Using gravity to explain gravity

hypnagogue

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This is a question I've always had about the conventional explanation for gravity... I read something recently (either here or elsewhere) that reminded me of it, and it still puzzles me, so maybe you guys can shed some light on this.

The conventional relativistic explanation of gravity goes like this: Imagine a stretched out rubber sheet; this is space-time. Place an object on the sheet and it will deform and curve downward in accordance to the shape and mass of the object; this curvature in space-time is what we call gravity. If we place another object on the sheet near the curvature, it will fall down the curvature 'well' towards the initial mass; this is analogous to the mechanism of gravitational attraction via curvature of space-time.

Now, what bugs me about this explanation is that in some respects, it begs the question-- that is, in trying to explain how gravity works in the model, we are using a demonstration that depends crucially on our intuition of the functioning of gravity in the real world. Now, I suppose we could superficially get around this by conducting the demonstration in outer space, using metallic objects and replacing the downward pull of gravity with the downward pull of an appropriately situated magnet. But this is still presuming the existence of an attractive force to explain the mechanism of an attractive force. Anyone care to clear up the confusion?
 
yeah baby! the whole point of physics is to explain esoteric things in terms of mundane things-the "gravity to explain gravity" is just to help you get a handle on things (the extra dimentions involved, I think).
 

chroot

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The rubber sheet is NOT an explanation for gravitation. It is an analogy. Like all analogies, it has its limitations.

The rubber plane is supposed to be two-dimensional space. The third dimension, in which the depressions live, is supposed to be time (roughly speaking).

In the real world, gravitation results from bodies trying to follow the straighest possible lines through curved space-time. The definition of a "straightest possible line" is, in fact, a line with maximal proper time. There is no need to invoke gravity to explain gravity, as you suspect. All that's necessary is a knowledge of curved spaces and the fact that Nature makes all bodies follow the straightest possible lines -- voila, you've got gravitation.

In the rubber-sheet analogy, the earth's gravity causes bodies to seek the bottom of a depression. In the real world, bodies seek to follow the straightest possible lines. This is the crux of the analogy. These are two different concepts, but they can be handled similarly by your brain. If you wish, you can think of earth's gravity on the rubber sheet as being analogous to a "force" that makes bodies in the real world follow the straightest possible lines.

- Warren
 

hypnagogue

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OK, but I guess this is the crux of the matter. Do we have any explanations, analogies, theories, etc. that account for why a body will follow the straightest line possible? Or do we just take this to be true axiomatically?
 
P

pmb

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The conventional relativistic explanation of gravity goes like this: Imagine a stretched out rubber sheet; this is space-time. Place an object on the sheet and it will deform and curve downward in accordance to the shape and mass of the object; this curvature in space-time is what we call gravity. If we place another object on the sheet near the curvature, it will fall down the curvature 'well' towards the initial mass; this is analogous to the mechanism of gravitational attraction via curvature of space-time.
That is not an explanation. That is a description. And that demonstrates spatial curvature. Not spacetime curvature. And gravity is not the same thing as spacetime curvature since there are gravitational fields with no spacetime curvature. E.g. a uniform gravitational field has no spacetime curvature.

Pmb
 

chroot

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Originally posted by hypnagogue
OK, but I guess this is the crux of the matter. Do we have any explanations, analogies, theories, etc. that account for why a body will follow the straightest line possible? Or do we just take this to be true axiomatically?
It is a feature of Nature. We also do not know why there are two kinds of electrical charge, or three kinds of colour charge. We don't know why there are four forces, instead of two or nineteen. Probably, these are meaningless, metaphysical questions. They probably will never have any answers. Invoke the weak anthropic principle if you wish.

- Warren
 
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Why there are analogies /similarities/ at all?
 
In the real world, gravitation results from bodies trying to follow the straighest possible lines through curved space-time. The definition of a "straightest possible line" is, in fact, a line with maximal proper time. There is no need to invoke gravity to explain gravity, as you suspect. All that's necessary is a knowledge of curved spaces and the fact that Nature makes all bodies follow the straightest possible lines -- voila, you've got gravitation.
Chroot,
Would you mind takin a step back and explaining what gravity has to do with following lines through space-time?
 

chroot

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Originally posted by Rockazella
Chroot,
Would you mind takin a step back and explaining what gravity has to do with following lines through space-time?
Imagine that two ants are on the equator of a sphere. Say there's about 90 degrees apart in longitude (because it's easy to visualize). Say the ants both begin walking north on the sphere, towards the pole. Each walk on a "great circle," which is the straighest possible line on a sphere (footnote 1). Now, even though each ant is walking on what is to him the straightest possible line, and even though both ants began walking in a "parallel" direction, they both find themselves at the pole at the same time. If they keep walking, they will, in fact, bump into each other.

If you look at the situation from the outside, the ants walked in straight lines, but wound up closer together as they walked. It is as if some force had pushed them together. This force is called "gravity."

Two bodies following geodesics (straightest lines) through curved spacetime will appear to be attracted to each other.

Footnote 1: a great circle is the largest kind of circle you can draw on a sphere; its center coincides with the center of the circle. The equator and all the lines of longitude are examples of great circles. When airplanes fly from one city to another, they also follow great circles, since great circles are the straightest possible lines along the curved surface of the earth.

- Warren
 
Imagine that two ants are on the equator of a sphere. Say there's about 90 degrees apart in longitude (because it's easy to visualize). Say the ants both begin walking north on the sphere, towards the pole. Each walk on a "great circle," which is the straighest possible line on a sphere (footnote 1). Now, even though each ant is walking on what is to him the straightest possible line, and even though both ants began walking in a "parallel" direction, they both find themselves at the pole at the same time. If they keep walking, they will, in fact, bump into each other.
Chroot,
This begins to give me an idea of what your saying, but I'm failing to see the significane of this example. Wouldn't the straightest possible line from the equator to the northpole be through the sphere? Why not tunnel? I dont see why space-time has to be considerd "curved". What's wrong with defining a straight line as the shortest possible line connecting two points? How can you place these surfaces in space?

I could probably ask a thousand more like that, but I wont(for now anyway).
 
Clip: "In the real world, gravitation results from bodies trying to follow the straighest possible lines through curved space-time."

- Warren

Hello Warren:
I have been trying for some time to understand curved space-time. This theory of gravitation is forceless, yes? If Earth causes curved space-time in nearby spaces and the Moon is trying to follow the straightest possible path which is curved around Earth, then why does it remain important that the Moon maintain a certain critical speed in order to remain in orbit? What do you think will happen if the Moon is slowed a bit in its orbit of Earth? What will happen after it is brought to a complete halt in its orbit of Earth?
Please explain the reasoning behind your forceless understanding.

Thanks,
 
I posted a similar question to this a year or so ago, I’d link to it but it seems to have been lost in various forum updates, is there an archive anywhere?

I’ll try and recount the conclusions but my memory is not brilliant so feel free to correct me.

Firstly some stuff about the rubber sheet analogy. The rubber sheet is a way of imaging 4D space-time. It accomplishes this by simply dropping one of the dimensions. The sheet is actually infinitely thin, the thinness of the sheet being the dimension we have lost, and any objects (planets etc..) do not sit on top of the sheet they are inside it.

Because we are viewing this 4D object from a £D perspective I’m not sure it’s correct to imagine objects moving within the sheet. We have X and Y dimensions and Z is this infinitely thin thickness of the sheet. We also have a bulge in the sheet (the gravity well caused by whatever massive object you want to imagine) and this bulge is pushing out into the 4th dimension from which we are viewing. If we are viewing from the perspective of the time dimension I doubt we can imagine the content of the sheet in motion – again feel free to correct me.

Despite the problems it’s still the best way of imaging space-time that I’ve come across so onto the gravity describing gravity bit. So, ignoring what I said in the last paragraph, imaging we have the Earth sitting in the centre of the sheet and we drop in the Moon. Now in a frictionless environment in order for the Moon to orbit you would need the slope of the bulge to be perpendicular to the earth (which I would class as infinite gravity) or, saying for example the angle of the slope is 45degress to the earth then half the orbital motion would come from the curved surface the Moon is travelling through and half would come what on Earth we would call gravity – like one of those charity boxes where your penny slowly spirals into the cash box but without friction on the surface.

The above example formed the crux of my original question and the answer I got was that the slope of the sheet is 90 degrees but it’s 90 degrees in 4 dimensions. I was never entirely happy with the answer but after spending a few days melting my brain trying to imagine a 4D surface bent by 90 degrees I accepted it.

This lead me on to another scenario similar to one mentioned above by another poster. We have Mercury orbiting the sun travelling around this perpendicular surface. If we were to double its speed it would break orbit and fly off into deep space but why would that be. The reason it was orbiting in the first place was that the only path it could take though space-time was a circle around the sun.

The answer I got to this one was that by doubling mercury’s speed we have changed its “perception” of space-time (it’s all relative you know ;) ), the slope is now not so severe and it can drift away.

Again this is all stuff I got from a couple of posts here some time ago so I’d be quite pleased if anyone wants to correct me (I was never 100% happy with it) or fill in the gaps.
 
Re: Re: Using gravity to explain gravity

Originally posted by pmb
And gravity is not the same thing as spacetime curvature since there are gravitational fields with no spacetime curvature.
Pmb
I thought relativity described gravity solely in terms of warped space-time?
 

chroot

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Originally posted by Rockazella
Chroot,
This begins to give me an idea of what your saying, but I'm failing to see the significane of this example. Wouldn't the straightest possible line from the equator to the northpole be through the sphere? Why not tunnel? I dont see why space-time has to be considerd "curved". What's wrong with defining a straight line as the shortest possible line connecting two points? How can you place these surfaces in space?

This is simply a matter of definition. For the ants-on-an-apple example, the entire universe is the surface of the apple -- tunneling through the apple is not allowed. This is in analogy to real four-dimensional spacetime, in which tunneling is (apparently) also not allowed. The surface of an apple is an example of a two-dimensional (and STRICTLY two-dimensional) curved space. Real spacetime is an example of a four-dimensional curved space.

- Warren
 

chroot

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Originally posted by Ethan Skyler

Hello Warren:
I have been trying for some time to understand curved space-time. This theory of gravitation is forceless, yes?
The bodies feel what physicists would call 'ficticious' forces, artifacts caused by their own inertia. Whether or not you consider such forces (which include the centrifugal force) 'real' or 'ficticious' is really a matter of semantics.
If Earth causes curved space-time in nearby spaces and the Moon is trying to follow the straightest possible path which is curved around Earth, then why does it remain important that the Moon maintain a certain critical speed in order to remain in orbit?
There is no critical speed. Orbits come in all shapes and sizes. When a body follows an eccentric orbit (a long stretched out ellipse), its speed is not constant. When it is close to the focus of its orbit, it moves much faster than when it is at the other end of its orbit. (Read up on Kepler's second law of planetary motion.) If you were to change the moon's instaneously velocity, it would simply begin moving in some kind of a new orbit.
What do you think will happen if the Moon is slowed a bit in its orbit of Earth?
It would begin orbiting in an ellipse, rather than the (nearly) perfect circle it now follows.
What will happen after it is brought to a complete halt in its orbit of Earth?
It would fall directly towards the earth's center, just like Newton's apple.

- Warren
 

chroot

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Re: Re: Re: Using gravity to explain gravity

Originally posted by MisterBig
I thought relativity described gravity solely in terms of warped space-time?
It does. pmb's statement is a bit misleading. In reality, there really is no such thing as a "uniform gravitational field." The only such thing that can be considered is the field in a very small region -- say, a small room. For all practical purposes, you could say that the field inside your bedroom is uniform, simply because it would take very, very delicate measurements to detect that, in reality, it is not.

- Warren
 
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Originally posted by chroot
In the real world, gravitation results from bodies trying to follow the straighest possible lines through curved space-time. The definition of a "straightest possible line" is, in fact, a line with maximal proper time.
This caught me. Warren, can you elaborate on this from perspective of proper time?
What does maximal proper time mean? Maximum # of clock ticks measured by onboard clocks? How do you visualise line with maximal proper time, can we talk about differing clock rates outside this line, in some sense?
Is then line of orbit around earth unique line that constitutes same reference frame with inertial object on that orbit?
 

chroot

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Originally posted by wimms
This caught me. Warren, can you elaborate on this from perspective of proper time?
What does maximal proper time mean? Maximum # of clock ticks measured by onboard clocks?
Yep, you got it. If you could somehow strap a wristwatch onto a photon, the photon would follow that path through spacetime that maximizes the time on its watch.

Some terminology: the time on its watch is called the proper time. Different paths have different proper times, so, really, the proper time is measure of the "length" of a path itself. The larger the proper time, the "straighter" is the path. (You might expect the reverse, that shorter proper times mean straighter paths, but it comes down to a minus sign in a matrix called the 'metric' at the heart of the theory.) In relativity theory, paths are called "intervals," and the intervals with greatest proper time are called 'geodesics.' You can tell your friends with great aplomb that:

Unaccelerated bodies follow geodesics, intervals of maximal proper time, through spacetime.
How do you visualise line with maximal proper time, can we talk about differing clock rates outside this line, in some sense?
The line of maximal proper time is actually the one you're used to -- baseballs arcing through the air follow them. So does the Moon.
Is then line of orbit around earth unique line that constitutes same reference frame with inertial object on that orbit?
I'm afraid that I don't know exactly what you mean by 'unique line' (all lines are unique), or by 'inertial object.' Try phrasing this a little differently, or provide some more detail.

- Warren
 
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It would fall directly towards the earth's center, just like Newton's apple.

- Warren [/B][/QUOTE]
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What do you see is the cause of the acceleration of the Moon's matter during this direct fall to Earth?
 

chroot

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Originally posted by Ethan Skyler
What do you see is the cause of the acceleration of the Moon's matter during this direct fall to Earth?
The ficticious force known as gravity, described in general relativistic terms as the curvature of spacetime.

- Warren
 

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