Implications of geodesiacs(philosophical)

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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,
sad
 
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  • #2
pervect
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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
JesseM
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My understanding of geodesics in simple terms is that an object follows a geodesic path generated by another object.
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
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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.
Are you saying that electricity, for example, is not directly affected by gravity?
 
  • #5
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which is determined by all the mass/energy in the region, not any one particular object.
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,
sad
 
  • #6
JesseM
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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?
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
pervect
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Are you saying that electricity, for example, is not directly affected by gravity?
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
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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.
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.
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.
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,
sad
 
  • #9
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I thought that geodesics described the paths of objects in a gravitational field.
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.

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

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.
I suspect that in order to develop a useful gravity field addition formula in GR we need something else than the manifold paradigm.
 
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  • #10
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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.
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 :biggrin: ).
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.
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,
sad
 
  • #11
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An actual moving body with non-negligible mass will disturb the metric (just as an actual electric charge will disturb an electric field).
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. :wink:
cheers,
sad
 
  • #12
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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.
ah, thanks for clearing that up.
I have trouble understanding what you are trying to say here, could you rephrase this?
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,
sad
 
  • #13
JesseM
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Then let me reiterate my assertion: The overall curvature of spacetime is independent of it's mass/energy distribution
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.
saderlius said:
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.
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.
saderlius said:
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.
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?
saderlius said:
It gives no mechanism whatsoever for how massive objects curve space/time.
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?
saderlius said:
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.
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.
 
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  • #14
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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,
sad
 
  • #15
paw
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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
JesseM
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Specifically which field equation do you propose contradicts my assertion. I would like to study it.
The Einstein field equations, the fundamental equations of GR. They can be written as:

[tex]R_{\mu \nu} - \frac{1}{2} g_{\mu \nu} R = 8 \pi T_{\mu \nu}[/tex]

where [tex]T_{\mu \nu}[/tex] is the stress-energy tensor, [tex]R_{\mu \nu}[/tex] is the Ricci curvature tensor, and R is the scalar curvature. See also the wikipedia entry on Einstein field equations.
saderlius said:
If an object occupies space and that space is curved, then wouldn't the object be warped along with the space it occupies?
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
Garth
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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?
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
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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,
sad
 
  • #19
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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.
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.
 
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  • #20
JesseM
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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 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.
 
  • #21
pervect
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The Stress E Tensor is an indicator, not a creator.
I don't see how you can say that. Conceptually, one can change the distribution of matter (the stress-energy tensor), and observe the resulting change in the geometry of space-time. It doesn't make a lot of sense within the context of current physical theory to reverse this, i.e. to say that one directly controls the geometry of space-time, and that the matter distribution is a consequence.

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,
sad
I've never seen the term "protodimension" used in any scientific paper that I can recall. Looking it up, the only reference I could find to protodimension was a wikipedia article about a RPG called "Dark conspiracy" (six percent relevance). Note that we try to stick to mainstream physics here, and not discuss personal theories.
 
  • #22
robphy
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Maybe a gravitational wave could be seen to be a good example of said pervasive pattern, but those are not yet proven.
"Demonstration of gravitational waves

A very important observation was made when the system had been followed for some years. This followed theoretical predictions made shortly after the original discovery of the pulsar. It was found that the orbit period is declining: the two astronomical bodies are rotating faster and faster about each other in an increasingly tight orbit. The change is very small. It corresponds to a reduction of the orbit period by about 75 millionths of a second per year, but, through observation over sufficient time, it is nevertheless fully measurable. This change was presumed to occur because the system is emitting energy in the form of gravitational waves in accordance with what Einstein in 1916 predicted should happen to masses moving relatively to each other. According to the latest data, the theoretically calculated value from the relativity theory agrees to within about one half of a percent with the observed value. The first report of this effect was made by Taylor and co-workers at the end of 1978, four years after the discovery of the binary pulsar was reported.

The good agreement between the observed value and the theoretically calculated value of the orbital path can be seen as an indirect proof of the existence of gravitational waves. We will probably have to wait until next century for a direct demonstration of their existence."

http://nobelprize.org/nobel_prizes/physics/laureates/1993/press.html
(The Royal Swedish Academy of Sciences has decided to award the Nobel Prize Physics for 1993 jointly to Russell A. Hulse and Joseph H. Taylor, Jr, both of Princeton University, New Jersey, USA for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation)
 
  • #23
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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.
The difference is in our understanding of how gravity works. You observe what appears to be matter affecting trajectories, but actually its the gravitational field which affects the trajectory of its own immediate matter, as well as other mass/energy quanta around it. My theory is not so absurd, its just as well supported by the data, though not as supported by our senses.
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.
That is your philosophy. Perhaps you are more content with the practicality of the theory, but i'm less content with it's philosophy.
thanks,
sad
 
  • #24
JesseM
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The difference is in our understanding of how gravity works. You observe what appears to be matter affecting trajectories, but actually its the gravitational field which affects the trajectory of its own immediate matter, as well as other mass/energy quanta around it. My theory is not so absurd, its just as well supported by the data, though not as supported by our senses.
Unless you can show that your idea has testable consequences, then it isn't a physical "theory" at all, but a philosophical interpretation (like I said, I don't see how any theory of physics can do anything but describe mathematical relationships between different things, not tell you which is the 'cause' and which is the 'effect', which doesn't even seem to be a well-defined question to me). And if it is the case that you're just arguing philosophy, you should be discussing it in the philosophy forum, not here.
saderlius said:
That is your philosophy. Perhaps you are more content with the practicality of the theory, but i'm less content with it's philosophy.
The theory doesn't have a philosophy as I understand it. In particular, it makes no claims about the matter/energy distribution "causing" the curvature of spacetime, although physicists may talk this way as a convenient shorthand; instead, it just describes the mathematical relationship between the two.
 
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  • #25
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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.
Common now, i call them how they lie- the common philosophy appended to the EFE are that gravity fields are generated from massive quanta- you admitted as much earlier. Besides, I can't help it if the natural course of physics points towards metaphysics, but i can help you to not avoid it or overlook it.
 

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