How exactly does gravity work?

[Sorcerer]

Don't - what he wrote is rubbish - and I am an Australian guy to if that makes any difference .

Thanks
Bill

Lol. I did say “this” Australian guy, for the record. Interesting possibly slightly xenophobic side-note regarding an Australian physics professor I had- he called out the rest of the physics department for having an example problem using a “koala bear.” It was pretty darn funny.

 

[bhobba]

What if you use the (-,-,-,+) sign convention? (Where space gets the negative sign) Does they change anything or is it irrelevant? I would guess in this case you’d actualy maximize it.

No.

See my explanation - it does not involve the signature of the metric. It's to do with the free particle Lagrangian which is the same regardless of the metric you use.

Thanks
Bill

 

[Patterner]

Unfortunately, I don't know anything about the math of all this. It's been about 37 years since high school trig, and that's as far as I went. And the first time a heard or saw the words "geodesic" and "worldline" was four days ago.

But can't this, at least the initial concept I'm trying to wrap my head around, be put into the words of a fairly simple thought experiment? I've heard Einstein was fond of them. :D Some of you may well be answering my question, but in terms I don't understand. So let me try this wording. Trying to make everything as unambiguous as possible.

Let's say there's a planet sitting in the middle of a section of flat spacetime. The only point of reference is a distant galaxy that looks like a star to the naked eye. Its pretty far away. Relative to this galaxy, this lone point of reference, the planet is not moving in space. It is not even rotating. It is moving in the dimension of time, but not the dimensions of space. It is utterly still.

The planet causes a spacetime curvature, as planets tend to do. That curvature has a certain size and shape, which is the result of the planet's composition, size, and whatever else affects the size and shape of spacetime curvatures. If we could inject die into this Curved Hunk o' Spacetime, we would be able to see it. But we can't, so we're stuck with our imaginations. A planet, surrounded by this lattice; this matrix; this CHoS.

We can also, in our minds' eyes, remove the planet from this scenario. Now we have a shimmering CHoS, sitting absolutely still, relative to the only point of reference.

Now getting back to the baseball. The CHoS is not there yet. Only a baseball is there, sitting still in flat spacetime. And who comes along but Galactus! From the distant galaxy, he sees the baseball. And, with his Power Cosmic, he creates our our old friend, CHoS, so that the very edge of it touches the baseball. He creates it so that it does not move, relative to the baseball, the Galaxy, and himself. All four things are, relative to each other, dead in space. No motion, of anything relative to anything, lead to the baseball being on the edge of this section of curved spacetime. But there it is.

My only question is this: Will the baseball move toward the spot that would be the center of the planet, the center gravity, if the planet was there? (If so, I assume through it, than probably pulled back again, through toward the spot it started, back and forth.) That is, does the presence of spacetime curvature, by itself, without the help of relative motion, magnetism, or any other darned thing, cause an object to move in the dimensions of space?

This all seems pretty simple and clear enough to me. I would expect a Yes or No answer is possible. But, not knowing enough about this stuff, maybe it's not?

 

[Ibix]

It is moving in the dimension of time, but not the dimensions of space.

The point is that this is a choice you make. You are free to choose that the planet is moving in space, simply by choosing to work in another frame. This is why the theory is called relativity - there's no such thing as "at rest" in any absolute sense. It's always relative to something. You've chosen some galaxy, but you can choose something else. One of the stars in the galaxy, perhaps.

 

[pervect]

The planet causes a spacetime curvature, as planets tend to do. That curvature has a certain size and shape, which is the result of the planet's composition, size, and whatever else affects the size and shape of spacetime curvatures. If we could inject die into this

I'm not sure I understand your question, but as far as your image goes, you might like http://www.eftaylor.com/pub/chapter2.pdf, an excerpt from Taylor's book, "Exploring Black Holes".

Nothing is more distressing on first contact with the idea of curved space-
time than the fear that every simple means of measurement has lost its
power in this unfamiliar context. One thinks of oneself as confronted with
the task of measuring the shape of a gigantic and fantastically sculptured
iceberg as one stands with a meterstick in a tossing rowboat on the surface
of a heaving ocean.

Were it the rowboat itself whose shape were to be measured, the proce-
dure would be simple enough (Figure 1). Draw it up on shore, turn it
upside down, and lightly drive in nails at strategic points here and there
on the surface. The measurement of distances from nail to nail would
record and reveal the shape of the surface. Using only the table of these
distances between each nail and other nearby nails, someone else can
reconstruct the shape of the rowboat. The precision of reproduction can be
made arbitrarily great by making the number of nails arbitrarily large.

In space-time, the nails are replaced by events. I'm not sure if you're familiar with events, they aren't terribly complicated. Events have a location and a time of occurrence. For example, if one was writing a police report about a crime, one might give the location (a street address, say), and a time and date of the crime. The street address is the location of the event, the crime, that tells where it occurred in space. Specifying the location of the event is not sufficient, however, we also need to know the time at which it occurred. Events are one of the most fundamental elements of space-time, replacing the "nails" in Taylor's rowboat, which only have a location in space, but do not have a time of occurrence.

The tricky part here is understanding what replaces the notion of the "distance between nails" on the rowboat. What is the equivalent "distantce" between events in space-time? The needed concept here is called the Lorentz interval. The Lorentz interval says that given two events in space-time, there is a single number that is simliar to a "distance", a number that is independent of the observer. A key part of why we need the Lorentz interval is a feature of special relativity called "the relativity of simultaneity". This feature says that whether or not two events occur "at the same time" depends on the observer, specifically the observer's state of motion, the observer's velocity. The end result is that we do not have a separate "spatial distance" and a "time distance" between two events that is the same for all observers. The spatial distance can change due to Lorentz contraction, the time "distance" can change due to the relativity of simultaneity. The Lorentz interval, however, does not change. It's the same for everyone, and it makes talking about what happens much, much easier.

I would guess offhand from what you write that you are not already familiar with these concepts (the Lorentz interval and the relativity of simultaneity). They both occurs in special relativity, which is much simpler mathematically than General relativity, though people still stumble over some of the needed concepts.

Myl recommendation to everyone is to understand special relativity first, before tackling General relativity. But I'd settle for people realizing that they should at least study special relativity in addition to general relativity.

 

[Nugatory]

That is, does the presence of spacetime curvature, by itself, without the help of relative motion, magnetism, or any other darned thing, cause an object to move in the dimensions of space?

I don't understand what you mean by "without the help of relative motion", because all movement in space is always relative motion - there is no other kind of motion.

But with that said, the answer to the rest of your question is that one thing and only one thing "causes" an object to move in the dimensions of space: and that one thing is which point in space you choose to define as not moving.

We've mentioned an object free-falling towards the surface of the Earth several times already in this thread. Choose the object to be at rest and the surface of the Earth is moving upwards through space; choose a point on the surface of the Earth to be at rest and the object is moving downwards through space. Either way the choice is purely a choice of point of view, with no physical significance.

In general the statement "X is moving through space" tells us only about the point of view of the person making that statement, and tells us nothing about what X is really doing. If you want to know that, you have to draw X's worldline, its path through spacetime. All observers, regardless of their point of view, will agree about which points in spacetime that worldline passes through, so there is no point-of-view problem in this description.

 

[Dale]

We can also, in our minds' eyes, remove the planet from this scenario.

You cannot remove the planet and keep the curvature of spacetime. The planet is the source of the curvature: no source -> no curvature. It is best to leave it.

our old friend, CHoS, so that the very edge of it

Hmm, there isn’t an edge. The curvature from a planet gets less and less the further away, but there is no edge where it suddenly goes to zero. I don’t think that the edge is helpful to your thought experiment.

That is, does the presence of spacetime curvature, by itself, without the help of relative motion, magnetism, or any other darned thing, cause an object to move in the dimensions of space?

This question is better answered by the following simplification of your scenario:

Consider a spherical non-rotating planet and a force-free ball initially at rest with respect to the planet in the vacuum some finite distance away from the planet. Neglect all other effects besides the curvature of spacetime due to the planet. Does the presence of spacetime curvature, by itself, cause the ball to move with respect to the planet?

The answer is: Yes

 

[Patterner]

You cannot remove the planet and keep the curvature of spacetime. The planet is the source of the curvature: no source -> no curvature. It is best to leave it.

Is there no hope of finding other means of curving spacetime, so we can put gravity wherever we want? Like on spaceships?

Hmm, there isn’t an edge. The curvature from a planet gets less and less the further away, but there is no edge where it suddenly goes to zero. I don’t think that the edge is helpful to your thought experiment.

One of the many less-than-fully-thought-out things I've posted in this thread. Still, there must be a distance from the Earth where it does not curve spacetime sufficiently to affect a baseball?

This question is better answered by the following simplification of your scenario:
Consider a spherical non-rotating planet and a force-free ball initially at rest with respect to the planet in the vacuum some finite distance away from the planet. Neglect all other effects besides the curvature of spacetime due to the planet. Does the presence of spacetime curvature, by itself, cause the ball to move with respect to the planet?
The answer is: Yes

Thank you!

 

[Patterner]

I would guess offhand from what you write that you are not already familiar with these concepts (the Lorentz interval and the relativity of simultaneity).

Lol. Indeed, I am not. Your post is the first I've ever heard of Lorentz. Thank you for the link. I'll see what I can make of it.

 

[Dale]

Is there no hope of finding other means of curving spacetime, so we can put gravity wherever we want? Like on spaceships?

You could always build planet sized spaceships.

One of the many less-than-fully-thought-out things I've posted in this thread. Still, there must be a distance from the Earth where it does not curve spacetime sufficiently to affect a baseball?

You could always specify some small speed and some large time where if over that large time the baseball has acquired less than the small speed, then you will call it “unaffected”. There would not be any edge, but at that point you would kind of shrug and say “who cares”.

However, setting a “who cares” radius and then asking about a baseball placed there will only lead to “who cares” answers. That is fairly uninteresting for us to write and uninformative for you to read, so I hope you don’t do it.

 

[David Lewis]

The only reason that objects follow the curve of a rubber sheet is because of the force of gravity. Take away the force of gravity and all bets are off.

It's a 2D model in 3D space, and you can see all the dimensions. If you are moving in a straight line in a universe that is curved in a dimension you can't see, you would feel a force.

Why does it lose some of its motion through time and gain motion in space?

The extent in one dimension decreases in the dimension it's rotating out of, and simultaneously increases in the dimension it's rotating into.

You cannot remove the planet and keep the curvature of spacetime.

The curvature will remain for a time. As a thought experiment, if you suddenly moved the Sun far away from the solar system, the curvature in the vicinity of Earth would remain unperturbed for about 8 minutes.

 

[Dale]

if you suddenly moved the Sun far away from the solar system,

You cannot do that either.

 

[PeterDonis]

If you are moving in a straight line in a universe that is curved in a dimension you can't see, you would feel a force.

No, you wouldn't. GR models spacetime in the presence of gravity this way (except for the part about being "curved in a dimension you can't see", which is not necessary, curvature can be intrinsic to a manifold and independent of any embedding into a higher dimensional space), and objects moving solely under gravity feel no force.

As a thought experiment, if you suddenly moved the Sun far away from the solar system

As @Dale pointed out, you can't do this. The qualfier doesn't get you off the hook; even in thought experiments, you can't violate the laws of physics, and suddenly moving the Sun far away from the solar system would violate the laws of GR (in this case, local conservation of stress-energy).

 

[Patterner]

You could always build planet sized spaceships.

That's an easy fix! :) Just don't go near any solar systems. Don't want to be causing tidal waves. Or pulling planets out of orbit.

However, setting a “who cares” radius and then asking about a baseball placed there will only lead to “who cares” answers. That is fairly uninteresting for us to write and uninformative for you to read, so I hope you don’t do it.

I will fight the urge. But I'm just trying to understand things. I guess the inverse square law won't let us say there is any distance at which the gravitational effect is 0. But still...

 

[Dale]

I'm just trying to understand things.

If you really do have a strong desire to understand, then you will need to put in some effort learning background concepts. I would recommend learning special relativity first, particularly from a source that teaches about four-vectors and has a strong emphasis on spacetime geometry.

 

[Patterner]

Any sources you particularly recommend?

 

[Nugatory]

Any sources you particularly recommend?

You could do worse than "Spacetime Physics", by Taylor and Wheeler.

 

[Dale]

Any sources you particularly recommend?

I was going to suggest Spacetime Physics also.

 

[A.T.]

Any sources you particularly recommend?

If you want an intuitive grasp of the concepts, with as little math as possible, try:
"Relativity Visualized" by Lewis Carroll Epstein

 

[Patterner]

Checking them out. Thanks.

 

[PeroK]

Checking them out. Thanks.

There are free texts on SR and GR here:

http://www.lightandmatter.com/

 

[Patterner]

Thanks again!