Space Dilation Interaction Between Two Masses

[MistySaa]

Edit: Disclaimer, this post contains faulty ideas

I'm a 'pedestrian' to physics trying to wrap my mind around various concepts of relativity, and one of those is a visualization of two, say, planets, say each starting at rest. By my understanding, their mass causes space to relatively compact/condense more and more closer to the planet. But of course if they're close enough to each other, they'll begin to accelerate towards each other. My conception of this was that, even though a given planet's gravitational 'field' of compacted spacetime did not cause it to move in any direction, the interaction of the two compacting 'fields' had a compounding effect in each other's (distant) spacetime vicinity, essentially multiplying off each other's manipulation of space such that it causes them to move through the space surrounding them. Or causing the space to flow past them and out from in between them, if it's relative in that way. Is this an accurate conceptualization of General Relativity/spacetime/gravity, and specifically the mechanism by which said two planets would accelerate towards one another through what we'd observe as 'space'? It's a concept I feel very compelled towards, in trying to cultivate my overall understanding of spacetime and such, but I haven't been able to find satisfactory results through searches to quell my curiosity.

 

[jerromyjon]

I like the "rubber sheet" analogy the best for visualizing gravity wells...

 

[Dale]

Is this an accurate conceptualization of General Relativity/spacetime/gravity

I don't recognize any relationship between the math of GR and what you wrote. Do you have a specific reference that discusses the "compression" idea or the "compounding" effect? It might help for us to read those sources and determine what they intended to convey.

 

[phinds]

I'm a 'pedestrian' to physics trying to wrap my mind around various concepts of relativity, and one of those is a visualization of two, say, planets, say each starting at rest.

There is no such thing. You have to say at rest relative to WHAT? If you mean at rest relative to each other, that's fine, but you have to be specific.

By my understanding, their mass causes space to relatively compact/condense more and more closer to the planet.

(1)Space is not a thing that can "compact/condense" and in any event, (2) you mean spacetime, not space.

But of course if they're close enough to each other, they'll begin to accelerate towards each other.

That happen regardless of whether they are "close" or not.

My conception of this was that, even though a given planet's gravitational 'field' of compacted spacetime

Again, it doesn't.

... did not cause it to move in any direction, the interaction of the two compacting 'fields' had a compounding effect in each other's (distant) spacetime vicinity, essentially multiplying off each other's manipulation of space such that it causes them to move through the space surrounding them.

The gravitational attraction between the two requires the existence of both of them so I'm not clear what you mean here.

Or causing the space to flow past them and out from in between them, if it's relative in that way.

Space doesn't "flow". It isn't a thing that can do that sort of thing

Is this an accurate conceptualization of General Relativity/spacetime/gravity, and specifically the mechanism by which said two planets would accelerate towards one another through what we'd observe as 'space'?

see comments above

It's a concept I feel very compelled towards, in trying to cultivate my overall understanding of spacetime and such, but I haven't been able to find satisfactory results through searches to quell my curiosity.

Keep reading. It can be confusing at first.

Also, I should mention that your title makes no sense. There is no such thing as "space dilation". Things get farther apart but that's not any kind of dilation of space. Google "metric expansion"

 

[MistySaa]

I like the "rubber sheet" analogy the best for visualizing gravity wells...

I'm aware of that but I didn't think it addressed my queries about the precise nature of the gravity/spacetime interactions.

 

[phinds]

I'm aware of that but I didn't think it addressed my queries about the precise nature of the gravity/spacetime interactions.

It won't. It's an analogy, and like most analogies it has its flaws.

 

[Dale]

I like the "rubber sheet" analogy the best for visualizing gravity wells...

Almost nobody else here likes it, but to each his own.

 

[MistySaa]

What are 'gravity wells' if not contraction of spacetime? Is the 'curvature' concept something else entirely? Do you have a visual/spacial concept of the 'curvature', or do you basically rely on a very functional/abstract conceptualization?

And gravity is just mass (or energy) manipulating/distorting spacetime, so by what mechanism does that cause two planets to accelerate through spacetime towards each other? If not by... effectively reducing the amount of space between them, or something. Isn't the 'gravitational attraction' idea Neutonian and inaccurate?

 

[MistySaa]

I don't recognize any relationship between the math of GR and what you wrote. Do you have a specific reference that discusses the "compression" idea or the "compounding" effect? It might help for us to read those sources and determine what they intended to convey.

No, it was my attempt to make the 'gravity wells'/manipulation of spacetime/curvature concept more comprehensive and understandable, based on basic info/explanations, but it seems it's not right.

 

[Dale]

No, it was my attempt to make the 'gravity wells'/manipulation of spacetime/curvature concept more comprehensive and understandable, based on basic info/explanations, but it seems it's not right.

Yeah, I am sorry to be the bearer of bad news, but if this is your personal explanation then I would discard it entirely and go back to learning the existing material first before trying to simplify it. I think that pursuing a personal analogy like this will be a bigger and bigger obstacle to really learning the theory the longer that you spend on it.

 

[phinds]

What are 'gravity wells' if not contraction of spacetime? Is the 'curvature' concept something else entirely? Do you have a visual/spacial concept of the 'curvature', or do you basically rely on a very functional/abstract conceptualization?

And gravity is just mass (or energy) manipulating/distorting spacetime, so by what mechanism does that cause two planets to accelerate through spacetime towards each other? If not by... effectively reducing the amount of space between them, or something. Isn't the 'gravitational attraction' idea Neutonian and inaccurate?

Things in spacetime, absent any external force (and gravity is not a force in GR) travel on straight lines, but these "straight lines" are more formally called "geodesics" and they are defined by the geometry of spacetime and the geometry of spacetime is affected by mass. That's the simple way of saying that massive bodies "attract" each other by affecting the geometry of spacetime and creating straight lines towards each other, not by doing anything to "space" which, again, is not a thing, it's just a component of spacetime.

 

[PeroK]

I like the "rubber sheet" analogy the best for visualizing gravity wells...

That's definitely the best way to visualise a rubber sheet, where the balls move down under the influence of gravity. But, if the shape of the rubber sheet is gravity, then why don't the balls move up the sheet or stay where they are? What is the force pushing the balls down the sheet or stopping them moving wherever they like?

If you took that curved sheet onto the space station, the balls would no pay no attention to its shape!

 

[jerromyjon]

If you took that curved sheet onto the space station, the balls would no pay no attention to its shape!

On the space station, the sheet would be almost perfectly flat, unlike here on Earth where the "spacetime" sheet has a curve under it's own weight! Spacetime doesn't warp itself!

 

[PeroK]

On the space station, the sheet would be almost perfectly flat, unlike here on Earth where the "spacetime" sheet has a curve under it's own weight! Spacetime doesn't warp itself!

It wouldn't be flat if you pushed a mass down into it.

Anywhere, how is time involved in the rubber sheet analogy? Isn't the rubber sheet just a curvature of space?

 

[jerromyjon]

No, it was my attempt to make the 'gravity wells'/manipulation of spacetime/curvature concept more comprehensive and understandable, based on basic info/explanations, but it seems it's not right.

I think the "compounding" you were trying to describe is when two masses approach each other the combined well is deeper, but as two masses circle closer some of the "warping" is dissipated as gravitational waves...

Anywhere, how is time involved in the rubber sheet analogy?

Time is still time... a two dimension plus time representation uses the third spatial dimension (that we see) as a representation of the amount of "warp" which has to be imagined as a fourth spatial dimension in three dimensions plus time, also known as "spacetime".

 

[PeroK]

I think the "compounding" you were trying to describe is when two masses approach each other the combined well is deeper, but as two masses circle closer some of the "warping" is dissipated as gravitational waves...

Time is still time... a second dimension plus time representation uses the third spatial dimension (that we see) as a representation of the amount of "warp" which has to be imagined as a fourth spatial dimension in three dimensions plus time, also known as "spacetime".

Well, we'll have to disagree. The rubber sheet analogy, in my opinion, is highly misleading for many reasons - not least because it cannot represent the curvature of time at all (only of space) and it clearly represents gravity as a force pushing things "down" along a curve. That is Newtonian gravity, not General Relativity! Without Newtonian gravity in the picture, there is no reason for a ball to move down the sheet rather than up the sheet - or to stay where it is.

 

[jerromyjon]

it cannot represent the curvature of time at all (only of space) and it clearly represents gravity as a force pushing things "down" along a curve.

To someone who might think gravity just "instantly pulls things together at a consistent rate", it should certainly show them how masses accelerate towards each other, with the force increasing as they approach...
Does general relativity include the warping of time?

 

[phinds]

Does general relativity include the warping of time?

What do you mean by "the warping of time"?

 

[jerromyjon]

The rubber sheet analogy, in my opinion, is highly misleading for many reasons - not least because it cannot represent the curvature of time at all (only of space)

That's why I asked...

 

[PeroK]

To someone who might think gravity just "instantly pulls things together at a consistent rate", it should certainly show them how masses accelerate towards each other, with the force increasing as they approach...
Does general relativity include the warping of time?

A particle moves in GR not because of a force but by following the Lagrangian principle of trying to maximise the spacetime distance it travels. In the absence of gravity, this reduces to constant velocity (in a straight line).

Mass curves spacetime in the sense that the distance between points in spacetime depends on the mass and the spatial "distance" from the mass. The curvature due to a spherical mass like the Earth or the Sun affects both the time and space coordinates.

This is hard to visualise, I agree, and it takes some mathematics to go from the equations of spacetime curvature to the familiar equations of motion - which are very similar to the Newtonian equations.

Personally, I feel you have to bite the Lagrangian bullet when presenting GR and at least give some explanation of why things move. The problem is that the naive student or lay-person will accept the rubber sheet because it is so close to Newtonian gravity. Whereas, the more perceptive student will ask: "but, if there is no force, why should a particle choose one path over another"? Things only follow a shape if they are constrained by that shape (like a ball attached to a wire) or a force compels them (like gravity on a rollercoaster). And, since particles are clearly not attached to spacetime and there is no force, why do they follow the paths they do?

In short, the problem with the rubber sheet analogy is that it stops you really thinking about why things move in the absence of a force.

 

[PeterDonis]

What are 'gravity wells' if not contraction of spacetime?

In the simplest case, a static "gravity well", it can be visualized as a bowl, with the gravitating mass filling the bottom of the bowl. The "amount of space" in the bowl is, if anything, "expanded" compared to flat spacetime, not "contracted". (Note that this is still a highly heuristic picture, which has significant limitations; but it at least gets across one key aspect of how a "gravity well" works.)

Is the 'curvature' concept something else entirely? Do you have a visual/spacial concept of the 'curvature', or do you basically rely on a very functional/abstract conceptualization?

Spacetime curvature is tidal gravity, which has a direct physical realization. In the simple case of a static, spherically symmetric mass, tidal gravity has two main components, radial and tangential.

For the radial case, imagine two rocks high above the Earth, at slightly different altitudes but along the same radial line, that get released from rest at the same instant. The two rocks will slowly diverge (i.e., get farther apart), because of the slight difference in the strength of the Earth's gravity between their altitudes. This corresponds to negative spacetime curvature.

For the tangential case, imagine two rocks high above the Earth, at the same altitude but slightly separated tangentially, that get released from rest at the same instant. The two rocks will slowly converge (i.e., get closer together), because of the slight difference in the direction of the Earth's gravity between them. This corresponds to positive spacetime curvature.

gravity is just mass (or energy) manipulating/distorting spacetime, so by what mechanism does that cause two planets to accelerate through spacetime towards each other?

The planets don't "accelerate through spacetime". They are in free fall, with zero proper acceleration. Their paths are geodesics of the curved spacetime geometry caused by their masses.

With a particular choice of coordinates, the planets have nonzero coordinate acceleration (which could be thought of as "acceleration through space", where "space" is according to the coordinates that were chosen), but that's because of the choice of coordinates.

If not by... effectively reducing the amount of space between them

If the planets are in stable orbits around each other, the "space between them" can stay constant (at least on average, if the orbits are elliptical). Yet their masses still affect the spacetime geometry. So no, thinking of their effect on the spacetime geometry as "reducing the amount of space between them" doesn't work.

A key idea you seem to be missing is that spacetime geometry isn't something that "changes with time". It is a 4-dimensional geometry that includes time as one of the dimensions; so the entire history of whatever system you are studying (the planets, in this case) is already included in the spacetime geometry.

Isn't the 'gravitational attraction' idea Neutonian and inaccurate?

It's an approximation that works ok for low speeds and weak gravity (small spacetime curvature). But if you're trying to understand how GR models gravity using spacetime curvature, no, it's not an accurate idea.