Arcadian Functor

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Marni D. Sheppeard

Tuesday, March 27, 2007

Countdown II

Oh, all right, I can't resist. For the conference countdown, let us ponder the fact that the correspondence between the prime three and the simple particles may give us an M theory derivation of the baryonic mass fraction, which would agree with Louise Riofrio's result of $\frac{\pi - 3}{\pi}$.

6 Comments:

Anonymous Nosy Snoopy said...

Bonjour, mademoiselle D'Sheppeard :)

Do you like this paper http://arxiv.org/abs/hep-th/0008217?

March 28, 2007 4:51 AM  
Blogger Kea said...

Thank you very much, nosy snoopy. I had not seen this paper before, although I have come across something by Schlesinger. Indeed, M Theory is turning out to be very much like that. The phrase heirarchy of quantizations is exactly what we are seeing with our p-adic logic. My personal version of the principles is a bit different, however.

I have been using (1) the idea of measurement geometry, inspired by Gray's work on the categorical comprehension scheme (but this could be interpreted in terms of deformed Turing machines, I suppose) and (2) the Machian principle of inertia, which appears as the web of dualities in String theory.

Are you by any chance the author?

March 28, 2007 11:43 AM  
Blogger Kea said...

nosy snoopy, I see that you have also been snooping about Aaronson's blog. What is your angle here? P = NP ? The Riemann hypotheis? Everything else?

March 28, 2007 1:15 PM  
Blogger Matti Pitkanen said...

Hierarchy of quantizations appears also in TGD framework at several levels.

Infinite primes are constructed by repeatedly second quantizing a super-symmetric arithmetic quantum field theory with fermion and boson states labelled by primes.

At the lowest level the number theoretic counterpart of Dirac sea is formed as the number

P=X +/- 1


where X is the product of all finite primes. The interpretation is that all negative energy states labelled by finite primes are populated. This number is obviously prime since P mod p=+-1 for any prime p.

More complex infinite primes are constructed by kicking fermions from the Dirac sea. For instance, P=nX/s + ms, where m is product and s a square free product of primes p not dividing n gives an infinite prime. Also more general infinite primes are possible.

At next step one forms X_1 as a product of all infinite primes obtained in this manner and forms infinite primes in the same manner. The process can be continued indefinitely and gives rise to infinitely repeated second quantization.

The proposed interpretation is that this hierarchy has hierarchy of space-time sheets containing space-time sheets containing .... as a space-time correlate. The finite primes appearing in infinite prime at lowest level label light-like partonic 3-surfaces associated with space-time sheet. The larger the size of partonic 2-surface, the higher the level in the hierarchy would be.


With respect to p-adic topologies all these infinite primes, integers, and rationals are finite so that the attribute "infinite" is only relative.

The really fascinating aspects of this generalization of number emerge when one adds to real numbers the ratios of infinite integers which are units in the real sense. These real units have arbitrarily complex number theoretic anatomy so that single number and thus also space-time point can have an arbitrarily rich structure and ability to represent practically anything in its structure.

This leads to the general vision that the world of classical worlds (space of lightlike 3-surfaces in M^4xCP_2) is representable is imbeddable to the space formed by these units so that everything reduces to the level of imbedding space through the generalization of the notion of number. By quantum classical correspondence also ground states of all possible superconformal representations (sorry for very loose but economical terminology) correspond to these units.


The category theoretical formulation of this Brahman=Atman identity might be an interesting excercise.

Best,
Matti

March 28, 2007 5:24 PM  
Anonymous nosy snoopy said...

Kea said:
...
Are you by any chance the author?
...
What is your angle here? P = NP ? The Riemann hypotheis? Everything else?


OK, I'll tell you everything about me.
Certainly I'm not the author. I am just a little curious dog and everything I have got and everything I can trust is my own little nose. :)
I've read all your blog posts, truth to say I don't even understand what you are asking me about all those Riemann's, P=NP and all the more everything elses. :(
I've recently become obsessed with only one question. This is what I've found while spooring the answer:
Sniff,sniff,sniff ...Ed Witten's paper "Magic, Mystery, and Matrix". He says that in string/M-theory besides Plank's constant we have also $\alpha'$ constant which is the size of a string, so it seems that string/M-theory is (if we can say so) even more nondeterministic than ordinary quantum theory. And I know (I don't say I understand) how to tell the difference between deterministic classical theory and nondeterministic quantum theory is by some Bell test experiment. So what follows? Is the question: How to tell the difference between even more nondeterministic string/M-theory and ordinary quantum theory? May be it is some type of Bell test experiment too?
Sniff, sniff, sniff... Smells like Grothendieck's constant to me?
But I don't again understand everything yet. May be you, Kea, will give to us desirous and curious "The Special M-theory lesson about Grothendieck's constant"? I would want to know very much if my nose betrayed me or not.

:)

March 29, 2007 4:46 AM  
Blogger Kea said...

nosy snoopy, as far as I can tell you have a first rate nose. Good luck with your sniffing. Grothendieck is behind many of the core ideas in M theory. And all numbers, not just Grothendieck constants, will have a place in our classical reality, because our classical reality is mathematics.

March 29, 2007 7:51 AM  

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