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Notes

[Sunday 14 December 2008 - Saturday 20 December 2008]

[Notebook: DB 65 Symmetric U]

[page 21]

Sunday 14 December 2008

What appears to be emerging, if we take Landauer's hypothesis (that all information is represented physically) in conjunction with the symmetric Universe is that the Universe does all its processing (computation) before our very eyes, and that the substratum of continuous mathematics with which we try to explain all this is an unnecessary throwback to the puppet days of the Universe when it was considered to be a non-divine continuum manipulated by a divinity, rather than a logical continuum fully explained by its own logical operations.

'The classical notion of field originated in attempts to avoid

[page 22]

the idea of action at a distance in the description of electromagnetic and gravitational phenomena. Streater & Wightman page 96.

One consequence of the continuous transformation approach assumed by relativistic quantum theory is that spacetime is reduced from being a participant in the universal process to be a homogeneous backdrop, as envisaged by Lonergan's notion of empirical residue. We might find it more productive to consider spacetime an 'emergent' phenomenon arising from the nature of the symbolic computations carried out by the Universe using the creation and annihilation of 'bonds' ie communications between information carrying physical particle.

'Since in quantum mechanics observables are represented by hermitean operators which act on the Hilbert space of state vectors, one expects the analogy in relativistic quantum mechanics of a classical observable field to be a set of hermitean operators defined for each point in space-time and having a well defined transformation law under the appropriate group.' Streater & Wightman

Here I wonder why we need to introduce Lorentz transformations at all, since they do not describe any real local changes in reality, but merely how phenomena in a moving frame look to a frame at rest. Admittedly, this might be of some importance in collision phenomena, since the outcome of a collision may depend on how the colliding frames look to one another, but most the important features of the 'look' are encoded in the relative 4-momenta of the colliding particles, and the outcome is controlled by the conservation of energy and momentum. What we need to do in a way is to see space and time as products of energy and momentum rather than the other way around, or rather that

[page 23]

they are the same thing. Here we have a glimpse of the idea that the unification of space and time in the concept of velocity, particularly the invariant velocity of light is more fundamental than either space or time alone, and the Lorentz transformation shows us how this emergence of space and time from velocity is controlled by relative velocity.

E = 1/2 mv 2, ie v = +- sqrt (2e/m ), E = mc 2 ie c = +- sqrt (E/m )

The equation we should be looking at is E 2 = p 2 + m 2.

Energy and the three components of momentum transform in the same way as space and time, as 4-vectors (and of course, vice versa). Thus energy and momentum form a coordinate system isomorphic to time and space. Lorentz transformations work the same when we substitute E for t and pi for x i.

These transformations look back to the time when the Universe was not differentiated into space and time or energy and momentum.

This idea leads us to wonder what quantum field theory looked like before the emergence of space and time as distinct entities, and the answer appears to be ordinary non relativistic quantum mechanics or its network equivalent, where we think of a logical rather than a spatial network.

The velocity of light dates from the days when the length of all 4-vectors was zero, ie before the invention of spacelike separation, which is the equivalent of having causally independent 'particles' or systems, ie a Universe (nothing outside = no outside Universe) differentiates into two Universes.

[page 24]

Between 1 space and 4 space lies 2 space, the realm of action and angular momentum, both with dimensions ML2T-1.. In 2D space, we can only have rotation about 1 axis, since there is only one, and this looks just like spin 1/2, 1 axis, 2 directions of rotation [2 directions of time?]

By thinking of the Universe as a layered network we have a way of thinking about (ie representing) the creation of the Universe, since each layer uses the layer beneath it as a set of processes from which it can concoct its own processes. So building a computer network, we can start with a nand gate and work from there.

The quantum mechanical [space] is linear, ie flat, and one can only have a flat closed system if it has only one dimension, ie a loop, in logical terms a periodic function or group.

My house is pervious, so I am affected by influxes of wilderness, rain, draughts, dust, mice, rats, snakes, lizards, possums, flies, mosquitoes etc etc.

The only things that really interest us about quantum field theory are the eigenvalues of the operator fields that we construct in spacetimes because they are what we observe..

These operators can become extremely complex as we strive to make field theory closed and consistent, but we assume (given the structure of mathematics) that there is enough variety in the symmetric network to enable one to one correspondence between eigenvalues of the operator filed and symbols in the network.

[page 25]

The representation of continuity.

We may think of mathematics (and writing in general) as an effort to represent ideas that appear out of the continuum of mind into the definition of consciousness. An important feature of being human is our growth with age in the number of things we can represent, ie the number of concepts one can grasp.

Now we estimate that there are a countably infinite number of observable eigenvectors in any connected locality in spacetime (ie inside a light cone). In the early Universe, this might be 2, so the world expressed itself in two eigenvectors, that is a two symbol alphabet. These eigenvectors are associated with eigenfunctions, themselves encoded as vectors.

In the spin 1/2 world it takes 1 quantum of action to flip a bit.

Comparing angular motion to linear motion we find distance <--> phase, velocity <--> angular velocity, momentum <--> angular momentum etc.

We might say that all velocities in a curved space are 'angular velocities', which need to be divided by the radius of the space to give a true angular velocity. The Universe was always curved but as it expands its curvature gets less, but it leaves copies of its earlier states behind (like the 2D world of the electron) in which the electron may be either spin up, or spin, down, electron or positron.

Make little bits of progress where possible, like doing jigsaw.

[page 26]

Fields in quantum field theory seem to play the part of gods, dei ex machina, assumed to exist to produce the results we observe.

Monday 15 December 2008

Feynman vol I, 25-6 'The numerical method is the most powerful method of all and can solve any equations. It is only when we have a simple problem that we can use mathematical analysis. [A shot in the arm for the symmetric network].

'Mathematical analysis is not the grand thing it is said to be: it solves only the simplest possible equations. As soon as the equations get a little more complicated, just a shade - they cannot be solved analytically. But the number method which was advertised at the beginning of the course, can take care of any equation of physical interest.'

We construct a leak-free argument by blocking all the holes so that the probability of the conclusion following from the premisses is 1 and there is no probability that the premisses lean in some cases to some other conclusion. Probability is the incompressible fluid in quantum mechanical circuits and it is closely akin to energy. It can be stored through times as potential and flow from one point to another. The essence of survival is manipulating probabilities so that 'good' things happen and 'bad' things don't. This is the essence of occupational health and safety, building impenetrable barriers to bad outcomes.

Fermat's principle of least time, Feynman, I, 26-3. Fermat's principle - Wikipedia

Quantum mechanics works things out by adding amplitudes and

[page 27]

Fermat's principle is a consequence of seeking a constant path integral. Paths where phase varies rapidly tend to cancel, which regions where phase is identical or close, amplitudes add 'constructively', ie 'cooperatively'. So we conclude from the path integral method that cooperation is the key to what actually happens and microscopically non-cooperatve systems are unlikely to lead to a macroscopic result. When we move to the computational view we think in terms of 'in phase' and 'out of phase' parallel computations, but in this case we can also handle complex non-linear situations like the operation of a car engine that depend not on simple linear addition of amplitudes but on breaking a large computation down into small sequential units (subroutines) that create the whole process, So we might say

Quantum mechanics has no subroutines or perhaps it behaves bosonically rather than fermionically.

In quantum mechanics all superpositions are simultaneous, there is no time ordering. (?)

Time division multiplexing = delay division multiplexing = ordering by distance (the most intuitively fundamental form of ordering).

Turing's delay line computer? Pilot ACE - Wikipedia So delay creates space, space creates delay. Polkinghorne Quantum Physics and Theology, Yale U Press. Polkinghorne

International Society for Science and Religion ISSR

GROWTH = CREATION

[page 28]

Spacetime derives from action-energy-momentum rather than vice versa' spacetime is more directly visible to us. Energy/momentum are a more spiritual isomorphism of the same structure and carry the seeds of infinite dimension al reality, (ie infinite degrees of freedom) whereas spacetime stops at 4.

PAIN = EDUCATION (keeps us on the straight and narrow).

Tuesday 16 December 2008

Polkinghorne a disappointment, a physicist turned Christian trying to justify his decision which seems rather narrow and lacking in vision. He sees the world as a special creation of a god rather than as god itself. An inspiration to write something which will redirect his faith from an ancient myth to the Universe that bore him.

Wednesday 17 December 2008
Thursday 18 December 2008

The last step before being exactly right is to be exactly wrong.

Lightness of rein. Mathematically we define lightness of rein with approximation to a complete set of states by effectively allowing it to do whatever it wanted to, constraining it not at all. But in this case vases would be useless. Utility requires constraint, To use the worker you must constrain him [and the wage is supposed to compensate for the constraint]

[page 29]

The ideal human situation is to have someone else do all the work. One way to measure the power of an individual is the number of people that work for it.

Polkinghorne purports to be both a Christian and a quantum mechanic, and he spends a whole chapter explaining how quantum mechanics and theology are independent of one another, sharing only the methodology of critical realism applied to quite distinct data sets: the Universe as observed by humans and the Bible. The Bible is part of the observable Universe, and many observe it.

An oscillator feeds of itself and will run forever it it is not damped. If there is damping, input power is needed to keep it going. POWER = RATE OF LOSS to maintain steady state.

People who think they are too good for the world are dangerous cargo on a fragile planet and their ideas must be constraining to improve our chances of survival, a task both for education and legislation. This is the sort of control exerted by churches which are organizations oriented to their own survival like any other by recruiting adherents, believers, donors, workers, missionaries and so on. Dupont selling chemicals is no different from Frances Xavier selling Christianity . [It is quite possible that those who buy the chemicals are doing a better deal.]

Physics describes the Universe at the cardinal level of abstraction, yielding probabilities as ratios of counts.

Everyone wants to be a legend in their own mind but society works against this, declaring legends to be relatively rare and therefore that the majority are not-legends.

[page 30]

Can we sum up Quantum Physics and Theology as a pathetic attempt by a physicist who has sold out to Christian theology trying to fight off the growing power of quantum mechanics as the heart of theology.

Quantum mechanics is not so much physics as metaphysics: it tells us how things must be (not much) but not how they actually are. Quantum mechanics has to be supplemented by evolution, the interplay of genotype and phenotype to explain the Universe as we find it.

The ancient religions are considerably tighter than modern liberal society, and this is a source of conflict. A well formed theology should be able to optimize the tightness and we hypothesize that quantum mechanics will be the result.

We have seen two big jolts in the history of mathematics, incommensurability and Cantor. Incommensurable magnitudes - Wikipedia, Transfinite numbers - Wikipedia

Bookwork and survival: I do my bookwork, I get my money, I survive. Genotype and phenotype.

. . .

Quantum mechanics is, in Christian terminology, a total slut, it will go with anybody. This is what we mean by a complete set of states.

Friday 19 December 2008

[page 31]

The Pope, celibate as he is, would like to dictate who, how and why we fuck.

The fundamental question is why do we bond? From necessity; for pleasure.

PLEASURE <--> HEADROOM (SPACE)

Our fundamental desire is for space, lebensraum.

From an evolutionary point of view the main game in town is the mating game. based on predictions of the survival and success of offspring.

The traditional churches trivialize the importance of religion by conceiving it as directed toward another life not like this, whereas our real concerns are with real life as it is and any ideas that things should or could be different are not considered.

We want to change the world. Is that a good idea or a bad one?

The world is full of difficult subjects , and one of the keys to survival might be to have the courage to take on difficult subjects.

RELIGION = THERMODYNAMICS

ie how to control what happens, ie how to control reactions.

[page 32]

Force transmits momentum Feynman I 39-3 'A certain amount of momentum per second will pour into the piston (from the gas), and it will start to move. To keep it from moving we must pour into it the same amount of momentum per second from our force. Of course, the force is the amount of momentum per second from our force.' Feynman

As I understand the rules, the only time Catholics are allowed to fuck is if they intend to breed more Catholics.

Saturday 20 December 2008

Communication ==> quantization in space (space division multiplexing)
Network ==> quantization in time (time division multiplexing)

Going to sleep? Why? No stimulus? Too much food?

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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!)

Feynman, Richard P, and Robert B Leighton et al, The Feynman Lectures on Physics (volume 1) : Mainly Mechanics, Radiation and Heat, Addison Wesley 1963 Foreword: 'This book is based on a course of lectures in introductory physics given by Prof. R P Feynman at the California Institute of Technology during the academic year 1961-62. ... The lectures constitute a major part of a fundamental revision of the introductory course, carried out over a four year period. ... The need for a basic revision arose both from the rapid development of physics in recent decades and from the fact that entering freshmen have shown a stewady incrase in mathematical ability as a result of improvements in high school mathematical course content.' 
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Polkinghorne, John, Quantum Physics and Theology: An Unexpected Kinship, Yale University Press 2008 Amazon Product Description 'Despite the differences of their subject matter, science and theology have a cousinly relationship, John Polkinghorne contends in his latest thought-provoking book.  From his unique perspective as both theoretical physicist and Anglican priest, Polkinghorne considers aspects of quantum physics and theology and demonstrates that the two truth-seeking enterprises are engaged in analogous rational techniques of inquiry. His exploration of the deep connections between science and theology shows with new clarity a common kinship in the search for truth.   The author identifies and explores key similarities in quantum physics and Christology. Among the many parallels he identifies are patterns of historical development in quantum physics and in Christology; wrestling with perplexities such as quantum interpretation and the problem of evil; and the drive for an overarching view in the Grand Unified Theories of physics and in Trinitarian theology. Both theology and science are propelled by a desire to understand the world through experienced reality, and Polkinghorne explains that their viewpoints are by no means mutually exclusive.' 
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Streater, Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2005 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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Links
Fermat's principle - Wikipedia Fermat's principle - Wikipedia, the free encyclopedia 'In optics, Fermat's principle or the principle of least time is the idea that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light.[1] Fermat's Principle can be used to describe the properties of light rays reflected off mirrors, refracted through different media, or undergoing total internal reflection. It can be deduced from Huygens' principle, and can be used to derive Snell's law of refraction and the law of reflection.' back
Incommensurable magnitudes - Wikipedia Incommensurable magnitudes - Wikipedia, the free encyclopedia 'The Greek discovery of incommensurable magnitudes changed the face of mathematics. At its most basic level it shed light on a glaring contradiction within the then current Greek conception of mathematical thought, which eventually resulted in a reformulation of both the methods and practice of mathematics in general. These reformulations brought about a new era in mathematics, and were the first stepping stones of some of our most important modern day conceptions, such as calculus.' back
ISSR International Society for Science and Religion 'About ISSR ISSR was founded in 2002 under the inaugural presidency of mathematical physicist and Anglican priest Sir John Polkinghorne. The Presidency subsequently passed to Professor George Ellis and then to Sir Brian Heap. The current President is Professor John Hedley Brooke. Aims Our central aim is the facilitation of dialogue between the two academic disciplines of science and religion, one of the most important current areas of debate in terms of understanding the nature of humanity. This includes both the enhancement of the profile of the science-religion interface in the public eye, as well as the safeguarding of the quality and rigour of the debate in the more formal, academic arena.' back
Pilot ACE - Wikipedia Pilot ACE - Wikipedia, the free encyclopedia 'The Pilot ACE was one of the first computers built in the United Kingdom, at the National Physical Laboratory (NPL) in the early 1950s. It was a preliminary version of the full ACE, which had been designed by Alan Turing. After Turing left NPL (in part because he was disillusioned by the lack of progress on building the ACE) James H. Wilkinson took over the project, Harry Huskey helped with the design. The Pilot ACE ran its first program on May 10, 1950 and was demonstrated to the press in December 1950' back
Transfinite numbers - Wikipedia Transfinite numbers - Wikipedia, the free encyclopedia 'Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were nevertheless not finite. Few contemporary workers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use.' back

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