How exactly does gravity work?

[TheNerdyBushman]

how does gravity actually work? i understand the accepted theory is that mass bends space-time, how ever, the more i think about it, the more stupid the theory becomes to me. its just seems a bit "primitive"...ill explain.

if planets orbit around suns due to the sun bending space, then why do the planets and the suns collide together? if gravity is the bending of space then there must be a counter force that prevents two massive objects in orbit from colliding together.
plus, if gravity really is the bending of space, then it would be impossible for a massive object to move along the curved space without an initial force present to make it move. there must be some type of force that acts on massive objects besides the bent space. think about it, even if a large mass does bend space, then there is still no reason why smaller masses would move in orbit around the larger mass...to me, it seems like the smaller mass should simply just sit still in the bent space unless there is a active force that actually makes it move...i like to think of it this way, imagine a astronaut in space has a flat sheet of metal with a large, round dent in its center, now imagine the astronaut placed a small ball on the part of the sheet that is bent, what do you think happens? the ball will not just magicly start moving along the bent sheet because there is no active force that causes it to move in the first place...

 

[A.T.]

the ball will not just magicly start moving along the bent sheet because there is no active force that causes it to move in the first place...

 

[Nugatory]

if planets orbit around suns due to the sun bending space,

It's due to the sun's mass bending space-time, not space. That's a really important distinction because...

then why do the planets and the suns collide together? if gravity is the bending of space then there must be a counter force that prevents two massive objects in orbit from colliding together.

The planets don't collide with the sun because their paths through spacetime (called a "worldline") don't intersect the worldline of the sun.

plus, if gravity really is the bending of space, then it would be impossible for a massive object to move along the curved space without an initial force present to make it move. there must be some type of force that acts on massive objects besides the bent space. think about it, even if a large mass does bend space, then there is still no reason why smaller masses would move in orbit around the larger mass...to me, it seems like the smaller mass should simply just sit still in the bent space unless there is a active force that actually makes it move...

An object can sit still in space, but it can't sit still in spacetime. Even if you don't change your position in space, time is still passing for you so you are constantly moving forward in the time direction.

i like to think of it this way, imagine a astronaut in space has a flat sheet of metal with a large, round dent in its center, now imagine the astronaut placed a small ball on the part of the sheet that is bent, what do you think happens? the ball will not just magicly start moving along the bent sheet because there is no active force that causes it to move in the first place...

The sheet is an example of curved space, not curved spacetime. You'll have to get that picture out of your mind or it will just keep confusing you. A.T.'s apple video is a much better way of thinking about it.

 

[Bandersnatch]

You're confusing gravity with momentum. Body A will orbit body B if it was given some momentum relative to B in earlier interactions. In case of planetary systems and galaxies, this is provided by the virtue of conservation of momentum of an initially-rotating cloud of gas (so in terms of dynamics, gravity acting on uneven distribution of matter).
It's exactly the same in general relativity as with Newtonian gravitation - if you placed a planet next to a star without giving it some momentum, it'd fall straight in. This in no way contradicts the Newtonian description of gravity as a force.

Furthermore, gravity is the curvature of space-time, not space. Notice that that's what A.T.'s videos depict.

 

[PeroK]

i like to think of it this way, imagine a astronaut in space has a flat sheet of metal with a large, round dent in its center, now imagine the astronaut placed a small ball on the part of the sheet that is bent, what do you think happens? the ball will not just magicly start moving along the bent sheet because there is no active force that causes it to move in the first place...

This is, I believe, a big issue with the rubber sheet analogy. 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.

In the absence of a force, therefore, what would induce a particle to move with a particular acceleration?

The answer lies in a formulation of mechanics using the Lagrangian principle. For example, in classical mechanics you can look at Newton's second law in two ways:

a) A particle accelerates under a force in inverse proportion to its mass.

b) A particle moves in order to minimise a thing called the Lagrangian (which involves its kinetic and potential energies).

And, these two can be shown to be equivalent.

Now, principle a) cannot be applied when gravity becomes spacetime curvature. But, the Lagrangian principle b) can be generalised. And, in fact, b) becomes:

b*) A particle moves in such a way as to maximise the amount of (proper) time it experiences.

You probably need to study some Relativity to appreciate what b*) really means. But, that is the principle that induces a particle to move under the influence of gravity.

 

[TheNerdyBushman]

the first video is exactly what i needed to know, gravity now makes complete sense to me, thanks!

its crazy to think about this concept, i now see that motion is a complete illusion, very interesting...

i can't help to think that there must be a way we can use this concept and maybe convert the movement of time into energy or somehow manipulate space to travel through time itself...a man can dream can't he? lol

 

[TheNerdyBushman]

how does gravity actually work? i understand the accepted theory is that mass bends space-time, how ever, the more i think about it, the more stupid the theory becomes to me. its just seems a bit "primitive"...ill explain.

if planets orbit around suns due to the sun bending space, then why do the planets and the suns collide together? if gravity is the bending of space then there must be a counter force that prevents two massive objects in orbit from colliding together.
plus, if gravity really is the bending of space, then it would be impossible for a massive object to move along the curved space without an initial force present to make it move. there must be some type of force that acts on massive objects besides the bent space. think about it, even if a large mass does bend space, then there is still no reason why smaller masses would move in orbit around the larger mass...to me, it seems like the smaller mass should simply just sit still in the bent space unless there is a active force that actually makes it move...i like to think of it this way, imagine a astronaut in space has a flat sheet of metal with a large, round dent in its center, now imagine the astronaut placed a small ball on the part of the sheet that is bent, what do you think happens? the ball will not just magicly start moving along the bent sheet because there is no active force that causes it to move in the first place...

after giving this some thought, i can not accept that time is the cause of this illusion of motion. time is a perception of the mind, i do not believe that time acts like a physical force, pushing objects through space in a strait direction. instead, doesn't it make a lot more since to say that the expansion of space with in our universe is the cause of the motion we perceive?

 

[Nugatory]

fter giving this some thought, i can not accept that time is the cause of this illusion of motion. time is a perception of the mind,

Motion is not an illusion and I'm not sure where you got the idea that it is. The only thing that is slightly surprising about motion (and it's not that surprising - Galileo discovered this in the 16th century so we've had the best part of five centuries to get used to it) is that motion is always relative. It makes no sense to talk about something moving at a particular speed (including the special case of speed equal to zero, which we call "at rest") without saying what that speed is relative to. I'm sitting in my chair typing this... Am I at rest? Yes, according to the dog who is asleep on the floor next to me... but the chair, floor, me, dog are all attached to the surface of the rotating earth... and that Earth is orbiting the sun, which is moving through interstellar space. So is my speed zero 9relative to the surface of the earth? A few miles per second relative to the sun? Or something completely different relative to the center of the galaxy? Or something even more different relative to the Andromeda galaxy?

instead, doesn't it make a lot more since to say that the expansion of space with in our universe is the cause of the motion we perceive?

No, and a moment's reflection should convince yourself of that. How could the expansion of the universe account for the way that the worldline of the free-falling apple and the surface of the Earth converge in A.T.s video? Where exactly is the expansion taking place, how much expansion is needed and how does that compare with the known rate of expansion (google will find that number for you), and is that consistent with the observed motion of other objects in the vicinity?

 

[Mister T]

if planets orbit around suns due to the sun bending space, then why do the planets and the suns collide together?

If you instead model gravity as a force that pulls the planets towards the sun, you still have this same issue to resolve.

to me, it seems like the smaller mass should simply just sit still in the bent space unless there is a active force that actually makes it move...

It does seem that way until you learn that Nature doesn't behave the way it seems it should. It behaves the way it behaves with no regard to what we humans think about it.

What happens is that objects don't necessarily move in the direction of the force exerted on them.

i like to think of it this way, imagine a astronaut in space has a flat sheet of metal with a large, round dent in its center, now imagine the astronaut placed a small ball on the part of the sheet that is bent, what do you think happens? the ball will not just magicly start moving along the bent sheet because there is no active force that causes it to move in the first place...

No, but what if the sheet is in motion? What if the sheet and the ball share the same motion?

What people have concluded is that all that matters is the relative motion. Do the ball and the sheet move relative to each other? That's the issue.

 

[A.T.]

the video claims this is due to the object traveling forward through time, thus, the object is not actually moving through space,

Watch it again. Initially it's advancing only through time, but due to the space-time geometry it deviates towards the spatial dimension, and starts advancing in space.

...the space itself is still expanding even if it is bent by a massive object...

Thats irrelevant here. The massive object just curves space-time such that locally straight worldliness deviate towards it. Play around with this applet to see how it works on wider scale:
http://www.adamtoons.de/physics/gravitation.swf

You will find more illustrations here:
http://www.relativitet.se/Webtheses/tes.pdf

 

[Ibix]

the video claim that the object at rest is actually moving forward through time, but to us the object doesn't seem to move at all because we are also moving forward through time at the same pace as the object we are observing

In addition to A.T.'s comment, note that it's perfectly possible to have an object moving relative to you in flat spacetime. It's just not the case that the animation shows.

And if you want to consider motion to be an illusion, may I suggest that the next time you stub your toe you remind yourself that motion is an illusion, so the collision and resulting pain must be illusions too.

 

[TheNerdyBushman]

Watch it again. Initially it's advancing only through time, but due to the space-time geometry it deviates towards the spatial dimension, and starts advancing in space.Thats irrelevant here. The massive object just curves space-time such that locally straight worldliness deviate towards it. Play around with this applet to see how it works on wider scale:
http://www.adamtoons.de/physics/gravitation.swf

You will find more illustrations here:
http://www.relativitet.se/Webtheses/tes.pdf

thanks! ill watched it again, how ever, it still seems to suggest that an object moving through time is what gives it the illusion of motion.

and as for what you say is irrelevant, its actually not lol. you took that quote from something i was explaining to nugatory XD

i was explaining my reasoning behind thinking that the expansion of space could cause the motion of planets orbiting a larger mass. just keep in mind that through out history, physics, science and our understanding of the universe keeps constantly changing, many times in history has our beliefs about physics and science turned out to be wrong, even though we were so sure of ourselves at the time.i just mean that its easy to confuse and misunderstand certain things that we think we know beyond a shadow of doubt. for instance, if a objects passage through time along the surface of bent space, it would be easy to think that if the expansion of space pushed an object at the same pace, you probably wouldn't be able to tell the difference between time and expanding space being the initial force and/or cause of motion.

 

[A.T.]

...the expansion of space could cause the motion of planets orbiting a larger mass...

No expansion is needed for this.

 

[TheNerdyBushman]

No expansion is needed for this.

well I am glad you have it all figured out.

 

[Mister T]

just keep in mind that through out history, physics, science and our understanding of the universe keeps constantly changing, many times in history has our beliefs about physics and science turned out to be wrong, even though we were so sure of ourselves at the time.

People who study physics beyond the freshman level learn that lesson and carry it with them for the rest of their lives.

i just mean that its easy to confuse and misunderstand certain things that we think we know beyond a shadow of doubt.

Once you learn the lesson mentioned above you never, and I mean never, think you know something about Nature "beyond a shadow of a doubt".

 

[Dale]

Let's please stop the discussion about motion as an illusion. I have deleted several of the previous posts about it and will delete all subsequent posts about it.

 

[Ostrados]

What the OP may not know is that it was proven experimentally many times that large objects in space indeed curve spacetime. And there are even practical uses for this phenomena, for example gravitational lensing is used in modern astronomy to see a far away galaxy behind another galaxy by exploiting spacetime bending:
http://www.cfhtlens.org/public/what-gravitational-lensing

I am strong believer in GR and I admire Einstein's gravity model, however I struggle when thinking about how this works on small scale. For example imagine a 20kg rock floating in free space with no gravity around, can the rock cause enough bending to have any gravitational effect on small objects around it, it seems to me that gravity does not exist on small scale.

 

[Ibix]

The Cavendish experiment to measure G works using the gravitational interaction between objects in that range. So yes, gravity works for small masses. Why wouldn't it?

 

[Ostrados]

The Cavendish experiment to measure G works using the gravitational interaction between objects in that range. So yes, gravity works for small masses. Why wouldn't it?

Lol I was just reading about the Cavendish experiment, so yes gravity works on small scale.

 

[Patterner]

I really don't know if I understand it yet. My best understanding goes a little something like this... There is no "force" of gravity. There is nothing reaching out from one thing to another. Newton's First Law of Motion says a body at rest will remain at rest unless an outside force acts on it, and a body in motion at a constant velocity will remain in motion in a straight line unless acted upon by an outside force. However, that only applies to flat spacetime. Because a body is never truly at rest; it is moving through the time dimension even if it is not moving through any of the three space dimensions. In flat spacetime, motion through the time dimension does not cause motion through any of the space dimensions. But in curved spacetime, it does. When a car going north at 50 mph turns so that it is going northwest at 50 mph, it loses some of its northward speed in order to have some westward speed. And, in curved spacetime, a body loses some of its speed through time in order to have some speed through space.

Is that right? If not, I'd appreciate some help!

If that is right, I still don't understand why it happens. Why must there be motion in a physical dimension in curved spacetime when there need not be in flat spacetime?

 

[PeroK]

If that is right, I still don't understand why it happens. Why must there be motion in a physical dimension in curved spacetime when there need not be in flat spacetime?

In Newtonian physics things move according to the forces acting on them. But, a french mathematician called Lagrange reworked Newtonian mechanics into a formulation where things move in order to minimise a quantity called the Lagrangian. Lagrange's formulation of mechanics can be shown to be entirely equivalent to Newton's. But, the underlying reason for motion is somewhat different.

When you move to the theory of General Relativity (GR), there are no forces, so you cannot apply Newton's laws. But, you can apply the Lagrangian principle that nature acts in order to minimise or maximise certain quantities. In GR the quantity being maximised is the "proper" time that a particle experience. This, therefore, is the defining law of GR in respect of the paths that particles take.

In the special case of flat spacetime a particle maximises its proper time by, you guessed it, remaining at rest or moving with constant velocity (in a straight line).

 

[Patterner]

I appreciate your response. But OY! Lol. What the heck is '"proper" time'? And why must there be motion through a dimension of space when spacetime is curved in order to maximize it?

 

[PeroK]

I appreciate your response. But OY! Lol. What the heck is '"proper" time'? And why must there be motion through a dimension of space when spacetime is curved in order to maximize it?

"Proper" time is the time that the particle experiences. Rather than someone else's measure of time. The local spacetime can be flat or curved. In either case the particle moves in order to maximise its proper time (the time it experiences).

That's the Lagrangian principle for motion. In Newtonian gravity there is nothing "touching" the Earth that moves it in its orbit. You end up with a similar situation that a particle moves in response to a gradient in gravitational potential, which is no less mysterious if you think about it.

How the heck do you think Newton's gravitational force transmits itself?

 

[Patterner]

Why would the time it experiences not be proper if it moves through the dimension of time but not any of the dimensions of space when spacetime is curved, but it is proper when spacetime is flat? (Does that wording make sense? Difficult to phrase my question clearly.)

 

[anorlunda]

My best understanding goes a little something like this... There is no "force" of gravity.

I think your confusion stems to that statement.

There is another definition of force that you may not have heard of yet. $F=\frac{dV}{dx}$ where V is potential energy and x is position. We call it a gradient. You can also call a hillside a gradient. The gradient of the hill in a gravitational field creates a force that accelerates the ball downhill. There is no need for objects to reach out and touch each other to make a potential energy gradient.

It takes work to lift a book from a lower shelf to a higher shelf. That means the book has more potential energy on the higher shelf. If the book is free to fall back down it will because free objects always move to the lowest energy if they can (in other words, downhill). So you can use that force from the potential gradient $F=\frac{dV}{dx}$ in Newton's Second Law $F=ma$ to see how the gradient creates motion, even if the object was initially motionless.

 

[PeroK]

Why would the time it experiences not be proper if it moves through the dimension of time but not any of the dimensions of space when spacetime is curved, but it is proper when spacetime is flat? (Does that wording make sense? Difficult to phrase my question clearly.)

"Proper" is perhaps not the best word that could have been chosen. The German is "Eigenzeit", I believe, which much more conveys the idea of being characteristic of that particular particle. In any case, "proper" only means the particle's own measure of time.

In fact, "proper time" is also the spacetime distance that the particle travels. This ties in with your idea that a particle at rest (in your reference frame) is moving only through your time dimension and not through your spatial dimensions. And a particle that is moving (in your reference frame) is moving through your time dimension and your spatial dimensions.

 

[A.T.]

Newton's First Law of Motion says a body at rest will remain at rest unless an outside force acts on it, and a body in motion at a constant velocity will remain in motion in a straight line unless acted upon by an outside force.

You can generalize this like this:

If no net force acts on the body it's worldline (path in space-time) is straight.

This applies to both, Newtons and Einsteins gravity models. What is different, when the above is the case: hanging apple (Newton) or falling apple (Einstein):

 

[Mister T]

Newton's First Law of Motion says a body at rest will remain at rest unless an outside force acts on it, and a body in motion at a constant velocity will remain in motion in a straight line unless acted upon by an outside force. However, that only applies to flat spacetime.

It is better to replace Newton's First Law with the Principle of Relativity. The latter is really the modern view of the former. All inertial reference frames are equivalent.

Because a body is never truly at rest; it is moving through the time dimension even if it is not moving through any of the three space dimensions.

This makes no sense. To move means to change position.

 

[bhobba]

Ok here is the technical rundown why gravity is space-time curvature. Its not at the B level - but it can't really be explained at that level why its pretty much inevitable. The OP probably will not understand the detail, but hopefully will get a gist.

If we consider flat-space time then let's try to construct a theory of gravity.

We will base it on electromagnetism in special relativity - ie flat space-time - the most elegant form of EM probably being the so called Lorentz gauge formalism. In this formalism ∂u∂uAv = 4π ∂vJv and ∂uAu=0. Au and Ju are first rank 4 tensors - you can look up what they are physically - but its not important to this. Just for the heck of it let's write a similar equation in second rank tensors Φuv instead of first rank ones like Au, so you have ∂u∂uΦjk = -kTjk and ∂uΦuk=0 - k is a constant to be determined. I haven't at this point said anything about Φ or T - we will see what happens if you mathematically analyse it. Define huv = Φuv - 1/2 ηuvΦ.

When you chug through the math you find something very interesting - the equation describing huv is invariant to very small changes of coordinate systems. Well since any coordinate system can be broken into a lot of small changes from another coordinate system this leads to the equations should be invariant to changes in coordinate systems. But that is very intuitive anyway - coordinate systems are man made - nature doesn't decide them - since we choose them, equations should not really change when they do - it's called the principle of invariance. So really you should write the equations in general coordinate systems from the start. We will not only assume that but make no assumption about if space-time is flat or not. In curved space-times an assumption is made - just like if you had some curved sheet in 3 dimensional space - small areas of it can be considered flat - in curved space-time small areas are considered flat space-time. Ok let's do that. When you do you find some interesting things. First the equation of motion of a particle at low speeds and small huv is exactly the same as a gravitational field with a simple relation to huv - in particular h00 - Φ = 1/2 k h00 where Φ is the gravitational potential. Hmmm - maybe this has something to do with gravity. Ok let's see what Tuv is - it turns out T00 is the mass density, p. But we know the equations have to be the same in any coordinate system. In small areas in curved space-time, its flat and SR holds - so the equations ∂u∂uΦjk = Tjk and ∂uΦuk=0 must hold. So we start to chug through the math again to find an equation that is the same in any coordinate system but in small areas reduces to the flat space time equations. The equation is Guv = -1/2k^2 Tuv. Guv is called the Einstein Tensor defined by Guv = Ruv - 1/2 guv R (guv is called the metric - and is defined as guv = ηuv + k huv). Ruv, called the Ricci tensor is a measure of the spaces curvature. R, is called the Ricci scalar, and is also a measure of curvature - so the Einstein Tensor is a measure of curvature. Suppose we have a dust of particles then Tuv is called its called the stress energy tensor of the particles, and T00 in flat space-time is the mass density. So we have the amazing result - space-time is curved by mass.

Its virtually inescapable if you follow where the math leads.

Thanks
Bill

 

[Patterner]

Sadly, though I surely appreciate everyone's posts, and will read them repeatedly, I'm no closer to understanding. Why can an object in the center of the flat spacetime grid sit still, moving only in the dimension of time, yet it must move in the dimensions of space in the curved spacetime grid?

 

[Ibix]

Motion is relative. So in either curved or flat spacetime an object can always regard itself as stationary. Note that your diagrams are potentially somewhat misleading in this context, because they show a grid that something might move relative to - but there's no such thing in spacetime. Unless you build one out of girders.

I think what you want to ask is why do objects follow curved paths in curved spacetime. The basic answer to this is "that's what they do". Why do things travel in straight lines in flat spacetime? It's just what they do. We can explain this in terms of extremising the action (the Lagrangian methodology @PeroK mentioned), but this is merely a mathematical way of saying "because they do".

At some point, you run into the fact that we don't know everything. General relativity simply models spacetime as an entity whose rules of geometry depend on mass and energy. Things follow curved paths because the geometry is not Euclidean. But why that should be, we don't know.

 

[Dale]

Why can an object in the center of the flat spacetime grid sit still, moving only in the dimension of time, yet it must move in the dimensions of space in the curved spacetime grid?

Objects in either grid can follow the time dimension of the grid. To follow the straight grid the object’s worldline must be straight. To follow the curved grid the objects worldline must be curved.

 

[Patterner]

I think what you want to ask is why do objects follow curved paths in curved spacetime.

I don't think that's it. I can understand that, if spacetime is curved, anything moving in that curved chunk of spacetime must follow the curve. A ball rolling down through a curved tube can only follow the path of the tube. What I *think* I want to ask is why do objects *have* to move in curved spacetime if they do not have to move in flat spacetime. Things can exist in curved spacetime without moving in the dimensions of space. The apple on the tree is doing so. It moves only in the dimension of time, because the tree is holding it still in the dimensions of space. But why MUST it begin to follow the curved spacetime when the tree let's go of the stem? Why does it not simply stay at the spot on the curve where it has been all along? It was not moving in space before. All of its lightspeed motion was in the dimension of time. Why does it lose some of its motion through time and gain motion in space?

The basic answer to this is "that's what they do". Why do things travel in straight lines in flat spacetime? It's just what they do. We can explain this in terms of extremising the action (the Lagrangian methodology @PeroK mentioned), but this is merely a mathematical way of saying "because they do".

At some point, you run into the fact that we don't know everything. General relativity simply models spacetime as an entity whose rules of geometry depend on mass and energy. Things follow curved paths because the geometry is not Euclidean. But why that should be, we don't know.

I can appreciate such answers. And, once we get down to the bottom of current human knowledge, I can accept it. But I don't think that's the case here. It cannot be the case that what I'm wanting to know is either not known, or seriously being looked into. I think the problem is that my question, my confusion, is not being understood. I have a feeling there's some bit of information that is so obvious, or so basic to all this that it's among the first things taught, that nobody thinks I don't have it. But I don't! LOL

 

[Nugatory]

What I *think* I want to ask is why do objects *have* to move in curved spacetime if they do not have to move in flat spacetime. Things can exist in curved spacetime without moving in the dimensions of space.

The term "moving in space" always means "moving in space relative to something", whether the spacetime is curved or not. The apple hanging on the branch is not moving in space relative to an observer standing on the ground; but an observer on Mars looking at the apple through a telescope will say that it is moving (along with the rest of the earth) through space at a speed of many kilometers per second.

Break the stem and let the apple fall, and now the apple will be moving in space relative to the surface of the earth; but it will not be moving through space according to an observer falling along with the apple.

 

[Dale]

What I *think* I want to ask is why do objects *have* to move in curved spacetime if they do not have to move in flat spacetime.

Based on your statements I think that your question is actually about curved grid lines (coordinates) rather than curved spacetime. If you have coordinates where the time axis is straight then objects that follow the time axis must have straight worldlines. If you have coordinates where the time axis curves then objects that follow the time axis must have similarly curved worldlines.

An apple on a stem has a curved worldline and an apple in free fall has a straight worldline.