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Notes

[Notebook: Transfinite Field Theory DB 56]

[Sunday 30 November 2003 - Saturday 6 December 2003]

Sunday 30 November 2003

[page 29]

Monday 1 December 2003

What are the salient points of quantum mechanics to be included in an article on transfinite quantum mechanics = metaphysics?

SPACES
PROCESSES (= CHANGES OF SPATIAL STRUCTURE)

Binding and loosing spaces and processes.

+ NORMALIZATION (inner product space) to aleph(0

Then 'a note on complex numbers' and 'closed process'

Features of energy:

1. measure (inter alia) of processing rate)

2. Exponential statistics of occupation of energy levels exp(kT/h nu) (Planck)

3. Conservation/symmetry with respect to time.

Changing time/constant energy.

Changing energy ==> force, acceleration, communication (free fall = out of communication) In a sense it does not exist, since to know about it we must communicate with it and as soon as we communicate with an inertial frame it is no longer inertial. An inertial frame is a platonic idea, a mathematical fiction, part of the hard external skeleton of the Universe that is empirically inaccessible to us.

As is (Lonergan) the ideal wheel and the core of Archimedes experiment. We use statistics to decide whether the observed facts are pointing to the existence of hidden hard mathematical boundaries.

[page 30]

Idealism (and the two year old mentality in general) does not take momentum into account. Structures take time and energy to change, and the calculating mind devotes itself not to complaining that things are unsatisfactory, but to plotting the shortest course to a satisfactory state.

Tuesday 2 December 2003
Wednesday 3 December 2003
Thursday 4 December 2003
Friday 5 December 2003
Saturday 6 December 2003

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Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Aristotle, and P H Wickstead and F M Cornford, translators, Physics books V-VIII, Harvard University Press,William Heinemann 1980 Introduction: 'Simplicius tells us that Books I - IV of the Physics were referred to as the books Concerning the Principles, while Books V - VIII were called On Movement. The earlier books have, in fact, defined the things which are subject to movement (the contents of the physical world) and analyzed certain concepts - Time, Place and so forth - which are involved in the occurrence of movement.' Book V is a further introduction to the detailed analysis in Books VI - VIII. Book VI deals with continuity, Book VII is an introductory study for Book VIII, which brings us to the conclusion that all change and motion in the unvierse are ultimately caused by a Prime Mover which is itself unchanging and unmoved and which has neither magnitude nor parts, but is spiritual and not in space.' 
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Cercignani, Carlo, Ludwig Boltzmann: The Man Who Trusted Atoms, Oxford University Press, USA 2006 'Cercignani provides a stimulating biography of a great scientist. Boltzmann's greatness is difficult to state, but the fact that the author is still actively engaged in research into some of the finer, as yet unresolved issues provoked by Boltzmann's work is a measure of just how far ahead of his time Boltzmann was. It is also tragic to read of Boltzmann's persecution by his contemporaries, the energeticists, who regarded atoms as a convenient hypothesis, but not as having a definite existence. Boltzmann felt that atoms were real and this motivated much of his research. How Boltzmann would have laughed if he could have seen present-day scanning tunnelling microscopy images, which resolve the atomic structure at surfaces! If only all scientists would learn from Boltzmann's life story that it is bad for science to persecute someone whose views you do not share but cannot disprove. One surprising fact I learned from this book was how research into thermodynamics and statistical mechanics led to the beginnings of quantum theory (such as Planck's distribution law, and Einstein's theory of specific heat). Lecture notes by Boltzmann also seem to have influenced Einstein's construction of special relativity. Cercignani's familiarity with Boltzmann's work at the research level will probably set this above other biographies of Boltzmann for a very long time to come.' Dr David J Bottomley  
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Chaitin, Gregory J, Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, World Scientific 1987 Jacket: 'Algorithmic information theory is a branch of computational complexity theory concerned with the size of computer programs rather than with their running time. ... The theory combines features of probability theory, information theory, statistical mechanics and thermodynamics, and recursive function or computability theory. ... [A] major application of algorithmic information theory has been the dramatic new light it throws on Goedel's famous incompleteness theorem and on the limitations of the axiomatic method. ...' 
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Chaitin, Gregory J, Algorithmic Information Theory, Cambridge UP 1987 Foreword: 'The crucial fact here is that there exist symbolic objects (i.e., texts) which are "algorithmically inexplicable", i.e., cannot be specified by any text shorter than themselves. Since texts of this sort have the properties associated with random sequences of classical probability theory, the theory of describability developed . . . in the present work yields a very interesting new view of the notion of randomness.' J T Schwartz 
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Cohen, Paul J, Set Theory and the Continuum Hypothesis, Benjamin/Cummings 1966-1980 Preface: 'The notes that follow are based on a course given at Harvard University, Spring 1965. The main objective was to give the proof of the independence of the continuum hypothesis [from the Zermelo-Fraenkel axioms for set theory with the axiom of choice included]. To keep the course as self contained as possible we included background materials in logic and axiomatic set theory as well as an account of Gödel's proof of the consistency of the continuum hypothesis. . . .'  
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Dirac, P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechaincs, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)  
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Job, The Book of Job in The Jerusalem Bible, Darton Longman and Todd 1966 Introduction: 'The Book of Job is the literary masterpiece of the [Biblical] Wisdom movement. . . . The author of the Book of Job . . . is without doubt an Israelite, brought up on the works of the prophets and the teachings of the sages. . . . The writer puts the case of the good man who suffers. This is a paradox for the conservative view then prevalent that a man's actions are rewarded or punished here on earth.' (pp 726, 727) 
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Lonergan, Bernard J F, Insight : A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '... Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding' 
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Schwartz, Laurent, and Israel Schwartz, Introduction to the Theory of Distributions. Based on lectures given by Laurent Schwartz, University of Toronto Press 1952  
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Spence, Jonathan D, The Death of Woman Wang, Penguin • ISBN-13: 978-0140051216 1978 Amazon customer revview: 'Although some may consider historical texts dull or dry, the ideas and situations DEATH OF WOMAN WANG confronts are timeless and universal. The thought-provoking stories of the Chinese county of T'an-Ch'eng in the 17th Century bring the reader directly into the course of history. The tales of woe, romance, and murder bring this distant setting boldly alive while secretly educating the reader about the details of Chinese governements. This is one book that will change your opinion of history and historical novels'. 'Possecomitatus' 
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Streater, Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2000 Amazon product description: 'PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.' 
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Streater, Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2000 Amazon product description: 'PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.' 
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West, Morris L, The Shoes of the Fisherman, Toby Press 2003 Amazon Product description 'A pope has died, and the corridors of the Vatican hum with intrigue as cardinals from all over the world gather to choose his successor. Suddenly, the election is concluded with a surprise result. The new pope is the youngest cardinal of all - and a Russian. Shoes of the Fisherman slowly unravels the heartwarming and profound story of Kiril Lakota, a cardinal who reluctantly steps out from behind the Iron Curtain to lead the Catholic Church and to grapple with the many issues facing the contemporary world. This is a reissue of a firm favorite, of which millions of copies have been sold worldwide. The 1968 film based on the book won best film at the National Board Review and was Golden Globe and Oscar nominated.' 
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Papers
Chaitin, Gregory J, "Randomness and Mathematical Proof", Scientific American, 232, 5, May 1975, page 47-52. 'Although randomness can be precisely defined and can even be measured, a given number cannot be proved random. This enigma establishes a limit in what is possible in mathematics'. back
Zurek, Wojciech Hubert, "Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer in the transition from quantum to classical", Physical Review A, 76, 5, 16 November 2007, page . Abstract: 'Measurements transfer information about a system to the apparatus and then, further on, to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide a framework for 'wave-packet collapse', designating terminal points of quantum jumps and defining the measured observable by specifying its eigenstates. In quantum Darwinism, they are the progenitors of multiple copies spread throughout the environment &mdash the fittest quantum states that not only survive decoherence, but subvert the environment into carrying information about them &mdash into becoming a witness.'. back
Links
Book of Job - Wikipedia Book of Job - Wikipedia, the free encyclopedia 'The Book of Job . . . is one of the books of the Hebrew Bible. The Book of Job is a didactic poem set in a prose framing device. The Book of Job has been called “the most profound and literary work of the entire Old Testament”.[1] The numerous exegeses of the Book of Job are classic attempts to address the problem of evil, i.e. the problem of reconciling the existence of evil or suffering in the world with the existence of God. Scholars are divided as to the origin, intent, and meaning of the book.' back
Georg Cantor - Wikipedia Georg Cantor - Wikipedia, the free encyclopedia Georg Ferdinand Ludwig Philipp Cantor (March 3 [O.S. February 19] 1845[1] – January 6, 1918) was a German mathematician, born in Russia. He is best known as the creator of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware' back
Job - U of Virginia Job, Bible, KJV back
Limit (mathematics) - Wikipedia Limit (mathematics) - Wikipedia, the free encyclopedia 'In mathematics, the concept of a "limit" is used to describe the behavior of a function as its argument or input either "gets close" to some point, or as the argument becomes arbitrarily large; or the behavior of a sequence's elements as their index increases indefinitely. Limits are used in calculus and other branches of mathematical analysis to define derivatives and continuity.' back
Stanford Encyclopedia of Philosophy Descartes' Ontological Argument 'Descartes' ontological (or a priori) argument is both one of the most fascinating and poorly understood aspects of his philosophy. Fascination with the argument stems from the effort to prove God's existence from simple but powerful premises. Existence is derived immediately from the clear and distinct idea of a supremely perfect being. . . . ' back
Zeno's paradoxes - Wikipedia Zeno's paradoxes - Wikipedia, the free encyclopedia 'Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.' back

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