Notes
[Sunday 13 april 2008 - Saturday 19 April 2008]
[Notebook: DB 63 aTheology]
[page 85]
Sunday 13 April 2008
Quantum field theory is a bit like Thomism, where everything is cut and dried and we gloss over difficulties so as to keep the general drift intact. Thomism is constrained by the need to fit the Roman Catholic Church, quantum field theory by the need to model observations understood in terms of quantum field theory.
[page 86]
Transform = change of point of view. We cannot transform reality which (in the classical Einstein view) is what it is, invariant.
Gravitation can 'see' what it going on in an isolated quantum system without 'collapsing' the wave function.
Feynman's (and Dirac's) integration over paths seems a bit wasteful, since first we create an infinity of possible paths (one of which is realized), each represented by a phase increasing at some rate between 0 and infinity, and an amplitude, so that when we add all the paths ('integrate') in a time (phase) ordered manner, the result is the actual path. The network approach would like to do away with this redundancy by finding the actual algorithm (Turing machine, transformation) that takes us directly from the initial to the final state. This is the approach of quantum computation which instead of imagining a continuous line of operators stretched from an input qubit to an output qubit simply compresses the line into a point, an operator called a gate.
So why is the path integral so useful? First because it shows us how to import the ideas of the tried and true classical methods of calculus into the new physics made necessary by observations. Physicists use the natural world as their touchstone as Christian theologians use the Bible. This is the primary article of faith in both regions. Both faiths are testable by their outcomes. The outcome of the Christian faith is that some of our specific knowledge of God is encoded in the Bible, and the total task of theologians is to decode this information using
[page 87]
the tools allowed to them by their institutional masters. Although Christian theologians allow that there is some knowledge of God available from knowledge of our world and ourselves, this knowledge is severely limited and tells us nothing that revelation does not tell us about God.
The alternative, which we use here, is much richer. It tells us that all experience is experience of God, and that the Bible records an infinitesimal fraction of this experience from limited human space and time. Since every experience is a historical document, it seems [un]likely that such a small sample as the Bible can tell us much about God.
The basic problem with the Christian approach is that it is very unlikely to be true because it is one of the millions of often contradictory world views that have been developed and propagated over the space-time range of Homo sapiens. This contention justifies searching for a reality (rather than a book) based search for a consistent theology, ie one that can look squarely at all human experience without any political or institutional bias.
Hobson: 'The invariant interval between A and B along n arbitrary path is then given by
where the integral is evaluated long the particular path under consideration. Clearly, to perform the integral we must have a set of equations defining the spacetime path.' page 13-14. Hobson
[page 88]
Another path integral.
We parametrize relativistic world lines by the proper time tau which is equal to the observed time only in the rest frame of the moving particle. We parametrize quantum world lines by a phase, theta, which is monotonically increasing like tau but whereas tau has a single value, d theta / d tau can range from 0 to infinity, and the path integral method computes the amplitude of a point as the sum of the amplitudes contributed by every frequency.
tau is a scalar, world line is 4D.
PROPER TIME = LOCAL TIME (ie relatively at rest time)
Massless particles do not have proper time since ds2 = 0, i delta tau = 0.
Doppler effect: changing distance between source and sink changes the frequencies observed at source and sink.
Physics, the study of God's body, gives / reveals to us an alphabet in which, ultimately, all the features of god are expresses.
REVELATION contains PHYSICS, ie PHYSICS is an element of REVELATION.
This is true in Christianity, since we need physics to read the Bible.
I have gone from NATURAL RELIGION is an element of CHRISTIANITY to CHRISTIANITY is an element of NATURAL RELIGION.
[page 89]
or better X contains N to N contains X.
Christianity is brand X.
In the real world, brands compete or collude.
Natural religion commutes with all brands because it is 1 and 1X = X 1, no matter what.
Electromagnetism needs sources and sinks because it is 2D? Gravitation can be source free in 3D.
Every different frame of reference gives a different meaning to a physical point (eg an atom in a protein or an ice block) even though gravitation is blind to this meaning, seeing no order but only symbols with energy.
Einstein page 123: 'The following statements hold generally: every physical description resolves itself into a number of statements, each of which refers to the space-time coincidence of two events A and B. In terms of Gaussian coordinates, every such statement is expressed by the agreement of their four coordinates x1 , x2 , , x3 , x4,. Thus in reality, the description of the time-space continuum by means of Gauss coordinates completely replaces the description with the aid of a body of reference, without suffering from the defects of the latter mode of description; it is not tied down to the Euclidean character of the continuum which has to be represented. Einstein
page 125: 'In gravitational fields, there are no such things as rigid bodies with Euclidean properties.'
[page 90]
Monday 14 April 2008
We may think of gravitation as the communication of a carrier without any modulation, ie an 'empty' message.
If gravitation is the physical layer of the Universe what is the next layer? Intuition (mine) suggests the electromagnetic field and the photon. Photons count energy (as do all quantum processes) so we imagine that the first bifurcation into observer and observed is via the differentiation of energy into the quantum of action and a count of quanta. This intuition is based on the observation that all measurements in the quantized world are counts. So we get the first equation in the Universe, E = h bar . little omega, which relates action, energy and time [frequency]. We might call this epoch the 'invention of time', and the foundation of proper time and phase which are the classical and quantum parameters used to map the order of physical events in the history of the Universe. With the invention of time came the invention of history and temporal order.
A photon is a source free flow, a completely dynamic harmonic oscillator which illustrates the classical relationship between potential and kinetic energy, showing that both have aspects of potential and kinetic energy. The observable is a count per unit time which we call energy. Each cycle of oscillation counts as a quantum of action, and we find that energy == quanta counted per unit of time.
ENERGY - PRIME MATTER. The difference between here, [and] Aristotle and Thomas is that here 'prime matter' is
[page 91]
not the ultimate in unformed passivity, but rather like the ultimate in unformed activity.
. . .
As my confidence grows I stick my head up in various fora. The promotional phase has begun. I am following the trajectory of creativity that I am trying to describe and loving it. In other contexts recursion leads to orgasm, the chain reaction that epitomizes the creation of the Universe in eg Tantra Philip Rawson. Rawson
Rawson page 7: 'Thought, in the sense of ordinary logical and very useful reasoning, Tantra sees as one of the chief causes for people gradually becoming disillusioned and miserable in what they believe to be their world.'
'Tantra is an Indian cult: but since it has evolved continuously from the remotest antiquity it is not limited to any particular Indian religions which arrived later on the historical scene.'
Ie a hardware layer of religion which has become so abstract in the Christian religion that it is inclined to reject ecstasy of all but the most 'spiritual' kind. Ordinary sexuality has been transformed into an exclusive mysticism.
Page 8: 'If you don't do what your Tantra prescribes, then you will never get the point.' The difference between money and work.
[page 92]
Rawson page 8: 'What [Tantra] describes and maps is a world of realities, a world that can only be visited by following the maps. It is there to be found; but someone who has not visited it can have no idea what it is like. For there is no way of examining it from the outside. It is what we are -- although we do not usually realize the fact -- and we can never step out of it to take an analytical view.'
The layered network model would seem to suggest that at least in imagination we can always step up from the layer we are in to a higher layer that enables us to see meaning in our history.
page 9: A good dichotomy ''You must abstain from all enjoyment, mortify the flesh, and obey the commands of a jealous Father-God' vs 'Raise your your enjoyment to its highest power, and then use it as spiritual rocket-fuel.' A wasteful use of fuel maybe, but natural religion would opt for the Tantric alternative. So more drug. Tea.
page 9: 'Tantra has always believed that our failure to grasp time lies at the root of all other human failures.'
[Christianity might say the same about eternity]
Another cult that assumes that without its help we are failures?
'To see the nature of time I to understand the process of Genesis, that ladder of descending stages from the Origin through the evolution of the cosmos. Once we grasp that, we can, so to speak, reverse the machine for ourselves, and climb back up the ladder to Genesis.
So seeing the unity of the whole.
[page 93]
History is created in the present building on the past. We can look at things from a comoving present or from a backward or forward looking past.
Rawson page 12 'We will never be able to find the origin or causes of all things 'out there', among older projected things. Their origin is in the projection-mechanism itself, that is to say within the psycho-physical organism.'
A bit solipsist? The past exists in the present through things (spaces) that are invariant in time, ie texts (like the Tantras) which record past events (like the isotopic composition of rock samples or our own DNA).
page 14: Pavaritti - 'turning back up' past creates present / present creates past.
We may see all communication as a one way track between past and present; all decoding as the reconstruction of the past from the resent. Present and past are joined by space. Space joins times, ie space is a wormhole in time.
Rawson page 14: 'The seed may be symbolized in the Shri Yantra by a central dot, the original point of energy which has location but no magnitude', usually depicted as white; it makes its fundamental originating movement in the shape of a female, downward-pointing triangle which is red. From this original couple, the white and the red, evolves a series of interwoven triangles, four male (upward-pointing) and four more female (downward-pointing). Their interpenetration produces circuits of lesser triangles which represent the subdividing of the original creative energies into more definite forces.'
[page 94]
Rawson page 15: '. . . yantra ... means any physical form which can carry a charge of symbolism.'
To us, this is any physical form capable of embodying information a la Landauer. Landauer
'[Mahakala and Kali] together are the creative functions of the unimaginable Brahman, the Parasamvit, the Supreme Truth, which encloses and projects all that can possibly exist throughout Universes and star systems, 'numberless as the sand grains in the Ganges'.'
page 17: '. . . every human act of love us a shadow of the cosmic art, and the more completely it is carried out the closer it may come to the divine primal act.'
We would say that from the point of view of pure act, every act is identical to the 'divine primal act' and is a realization of the initial singularity in the present.
A set which is a member of itself? Distinguished by cardinal number?
page 20: '. . . wholes come first and generate their parts . . . All causes lie in wholes, not in the accidental relations between inferior parts.'
page 24: 'Tantra cultivates artistic experience for its own sake.
[page 95]
Rawson page 29: 'For according to Buddhist ideas, one must not look for 'higher objects' like deities on which to fix one's mind; one must learn instead to live ultimately in a state in which all objects, even 'higher' ones are abandoned as illusions, dissolved into an immense seamless web of relations, in which there is neither space nor time.'
Few religions seem to like space and time, but otherwise very network 'web'. Natural religion might be thoroughly syncretist, looking for a coherent harmonizing of all religions.
Hobson et al: We may relabel the points of a manifold by performing a coordinate transformation.
Point = event = transmission of a message defined by source, content, destination, a 3D space for defining all the messages in a network. Add time of transmission ' reception and we have something that could be mapped to a 4D space not necessarily continuous. The space need not be continuous, but for real manifolds the coordinate transformations must be continuous and differentiable.
oportet distinguere - we must break all symmetries to get at reality.
Getting of wisdom = solving the problems posed by one's life. This obviously has different degrees of difficulty in different lives. We might suppose on the one hand a completely stable society in which every person has a valuable niche. Presumably in such a society the acculturation of children from birth would fit them uniquely for their place in society and their life would run from birth to death without any
[page 96]
perceptible problems, something like Heaven, the City of God. Augustine of Hippo - Wikipedia, Augustine On the other hand one might be born in the midst of war, famine and disease with no end of troubles ended by an early death. In the first case we might say that there is no wisdom because there were no problems. In the second case one would expect wisdom to be maximized because each near death experience may show more clearly how to avoid death. I am somewhere in between these extremes, having been acculturated in a religion and theology that have proved (to me) to be made of straw. I feel now that I have solved the problem to my own satisfaction. I feel that I have my wisdom now and can propagate it to others who are stretched on the horns of contradiction between acculturation and reality, what we have been taught to be true, and how we find things in our own lives.
To get wisdom is to come to a state of intellectual rest or equilibrium where there are no fundamental problems awaiting solution, although there may be an infinity of problems involved in the detailed application of the wisdom.
The formation of every nation requires the subjugation of peoples, insofar as a nation is bigger that a people and nation formation involves homogenization. Need it? Hussein
Electromagnetic radiation is source free and infinite in range. The advent of electric charge carried by particles localized electromagnetic radiation by creating sources and sinks, ie nodes. The development of nodes quantized the radiation?
[page 97]
Of course the next step after the getting of wisdom , as most prophets seem to demonstrate, is campaigning to get the wisdom implemented, which may not always be a good thing of the prophet is misguided. It seems to be, however, a feature of a good society that people who are under pressure or in pain be encouraged to speak by being listened to. This is the mechanism of load balancing which, we suppose, should be implemented among peers.
Hobson page 31: 'It is the assignment to each point in the manifold of a distance between points with infinitesimally different values of the coordinates that determines the local geometry of the manifold.
A relationship between artificial [arbitrary] coordinates and real distances.
'The metric functions gab(x) can be considered as the elements of a position dependent N x N matrix. Hobson page 32.
The invariance of the interval ds2 defines the relationship between coordinate transformations and the metric.
page 33: Intrinsic and extrinsic properties of a manifold. Extrinsic are added by the way it is embedded in a more complex space. Sop 4-space may be extrinsic to gravitation and rely on the existence of fermions. Each layer of a network adds extrinsic properties to the intrinsic properties of the layer below it, and its own intrinsic properties are extended by the layer above it.
The wisdom business: something for a not for profit non-governmental organization.
Governments move societies by spending decisions [and spin].
[page 98]
I begin to preach when I believe my own beliefs. It is up to my hearers to decide whether they will believe my beliefs, or a modified version of them, or reject them.
Tuesday 15 April 2008
Calculus: infinitesimal = linear
A prominent feature of quantum mechanics is that boundaries create structure, so that eg the complex electronic structure of an atom arises from the potential created by the nucleus. This principle appears to hold across the board, so when we put constraints on something we induce certain structures. So gravity induces much of the structure in plants and animals, and the boundaries imposed by the Bible create structures in the behaviour of believers and so on.
This feature is best illustrated by wave mechanics, where we require that the wave motion be zero at boundaries so that only discrete frequencies (energies are favoured by the principal note and harmonics in a vibrating string. In quantum mechanics the boundaries imposed by potential constrain the frequencies (kinetic energies) of recursion of states within the atom represented by periodic wave functions.
Things happen because they can, ie all inhibitions are removed. Presumably with no inhibitions the Universe would be over in a flash. (reference)
[page 99]
Evolution and the Euler-Lagrange equations. Hobson page 78 sqq.
We assume proper time to be the basic coordinate and express everything as a count of proper time [whose intervals are held to be invariant]
Wednesday 16 April 2008
Things happen because they can. Processes are halted by lack of resources, ie there is an inhibition (and 'energy barrier' too strong (high) to be overcome with available resources). One may be inhibited from opening a container because its lid is too tight. This situation may be overcome with a tool. One may be confronted with a calculation too complex to do 'by hand'. The appropriate tool here is a computer.
Possibility or potential is thus an active ingredient in process, since the process will occur if there are no inhibitions. Here lies a key difference between natural metaphysics and Catholic metaphysics. Following Aristotle, the Church defines potential to be passive, ultimately requiring a divine agent. Natural religion makes the Universe pure act, but analyzes that act into actual and potential energy which are not independent but bound by the conservation of energy, ie kinetic + potential = 0 [kinetic - potential = Lagrangian]
In general barriers are overcome by force and / or cunning.
We begin by fiddling with things. The important design point is to make things as fool proof as possible to minimize the probability that fiddling will lead to error (damage, injury). Good software (eg) is foolproof and 'intuitive'.
[page 100]
Hobson page 114: ' . . . the notion of an orthonormal set of basis vectors at any point in spacetime is of fundamental importance four our description of observers. Zurek
If you live in a Universe like this [is] what you will see (by which we mean what will be your experimental input in all models). The classical stance is that everything exists independently of observers, and that each observer observes this invariant whole from a different personal frame of reference, the inertial frame in which we are are subject to no outside forces (distortions) our true self.
We travel through time at the velocity of light. All clocks on photons look stopped to us, but what do they look like to the photon? Frequency = energy.
Have long since thought that massless particles can have no visible internal process (they seem to be outside time) and so their personalities have no inner process but are completely determined by their environment. Photon and graviton. Since neutrinos have mass they can change in flight; since they change in flight they have mass.
One Universe = many ways of looking at it = many Universes.
Hobson page 135: 'We will see that a consistent theory of electromagnetism follows from saying that there exists a pure 4-force that depends linearly on the 4-velocity and also on a certain property f a particle, namely its charge q.
[page 101]
PORNOGRAPHY = REDUCTIONISM
Thursday 17 April 2008
Physics proceeds on the basis that a) we need some sort of coordinate system to describe the world; and b) the real physical world is independent of any coordinate system. The result of these two propositions is that all Gaussian coordinate systems are equivalent and this equivalence is embodied in tensors which act as inverses of the coordinates so that the tensor expression of the physical law is invariant under transformations of coordinates.
We might find a few flaws in this. Why can't we express laws of physics directly in terms of the agents involved without using coordinates as a medium; and if we do use coordinates, do the coordinates transformations have to be continuous?
The invariant interval is the fixed point in tensor transformations, and serves to mediate between the coordinate system and the real physics, The invariant interval is expressed by a combination of the metric tensor at a point and two coordinate intervals, ds2 = gmnxmxn.
What is the difference between I'm in love (perhaps with an unwitting person) and we're in love? In communication terms we have been through the handshaking stage and re busy sharing messages in a growing set of common codes, ie getting to know eachother.
[page 102]
We don't hear much of tensors in quantum theory, although it is full of transformations. What is the fixed point in quantum transformations? conservation of probability. This constrains the wavefunction via the mechanism of interpretation |<x >|2 is the normalized probability that we will observe |x >. The special thing about quantum mechanics is how we compute probabilities. What does this (rather counterintuitive) procedure mean?
The plan here is to interpret gravitation and quantum mechanics as networks. Gravitation is the power network, a totally unmodulated carrier of energy.
The mainstream idea is to work by day and sleep by night. Early to bed ad early to rise makes a person healthy, wealthy and wise. This may be true for diurnal people but there are as we might expect, nocturnal people as well, living by the inverse algorithm late to bed . . . .
Quantum mechanics begins with the assertion that the probability of the Universe is 1, that is it exists. Then we multiplex that 1 in communication space and map the resulting multiplexation into space time where we can observe the actual calculations that make the world go, bust as we can (in principle) observe the working of an ordinary digital computer. These observations are explained by the hardware and software that define the computer.
The aim of the transfinite oscillator is to draw a tree tracing every possible like of action in the Universe. This is tree is both a static and a dynamic entity, for ℵ0 quanta of action
[page 103]
are flowing along the 'path' parametrized by the age of the Universe in units of proper time. The evolution of the Universe proceeds by localization. The velocity of light and its consequent light cones partition the set of correlations in the Universe along a spectrum 0 to 1.
LOCAL = a) inertial; b) frequent communication - strong energy flow.
Gravitation is the network localized by c. Photons [gravitons?] are the primary carriers of energy. The location of a photon [graviton?] and its frequency re measured by frequency or energy. Energy can be varied in quanta by a continuous range of frequencies ranging from (say) 1 to 0. normalized by the constant ℵ0 . h bar.
Tantra, like Yoga, tends to limit the range of human actions considered enlightening, whereas natural theology and religion would embrace all action to learn from it and guide ourselves accordingly.
WISDOM = TRUE ENLIGHTENMENT
Those who attempt enlightenment by withdrawing from everyday experience may be prone to delusion. Our experiences are the observations which fix our position in life. The static framework of the world is embodied in the messages passing around it whose archetypes are photons, or more generally particles with no rest mass and so no rest existence.
If our models and interpretations are good they will fit
[page 104]
the experience of us living in the midst of the system modelled.
Electromagnetism: f = qF.u, f = electromagnetic four force, u is particle's 4-velocity . . . q its charge, ie a scalar coupling constant between f, F and u, and F the electromagnetic field tensor.
The mathematical theory or waves or periodic functions allows us to see the many similarities between sound and quantum mechanics. An oscillator is any physical system that can be modelled with a periodic function. This turns out to be everything except the Universe as a whose, which may expand monotonically forever.
Quantum mechanics, via the path integral method, is directly concerned with communications between states. This does not prima facie require spacetime, but we eventually have to map it onto the classical spacetime where real observations are made. So quantum mechanics is concerned with the actual core of the event whose space-time location is irrelevant. The quantum event is the invariant that must be mapped into the laboratory frame.
Forced vs free communication: compulsory education, rape etc.
Physical laws are all expressed as equations. Human laws are expressed as commandments: 'thou shalt not x, ie you shall equal not doing x.
[page 105]
An equality says two expressions are in some sense degenerate equals equal. 'equal' = 'degenerate'. Degenerate = universal = symmetrical.
Hobson page 136: '. . . we must now construct the field equations of the theory, which determine the electromagnetic field tensor F(x) at any point in spacetime in terms of charges and currents. To construct these field equations, we must first find a properly relativistic (or covariant) way of expressing the source term. In other words, we need to identify the 4-tensor, defined at each event in spacetime, which acts as the source of the electromagnetic field.'
The Universe is a market. They will be best placed to buy energy who can make the most out of it.
money = action. Actions per hour = energy = dollars per hour. We measure frequency in Planck's per second = energy.
How doe the uncertainty principle relate to transfinite arithmetic, where ℵ0 + ℵ0 = ℵ0, . . . c + c = c.
The study of any system is a study power, that is the flow of energy per unit time. How do we relate political power to physical power? Political power is the ability to correlate people's beliefs and actions. [to bring out the boson in them]
Quantum statistics all lies in the simple phrase p = | x >|2. Why is this? What does it mean? Particularly given that x is a complex number so |x >|2 = |x > <x| *. First, the construction of wave functions by superposition, there are two numbers to be added, the coefficients of the real
[page 106]
and imaginary basis vectors of the amplitudes (complex numbers) to be added Imaginary reminds us of time, so perhaps we might see the complex plane as one axis of time and one axis of space. This addition is simple arithmetic and does not exhibit any of the special properties of complex numbers.
The Argand diagram is a two dimensional Minkowski space?. . .
This is all wrong. . . .
So what is the difference between a 2D Minkowski space and the complex plane? The time axis is real [in the Minkowski space] and the complexity is introduced by the metric.
Distance is measured by the absolute value |z | = square root (x2 + y2)
[page 107]
whereas in Minkowski space |delta s | = + square root (x2 - t2).
Instantaneous phase has two degrees of freedom. Why is probability a quadratic function of amplitude? Perhaps because the probability we measure is for the complete event which has two stages represented by |x > and |x >*. We know that
so we are talking about the probabilities of getting a message from x to y and back again.
<x |y > is a dot product. If xi are the components of <x | and yi of |y >, <x |y > = sumi xiyi.
But still, what does it mean? Why is an amplitude represented by a complex number and what does this tell us about the world? Sleep on it.
Friday 18 April 2008
A complex number encodes two real numbers with special multiplication rules, so we can think of a quantum history in three dimensions, one corresponding to phase, and one to each of the real and imaginary axes so that what we see is a helix. Many helixes of different amplitudes and frequencies may be represented by the same set of axes and added up to give a resultant (superposed) helix with variable (ie modulated) amplitude and a wide spread of frequencies. Stationary states are represented by a single sharp frequency.
[page 108]
A similar scenario concerns particle and antiparticles, whose direction of rotation of phase is opposite so when they meet they annihilate, ie their probability drops to 0.
As with classical probabilities, when there are two indistinguishable ways for an event to happen, the probabilities associated with each path add, but in the quantum case this interference or addition is vectorial and so the sum may be less than the individual vectors. This only has meaning in terms of absolute values |z | = square root (x2 + y2) since complex numbers in themselves are not ordered and z1< z2 has no meaning.
What we are talking about in superposition is 'mutual modulation' some sort of duality. The fact that complex numbers are continuous means that they are error prone. Two independent error prone variables combine to control the probability of emission of an error resistant particles.
PROBABILITY = UNCERTAINTY
Maximum uncertainty = equiprobability.
In quantum mechanics we might say that the event is inevitable but uncertainty lies in when and where, ie in mapping the event onto spacetime so delta x . delta p = h bar. So the probability that I will actually mate with someone is close to 1, but when an where us an uncertain function of circumstances like my closeness to a potential mate.
Feynman page 3-2: '. . . how much can be deduced from so little.'
[page 109]
In quantum mechanics p = |<a |b >|2. ie dot product <x |y > = sumi xiyi. => 0. In special relativity (delta s )2 - (delta t )2 = (delta s )2 + (i delta t )2 = -1 =< (delta s ) =< 1.
Put these together and we have a quantum field theory, where relative velocity of superposing particles affects their interaction, but 'particle' carries its amplitude in its own rest frame.
Everybody's laws of physics look the same in their own rest frame. Particle can only interact (an event) when the spacetime interval between them is zero, so my retina and a distant supernova may occupy the same point (event) in spacetime. [united by the null trajectory of a photon]
Bosons date from the days when the Universe had no space, only time, energy, frequency, all elements of the broken symmetry of action. What we speculate to be the first differentiation in the Universe. So we have action = energy . time, 1 / action = action; 1/time = frequency = energy; 1.energy = time, elapsed time, interval. So energy and time act like dual bases for action, tensors of rank zero.
Perhaps we can say there are an infinity of rolled up spaces represented by all the basis vectors of the Hilbert space of the Universe. Why are the 4 unrolled macroscopic? Because they date form the time when macroscopic was microscopic, ie space = memory = fixed point did not exist, or in fact existed as one point, the initial singularity, a boson. A boson is a message, something that can be 'parallel transported' through space and sees no space or time. In it death and life are the same think. The archeboson states of the Universe are massless. Mass . . .
[page 110]
. . .
Now can this quantum interval be mapped to spacetime. Here we have a problem since causality (Einstein) = interval 0 --> infinite energy. But we re saved by the uncertainty principle since delta E (ie delta frequency) . delta t = h bar. So the closest we can get to 0 is a quantum of action. So we might say h bar / 2 = 0. What is going on inside this interval is not observable because it is deterministic (Turing machine) and deterministic processes do not stop and talk. To stop and talk is to get new ideas and quite probably to off in a direction other than where one was going before stopping. Complex.
So a boson, like a photon, is described by Maxwell's equations in one complex dimension, where we might say that electric is real (there are charged monopoles) and magnetic is complex (we have yet to observe a magnetic monopole).
where algorithms can be represented by the 2D identity matrix . . . if we obey the laws of complex multiplication.
There are aleph(n) different massless boson states corresponding to aleph(n) different frequencies, at least in the Platonic world of mathematics where frequency is a real
[page 111]
number. But how many can the Universe actually distinguish, given the uncertainty principle. Let us say a countable infinity, ℵ0 , which may be any natural number depending on the machine infinity of the system we are discussing. These boson states vary through time but all at one superposed point in space. We may plot them on a line parametrized by proper time interval. Spin and helicity? Wait. So much for bosons.
Fermions and space are the next break in universal symmetry.
When the Universe adds space to its structure, we find that massless bosons have no rest state.
From the user's point of view, all the dimensions in a compute are rolled up (cyclic) except the input and output streams which are extended in spacetime. Dimension - degree of freedom.
Amplitudes: product = serial events; sum = parallel events.
Amplitudes represent possibilities and we might say that the product of two possibilities gives another possibility. The product of a possibility with itself gives a probability.
How possible? is measured by phase. Completely in phase probability = 1, completely out of phase probability = 0.
PHASE - HARMONY PEACE - HARMONY ie acting in phase with one another in a time and space ordered process like manufacturing a car in a car factory or a protein in a cell.
[page 112]
Feynman page 4-3: 'Why is it that particles with half-integral spin are Fermi particles whose amplitudes add with a minus sign, whereas articles with integral spin are Bose particles whose amplitudes add with the positive sign. . . . An explanation has been worked out by Pauli from complicated arguments of quantum field theory and relativity. Pauli
The pre-science / science paradigm change was equivalent to the change from accepting the authority of texts to accepting the authority of observations. A text is a transformation of the experience of the author based on some internal parameters of the author. These internal parameters (in the pre-science approach) are determined by the needs or state of the author. Such needs may be staying in power for a ruler, or expressing strong feeling for a prophet [or just to make a living]. Such transformations, while telling us something about the author, are rather arbitrary and impress this character on their texts, which are thus poorly correlated with the invariant world inhabited by the authors [and their readers].
We think of space as memory. Memory has both cost and benefit. The cost is the cost of error correction (keeping the memory 'pure' or invariant) and the benefit is the more complex algorithms which can be developed when memory is available. The Church, by maintaining as invariant deposit of faith, provides itself with a paradigm for reaping the benefits it needs for survival and growth, like a virus or any other organism.
Science by passes the text and the authority and goes straight to the source.
[page 113]
Science has shown us the size and power of the Universe so that it no longer carries much weight that it was made just for us, or that some ancient human error deranged the entire system.
The core of te Roman Catholic Church is an institutional transform of experience. The transform serves the purposes of the Church in just the same way s my physiological transform of my food for my own benefit.
Saturday 19 April 2008
Pauli: The Connection between spin and statistics. Pauli
Physics looks for those thing which are invariant under various transformations believing (with plenty of evidence) that knowledge of invariants gives us the key to understanding the past and predicting what is predictable in the future.
I am gradually transforming this project from play to work while converting ditch digging and allied trades from [work to play].
Einstein made his scientific view explicit in his study of invariance in communications through space and time and the general idea has spread. Invariant = universal = symmetrical.
The very existence of invariants points to the layered structure of the Universe.,
So we look for invariants in the HIV in order to design vaccines against it.
[page 114]
INVARIANT = MEMORY
Communication falls into two categories. The first, we will call the physical layer, concerned strictly with the communication of information. Whether this be ink or electronics is irrelevant to the abstract invariant theory of communication.
ACU EJournal of Theology: On the existence of God. ACU
It remains a scandal to me that theology is but a sub-faculty of the Australian Catholic University, whereas in the 13th century [ancestor] the Theology faculty would have been its raison d'etre and the ultimate user of all the output of lesser faculties. This bit of nostalgia is motivated by my erstwhile membership of the Order of Preachers which still remembers its role in medieval universities through such personalities as Albert the Great, and Thomas Aquinas, both saints of the RCC along with the founder of the order Dominic Guzman. Albertus Magnus - Wikipedia, Thomas Aquinas - Wikipedia, Saint Dominic - Wikipedia
This situation and many others including a growing personal conviction, motivates me to propose a paradigm change in the methods and assumptions of theology.
This observation may not be considered scholarly but they nevertheless convey data about the author that may help in interpreting what follows.
The purpose of science is to track reality. With a good knowledge of the ways of the world we are best equipped to steer our own courses in the space of life, a message space.
[page 115]
What is observable is physically encoded messages, like the embodiment of this essay. Among the observables is the Bible. Some of us take the decoding of the Bible very seriously and give that set of data far greater weight than any other of the millions of books and the countably infinite other sets of data.
DECODING: Meaning; Weight.
The 24 These are the Lagrangian of the Standard Model of God. Or maybe not, but we take as our guide Feynman's observation that theories not reducible to a Lagrangian are apt to lead to contradiction. Feynman
Feynman Gravitation page 81: There is apparently no successful theory which is not derivable from a variational principle which starts from a Lagrangian or Hamiltonian functional (which are equivalent. It is not certain whether the failures of non_Lagrangian theories reflect some fundamental truth about nature.' [maybe that evolution by natural selection (variation) operates at all levels of complexity and is the heart of intelligence]
Marketing: Sex and Quantum Electrodynamics
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