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Thank you so much for your reply!

Indeed, Greene is only speaking in the interview of the conventional, compactified Kaluza-Klein extra spatial dimensions, but in his presentation on PBS (I think it was) he also spoke of the higher dimensional theories, inter-dimensionality and included Cumrun Vafa in the program (extra time dimensions). For that reason, I believe he is open to the other theories as well.

Plus, he said this in the article:

I think, however, and many physicists agree, that that sense of time flowing that we all feel through memory is actually an illusion. Every moment is as real as every other. Every "now," when you say, "this is the real moment," is as real as every other "now"—and therefore all the moments are just out there. Just as every location in space is out there, I think every moment in time is out there, too.

At bottom, space and time transform. Time is geometric. That is the point of the Lorenz transformation and special relativity. General relativity makes it more complicated because it speaks to the warping of space/time and is even more problematic for causality than special relativity. Nevertheless, where there is space, there is time and vice versa thus each point constitutes a space/time history (Hilbert space) even without an extra temporal dimension. But an extra time dimension itself simplifies a host of other problems (duality, non-locality, superposition, etc.) In all fairness, it does so at the expense of causality (which is already on life support from non-locality anyhoot)! Nevertheless, IMHO it is a much better theory.

But I digress...

I certainly do agree with you that it is premature to count the dimensions or to characterize them in terms of number of spatial and number of temporal or to require that they be in total compactified or higher dimensional!!!

At bottom, space and time transform. Time is geometric. That is the point of the Lorenz transformation and special relativity. General relativity makes it more complicated because it speaks to the warping of space/time and is even more problematic for causality than special relativity. Nevertheless, where there is space, there is time and vice versa thus each point constitutes a space/time history (Hilbert space) even without an extra temporal dimension. But an extra time dimension itself simplifies a host of other problems (duality, non-locality, superposition, etc.) In all fairness, it does so at the expense of causality (which is already on life support from non-locality anyhoot)! Nevertheless, IMHO it is a much better theory.

Give me that extra time dimension then, Alamo-Girl! It seems clear to me that a more elaborated concept of time, “a much better theory” needs to be found in order to explain such things as duality, non-locality, and superposition, which have been observed under laboratory conditions. Even under laboratory conditions, these phenomena would seem to require superluminal velocities in order to occur. I gather the speed of light is posited as a universal constant/constraint in relativity theory, such that were two entangled particles from “opposite ends of the universe” to get together for a spontaneous “love fest,” and this happens instantly, spontaneously, we can’t explain under either Newtonian or Einsteinian theory how that could have happened.

In such scenario, travel time would be nil; time would seem to be a null factor with respect to such effects – if we understand time as measurable in terms of particular configurations of velocity and mass, moving from point A to point B through a topography featuring other “massive” (more or less) objects capable of “exerting gravity effects on passing bodies.” And thereby causing the space through which the primary “space-time body” is moving “to curve.” Which would seem to suggest that a more massive body can affect the mass and velocity of “passing” objects moving relative to it.

I’m with you, Alamo-Girl: Geometry is the very language we need to describe such relations. Geometry seems to propose most useful language for describing the features of the reality that man and nature seem to be commonly, collectively subject to.

I figure that the various geometries as originally conceived and described were personal visions – from Euclid and his ancestors in Pythagoras, Heraclitus, Plato, et al., to the present day. That is, a novel geometry elaborated represents the singular vision of the particular geometer who articulated it. And in an honest culture, such products of mind and spirit are not any kind of fly by night routine.

Just to give an example: Reimann conceived a particular geometry that flew in the face of Euclidean orthodoxy. Apparently, this was a gift received via imagination and experience. Yet far from being a merely “subjective belief,” it appears that Reimann’s geometry referred to real things far beyond Reimann’s “subjectivity.” For when Einstein needed a conceptual base for his speculations into relativity theory, he picked Reimann’s geometry “right off of the shelf”: For it furnished “the best description” of what Einstein in his deepest, most intense mediations and reflections “encountered” as “already out there” in reality. Thus I imagine the geometer as a type may be more artist than scientist. And so given their invaluable achievements, both Reimann and Einstein were great artists as well as great scientists/mathematicians.

Alamo-Girl, you and Thermopylae have broached a number of issues today that I want to think about some more before I reply. When I come back, maybe the problem would be: “What must have been loaded into the Singularity of pre-Space/Time-Zero, such that a living universe of the particular configuration we now observe (in all its harmonious branches) could possibly become the way that it is, and continue to maintain in that way?”

This to me is the single most fascinating question that can be asked.

The string theorists are trying to work this problem from the inside out. Do you suppose there is any way this same problem could be worked from the outside in?

That is from the Whole to the Part, instead of the other way around?

Just wondering, asking. But then I must be famous for my dumb questions by now. Oh, well…. Good night to dear A-G and T! God bless you and all of yours….