Re: Attraction VS geometry
- From: Tom Roberts <tjroberts@xxxxxxxxxx>
- Date: Tue, 15 Nov 2005 22:29:45 GMT
I agree with much, but by no means all, of what you write. I'll only comment on the differences.
jambaugh wrote:
In the end it is as
improper to say gravity is "all geometry" as it is to say gravity is "a
dynamic force in a flat space-time geometry".
In "the end" we have only physical theories to understand the world we inhabit. We haven't yet reached "the end" of physics. In GR, gravity is most definitely "all geometry" (see below).
Both are incorrect (scientifically) in that they assert metaphysical facts apart from what can be empirically determined. The proper statement is that dynamic forces and geometry are inseparable. Each is defined relative to the other in the context of empirically determined phenomena.
Such things can only be stated in the context of some specific theory of physics. Without such a theory, there is no real meaning to words like "geometry", "dynamic forces", etc. Apparently you are implicitly assuming some nebulous mishmash abstracted from some collection of theories you have seen. Rather than doing that, it is MUCH better to explicitly state your theoretical context, so readers can share your context and know what your words mean.
I do so: I am discussing GR.
Finally let me point out that Einstein did not invent the geometric
component to dynamics. We have always implicitly assumed a base
geometry in which dynamic forces occur. The geometry is effectively
the "zero dynamic" default.
Not by "default", but rather that's what Newton implicitly assumed.
[In this respect, metaphorically, Einstein was the first fish to observe the water (i.e. recognize that geometry could be dynamic -- Riemann had some inklings, but never followed up).]
Newton's first law " 'free' spatial orbits are straight lines" is an assumption of flat Euclidean spatial geometry. This Einstein carries over into SR with its flat pseudo-Euclidean geometry, "Free orbits are straight world-lines".
Yes. Einstein had not yet had his epiphany.
What Einstein did in GR is point out that we observe geometry in the same way we observe dynamics, by the behavior of moving bodies.
Yes.
In effect the "zero force" case is one of convention and relative to
the ad hoc choice of implicit geometry. He demonstrated that for
gravitation we can set the geometry such that the actual behavior of
test particles in the presence of gravitational masses can be reduced
to this "zero force" case. (strong equivalence principle)
This is not arbitrary as you seem to think. In GR one cannot ascribe gravitation to some dynamic "force" and still retain objects in the math that can correspond to physical phenomena. That is, as long as one represents paths by tangent _vectors_, then gravitation MUST be subsumed inside the covariant derivative, and not in any force term. The variability you seem to think is possible abandons the symmetries of the theory.
But one
could as easily** work in an Einsteinian theory where there is both
curved geometry and "physical" gravitational forces.
This is not "easy" at all -- to do that you must abandon vectors and tensors. You will necessarily find that your "physical gravitational forces" cannot possibly be _physical_ because they are inherently coordinate dependent.
It is a matter of
splitting the structure term in the covariant derivative arbitrarily
into "geometric connection" and "dynamic force" components.
And in doing so, abandoning the tensor character of the equations. If gravity is some "dynamic force" then it must enter into T (the energy-momentum tensor), and that means that Del.T is no longer zero, and G (the Einstein curvature tensor) no longer equals T, etc. This completely destroys the equations of GR as we know them, for no discernable gain -- in fact, for a CONSIDERABLE _LOSS_ because the equations you will end up with won't be coordinate independent.
But in the
end the proper treatment is to leave geometry and gravitational
dynamics intertwined.
No. The proper treatment is to leave GR alone -- it _naturally_ describes gravitation as geometry. So one should _naturally_ not attempt to do something completely different.
footnote: ** 'as easily' conceptually the math would likely be worse.
No, the math would be non-tensor and outrageously inpenetrable. GR is difficult enough, without such attempts to obfuscate its basic principles further. It's first principle is general covariance (aka coordinate independence), and your equations won't display that.
The main point of tensors is that they are coordinate independent, and so can represent physical phenomena (which of course are inherently independent of coordinates). If you attempt to pull "gravitation" out of the covariant derivative and put it into the "force" term of the equations of motion, and into the energy-momentum tensor, then NONE of the quantities in your equations will be tensors, and NONE of them can sensibly represent physical phenomena. That's crazy....
All that said, I repeat: I am discussing GR. GR is clearly not the whole story, and in some as-yet-unknown theory gravitation may very well be some sort of "dynamic force" -- in fact there are inklings of a grand synthesis between GR and the standard model of particle physics in which that would be so, but this has not yet produced any coherent theory....
Tom Roberts tjroberts@xxxxxxxxxx .
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