Curvature or Force?

[Riogho]

I've heard two opposing views of gravity, and many compilations. The first being:

 

That gravity acts upon a static background and is a force that is there because of mass and it just is.

 

And the second being that the curvature of spacetime because of mass causes objects to follow different paths making it seem they are 'attracted' to each other.

 

Obviously, the first one is wrong, and has been disproven by GR and experiments since then. However, the second seems to be a common conception, but I don't understand how that would work. Because if something is merely curvature and I were to have a large body say, a black hole who influences much space around it to have curvature, (the black hole is at rest), and then I have me, standing 100m away from the black hole, at rest, would I fall into the black hole?

 

If we were both at rest there would need to be energy required to push me into the black hole, curvature of space isn't energy...

 

And of course, the curving of space wouldn't cause me to 'fall' into the black hole because 'falling' is an effect of gravity.

 

I'm utterly confused, and I am sure other people are as well.

 

Clarification please?

[swansont]

It doesn't take energy to push you into the gravity well, it takes a force. And the curvature acts like a force, because your motion is changed by the gradient of the surface, though one of the results of relativity is that a constant acceleration (i.e. freefall) is inertial.

[Riogho]

But there is no motion, I am at rest.

[Klaynos]

But there is no motion, I am at rest.

 

Once you start moving towards the centre of mass you are not.

[Riogho]

But... what makes me move?

[Klaynos]

The gravitational force, which is the same as the curvature of space, or the curvature acts as a force...

[Riogho]

So gravity is both a force AND curvature?

 

Or Curvature IS a force?

[swansont]

So gravity is both a force AND curvature?

 

Or Curvature IS a force?

 

Two ways of looking at the same thing. Either you use forces or you use geometry to explain the motion.

[pioneer]

Here is something I don't understand. If we use classical gravity, the gravity force in the center of a sphere is zero due to force vector canceling. So if we started at a distance from a spherical mass, like the earth, and plotted gravity, it would start near zero (extreme distance), increase to the surface, and then decrease again to zero in the center.

 

If we use the analogy of GR being sort of a well in the fabric of space-time, should this well have a peak in the center? In other words, based on classic gravity, the flat fabric of space-time has zero gravity at far distance. It also has zero gravity in the center so these two places should have the same height in the fabric of space-time. The well part gets a deep as it can at the surface, and then has to climb again to account for lowering gravity=GR as we move toward center.

 

I know that GR does not use a peak in the center of the well, even though doing a gravity measurement in the center should imply this. The next question is, is this peak virtual and the source of the GR affect?

 

One way to address this is with the wave-particle duality. If we assumed just particles, for the sake of argument, all mass points in a sphere would be exchanging particles, with the center having the lowest d summation. If we assume just waves, for the sake of argument, this gives us a result that is more in line with observation, with the waves canceling in center. Here is the paradox for the virtual peak. Because of the wave-particle nature both have to be in agreement. This means that even if particles converge on center, they can not appear in center to be consistent with the waves. This does not mean loss of energy. It means they have to appear elsewhere in a way that this also consistent with the wave addition. The result is the GR affect, with contracted space-time able to store this energy.

[smooth]

I prefer goemotrical view...

 

[swansont]

Here is something I don't understand. If we use classical gravity, the gravity force in the center of a sphere is zero due to force vector canceling. So if we started at a distance from a spherical mass, like the earth, and plotted gravity, it would start near zero (extreme distance), increase to the surface, and then decrease again to zero in the center.

 

If we use the analogy of GR being sort of a well in the fabric of space-time, should this well have a peak in the center? In other words, based on classic gravity, the flat fabric of space-time has zero gravity at far distance. It also has zero gravity in the center so these two places should have the same height in the fabric of space-time. The well part gets a deep as it can at the surface, and then has to climb again to account for lowering gravity=GR as we move toward center.

 

 

AFAIK it would be flat where the force goes to zero, and lower than the surroundings, because it's at a lower potential.

[Obelix]

But there is no motion, I am at rest.

 

I'm afraid "you are not thinking 4 dimensionally", as John Lithgow often said in "Back to the future".

 

1) It is not Space that is curved, it is SPACETIME (4 dimensions).

 

2) If at rest in a three dimensional space, be it curved as, e.g., the sides of a pit, one needs a force to get him/her rolling downwards.

 

3) In 4 dimensional SPACETIME, on the other hand, it s a principle of its GEOMETRY that paricles/bodies not influenced by anything except the gravitational field, move along TIMELIKE GEODESIC CURVES. This is a GEOMETRIC PROPERTY, as particles/bodies are themselves GEOMETRIC FEATURES of Spacetime, according to Einstein's Gravitational Field Equations. In other words: The geometric features of spacetime called material particles satisfy the equations of timelike geodesics:

 

[math]\frac{d^2x^\alpha}{ds^2} + \Gamma^{\alpha}_{\beta\gamma}\frac{dx^\beta}{ds}\frac{dx^\gamma}{ds}=0 \Leftrightarrow \frac{d^2x^\alpha}{ds^2} = - \Gamma^{\alpha}_{\beta\gamma}\frac{dx^\beta}{ds}\frac{dx^\gamma}{ds}[/math]

 

the indices running over the values: [math]0[/math] (time coordinate) and [math]1, 2, 3[/math] (spatial coordinates) whereas summation is understood over repeated indices ("dummy indices"). The second half of this relation gives the acceleration ([math]\frac{d^2x^\alpha}{ds^2}[/math]) of the material particle.

 

4) Nowthen: Suppose Spacetime is curved, i.e. the quantities [math]\Gamma^{\alpha}_{\beta\gamma}[/math] (Levi - Civita connection coefficients) are not all zero. In that case, even if the spatial velocity is initially zero ([math]\frac{dx^\alpha}{ds} = 0, \alpha = 1, 2, 3[/math]) , this is NOT the case with the temporal velocity ([math]\frac{dx^0}{ds} \neq 0[/math] - no material particles can stand still in time!) Hence, from our equation above:

 

[math]\frac{d^2x^\alpha}{ds^2} = -\Gamma^{\alpha}_{00}\frac{dx^0}{ds}\frac{dx^0}{ds} \neq 0[/math] for [math]\alpha = 1, 2, 3,[/math] i.e., even if, initially, the particle is at rest (in space) it will accelerate, in general (that is, if [math]\Gamma^{\alpha}_{00}[/math] are NOT zero for all spatial values [math]\alpha = 1, 2, 3[/math]) as a result of the GEOMETRY of spacetime.

 

5) Motion along geodesic curves manifests itself in 3 dimensions by falling down the gravitatonal field.

 

I hope this has helped you out!

[NeonBlack]

Obelix, welcome to SFN. I didn't realize that falling into the magic potion when you were a baby also made you smart.

Do not be suprised or upset if few people find your post enlightening. It's probably a bit too advanced for this thread. I think a more hand-waving or "cartoon" description would be more appropriate.

[swansont]

I'm afraid "you are not thinking 4 dimensionally", as John Lithgow often said in "Back to the future".

 

John Lithgow wasn't in "Back to the Future;" he might have said that in "3rd Rock from the Sun." Christopher Lloyd was Doc Brown in all of the BTTF movies.

 

Obelix, welcome to SFN. I didn't realize that falling into the magic potion when you were a baby also made you smart.

Do not be suprised or upset if few people find your post enlightening. It's probably a bit too advanced for this thread. I think a more hand-waving or "cartoon" description would be more appropriate.

 

I don't think that bringing rigor and more advanced analysis into a discussion should be discouraged. If you have questions about it, you can ask them.

[NeonBlack]

I think you know that's not what I meant Swanny. Since he is a new member, he probably does not know the usual level of discussion here and I did not want him to be discouraged by lack of response to his thread. Don't worry. At the time I made the post, I also pm'ed him asking him to start a new thread.

[Obelix]

Obelix, welcome to SFN. I didn't realize that falling into the magic potion when you were a baby also made you smart.

Do not be suprised or upset if few people find your post enlightening. It's probably a bit too advanced for this thread. I think a more hand-waving or "cartoon" description would be more appropriate.

 

Oooops!...I'm a bit hopeless when it comes to pictorial or intuitional description of Physics.

 

I remember, when I was in Imperial College / London (1993) attending the class of Chris Isham (anybody knows him?) he had made a distinction between those people who prefer description in terms of Analysis, and those who choose Geometry and / or pictures in general. He had said that the latter ones are those who typically will live up a party, dance, talk with people of the opposite sex, and generally have a good time, whereas the former ones are what he called "party poopers" (I'm not sure those were his exact words - English is not my mother tongue). That is, people who prefer Analysis are the ones who will just simply sit isolated in a party and do nothing...

 

When I heard all that I was astonished - I was hearing an EXACT description of myself! (In fact I had had a recent experience of a party where I had felt very isolated and very dissapointed, whereas Analysis had always been my favourite way, and it still is...) So when Isham asked us to tell him frankly if any of us was a "party pooper", I immediately raised - no, actually launched my hand, nearly under his nose (I was sitting on a front desk). It was obvioys he didn't expect anything like that. The class rolled down with laughter...

 

Seriously now: I understand there are threads for people who want rigor and threads "for the layman". How can I tell which is which?

 

Besides, how could I tell that Riogho was not asking for a mathematical answer?

 

John Lithgow wasn't in "Back to the Future;" he might have said that in "3rd Rock from the Sun." Christopher Lloyd was Doc Brown in all of the BTTF movies.

 

It was definetely in "Back to the future". I wasn't sure it was John Lithgow, but he looked like him.

 

What movie was "3rd rock from the Sun"? Is there a relative web site?

[iNow]

What movie was "3rd rock from the Sun"? Is there a relative web site?

Hi Obelix,

 

It was a television show.

 

http://www.3rdrock.com/

http://en.wikipedia.org/wiki/John_Lithgow

 

 

Also, any chance you could start posting in regular forum font?

 

Right now, it feels like you're yelling at me, and I get a headache reading your posts (and strangely, it has zero to do with the content of your posts and everything to do with the formatting). Thanks in advance!

[Riogho]

You're actually not at rest because time itself is moving? And since you are in time... your point on a 4 dimensional-graph would be moving...

 

I think... o.o

[iNow]

You're actually not at rest because time itself is moving? And since you are in time... your point on a 4 dimensional-graph would be moving...

 

This seems strangely self-referential and circular. Can you elaborate? Is time just the name you've given to your car?

[NeonBlack]

I think he means to say that in GR, gravitational field is curvature not of space, but of space-time.

And you are always moving through time.

[Riogho]

Yea, what he said

[Obelix]

I think he means to say that in GR, gravitational field is curvature not of space, but of space-time.

And you are always moving through time.

 

I would say that, according to Einstein's field equations, space and time are interrelated dynamically. They both evolve, and whatever happens to one of them influences the other. This is unlike Newtonian space and time, which are static, non - evolving, and independent from each other.

 

In G.R., as time moves on, that has an impact on space, causing objects to gravitate and move, even if they are initially at rest.

 

Hey, iNow, what's wrong with this font? I find it attractive and definetely easier to read. And why on earth did it feel I was "yelling at...YOU"??? I didn't even quote you!

[Blue Fire]

... [snip]

And you are always moving through time.

Unless, of course, you are a photon, in which case you would be moving entirely through space and not through time. It may be helpful to note that everything moves through spacetime at c. Of course, for most things, movement consists of some movement through space and some movement through time - sort of like traveling northeast in a car. Some part of your motion is north and some part is east. And some things like light travel due east (assuming east is space) with no motion north (time).

[swansont]

 

Hey, iNow, what's wrong with this font? I find it attractive and definetely easier to read. And why on earth did it feel I was "yelling at...YOU"??? I didn't even quote you!

 

Others disagree, and there's definitely no need to go to "4" on the font size. Please change your browser setting if you need larger type.