vol 7: Notes
2007
Sunday 30 December
Site map
Directory
Search this site
Home
1: About
2: Synopsis
3: Development
Next:
Previous: Notes 2007 Toc
... to restore theology to the mainstream of science
Notes
[Notebook: DB 62 Interpretation]
[Sunday 30 December 2007 - Saturday 4 January 2008]
[page 88]
Sunday 30 December 2007
If the operator is passed a time value, the frequency of its response is measured in energy. If a space value, the return is in momentum, if a number, the return is in action.
When I first became acquainted with computers (6809 chip, 1970's) the most difficult abstraction for me to comprehend was the distinction between logical and physical addressing. Motorola 6809 - Wikipedia Quantum information theory brings these two ideas together in that the physics is the logic, ie the logic is embodied in the physics. The conceptual problem now (closely related to the 'collapse of the wave function') is to map the continuous models of physics onto the discrete models of logic.
Although the not operator is a discrete function, it can be made to look continuous in a more complex system and represented by a wavelike Hamiltonian because it may be called at any moment and the random superposition of these discrete calls may look like a continuous wave. This is analogous to the idea that although each individual Turing machine is a deterministic entity a network of Turing machines becomes indeterministic because they may interrupt one another at random moments in their individual processes. This ideas is expressed more satisfactorily by saying Turing machines in a network may be concatenated in random order, since then we do not have to interrupt a
[page 89]
deterministic process, a rather self-contradictory idea. The superposition of a set of not operators called at different moments is what looks like a continuous wave.
We represent reversible Turing machines by matrices and the deterministic processes of quantum theory by 'matrix mechanics'.
Another analogy by which the appearance of continuity may arise is the decoupling between meaning and symbol. So any program may call any subroutine and give it any meaning it likes. So it is with natural languages, naming and mapping in general, so that the same object may have an infinity of different names in different languages and the same linguistic symbol may be mapped to an infinity of different objects.
The binary world is modelled (at its most abstract) by connection and disconnection.
Quantum mechanics explains the structure of the world by showing what can and cannot happen. All events are digitized and things can only happen in a digital way, eg de Broglie's hypotheses explains the stationary states ('packets') of the atom by the requirement that integral numbers of waves fit into certain spaces. So confinement digitizes.
Monday 31 December 2007
Tuesday 1 January 2007
Ehrenfest's adiabatic hypothesis: If a system is affected in a reversible adiabatic way, allowed motions are transformed into allowed motions.' Bohr: 'Principle of mechanical transform ability'.
[page 90]
Van der Waerden p 4-5. van der Waerden
Wednesday 2 January 2007
Thursday 3 January 2007
Friday 4 January 2007
Hopefully, the point of view developed by Zurek (2007) is the final plank necessary to develop the logical (digital ) view of the universe proposed in these pages. Zurek
The trouble for physics lies in the first postulate of quantum theory, that the quantum state of a system is represented by a vector in its Hilbert space. The trouble arises from the continuity assumption embodied in this postulate, since continuity is part of the definition of Hilbert space (von Neumann). von Neumann
Further postulates: second unitary evolution
Third immediate repetition of a measurement using the same
measurement operator yield the same outcome.
Zurek page 1: 'These first three postulates indicate no bias - they treat every state [every vector] in the Hilbert space of the system on an equal footing.'
That is, they do not partition the message space into 'legitimate' and 'illegitimate' (erroneous) messages as required by Shannon's theory if we are to have error free transmission of messages. Shannon, Khinchin
Zurek: 'By contrast, the last two postulates, (iv) measurement outcomes are restricted to an orthonormal set { |sk|>} of eigenstates of the measured observable
[page 91]
(i.e. measurement does not reveal the state of the system because it limits possible outcomes to the preassigned outcome states) [as we do in error resistant coding] and (v) the probability of finding a given outcome is pk = |<sk || psi >| 2 where | psi > is the [assumed by postulate (i)] preexisting state of the system are at the heart of long standing disputes on the interpretation of quantum theory.'
'The aim of this paper is to point out that already the (symmetric and uncontroversial) postulates (i) - (iii) necessarily imply selection of some preferred set of orthogonal states, that they impose the broken symmetry that is at the heart of postulate (iv) - although they stop short of specifying what this set of outcome states is and obviously cannot result in anything non-unitary (eg the actual collapse).
Here we see logical continuity at work 'defeating' the classical 'argument from continuity' that is inherent in the postulate of unitarity.
Saturday 5 January 2007
How much control is a legitimate and much debated question. Since experience suggests that too much can be as bad as too little, the problem presumably has an optimum.
The universe is a real time system whose elements must be 'tuned' to certain frequencies for processes to work properly. The fundamental structure of the universe is the arithmetic of energy (cardinal) reflecting the logic of process (ordinal).
[page 92]
'The atoms of Newton and Boyle are hard little balls, Euler's atoms like musical instruments.' Park, quoted in Sacks Tungsten p 82 n. Sacks
Further reading
Books
| Christie, Agatha, Murder on the Orient Express, Berkley Publishing Group 2000 Amazon: 'This beautifully crafted murder mystery ranks among Agatha Christie's finest. The dapper Belgian detective finds himself investigating the murder of an American businessman on board the Simplon Orient Express. The death occurs in a a manner that implicates one of the twelve passengers in the Stamboul-Calais coach. Poirot carefully interviews the suspects, all of whom have cast-iron alibis. The case appears impossible to solve, until Poirot, using nothing but his wits and a few tiny, seemingly insignificant clues (including a monogrammed handkerchief, a pipe-cleaner, and a Hungarian passport), assembles one of his most brilliant explanations.' A reader from Anaheim, California. Amazon back |
| Khinchin, A I, Mathematical Foundations of Information Theory (translated by P A Silvermann and M D Friedman), Dover 1957 Jacket: 'The first comprehensive introduction to information theory, this book places the work begun by Shannon and continued by McMillan, Feinstein and Khinchin on a rigorous mathematical basis. For the first time, mathematicians, statisticians, physicists, cyberneticists and communications engineers are offered a lucid, comprehensive introduction to this rapidly growing field.' Amazon back |
| Lo, Hoi-Kwong, and Tim Spiller, Sandra Popescu, Introduction to Quantum Computation and Information, World Scientific 1998 Jacket: 'This book provides a pedagogical introduction to the subjects of quantum information and computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault tolerant quantum computation, as well as some experimental aspects of quantum computation and quantum cryptography. A knowledge of basic quantum mechanics is assumed.' Amazon back |
| 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' Amazon back |
| Sacks, Oliver, Uncle Tungsten: Memories of a Chemical Boyhood, Vintage 2002 Amazon editorial review From Publishers Weekly 'Sacks, a neurologist perhaps best known for his books Awakenings (which became a Robin Williams/Robert De Niro vehicle) and The Man Who Mistook His Wife for a Hat, invokes his childhood in wartime England and his early scientific fascination with light, matter and energy as a mystic might invoke the transformative symbolism of metals and salts. The "Uncle Tungsten" of the book's title is Sacks's Uncle Dave, who manufactured light bulbs with filaments of fine tungsten wire, and who first initiated Sacks into the mysteries of metals. The author of this illuminating and poignant memoir describes his four tortuous years at boarding school during the war, where he was sent to escape the bombings, and his profound inquisitiveness cultivated by living in a household steeped in learning, religion and politics (both his parents were doctors and his aunts were ardent Zionists). But as Sacks writes, the family influence extended well beyond the home, to include the groundbreaking chemists and physicists whom he describes as "honorary ancestors, people to whom, in fantasy, I had a sort of connection." Family life exacted another transformative influence as well: his older brother Michael's psychosis made him feel that "a magical and malignant world was closing in about him," perhaps giving a hint of what led the author to explore the depths of psychosis in his later professional life. For Sacks, the onset of puberty coincided with his discovery of biology, his departure from his childhood love of chemistry and, at age 14, a new understanding that he would become a doctor. Many readers and patients are happy with that decision. (Oct.)Forecast: This book is as well-written as Sacks's earlier works, and should get fans engrossed in the facts of his life and opinions. Look for an early spike on the strength of his name, and strong sales thereafter.' Copyright 2001 Cahners Business Information, Inc. Amazon back |
| Shannon, Claude, and Warren Weaver, The Mathematical Theory of Communication, University of Illinois Press 1949 'Before this there was no universal way of measuring the complexities of messages or the capabilities of circuits to transmit them. Shannon gave us a mathematical way...invaluable...to scientists and engineers the world over." Scientific American http://www.amazon.com/exec/obidos/ASIN/0252725484/tnrp">Amazon back |
| van der Waerden, B L, Sources of Quantum Mechanics, Dover Publications 1968 Amazon Book Description: 'Seventeen seminal papers, dating from the years 1917-26, in which the quantum theory as wenow know it was developed and formulated. Among the scientists represented: Einstein,Ehrenfest, Bohr, Born, Van Vleck, Heisenberg, Dirac, Pauli and Jordan. All 17 papers translatedinto English.' Amazon back |
| von Neumann, John, and Robert T Beyer (translator), Mathematical Foundations of Quantum Mechanics, Princeton University Press 1983 Jacket: '... a revolutionary book that caused a sea change in theoretical physics. ... JvN begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which vN regards as the definitive form of quantum mechanics. ... Regarded as a tour de force at the time of its publication, this book is still indispensible for those interested in the fundamental issues of quantum mechanics.' Amazon back |
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, 052110, 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--the fittest quantum states that not only survive decoherence, but subvert the environment into carrying information about them--into becoming a witness.'. back |
Links
| Motorola 6809 - Wikipedia Motorola 6809 - Wikipedia, the free encyclopdia 'The Motorola 6809 is an 8-bit (arguably, an 8/16-bit) microprocessor CPU from Motorola, introduced circa 1979. It was a major advance over both its predecessor, the Motorola 6800, and the related, MOS Technology 6502.' back |
Click on an "Amazon" link in the booklist at the foot of the page to buy the book, see more details or search for similar items
Related sites:
Concordat Watch
Revealing Vatican attempts to propagate its religion by international treaty
