# Implications of geodesiacs(philosophical)

1. Mar 29, 2007

Implications of geodesics(philosophical)

My understanding of geodesics in simple terms is that an object follows a geodesic path generated by another object.
However, this seems to muddle causality: An object follows the path of a space-like geodesic set by a larger body, yet that larger body follows its own geodesic of a larger system, and that the geodesic of a larger one, possibly ad infinitum. Since geodesics are patterns in spacetime itself in which energy roams, they must be primitive to their occupants. Here is a proposition which to my knowledge doesn't contradict the working principals:
Rather than geodesics being generated from matter, perhaps matter congregates at certain geodesics, according to a natural pattern. Thus, certain smaller gravity well charters fall within the larger geodesic charter, while matter congregates at each well according to the natural formula.

cheers,

Last edited: Mar 29, 2007
2. Mar 29, 2007

### pervect

Staff Emeritus
It is only small (and non-spinning, as it turns out) "test bodies" that follow geodesics.

An actual moving body with non-negligible mass will disturb the metric (just as an actual electric charge will disturb an electric field).

One has to solve Einstien's field equations to find the solution when one has two massive bodies. This is a difficult task.

3. Mar 29, 2007

### JesseM

This is a little unclear. Whether a path is a "geodesic" or not depends on the curvature of spacetime, which is determined by all the mass/energy in the region, not any one particular object. Just as you can talk about the shortest path between two points on a curved 2D surface like the surface of a sphere (the shortest path between points on a sphere is always a section of a great circle on that sphere), so you can talk about the spacetime path between two events with the extreme value of proper time (usually the maximum value), and that is the "geodesic" between those events.

4. Mar 29, 2007

Are you saying that electricity, for example, is not directly affected by gravity?

5. Mar 29, 2007

Because of my untested ignorance, i see no reason that you should make the above extrapolation. Just because you know that the curvature of spacetime is closely associated with the amount of mass/energy in a region doesn't mean that mass/energy determines the curvature. My proposition is that the curvature determines the amount of matter/energy which congregates there.
bass akwards. Why am i wrong?
cheers,

6. Mar 29, 2007

### JesseM

I'm not an expert in GR, but I believe that if you know the distribution of matter/energy (given by the stress-energy tensor), that uniquely specifies the curvature of spacetime. It might be true that you could also go in reverse, determining the distribution of mass/energy given the curvature of spacetime, although experimentally it's obviously a lot easier to measure the distribution of matter/energy. If it's true that the matter/energy distribution and the curvature each uniquely determine the other in the Einstein field equations, then I suppose you'd be free to say that "the curvature determines the amount of matter/energy which congregates there", just as you'd be free to say "the distribution of matter/energy determines the curvature"--both statements would be valid mathematically. But if you're somehow proposing that the first would be true while the second would be false, then I don't understand your argument. I also don't understand why you talk as if each geodesic is determined by a particular larger object (when you said, for example, that 'An object follows the path of a space-like geodesic set by a larger body, yet that larger body follows its own geodesic of a larger system, and that the geodesic of a larger one, possibly ad infinitum'), rather than being determined by the overall curvature of spacetime or the overall distribution of matter/energy.

7. Mar 29, 2007

### pervect

Staff Emeritus
No.

I am saying that the concept of a geodesic is the limiting case in which one considers very small non-spinning test masses.

If one wants to find the trajectory of a finite mass, one needs to use a different approach.

It turns out in practice that geodesic motion is an ecellent approximation in GR (interestingly enough, it's not so good in some other theories of gravity such as Branse-Dicke). But geodesic motion is just an approximation, it is not the ultimate defintion of how objects move. The ultimate defintion is contained in Einstein's field equations themselves. The tricky part is representing an "object" in the EFE - the "object" has to be modelled as some sort of system that has a distributed stress-energy tensor.

The analogy to electromagnetism was intended to be just that - an analogy. Since you are apparently not familiar with this analogy, I don't think there's much point in explaining it in a lot of depth - it's just to point out that this sort of issue is not unique to GR.

8. Mar 29, 2007

sorry, i veered us off from my main inquirery. I thought that geodesics described the paths of objects in a gravitational field. Really what i should have addressed is the curvature of spacetime directly. What i am asking you is to refute my claim that the the mass/energy distribution in a plane is determined by the curvature of spacetime, while the curvature pattern itself is completely unaffected by the distribution of mass/energy.
sorry, miscommunication. I understand your analogy pervectly. I picked an electron arbitrarily because i know it to have chirality. You said a small particle with spin doesn't follow a geodesiac. What i thought u meant by this is that the formers are not subject to the "curvature of spacetime" which is what we call gravity, yes?
thanks for your patience,

9. Mar 29, 2007

### MeJennifer

Then you are mistaken.
Geodesics are the paths that particles without any mass or energy would follow if they were to exist. In reality all particles have mass or energy and thus they create their own gravitational field.
So in these cases we need to add those two fields in order to describe the relative motions between those two particles which respect to each particle's proper time.

I have trouble understanding what you are trying to say here, could you rephrase this?

I suspect that in order to develop a useful gravity field addition formula in GR we need something else than the manifold paradigm.

Last edited: Mar 29, 2007
10. Mar 29, 2007

Then let me reiterate my assertion: The overall curvature of spacetime is independent of it's mass/energy distribution because space/time itself is, logically, primitive to the values that it contains. Its a mathematical argument: a smooth dimensional plane doesn't have to take values into consideration at all, but on the other hand, values already assume a dimensional background. Thus, the background in which our mass/energy plays is primitive to- hierarchically superior to, the mass/energy value itself. For this reason, it seems erroneous to assume the curvature of spacetime is affected by the distribution of mass/energy in the same way that mass energy is effected by the curvature of spacetime. Nobody has given me any reason to assume something so illogical given the data. Even if the equations as they are predict phenomena well, that in no way supports nor discredits my contention(to my knowledge ).
Sorry, more ignorance on my part, getting terms confused... I phrased that wrong. What i was trying to say is that even those massive objects which are supposedly warping the fabric of spacetime around them are themseves being warped by another massive object. This idea has always bothered me because it doesn't explain the connectivity between things very well, because it makes every massive object out to be its own gravitational well. It gives no mechanism whatsoever for how massive objects curve space/time. My explanation does explain the connectivity, in that the wells are charters, and also clears up the mechanism- the charter is preset according to natural formula, and it also clears up the hierarchal logic problem.
cheers,

11. Mar 29, 2007

Ahhhh i see better your argument, says the blind student. You are saying that since a massive vector disturbs the metric of a geodesic path through a gravitational field, that indicates that massive objects generate their own gravitation fields which conflict with those of others.
I don't think that conclusion is necessitated by the evidence you provided. Also the electric field analogy doesn't account for the connectedness of all massive objects in space.
Rather, one gravity well charter is drawn into the immediate effect of another, and they align fields to account for the respective strength of each. Basicly, I'm saying that even if there were no energy/matter around to populate them, there could still be little patterns moving around in the fabric of spacetime.

I know this at first seems to be a mystical approach, but i see it as a plausible explanation given the empirical data. Or just as plausible and no more mystical than string theory, at least.
cheers,

12. Mar 29, 2007

ah, thanks for clearing that up.
sure. i've said basically what you just said in the bottom of the previous quote regarding the addition of fields, except that i've taken it to a fuller understanding of it's inherent implication. What i'm saying is that the fields work independently of the particles. Read my post to Jesse right below your post for the logical reason to suspect this.
thanks,

13. Mar 30, 2007

### JesseM

According to what theory of physics? Not general relativity obviously, since the Einstein field equations give a precise mathematical relationship between the curvature tensor at each point and the stress-energy tensor at that point.
Saying that one thing is "logically primitive" doesn't sound like a mathematical argument, it sounds like some sort of philosophical argument. Sure, if you ignore the laws of physics, you can have any sort of curved spacetime manifold you want without defining a matter/energy distribution on it; is that all you're saying? But according to the laws of physics which have the best empirical confirmation, ie general relativity, the curvature of spacetime and the matter/energy distribution are coupled to one another by the precise mathematical relationship given in the Einstein field equation.
How can an "object" be warped? It's spacetime that's warped in general relativity, and the curvature at each point is can be exactly determined by the stress-energy tensor (the distribution of matter/energy) according to the Einstein field equation. Are you saying that you think this equation is wrong? What alternate equation can you propose that fits the empirical data so well?
Physics doesn't give "mechanisms" for anything, just mathematical relationships between various things which constitute the "laws of physics". What is the "mechanism" for a charged particle being moved around by an electromagnetic field, for example?
If you're proposing a mathematical relationship between the curvature and the stress-energy tensor which can be different than the one given by the Einstein field equation, then you have the problem of giving an alternate explanation for the abundant empirical data that seems to fit the predictions of GR so well.

Last edited: Mar 30, 2007
14. Mar 30, 2007

Specifically which field equation do you propose contradicts my assertion. I would like to study it.
If an object occupies space and that space is curved, then wouldn't the object be warped along with the space it occupies?
thanks,

15. Mar 30, 2007

### paw

sad, you are apparantly claiming that spacetime, in the absense of mass and energy, is somehow curved/dimpled in some way that exactly matches the physical reality we observe. You seem to claim that mass/energy then somehow congregates in those curves/dimples.

That may seem fine to you but it begs a much bigger question. Why!

Conventional GR doesn't have this problem. The presense of matter/energy causes the curves/dimples. Your postulate doesn't. A quick application of Occams Razor will tell you the conventional explanation is the best one in the absense of any evidence to the contrary.

Are you aware of the quote that 'extraordinary claims require extraordinary evidence'?

16. Mar 30, 2007

### JesseM

The Einstein field equations, the fundamental equations of GR. They can be written as:

$$R_{\mu \nu} - \frac{1}{2} g_{\mu \nu} R = 8 \pi T_{\mu \nu}$$

where $$T_{\mu \nu}$$ is the stress-energy tensor, $$R_{\mu \nu}$$ is the Ricci curvature tensor, and R is the scalar curvature. See also the wikipedia entry on Einstein field equations.
I don't know if there's any standard definition for what it means to say an object is "warped"--are you talking about internal stresses in the object due to gravitational acceleration?

17. Mar 30, 2007

### Garth

Well, the concept of gravity wave detectors, either the beam or laser type, depends on the idea that a gravity wave passing through the apparatus will 'warp' the cylinder of solid metal making it 'ring', or that it will 'warp' the ground and vacuum tubes of the, say LIGO, detector, momentarily changing the length of one half-beam light-path relative to the other half beam light-path orthogonal to it.

Garth

18. Mar 30, 2007

ah, thanks Jesse- right after i posted my request, i figured i should just look it up on wiki, srry for the hassle. As i just posted to Paw in post #18: The EFE simply describes a mathematical relation between the matter/energy distribution and the curvature of spacetime. It doesn't prove that the curvature is caused by the stress E tensor, it just shows u can generally predict the curvature based on the stress E tensor. The Stress E Tensor is an indicator, not a creator.
I see another problem in the conventional philosophy which treats time as a 4th dimension, but i haven't yet figured out how to rewrite the equations to express time as a protodimension instead.
cheers,

19. Mar 30, 2007

### Thrice

What's the difference? We're trying to predict paths an object will follow based on how much matter/energy there is nearby. We observe that matter affects the trajectories of other matter & we call that force gravity. You're basically maybe there's something else that causes gravity. Well yeah that's how empirical knowledge works & paw was right to invoke occam's razor. There's always an infinite number of unfalsifiable 'theories' around each observation. Maybe I'm "really" typing on a tree branch & fairies are making me think it's a computer.

Much of philosophy is junk, but they really should teach this stuff in classrooms. You might even see fewer people subscribing to their local mythology.

Last edited: Mar 30, 2007
20. Mar 30, 2007

### JesseM

It seems to me that all that any law of physics ever written has ever done is describe a mathematical relationship between one thing and another. "Cause" as you are using the word would seem to belong to metaphysics, not science, unless you can think of a way to experimentally test whether a given mathematical relationship represents one thing "causing" another.