Recently, I have been discussing Einteinian and Whiteheadian cosmology with Gary Herstein, who is author of

*Whitehead and the Measurement Problem of Cosmology*. (http://www.amazon.com/Whitehead-Measurement-Problem-Cosmology-Process/dp/3937202951) I strongly recommend it for process metaphysics and those concerned with speaking of process metaphysics in terms of contemporary cosmology, although the book is focused on the latter.
I have always struggled to understand Einstein's view of space-time and gravity. I suppose that we're all seen the curved space models, which is what I always imagine. While I get the idea, I never understood

*why*and short of actively studying cosmology--us philosophers already have long reading lists--I wondered if I would ever understand it. I then had an insight.
Gravity is the connectivity of space.

(For "connectivity," see http://mathworld.wolfram.com/SimplyConnected.html and for the "connectivity of space," see http://mathworld.wolfram.com/ConnectedSpace.html.)

I asked Gary and he said that I was on the right track. However, he noted that Whitehead criticized Einstein's theory, and said that the way I framed the question was "making the Einstein & SMC (Standard Model of Cosmology) move of equating the physical with the geometrical." This employs only "one metric tensor," whereas Whitehead's was "bimetric." He also mentions the alternatives, Modified Newtonian Dynamic and Tensor-Vector-Scalar (which I've heard of). Now for his interesting comment.

Part of his critique was that these alternatives to the SMC "do not require the 'ad hoc' assumptions of miracle features like 'dark matter' and 'dark energy.'" This is as I always suspected: these strange phenomenon are likely artifacts of mathematics and if they have any reality are likely misrepresented.

For my part, I was thinking that blackholes might be a case where connectivity fails to be "simple connectivity" (see the link above), which may occur under extreme conditions. That is, parts of space are not longer "geometrically contiguous" even though they are "connected." This would be possible, upon my hypothesis, because gravity

*is*the connectivity of space, and gravity is not strictly geometric. If this doesn't seem plausible, then I ask someone to explain the plausibility of quantum teleportation and entanglement. Gary is right; geometric models appear insufficient.
A side thought. This hypothesis casts "time" as if it were a

*relative*positionality in space or connectivity. I am still musing upon this.
In their conversations at the Princeton Institute for Advanced Studies, Einstein and Gödel got onto the topic of time. Basically what they realized (and Gödel went so far as to provide a proof) was that in an Einsteinian universe (SMC) time does not really exist. It is, at best, an illusion due to the limitations of human cognition.

ReplyDeleteThe sheer incoherence of this conclusion ought, but itself, have been enough to refute the SMC. But physicists and logicians are not notes for the subtleties of their phenomenological analyses.

Whitehead's theory -- as developed in his Triptych of works on natural philosophy -- takes

timeas the primary natural phenomenon, and derives space (from what I've called his "multi-threaded" theory of time) as an emergent property of modalities of simultaneity.In any event, in order to have meaningful theory of measurement, it is necessary to have a stable system of transformations (a mathematical "group") that make quantitative comparisons at least logically possible. In spatial relations, this group is known as the system of congruences.

Since Einstein and the SMC collapse the contingent relations of physics into the necessary relations of geometry, we have no way of knowing what these transformations are in the SMC universe until we first know the complete distribution of matter and energy in the cosmos. The only way we can know THIS, however, is through accurate measurements. And here we have the problem: we can't have accurate measurements until we already know all there is to know about what it is we want to measure in the first place. As Whitehead observed, we must first know everything before we can know anything.

Thanks, Gary.

ReplyDeleteMore Whitehead was already on my reading list.

I wish to clarify my previous comment on the relativity of time. I did not mean "relative" in the usual connotation in Einsteinian relativity (as little as I profess to understand it). Rather, I was trying to think connectivity as prior to spatiality (distance) and a time as descriptive of two connected points. But you're right; this makes time derivative and conflicts with my other hypotheses about time.

Elsewhere, I have thought time as emergent order, i.e., the creative structuring of chance, which is nontrivial in a metaphysics where order is generative of potentiality. The synchronic moment is time, while the diachronic moment is history. I will have to consult what you say on time.

Also, for those unfamiliar with a mathematical group, see http://mathworld.wolfram.com/Group.html.

Certainly Whitehead sees time as emergent from more basic forms of metaphysical order ("prehension" and "extension"). A lot of Whiteheadians often seem not to get this notion, that time for Whitehead is a natural phenomenon that presupposes some fairly stringent rules of seriality (along any given thread), but serial relations themselves are not at all metaphysically primary.

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