B How Matter Bends Space & Slows Time: Physical Mechanism

[TheTuringTester]

Given that we know experimentally that time slows and space bends in the presence of matter, what is the actual physical mechanism that enables matter to bend space and slow time?

 

[deepalakshmi]

Maybe you should see this post:
https://www.physicsforums.com/threads/how-does-matter-bend-space.598210/

 

[PeroK]

Given that we know experimentally that time slows and space bends in the presence of matter, what is the actual physical mechanism that enables matter to bend space and slow time?

There is no mechanism. The Einstein Field Equations which relate the spacetime curvature tensor to the stress-energy tensor is an axiom of GR.

A successful theory of quantum gravity may give a more fundamental law, but physics generally doesn't provide mechanisms, but basic axioms or postulates. Look at Newton's laws, classical electromagnetism and quantum mechanics, for example.

 

[vanhees71]

I don't know what you call "mechanism". The theoretical foundation of GR is to make the proper orthochrounous Poincare symmetry of SR local, leading to theory of the gravitational interaction which is equivalent to describe it with a pseudo-Riemannian (or Einstein-Cartan) manifold as the spacetime model. In that sense the "geometrization of the gravitational interaction" is derivable by the same "mechanism" as all the fundamental interactions are described, i.e., as a gauge theory. The specialty of the gravitational interaction in contradistinction to the other interactions is that it "gauges" the spacetime symmetry.

 

[Dale]

There is no mechanism. The Einstein Field Equations which relate the spacetime curvature tensor to the stress-energy tensor is an axiom of GR.

I disagree. There is a mechanism and the EFE is the description of that mechanism. That it is an axiom in GR just means that we cannot express this mechanism in terms of anything else.

 

[phinds]

Given that we know experimentally that time slows and space bends in the presence of matter,

Just so you are clear, time does NOT slow for the person experiencing it. That is, if I am very low in a gravity well and you are very high in the same well, you will see my clock tick more slowly than yours and I will see yours tick more rapidly than mine, BUT ... locally, we each will see our time ticking away at one second per second.

If we started off together and then you went up or I went down, there will be differential aging if later you come down to me or I go up to you. I will be younger. That's because our clocks will have ticked a different number of times, at one second per second, because we were on different paths through space-time.

 

[Ibix]

There is no mechanism.

I disagree.

Perhaps splitting the difference here, general relativity doesn't explain how mass and energy curve spacetime, but it describes the curvature that is generated. Whether the Einstein field equations (which do the describing of curvature) count as a "mechanism" or not is kind of up to you. For a host of reasons, though, most physicists believe there's a more fundamental theory to be found here which would hopefully say how it works.

However, note that physical theories always rest on some assumptions (in GR this is the local proper orthochronous symmetry that @vanhees71 mentions). So a more fundamental theory - probably a quantum theory of gravity - would have other questions that can't be answered within the theory. That's a bit turtles-all-the-way-down, I'm afraid, but that's the nature of scientific theory.

 

[TheTuringTester]

There is no mechanism. The Einstein Field Equations which relate the spacetime curvature tensor to the stress-energy tensor is an axiom of GR.

I think the root cause of my question is that I am trying to understand is if gravity is not a force, it's just the result of curved spacetime - do we have a name for the force that bends space and slows time and it is the same force acting equally - does time slow in exact proportion to space bending - and if not, is that force pulling on space and time through the same mechanism? I know I am struggling to put a classical visualization on something that might not have a classical definition, but I think there is value in that struggle to help light the path ahead to a more accurate visualization in baby steps from the concrete to the abstract.

 

[Ibix]

do we have a name for the force that bends space and slows time and it is the same force acting equally

We don't know the mechanism. I would be very surprised if it is anything like a force, though. I suspect you are thinking of the rubber sheet curved by a weight on it, which is a deeply evocative and almost entirely wrong picture you see in a lot of popsci.

does time slow in exact proportion to space bending

Space and time are fairly arbitrary distinctions we put on spacetime, which is the thing that's curved. And there isn't a single number to describe the curvature of space even when you've defined it, so there isn't really a sensible answer to this question.

I think there is value in that struggle to help light the path ahead to a more accurate visualization in baby steps from the concrete to the abstract.

There is no accurate visualisation of a curved 4d pseudo-Riemannian manifold. I gather one can prove that you can't draw a representation of one in any finite dimensional Euclidean space. There are visualisations of limited parts of one - forum member A.T.'s animation is a good one:

 

[PeroK]

I think the root cause of my question is that I am trying to understand is if gravity is not a force, it's just the result of curved spacetime - do we have a name for the force that bends space and slows time and it is the same force acting equally - does time slow in exact proportion to space bending - and if not, is that force pulling on space and time through the same mechanism? I know I am struggling to put a classical visualization on something that might not have a classical definition, but I think there is value in that struggle to help light the path ahead to a more accurate visualization in baby steps from the concrete to the abstract.

You should forget forces as they don't generalise beyond Newtonian mechanics. Spacetime is a geometric model.

The simplest example of curved spacetime is perhaps the geometry around a spherical star or planet. You can choose any number of coordinate systems to describe this geometry and often the first one is the Schwartzschild coordinates.

There's no deeper mechanism that to study the Einstein field equations for this physical scenario and deduce the Schwartzschild geometry from those.

There's no deeper way to say why spacetime has the geometry it has in that scenario. Solving the field equations is what physics is about.

That geometry replaces Newton's theory of gravity.

The obvious next question is why objects move as they do in this geometry. This requires another law to replace Newton's second law of motion. For GR we have a generalisation of the principle of least action. When you add that principle you get the expected planetary orbits. Although, of course, in extreme cases, the orbits may differ significantly from Newtonian predictions.

Things like gravitational time dilation and redshift of light can also be deduced from the geometry.

 

[Dale]

Whether the Einstein field equations (which do the describing of curvature) count as a "mechanism" or not is kind of up to you.

That is a good point. So let me explain how I think of "mechanisms".

If someone were to ask about the mechanism of how a lever works or how a spring works, then I would say that we describe the mechanism for a lever using the lever law, and we describe the mechanism of a spring using Hooke's law. Obviously, the description is not the mechanism itself, but when answering a question about a mechanism I can only answer with a description. So the correct answer to a question about a mechanism is a description of the mechanism, or a name that can refer to the description.

So how are mechanisms described scientifically? Because physics is so precise and deals with things that are outside the realm of everyday experience, we need a general way to describe mechanisms that is not subject to the vagueness of ordinary language or the limitations of everyday experience. Thus they are described through equations that match the result of scientific experiments. The lever law is $F_A/F_B=a/b$ and Hooke's law is $F=-kx$ where each of those symbols is interpreted in terms of physical experiments that can be performed and the law describes the relationship between the physical quantities. That is how we describe mechanisms in physics.

The EFE has that form, so the EFE is the scientific description of a mechanism, at least in my usage and understanding of the term "mechanism".

 

[Dale]

do we have a name for the force that bends space and slows time and it is the same force acting equally -

Yes, we call them the Christoffel symbols. In a non-inertial frame the Christoffel symbols give the fictitious forces, and in curved spacetime they give the equivalent of the Newtonian gravitational field.

They are coordinate-dependent meaning that they can be made to disappear locally by judicious choice of your coordinates.