E-Infinity & all:
I've been trying to understand this controversy between the E-Infinity group and the group that includes Renate Loll out of Germany. I hunted down and read the often-cited 2008 Scientific American article (July, "The Self Organizing Quantum Universe") that I understand some have accused Prof. Loll of plagiarizing from El Naschie's work. What am I missing here? - where is the evidence of plagiarism?
I have read in one or more of these 18 blog posts from E-Infinity about "spacetime fluctuations," which I have to assume mean fluctuations of "Cantorian spacetime." But that's not what Loll is writing about. Hers are quantum fluctuations, a theoretically well understood phenomenon of vacuum energy, i.e., the energy of space alone, not a spacetime. Because at the small scale, quantum mechanics is non-relativistic, no time is involved; however, such fluctuations require 2 dimensions of space. Quantum theory does not allow space collapsed to a point.
Now I get it, that points of the Cantor set are bigger than points of an ordinary line (and so, not collapsed), but I do not get how this fact imparts an extra dimension of time to a set which is intrinsically 1-dimensional, though compact. How does the El Naschie group get two dimensions from one? Loll's (et al) theory assumes 2 dimensions, acquiring another dimension of time by what she describes as a "stir fry" of self organization among a complex of spatial volumes of unknown structure (or even structureless), but too small to be measured by conventional integer dimensions. Yes, fractals.
Does the E-Infinity group have this or another derivation for "Cantorian spacetime?" Loll only gives the Cantor set (as well as the Sierpinski gasket and Menger sponge) as examples of fractal shapes; she doesn't assign causality to them.
" ... the universe must encode what physicists call causality. Causality means that empty spacetime has a structure that allows us to distinguish unambiguously between cause and effect." (I note that in my opinion she has abused the word "spacetime" here--space _does_have a structure if it includes a time metric; spacetime is itself a structure).
So you think I'm defending Loll, et al? - surprise - wrong! I disagree with her thesis.
I disagree with it for the same reason that I gave you for disagreeing with yours: scale dependence. My model is time dependent.
Although I also think that complex system self-organization is the key to the origin of the universe, I support scale invariance; i.e., field theory. Before Loll can move forward with her idea, she has to (as she does in the article) dismiss Euclidean gravity (implying continuous spacetime), and along with it, Hawking-Hartle imaginary time. Her computer models just didn't compute.
If Einstein, Hawking and I are right, though, space is more or less well behaved all the way from nothing to something and we get time (including imaginary, or complex, time) in a physically causative way as a result of feedback effects among self organized structures in a field matrix.
Anyway, I have no axe to grind. I just want to know what's objectively real.
Hey--by the way-- Loll says, "We are now in the process of probing even finer scales. One possibility is that the universe becomes self similar and looks the same on all scales below a certain threshold. If so, spacetime does not consist of strings or atoms of spacetime, but a region of infinite boredom: the structure found just below the threshold will simply repeat itself on every smaller scale, ad infinitum."
In a well behaved universe, that's not a possibility; it's a certainty. As I said in a 2006 conference paper,
". . . the net effect of random n-dimensional motion will appear +1 positive, backward or forward. SIGMA_d/3 = 1 is precisely the observational consequence we should expect when length 1 is preserved on a sphere of radius 1 even when we cannot be sure of the status of the metric diameter, the true state vector, until we measure the result. (insert quantum unitarity eqn., bracket/psi/psi/bracket = 1) The unitary measurement is local. That makes quantum mechanics, from a theoretical viewpoint, profoundly boring. That is, SIGMA_d/3 - 1 = 0."
The equations require some explanation that I won't get into here. Point is - boring is good sometimes. :-)
Tom