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Originally Posted by George
Although the coordinate view from the cart is just as valid as the coordinate view from the horse or the on-watcher, the erratic movement of the horse will cause coordinate changes.
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If the coordinates are the coordinates of the horse, then there is no coordinate change-- the erraticness (is that a word?) is manifested in the motion of everything
else, but not in the coordinates, they are just as smooth as silk (perhaps generated by radar ranging experiments from horseback). Now it must be granted that a coordinate system that suggests everything in the universe is moving in an erratic way
except the horse does great violence with causality concepts, but that is not a problem if one does not expect the coordinates to respect causality-- the only duty of the coordinates is to keep track of what is happening and provide a mathematical scheme for understanding and predicting what will happen next. They are not there to answer issues of causality, and whosoever uses them for that purpose is likely to be let down.
You might argue that if we have a breakdown in our understanding of the motion of a horse, it's best that it only affect the one thing, the horse, and allows us to get everything else right, rather than allowing us to get the horse right by default but incorrectly predict the motion of everything else in the universe. That's the advantage of using coordinates that respect causality, once you know what the causality is. But there may also be disadvantages-- such that the "superior" choice may be dependent on the problem of interest.
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For me, those that favor the Geocentric model don't appreciate what you've said, so I like the fact that the Earth jiggles as it rotates.
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I agree they don't, I am not defending the way Geocentrism gets applied as a philosophy or theology-- just how geocentrism is used to make Earth-frame calculations of things like weather patterns. For example, geocentrism allows us to speak of "wind" as if it was simply air movement, saving us from calling it air movement relative to the surface of the Earth. We then view hurricanes as caused by the "coriolis effect", rather than simply saying they occur because the air is already hurtling around the Earth at speeds upwards of half a km/s. It serves us to do so, even though it monkeys with the "real" causality rather badly (the coriolis effect is a coordinate force like the one that makes the universe lurch when the horse is erratic).
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Using Air mass movements, primarily, and other mass shifts cause the Earth to speed-up or slow down enough to be measurable (using quasar alignments, interestingly). For one to argue that the universe causes these changes, then they will find themselves in Sillyville trying to compare their causal arguments against a rotating Earth with its observable changes in air mass.
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Yes, coordinates don't give us causality, causality stems from something else. That I think is the main flaw in Geocentrism as a philosophy, as opposed to geocentrism in weather forecasting. There are ways of thinking of the gravitational influence of the air mass movements as affecting the rest of the universe (which is after all moving faster than light at large enough distances if one uses coordinates in which the Earth is not rotating), and then the influences are faster than the speed of light. But causality seems to know the difference between a "true" subluminal cause and this type of "ficticious" cause, so I think the issue of the causality is not as invariant as the coordinatization.
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I sense an indifference intrinsic to GR on this kind of issue and it seems counter to how the scientific method has worked before in developing prior theories. GR seems beautiful but cold (ok, that's subjective.
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It's hard for me to say, not being a GR expert, but my impression is that GR admits two separate types of causality. One is a kind of causal
illusion, akin to what are called "coordinate forces" and closely connected to the equivalence principle. For example, if you have straight line motion in Cartesian coordinates and you transform that into polar coordinates, it still qualifies as a geodesic, but it's curved in those coordinates, because azimuthal motion evolves naturally into radial motion without there being any true forces to make that happen. That's a "coordinate force".
Given the equivalence principle, all such coordinate forces are indistinguishable from gravity if you don't look too closely-- where looking closely means looking for the
tidal signature of real gravity (the shape of the vase, again). So what is the "cause" of the curved motion in polar coordinates? The coordinates themselves. That's not a "real" cause, as it need not reflect subluminal influences and identifiable agents. Similarly, the coordinates "attached to the horse" will also generate coordinate forces that affect the whole rest of the universe, whose "cause" is the erratic motions of the horse. It's a different kind of causality, but it's allowed in GR. Still, GR does not remove our ability to notice that there is another type of causality at play that obeys the subluminal speed limit and is describable in terms of real forces.
The question then is-- which type is
gravity, coordinate force or real force? I think the answer is, only
tidal gravitational affects are the "real" forces-- the
main affects of gravity on motion that we perceive are actually just coordinate forces, and are just as "imaginary" as the erratic motion of the horse "causing" everything in the universe to lurch in compensating ways.
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Not inferior in its utility or mathematical equivalence, but inferior when it attempts to interface, as Len Moran stated, with reality.
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I agree, and I see the source of that inferiority lying not in the coordinates themselves, but in any associated supposition that the coordinates are anything but arbitrary. Indeed, I've always felt the debate between the Copernican view and the Ptolemaic view (or better, Tycho Brahe's model) was not which object orbits which-- that's just a question of reference frame. It is whether or not the motion of the Earth is special in some way that is built into the fabric of reality, or whether or not reality is ambivalent to the motion of the Earth vis-a-vis the motion of any other similar rocky body in creation. The specialness comes from our choice of coordinates, not from nature, that's the real failing of Geocentrism.
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This is some tricky stuff for me, as you can guess, as I am uncomfortable about allowing subjective views imposing on science, so I am trying to be sure this superiority idea is not beyond the purview of science.
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There are pitfalls to avoid. The "superiority" of a coordinate choice can only be staked on convenience and preference of the practitioner, nothing else. The claim that the laws of nature themselves dictate the superiority of a certain coordinatization, simply because it gibes with causality, runs rather counter to the whole spirit of relativity.
For example, any coordinatization that generates what we would normally call a "force of gravity" (not differential stretching or squeezing, which are "real" tidal gravity effects) is similarly at odds with "true" causality, so would have to be labeled "inferior" in your general scheme. As such, a Cartesian coordinate system with origin at the center of mass of the solar system is also of the "inferior" type, as it has the Earth following a
curved path, despite the absence of a proper cause for that (it's a "coordinate force" stemming from using coordinates that do not respect the curvature of spacetime, making it appear that the Earth's geodesic curves despite there being no cause for that other than the coordinates themselves).