of any zero length paths between distinct points is enough to show the difficulty in trying to draw a diagram of Minkowski spacetime on a Euclidean sheet of paper.

Fortunately a sheet of paper is not Euclidean but just a (model of a) affine manifold, on which you can endorse any fundamental form you like. You are used to endorse a metric and make it to an Euclidean affine space (or plane since it's 2D) since elementary school. When learning special relativity sometimes teachers force you to draw Minkowski diagrams, and then you must forget the metric and substitute it by a fundamental form of signature (1,1), and then it's a Minkowskian (Lorentzian) affine plane. Our use of the affine plane as an Euclidean plane for 99% of the time makes it very hard for us to forget about the Euclidicity an read it as a Lorentzian plane, and that's why Minkowski diagrams are more cofusing than one thinks!

 

[talanum52]

The GR mechanism explicitly excludes such scenarios.

Then pair production can't happen instentaniously.

 

[talanum52]

If we ever saw a star pop into existence out of nowhere then GR would be falsified.

I saw one going out of existence, or at least it stopped shining.

 

[malawi_glenn]

Then pair production can't happen instentaniously.

GR is not a quantum theory you know.

I saw one going out of existence, or at least it stopped shining.

me too, it was your career ;)

 

[Ibix]

Then pair production can't happen instentaniously.

GR is not a quantum theory so should not be expected to make claims about quantum processes. And I don't think pair production necessarily violates conservation of energy anyway.

I saw one going out of existence, or at least it stopped shining.

Stopping shining does not mean its mass vanished. It is the latter that can't happen.

 

[malawi_glenn]

And I don't think pair production necessarily violates conservation of energy anyway.

Any evidence of pair production from "nothing" in general?

 

[Vanadium 50]

Then pair production can't happen instentaniously.

You are quicky moving out of the realm of asking questions, and into the realm of pushing a personal theory, a theory that will inspire people to describe with adjectives.

Pair production does not mean pairs appear out of nowhere. It means particles are produced by the interaction of other particles, like a photon and a nucleus.

If you didn't know this, you should have looked it up before posting. If you did know this and posted it anyway, well, people are going to use more adjectives then.

 

[PeterDonis]

For this to be the mechanism for explaining how new mass distorts space, one has to substitute for the stress-energy tensor a step function (Cu(x)).

You are misunderstanding what a GR spacetime model is. It is a model of spacetime. It already includes all "time variation" of everything in a self-consistent way. It is a global description of an entire history of a physical system (such as the universe). It is not a "snapshot" at an instant of time that then has to be evolved in time.

Note that you cannot just put a "new mass" into such a model; it won't be consistent. Mass cannot just appear out of nowhere. It has to be conserved. So if the only way for you to find a "mechanism" is to magically make a mass appear out of nowhere and then see what happens, you will never find any such mechanism in GR. Sorry.

If you insist on some kind of "time evolution" model in the context of GR, you would want to look at the ADM formalism, which @Dale mentioned in an earlier post. This is a way of generating a full spacetime model (the kind described above) by starting with conditions on a particular spacelike hypersurface ("space" at an instant of "time"), and then evolving things in time. But any result you obtain this way can also be obtained the "global" way, with a full spacetime model as described above. And any result you obtain this way still has to satisfy the conservation law I described above. The spacelike hypersurface on which you define your starting conditions has to be evolved backwards in time as well as forwards, in order to obtain a complete self-consistent solution.

Whether the ADM formalism would satisfy your definition of a "mechanism" is a matter of your personal preferences, not physics.

 

[Dale]

Then pair production can't happen instentaniously.

The stress energy for the pair production must already be present before the pair is produced.

 

[Nugatory]

Then pair production can't happen instantaneously.

No one has ever said that it does (except some pop-sci presentations that oversimplify to the point of misleading). As far as QM is concerned, at time $T$ we prepare a state that includes everything required for pair production (a sufficiently energetic photon and a convenient massive nucleus) and at some later time $T+\Delta T$ we observe that we have an electron-positron pair and that the momentum of the nucleus has changed. What happened between $T$ and $T+\Delta T$? Quantum mechanics won't tell us; that question cannot even be posed within the mathematical formalism of the theory.

Pair production conserves energy and momentum so the transition between the initial and final states does not have to violate any of the invariants of general relativity. This is a completely different situation than the "gravitating mass appears from nowhere" situation that you brought up earlier.

 

[Nugatory]

And I don't think pair production necessarily violates conservation of energy anyway.

It doesn't - full stop.
[Edited to unbotch the quote - sorry@ Ibix, the earlier unedited quote misrepresented what you said - my sloppy mousing]

 

[talanum52]

And I don't think pair production necessarily violates conservation of energy anyway.

Think about it: you have nothing and then you have mass-energy (and there is no negative mass). - Ignore this: you have initially some energy. Problem is: how did energy ultimately start to exist?

 

[Dale]

Think about it: you have nothing and then you have mass-energy

This is incorrect, as has already been explained to you by multiple people here. Energy and momentum are conserved with all of the stress energy of the pair necessarily being present before pair production.

Please do not repeat this false claim again.

 

[Ibix]

Think about it: you have nothing and then you have mass-energy (and there is no negative mass). - Ignore this: you have initially some energy. Problem is: how did energy ultimately start to exist?

If you mean "relativity doesn't describe the origin of the universe" then sure, that's well known. If you mean "pair production produces something out of nothing" then see the post above yours.

 

[malawi_glenn]

When did we measure the creation of say a pair of electron and positron out of "pure energy"?
(note that a photon can not convert it self to a pair of $e^-$ and $e^+$ alone, there needs to be a third particle, usually a proton, involved in order for both energy and linear momentum to be conserved).

 

[jbriggs444]

When did we measure the creation of say a pair of electron and positron out of "pure energy"?
(note that a photon can not convert it self to a pair of $e^-$ and $e^+$ alone, there needs to be a third particle, usually a proton, involved in order for both energy and linear momentum to be conserved).

It is my understanding, perhaps flawed, that photon-photon interactions are possible without an intermediary.

https://en.wikipedia.org/wiki/Two-photon_physics

Energy and momentum conservation are not a problem for this. If you can run an annihilation forward while conserving energy and momentum then the time reversal must conserve them as well.

 

[malawi_glenn]

Energy and momentum conservation are not a problem for this.

No its not. But $\gamma \to e^+ + e^-$ is.

 

[jbriggs444]

No its not. But $\gamma \to e^+ + e^-$ is.

But we are talking about $\gamma + \gamma \to e^+ + e^-$ here. What is the problem with that?

 

[Nugatory]

Whatever process we consider, it conserves mass-energy, does not imply any discontinuity in the stress-energy or Einstein tensors, and therefore does not conflict with GR - at least not the way @talanum52 is mistakenly suggesting.

And people... this is a digression. Back on track, please?