Hawking Radiation 4

By Roman Andie

Inclusions of HFFs and quantum groups characterised by quantum phases q= exp(i2pi/n) are very interesting and quantum Pascal triangle is characterised by such a phase and gives quantum variant of binomial coefficient as a result. One can imagine quantum variants for integers characterising all kinds of combinatorial objects: Do quantum variants of objects make sense in some sense? Probably some mathematicians has pondered also this question.

Only few days ago I realised that in order to have "quantum quantum theory" as a tool to describe finite measurement resolution, it is better to have quantum variants of fermionic quantum anti-commutation relations for the induced spinors. They have been formulated as I learned in five minutes from web.

These anticommutation relations however demand 2-D space/space-time! But just the well-definedness of em charge almost-forces 2-D string world sheets! And number theoretic arguments removes the "almost". In 4-D Minkowski space-time you do not get them!

In over-optimistic mood - officially allowed at morning hours - I can therefore conclude that the observation of anyons in condensed matter systems (assigned with 2-D boundaries) serves as a direct evidence for the localisation of induced spinors at 2-D surfaces and for large h_eff. I must however assume that also partonic 2-surfaces carry them- whether it is so has been an open question for a long time. 

• Language: English
• Publisher: Lighthouse Books for Translation and Publishing.
• Release date: Jan 24, 2018
• ISBN: 9783592132250

Book preview

HAWKING RADIATION 4

Roman Andie

LIGHTHOUSE BOOKS FOR TRANSLATION AND PUBLISHING.

Thank you for reading. If you enjoy this book, please leave a review.

All rights reserved. Aside from brief quotations for media coverage and reviews, no part of this book may be reproduced or distributed in any form without the author’s permission. Thank you for supporting authors and a diverse, creative culture by purchasing this book and complying with copyright laws.

Copyright © 2017 by Roman Andie

Published by Lighthouse Books for Translation and Publishing.

Interior design by Pronoun

Distribution by Pronoun

ISBN: 9783592132250

TABLE OF CONTENTS

Hawking Radiation 4 by Roman Andie

At 7:05 AM, Anonymous said...

Hawking Radiation

4

Roman Andie

Lighthouse Books for Translation and Publishing

HAWKING RADIATION 4 BY ROMAN ANDIE

Copyright 2017© by Lighthouse Books for Translation and Publishing.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical photocopying, recording, or otherwise without the prior permission in writing of the writer, or as expressly permitted by law, by licence, or under terms agreed upon with the writer. Enquiries concerning reproduction outside the scope of the above should be sent to the following email

Email: [e-mail]

ISBN 13: 9783592132250

ISBN 10: 3592132250

You must not circulate this work in any other form and you must impose this same condition on any acquirer.

5. Number theoretic universality for cognitive representations

1.By number theoretic universality p-adic zero energy states should be formally similar to their real counterparts for option B. For option A the states between which real—p-adic transitions are highly probable would be similar. The states would have as basic building bricks the elements of the Yangian of the super-symplectic algebra associated with these strings which one can hope to be algebraically universal.

2.Finite measurement resolution demands that all scattering amplitudes representing zero energy states involve discretization. In purely p-adic context this is unavoidable because the notion of integral is highly problematic. Residue integral is p-adically well-defined if one can deal with π.

p-Adic integral can be defined as the algebraic continuation of real integral made possible by the notion of p-adic manifold and this works at least in the real—p-adic intersection. String world sheets would belong to the intersection if they are cognitive representations as the interpretation of fermions as correlates of Boolean cognition suggests. In this case there are excellent hopes that all real integrals can be continued to various p-adic sectors (which can involve algebraic extensions of p-adic number fields). Quantum-TGD would be adelic. There are of course potential problems with transcendentals like powers of π.

3.Discrete Fourier analysis allows to define integration in angle degrees of freedom represented in terms of algebraic extension involving roots of unity. In purely p-adic context the notion of angle does not make sense but trigonometric functions make sense: the reason is that only the local aspect of geometry generalize characterized by metric generalize. The global aspects such as line length involving integral do not. One can however introduce algebraic extensions of p-adic numbers containing roots of unity and this gives rise to a realistic notion of trigonometric function. One can also define the counterpart of integration as discrete Fourier analysis in discretized angle degrees of freedom.

4.Maybe the 2-dimensionality of cognition has something to do with the fact that quaternions and octonions do not have p-adic counterpart (the p-adic norm squared of quaternion/octonion can vanish). I have earlier proposed that life and cognitive representations resides in real-p-adic intersection. Stringy description of TGD could be seen as number theoretically universal cognitive representation of 4-D physics. The best that the limitations of cognition allow to obtain. This hypothesis would also guarantee that various conserved quantal charges make sense both in real and p-adic sense as p-adic mass calculations demand.

posted by Matti Pitkanen @ 6:53 AM

8 Comments:

At 5:22 AM, Anonymous said...

It is joy to see how TGD keeps on evolving and boldly asking genuine questions.

For further evolution, as an informant of a bundle of conscious experiences I can’t identify with 2-dimensionality of cognition, and I suggest that that idea might simply arise from an entangled state with primarily visual sentient-cognitive state, (as also theory literally and etymologically means, from Greek verb theaomai, to watch, from which theater etc. are derived) ie. from cognitive entanglement and filtering with space-time sheet of sentience with visual 2D-character (binary mapping into lighted (and colored) pointillistic(!? a la certain impressionit painters) points vs. unlighted/dark points

A conscious body-sense feel of empathy (cf. negentropic entanglement) has very different geometric connotation from visual sensing. I, as an informant of this ‘thusly’ conscious experience, can best describe this as infinitely(?) dense point at heart chackra, where conscious sensations of good feel and bad feel locally alternate in various mixtures and intensities, surrounded with field-like extentions, for which the best mathematical analogy so far has been some kind of Dehn-ball. The ‘ball’ aspect sensing happens in 3-D and/or 4-D, and the ball-like field consists of n-dimensional dimension lines (cf. worm holes) allowing heart-local non-local empathy of good feel / bad feel entanglements also with other sentient beings and conscious informants.

According to most functional ethical theory and practice I’m aware or, the ‘good feel’ is the norm (universe=god=love) and the ‘bad feels’ are exceptions to the rule arising from breaking of strong entanglements aka attachments, such as actual loss of a love, or fear and worry of loss projected to some other space time sheet than ‘now’. Informant expressions such as heart-broken and without him/her/it, there’s an empty space within me", etc. gain very literal spatio-temporal interpretations. On the other hand, according to critical-ethical theory of global-local, the Universal Source of ‘good feel’ is already and always inside each heart and each and every point in space-time, and can be also consciously sensed-experienced when filters that cover it are removed.

One further comment, I associate intending with ‘focus’, and as the word in-tention suggests, the movement has more pointed character than that of planar mapping. If needs that give rise to intentions arise adelically, the most self-suggestive geometry of intentional targeting to fulfill the adelically metabolic need would be ideles. Or just ‘id-gesture’, as the Latin version of Freud goes. Note that when walking, the intention to not stumble and fall, and when stumbling, step dancing faster than conscious thought, is very carefully focused on the point of balance. :)

At 6:35 AM, [e-mail] said...

To Anonymous:

I have been very critical about string models. But I must admit that they have caught something very profound about the structure of existence. String world sheets and partonic 2-surface could be seen as maximal cognitive representations that one can have. One can of course have a lot of them.

One extremely nice feature is that conformal invariance implies the reduction of WCW for string world sheets and partonic 2-surfaces to the confromal moduli space for them. They are finite-dimensional and I have already applied these spaces in p-adic mass calculations.

Too many independent arguments lead to these objects so that I can only accept them. Strong form of holography, well-definedness of em charge, octonionic spinor structure making possible 8-D twistorilization, and commutativity of tangent spaces of objects in the intersection of reality and p-adicities, non-existence of p-adic variants of quaterions and octonions, fermions as correlates of Boolean cognition and the arguments forcing the to string world sheets, and so on….

The Book analogy is at work again. String world sheets define the back of the book with space-time surfaces in various p-adic number fields as pages.

It is surprising that the notion of negentropic entanglement allows also to seriously discuss about the quantum correlates of ethics and moral rules. In standard physics one has only events. NMP makes it possible to talk about deeds.

The question about precise form of NMP leads directly to the key question about which spiritual people have discussed for millennia: why God does allow Evil. I guess that the weak form of NMP allowing genuine free will in good and bad is the only mathematically consistent option.

At 7:14 PM, Anonymous said...

One feels and thinks that it would be nicer deed if one’s mode of experiencing would be received as empirical phenomenology that an explanatory function such as theory formulation aims to explain, instead of excluding and limiting theoretically allowed possible experience on grounds of theoretical presuppositions.

Neural networks have a filtering function, and yes, they have stringy character. We do not, however, presume or insist that full-body sentience (cf. e.g. magnetic bodies) and consciousness in themselves reduce to neural networks alone, rather, neural networks and their filtering and representing function in relation to conscious experience deserve also explanation and description as part of the larger picture, where view of inner and outer extensions of rationals is becoming less dualistic, and neural networks can’t be said to be absolute requirement for sentience and conscience (cf. plants, mushrooms, headless chickens, etc.).

Theory of mental representations has a more natural place at the level of neural networks than at the level of space-time sheets and undivided whole of sentience-consciousness, which has more ‘map=landscape" character than that of representation of externalized objects.

At 8:15 PM, [e-mail] said...

To Anonymous:

I see this somewhat differently.

When one thinks seriously about physics and consciousness, one sooner or later starts to talk about ontology, even when one is physicist;-). In my case new ontology emerged gradually: space-time as 4-surface of imbedding space, WCW, subjective existence as quantum jumps between objective existences, zero energy ontology, hierarchy of Planck constants, p-adic physics as physics of cognition (note that I have no dropped and intention;-)), WCW.

Even worse;-), if one is seriously building what one might call unification, eventually also the word epistemology creeps in, and one must seriously ponder what one can know. Uncertainty Principle to the discoveries of physical epistemology.

These two words are practically all that I know about philosophy as an academic discipline. Therefore I do not know the name of branch of philosophy studying what can be not only known but also expressed using language, that is mathematically. Let us temporarily call the field of philosophy X-ology.

In TGD framework the first X-logical discovery is the realisation that although space-time surface is 4-D and seems that all that we can say mathematically about quantum physics is expressible mathematically in terms of string world sheets and partonic 2-surfaces. Strong form of holography is another manner to say this. Or strong form of general coorinate invariance which explains it. Note that this is much more than string models can say - one would have only string world sheets.

One can have space-time surfaces full of string world sheets and get arbitrary precise description of space-time but it is not of course the same space-time anymore.

What one can known and say define what I call cognitive representations. X-ologist wold say that these string world sheets carrying fermions serving as correlates of Boolean cognition. They reside in the intersection of realities and p-adicities where also life and love as negentropic entanglement reside. These cognitive representations would defining all that universe can say about itself using language.

This is very practical statement. In principle one can build quantum physics predictions by using only the data associated with partonic 2-surfaces and string world sheets. Even better, conformal equivalence classes are enough. Infinite-D WCW is effectively reduced to finite-D spaces of moduli. In case of string world sheets just the positions of edges and angles at them! This is gigantic simplification and gives realistic hopes about calculable theory ( that is allowing to express mathematically what is