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

• talanum52
In summary: There is a difficulty in drawing a diagram of Minkowski spacetime on a Euclidean sheet of paper?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.See Feynman respond to the same question about something more pedestrian: magnetism.There is a difficulty in drawing a diagram of Minkowski spacetime on a Euclidean sheet of paper?Yes.
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.

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

talanum52 said:
General Relativity doesn't provide a mechanism.

Define "mechanism"

nasu, Vanadium 50, Dale and 3 others
malawi_glenn said:
Define "mechanism"
An animated picture of how mass distorts spacetime.

talanum52 said:
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.

malawi_glenn said:
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.

talanum52 said:
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)

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talanum52 said:
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.

nasu, Ibix, vanhees71 and 1 other person
I see an animated picture with general distances as a possible analogue to a mathematical equation.

You are asking for an analogy?

talanum52 said:
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.

talanum52 said:
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.

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

cyboman
Ibix said:
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.

PeterDonis said:
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.
PeterDonis said:
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.

Dale
Ibix said:
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.)

PeterDonis said:
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.

Ibix said:
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.

PeterDonis said:
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.

Dale
Ibix said:
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.

Ibix said:
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.

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.

FactChecker said:
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.

FactChecker said:
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
Dale said:
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.
Dale said:
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.

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.

weirdoguy and Motore
talanum52 said:
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?

FactChecker
talanum52 said:
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.

FactChecker
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.

talanum52 said:
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.

vanhees71 and malawi_glenn
talanum52 said:
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.

talanum52 said:
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.

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vanhees71
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.

dextercioby, vanhees71 and Dale
PeterDonis said:
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!

Dale said:
The GR mechanism explicitly excludes such scenarios.
Then pair production can't happen instentaniously.

Ibix said:
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.

talanum52 said:
Then pair production can't happen instentaniously.
GR is not a quantum theory you know.
talanum52 said:
I saw one going out of existence, or at least it stopped shining.
me too, it was your career ;)

phinds, Motore and vanhees71

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