Notes
[Sunday 15 March 2009 - Saturday 21 March 2009]
[Notebook: DB 66 Turing Field]
[page 25]
Sunday 15 March 2009
Wigner page 51: The principal theme of this discourse is the great difference between the relation of special relativity and quantum theory on the one hand, and general relativity and quantum theory on the other. . . . briefly, while there are no conceptual problems to separate the theory of special relativity from quantum theory, there is hardly any common ground between the general theory of relativity and quantum mechanics.' Wigner
This is because general relativity is a pre-quantum theory in which error is impossible and so quantization unnecessary.
'. . . it required the very ingenious work of Tomonaga, Schwinger, Feynman and Dyson to adjust quantum mechanics to the postulates of special relativity, and this was so far successful only on a working level.' Sin-Itiro Tomonaga - Wikipedia, Julian Schwinger - Wikipedia, Richard Feynman - Wikipedia, Freeman Dyson - Wikipedia
Wigner page 52: 'This is not so with the general theory of relativity. The basic premise of this theory is that coordinates are only auxiliary quantities that can be given arbitrary values at every event. Hence the measurement of position, that is, of space coordinates is certainly not a significant measurement in the postulates of general relativity are adopted; the coordinates may be given any value one wants.'
Except that coordinate transformations must be continuous within the meaning of continuity, defined on a C infinity manifold. Hawking and Ellis. Hawking & Ellis
page 53: If we want to put general relativity on speaking
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terms with quantum mechanics, our first task has to be to bring the statements of general relativity into such form that they conform with the basic principles of the general relativity theory itself. It will be shown below how this might be attempted.'
Wigner page 53: 'The relation between the special theory and quantum mechanics is most simple for single particles. The equations and properties in the absence of interactions can be deduced from relative covariance.'
On the other hand, an empiricist would say we know nothing in the absence of interaction.
page 53 (cont) 'Two cases can be distinguished: the particle either can or cannot be transformed to rest. . . . If the particle cannot be transformed to rest, its velocity must always be equal to the velocity of light. The rest masses of these particles is zero because a non-zero rest mass would entail an infinite energy if moving with light velocity.'
On the other hand (again) 'rest mass' is meaningless (and so can be assigned no value) for a particle that cannot be transformed to rest.
Wigner page 54: ', , , the statement that the spin is parallel to the velocity is a relativistically invariant statement: [for a particle with 'zero rest mass'] it holds as well if the particle is viewed from a moving coordinate system.
'. . . the statement that spin and velocity are parallel cannot be universally valid for a particle with finite rest mass [because it can be transformed to rest and spin has no velocity to be compared
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to].'
Wigner page 61: 'The approximate validity of laws of symmetry is therefore a very general phenomenon -- it may be a general phenomenon. We are reminded of Mach's axiom that the laws of nature depend on the physical content of the Universe, and the physical content of the Universe certainly shows no symmetry [?] This suggests -- and this may also be the spirit of the ideas of Yang and Lee -- that all symmetry properties are only approximate. The weakest interaction, the gravitational force, is the basis of the distinction between inertial and accelerated coordinate systems, the second weakest known interaction, that leading to beta decay, leads to the distinction between matter and antimatter.'
Can we say that symmetries at one peer level are broken in the next? From the point of view of information theory the most valuable symmetry is that of equiprobability, which leads to maximum entropy and maximum error free transmission rate.
page 62: 'Let us look at the question of how the equations of the general theory of relativity can be verified.'
What does equation mean? It is itself a meaning, the correspondence between various measurable parameters combined in various algebraic ways. In practical work, these algebraic expression may have countable infinities of terms. Simple expressions like F = ma, E = mc2 etc point to deep hardware properties of the world. Complex perturbation expansions encoded in Feynman diagrams suggest higher layers of the network, where large groups of peers exchange messages over the hardware.
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Wigner page 62: 'In relativity theory the state is described by the metric which consists of a network of points in space-time, that is a network of events and the distances between these events.' The simplest metric in 4-space can be expressed as a differential equation which, in effect, constrains the space by the simple requirements of continuity and correspondence with Newtonian physics, which relies on the conservation of action, energy and momentum. But quantum mechanics gives deeper meaning to these ideas. Energy is no longer a scalar quantity but a matrix of values which encode the rate of communication between different components of the vectors input to and output from this Hamiltonian or energy matrix. The Hamiltonian tells us how to encode these values and places a tight constraint on the values. Further theory is required to fix the actual values in the matrix.
We see that the mathematical formalism constrains the space of acceptable vectors and matrices operating in Hilbert space. This constraint once again arises from continuity. So the whole quantum field theory is worked out in terms of infinitesimal Lorentz transformations and the integration of an infinity of trajectories to assign probabilities to various outcomes given the input (often high energy beams of particles).
So we couple to the old theory by showing that quantum mechanics is an abstract version of the cosmic layered network of communication. We approach this through the Hamiltonian, as described above. But what is this telling us? Using it we can compute the traffic along all the fundamental interactions possible in the
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Universe, that is the interactions directly involving fundamental particles, without regard to the meaning that higher layers of the Universe attribute to various processes.
The Hamiltonian transforms vectors in a unitary way. This unitarity serves to establish the normalization of all sources across their alphabets so that for any given event the sum of the probabilities of possible outcomes in 1. This is the fundamental observational input which introduces a certain dynamic order into the universal process. We express this dynamism in the axiom probability is conserved, so that the flow of probability (energy, information) in the universal network is like the flow of an incompressible fluid in an infinite array of connected leak proof pipes. What is flowing is not a fluid in fact but can be treated mathematically as a fluid if we ignore the meaning of the messages so transmitted. The complexification of the energy operator models mathematically how the Universe comes to be in the unitary interior of the initial singularity.
Wigner page 62 (cont):' If we wish to translate these general statements into something concrete, we must decide what events are and how we measure distances between events. The metric in the general theory of relativity is a metric in space-time -- its elements are distances between space-time points, not points in ordinary space.'
page 63: The events of the general theory of relativity are coincidences, that is, we say, the logical exchange of a message through one element of the Universe "measuring" another, ie two entities entering a common basis state into the Hilbert product space of their individual bases. They learn to speak the same language, which involves a transformation
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matrix from one language to another.
'coincidences, that is collisions between particles.' This is the most physical expression of the reality of communication, concerned not with meaning, but with traffic. It is easy to measure traffic. It is harder to transform its meaning into one's own reference frame, that is to understand it. It is because all communications are encoded physically that the dense encoding of the Universe can nevertheless be measured by action, energy, momentum and normalization.
EVENT = COINCIDENCE is ds 2 = 0. For photons there is from our point of view one event because we see that for photons ds 2 = 0 always. They date from an era when the Universe was a harmonic oscillator of zero size but (let us say) ℵ0 states. This nomenclature is chosen because a state is a unique countable entity, and there are ℵ0 countable entities at the foundation of mathematics. Mathematics is the study of unlimited numbers so that we can be sure we can trust the limited numbers used by engineers, bankers and tradespeople.
LOCALIZATION = 4-MOMENTUM (PIXELLATION)
If we want to look at a very small (localized) event in spacetime we pour in the 4-momentum. The Universe is ill defined in regions of low 4-momentum, something of deep concern to everybody in the communication industry, where the detection of weak signals and the production of strong signals both contribute to larger and more secure networks.
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'. . . the establishment of a close network of points in space-time requires a reasonable energy density.
Stress-energy tensor. Stress-energy tensor - Wikipedia
Wigner (cont): 'However, it is not necessary to discuss this in detail because the measurement of distances between the points of a network gives more stringent requirements that the establishment of the network'.
Yardsticks are hard to work: 'It is desirable, therefore, to reduce all measurements in space-time to measurement by clocks.' This takes advantage of the underlying unity of the broken symmetry of space and time - ie time became the foundation for one dimension of space and one of time, and this little structure has now become the foundation (hardware) for 4-D spacetime.
It is incumbent on a manufacturer to produce a trustworthy and safe product that does the job effectively.
Wigner page 53: 'The distances of events which are in spacelike relation, and which would be measured more naturally by yardsticks, will have to be measured, therefore, indirectly.'
Spacelike distances can only be measured from backwards or forwards in time. We cannot look forward, so we have to look back after the light cones emanating from the spatially separated points have merged so that both can be seen at once.
page 64: 'It is interesting to consider the quantum limitations
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on the accuracy of he conversion of time-like measurements into space-like measurements . . . A more detailed calculation shows . . . that the conversion of time like measurements into space-like measurements is essentially free.'
Wigner page 64: 'We finally come to the discussion of one of the physical problems, the limitations on the accuracy of the clock.
page 65: 'For example a clock with a running time of a day and an accuracy of 10-8 second ( = 10-13 / sec) must weigh a gram for reasons stemming from the uncertainty principle and similar considerations. Oscillator 1013 + counter, 1 mg crystal, 1 mg silicon?
page 66: 'the reading requirement introduces only an insignificant numerical factor but does not change the form of the expression for the minimum mass of the clock.'
'The curvature tensor can be obtained from the metric in the conventional way if the metric is measured with sufficient accuracy.'
page 68: 'The result, as could be anticipated, is that the curvature of a point in space-time cannot be measured at all; only the average curvature over finite region of space-time can be obtained.'
'. . . the essentially non-microscopic nature of the general relativistic concept seems to us inescapable. '
What I would like to say is 'essentially non quantized'
page 69: Planck mass 20 micrograms.
[page 33]
'There is therefore a boundary in our experiments between the region in which we use the quantum concepts without worrying about their meaning in the face of the fundamental observation of the general theory of relativity, and the surrounding region in which we use concepts which are meaningful also in the face of the basic observations of the theory of relativity but cannot be described by means of quantum theory. This appears to be most unsatisfactory from a strictly logical standpoint.'
Goes to show that gravitation is more primitive than quantum mechanics.
Appendix I
Wigner page 69: 'It will be necessary, in this appendix, to compare various states of the same physical system. These states will be generated by looking at the same state -- the standard state -- from various coordinate systems.'
General relativity: does the action principle define the space or vice versa?
page 70: 'Two states of the system will be identical only if the Lorentz transformations that define them are identical. Under this definition the relationships which will be obtained will be valid independently of the properties of the particle.'
page 75: 'Luders has pointed out that, under certain very natural conditions, PCT belongs to the symmetry group of every local field theory (refs page 74)
[page 34]
The total energy and momentum of the initial Universe is zero, giving us ds2 = 0.
Probability density in space time = what are the odds of it happening in this space-time box.
Communication theory coupled with physics gives us limits on the resolution of the world.
Before the advent of space coordinate systems can only 'rotate' relative to one another, they cannot translate.
Special relativity only enters the scene with communication (observation) and error proofing. Without 'truth' the Universe cannot maintain its structure.
We divide coordinates into physical and theoretical. Changes of physical coordinates map some real change in the physical system, ie an observable change, like a change in relative velocity. Theoretical changes of coordinate system reflect instead the state of mind of the observer, who looks at things in the light of a different mathematical hypothesis about the generation of the data in hand.
The physicist is part of the discovery, which is why we remember those who develop fruitful ways of looking at things.
Curl = cross product only possible in 3D? Does this say something about the wiring?
Monday 16 March 2009
The mathematical marvel of the Newtonian era is vector calculus in three dimensions. Einstein showed us how to include time in the definition of a point and gave us 4D vectors. Quantum mechanics, on the other hand, moved into infinite dimensional complex 'spaces' that have an abstract measure of 'length' that only vaguely resembles normal geometrical length. Nevertheless it seems that the definition of length in quantum mechanics must in some way set the scale for 3D geometric length. The mathematics hints at it through the involvement of complex numbers and in fact (?) in 2D space geometric space and Hilbert space are mathematically isomorphic.
DISTANCE is proportional to PROBABILITY OF COMMUNICATION
At the simple level of physical space, we want to show that this us a consequence of quantum mechanics when we combine 2 2D spaces to make a 4D space in which the 2D spaces can 'measure' eachother. It is of the nature of measurement that it requires synthesis of the Hilbert spaces of the participant particles into their tensor product in order to gain the processing power [memory] necessary to make the measurement. A measurement in physical space corresponds to an act of insight in psychological space, symbolized by the diagonalization of the operator. I can see clearly now . . .
A feature of good fiction is consistency: the whole story hangs together, makes sense (in the end) without undue waffle. It makes sense because it illustrates the behaviour of 'credible' personalities.
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SCALAR (REAL) = LOCAL, OBSERVABLE IMMEDIATELY
Complex numbers, vectors, tensors and large algorithms in general require the synthesis of many scalar observation to reconstruct the components of the number [also require independent memory locations for storage]
Logic and action have a scalar relationship. The length of a process is the number of logical operations required to complete it.
In 3D space, the difference of something between two points is the dot product of the gradient of the something and the vector joining the two points.
Gradient = amount of change induced per logical operation [related
to the 'power' of the operation in the hierarchical system].
Vector = count of logical operations to go from A to B
in whatever algorithmic space we are using.
I am not a physicist and was thrown out of my theology school for nonconformity. My non-conformity was to hypothesize that god and the Universe were identical This strikes at the heart of the Christian business plan, which proposed a god utterly remote from this vale of tears who will make everything good for us in the end if we obey the Christian Church. They were wise to throw me out, since after 40 years of further thought, I think I was right.
From a practical scientific point of view, if god and the Universe are the same, physics, which studies the Universe, is part of theology, which studies god. The same goes for all the other sciences and in fact for all knowledge. On my
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hypothesis, since we are part of both the Universe and god, . . . every one of our experiences is experience of god. This does away with the need to look to the Churches for data about God.
So far so good, but how do we unify theology and physics, talk about god and talk about motion? At first this seems impossible. God is eternal (ie immutable, outside time) and the Universe is in ceaseless motion. QED. This hypothesis is beautifully developed by Thomas Aquinas in the first part of his Summa, and he will be my guide in what follows.
God may be eternal, but the Christian God is a living God, and life, according to the ancients, is self motion. How can God be both eternal and move? Easy, says Thomas, there are two sorts of motion, one from possibility to actuality, the other from actuality to actuality. The first is characteristic of the sublunary world, the latter characteristic of life in the divinity. Aquinas
Since we are inside god, our motion must fall into the latter category. The ancients made a mistake here which has been corrected by modern physics. Aristotle believed that potential was inferior to actuality, so that no potential could actualize itself and an unmoved mover was needed to keep the whole thing going. Unmoved mover - Wikipedia
Newton broke the ice, with his three laws of motion which define the barrier between dependence and independence. Newton's Laws of Motion - Wikipedia
Physical quantity = scalar field. Feynman II 2-7 Feynman
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Tuesday 17 March 2009
The standard approach is to Lorentz transform the fields before computing the amplitudes using Feynman diagrams. What would be the effect of reversing this order, [Lorentz] transforming the coordinates of the particles after the computation of probabilities.
Here we feel that quantum mechanics operates as a logical realm that exists before space, and to Lorentz transformations do not apply to it. It is only concerned with energy, frequency, time and in particular phase, that is the relative halting time and emission of messages by different processes. What we observe are particles and we observe them in 4-space. The relative velocities of observers is thus subject to Lorentz transformation.
The Father, observing himself, begets the Son. Aquinas 161
Our theorem: quantum mechanics is isomorphic to the transfinite computer network. At present an assumption, but if proven, a theorem. The arguments presented for this idea are informal and physical.
Let us say non-constructively isomorphic, insofar as the constraints imposed upon a network by memory, processing power and error control are the same constraints manifest in the quantum theory. So, as tried before, we can try to produce a dictionary:
phase = relative halting times of different processes operating at different clock rates 0 < nu < ℵ0.
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You ask what is the unit of ℵ0 and we say no unit because ℵ0 x ℵ0 = ℵ0 etc. At this level the Universe is cardinally indeterminate, we can see as much detail as we can look for, but the search requires us to devise a particular looking process (eg High Energy Physics) if we want to see certain things, fundamental particles. From this state the Universe builds up by looking at itself, a mysterious event that involved the collapse of the wave function [and the act of insight Lonergan].
In computer terms the collapse of the wave function is a decision. Quantum field theory, via Feynman (network) diagrams, shows that there is a tree of events(some 'virtual') behind every decision, the universal decision tree. Such a tree is rooted in an observed event and grows into the past, gradually expanding to include all the events within the light cone of the event of interest. Historians work in a similar way when they ask Why was the French Revolution?
From a quantum mechanical point of view we see this tree working in terms of the phases of the amplitudes for various events. Past computation cannot fully determine future events, so we have an uncertainty principle in the system [although there is no uncertainty about the past]. This seems ultimately to result from Gödel's incompleteness theorem there are true statements in a language which cannot be proven in that language, intersecting with Turing's theorem that there are incomputable functions. Both theorems have the black and white nature of mathematics but when implemented in the real world appear as different degrees of knowability and computability. Here time (which is absent from mathematics as practised) becomes of the essence. The animal that can work out what is going on in its environment and
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works out a successful plan to deal with it is on the road to survival.
Now we envisage the quantum-mechanical tree in communication network terms. We examine two points of contact, locality and uncertainty.
Because of the physical constraints on bandwidth, computations in the physical world are not carried out locally to infinite order. In fact locally a quantum mechanical system has no memory. It is only when space and memory develop that we can have non-locality. The non-locality arises because space and memory must be error free and so encoded in some way. Here we have the bootstrap better error correction = more memory = better error correction. We see this happening in our society, and we think that as social communications improve the ability of corruption to grow is decreased This was the idea behind 'naked money' (An essay on the divinity of money). An essay on the divinity of money
. . .
Locally the Universe can be modelled by 3D vector calculus, which assumes that space in 3D, continuous and measurable. Its deepest finding is that vectors may be operators that operate on other vectors. This system is linear in the sense that we can establish correspondences between
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numbers and 'distances' (which may be expressed geometrically, computationally, probabilistically (communication theory) etc.)
As we build up the layers of the network each layer becomes an invariant in the construction of the layer above it. The higher layer must maintain this invariance (the law) so as to be able to maintain itself on a relatively error free foundation. So I try to manage the economic side of my life so as to have time and energy to spare for this work.
Feynman II 25-5: '. . . the 'length' of the momentum four-vector of any particle is just the mass of the particle squared
. . .
. . . the mathematics encapsulates a feature of the world that we need to understand, that is that time is in some ways the analogue and in other ways the inverse of space.
Feynman page 25-7: '. . . the electric charge density rho and the current density j form a four vector jmu = (rho, j).
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Local 3-space can be stored in three memory locations, mx, my, and mz , which are in no way coupled and may be changed with complete independence.
. . .
Feynman page 25-11 'It is because the principle of relativity is a fact of nature that in the notation of four-dimensional vectors the equations of the world will look simple.'
These are the equations of the observed world in 4-space.
But maybe there is a boundary between particles and fields because the Turing field is universal and logically invariant which the particle world exists in Lorentz space.
page 26-2: '. . . we can summarize all the phenomena of electrodynamics either by writing Maxwell's equations or by the following series of remarks. (Remember them in case you are ever on a desert island. From them all can be reconstructed. You will of course know the Lorentz transformation; you will never forget that on a desert island or anywhere else)'
2D SPACE-TIME == SPIN
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Feynman cont: 'First, Amu is a four vector. Second, the Coulomb potential for a stationary charge is q / 4 pi epsilono r. Third, the potentials produced by a charge moving in any way depend only on the velocity and position at the retarded time. With those three facts we have everything.
The Theology Company: Searching for new theological ideas to complement the worlds ancient religious traditions with a view to developing a common religion, thus facilitating peace on earth.
Life depends on trust. And who can we trust? By definition God.
Physicists can only talk about remembered (invariant) things.
Wednesday 18 March 2009
3-space allows rotation and translation. 4-space allows the same in four dimensions. We may see rotation as coupling, like gearing. Turing machines are cyclic in their operations, different processes working at different frequencies. Because the buildup of computable functions is recursive we find the simpler processes occurring at a higher frequency than complex processes. So, if the system is linear we can say (frequency x complexity) of operation is a constant.
Cross product and curl are specifically three space operations, and they are connected to rotation, that is something conserved going around a closed curve.
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Rotation seems more fundamental than translation since it is naturally expressed by permutation, although this implies the existence of memory units to hold the permutation and processes to change the state of each unit. In the physicalization of mathematics we must supply a process to explain the implementation of the formal assumptions of mathematics, that there are unique addressable states, for instance.
What I would like to say is that Lorentz invariance is explained by coding delay in an error resistant network.
Feynman page 23-5: t 2 - x 2 - y 2 - z 2 . . . is invariant under what is called the 'complete Lorentz group' which means for transformations of both translations at constant velocity and rotations.
'. . . since this invariance is an algebraic matter depending only on the transformation rules . . . -- plus rotations -- it is true for any four-vector (by definition they all transform the same).'
ALGEBRAIC <-- ARITHMETIC
ALGEBRA contains ARITHMETIC
ALGEBRA ==> ARITHMETIC (and vice versa?)
Lorentz invariant quantity (scalar, vector, tensor) has the same value in all frames connected by a Lorentz transformation, eg divergence, gradient, etc.
All this revolves around the interval invariant under Lorentz transformation. What does this mean logically? We begin with a time (and cause) ordered sequence of events and instead of annihilating an existing event to create a new one, we leave the old one
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one in existence and create a new one so we have two events existing in parallel, but with different lifetimes. So the lifetimes of all the sub-events of the universal event are shorter than the life of te Universe, L = Y - V = 0, but this equation allows us to increase T and V without limit, provided only that they are equal.
Lorentz invariant means doesn't know anything about Lorentz transformations, ie it reflects something that precedes spacetime, which must be action. Action bifurcates into energy / frequency and two further bifurcations give us spin and 4-space. So we want to derive Minkowski metric from network functioning. All we need to do is to introduce a delay on every link.
Thursday 19 March 2009
Love conquers all, as does gravitation.
The foundation of physical theory is the arithmetic of the integers. Now we ask, which comes first, algebra or arithmetic? Algebra is generalized arithmetic in the sense that the only values established for its symbols arises from the algebraic relationships of its symbols, so a = b says (algebraically) that a and b may take any values, subject to the constraint that a = b. a and b may be anything formally imaginable and the = sign points to one or more features shared by a and b which may be somewhere between the trivial) and a huge number, as when we say Alice = Bob, where the names refer to human being with individual personalities but a vast amount of molecular and physiological community.
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As we imagine the transfinite numbers, the value of a number like aleph(n) is not fixed but is constrained or defined by being greater than aleph(n-1) and less that aleph(n+1). This vagueness looks a little algebraic, insofar as we can treat each transfinite cardinal whose range is given by the inequality above. The transfinite cardinals do not overlap in this definition, they are distinct.
On the other hand, the greater are constructed from the lesser, so that although there is no overlap by definition greater numbers contain the lesser and in communication terms we say that aleph(n) is the [cardinal of] the alphabet for aleph(m > n). The distinction by inequality is a cardinal distinction. The unity by containment is an ordinal unity. Which is as it should be, since order implies both distinction and relationship.
As the particles interact, we wonder what is going on in their minds, ie their control systems, and whether we can ever get in there. The answer seems to be yes because we too are interacting particles and we just have to establish the invariant algebraic properties of interaction and see how they apply to every case of action. These invariants are provided by the theorems of Cantor, Hilbert, Gödel, Turing and Shannon
Rest length and rest time are also invariant, insofar as every observer observes the same in his own frame.
Action is relativistically invariant, meaning that an action viewed in any frame is just an action, like the snap of a
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switch, a change of state. The reality of logical states is relativistically invariant, and so we expect them to be coupled in some way to the invariant interval ds 2 when we expand the Universe to space-time.
Most of an atom's volume is 'empty space'. The size of this empty space is ultimately dictated by Planck's constant and the uncertainty principle. In other words this space is in effect the mapping of a logical operation into 3-space.
Particleadventure.org. 'Gravity affects matter and antimatter the same way, because gravity is not a charged property, and a matter particle has the same mass as its antiparticle. Particle Data Group. Lawrence Berkeley National Laboratory
'If matter and anti-matter are exactly equal but opposite, then why is there so much more matter in the Universe than antimatter? Well . . . we don't know.'
It is like we drive on the left. Let us say that the first bifurcation in the Universe is from unity to matter-antimatter. A matter-antimatter pair is made of pure energy and 'annihilates' to pure energy, ie a stream of action abstracted from any higher process.
Quarks - fractional electric charge; colour charge. Six flavours of quark.
Hadrons composed of quarks; integral electric charge, no colour charge. Hadron = {baryon, meson}
Baryons qqq, mesons qq overbar.
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'Because a meson consists of a particle and an antiparticle, it is very unstable. The kaon (K*) meson behaves lives much longer than most mesons, which it why it was called "strange" and gave this name to the strange quark, one of its components.
'A weird thing about hadrons is that only a very very very small part of the mass of a hadron is due to the quarks in it.' [the rest is die to the conversation between the quarks?]
Quarks are sociable and exist only in composite particles with other quarks, whereas leptons are solitary particles.'
Bifurcations - matter / antimatter - 'prequarks' - mesons. As the two 'prequarks' matter and antimatter differentiated into six quarks and antiquarks, the complexity of the structures that can be built from them (hadrons, mesons) also grew.
'Physicists have noticed that some types of lepton decay are possible and some are not. In order to explain this they divided the leptons into three lepton families: the electron and its neutrino, the muon and its neutrino and the tau and its neutrino. The number of members in each family must remain constant in a decay. (A particle and an antiparticle in the same family 'cancel out' to make the total of them equal zero).
Muon and tau unstable and rare. Electron and three neutrinos are stable.
[page 49]
'. . . electron. muon and tau numbers are conserved. These and other conservation laws are what we believe define whether or not a given hypothetical lepton decay is possible.'
Three variables | three constants | conservation
Conservation of matter means that if you make one thing you cannot make another thing.
'Because neutrinos were produced in great abundance in the early Universe and rarely interact with matter, there are a lot of them in the Universe. Their tiny mass and huge numbers may contribute to total mass of the Universe and affect its expansion.'
'What is the difference between a force and an interaction?'
'. . . Strictly speaking, a force is the effect on a particle due to the presence of other particles [ie the modification of a message by previous messages]. The interactions of a particle include all the forces that affect it, but also include decays and annihilations that the particle might go through.'
'At a fundamental level, a force isn't just something that happens to particles. It is a thing which is passed between two particles.'
[Work (in 3-space) = force x distance moved]
'One important thing to know about force carriers is that a particular force carrier particle can only be absorbed or produced by a matter particle which is affected
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by that particular force.'
FORCE = COMMUNICATION PROTOCOL = LANGUAGE (Physically embodied in bosons).
Residual electromagnetic forces: Electromagnetic force - Wikipedia
Strong force - colour charge - gluon. Strong interaction - Wikipedia Both gluons and quarks have colour charge. Gluon - Wikipedia, Quark - Wikipedia Photons, on the other hands, are not charged and so do not interact electromagnetically.
'Quarks constantly change their colour charges as they exchange gluons with other quarks.
Three colour charges, red, green, blue for quarks, anti-red, anti-green and anti-blue for antiquarks.
red + green + blue = anti-red + anti-green + antiblue = white. Colour is conserved and gluon emission and absorption always changes colour.
'Quarks cannot exist individually because the colour force increases as they are pulled apart.'
'If one of the quarks in a given hadron is pulled away from its neighbours, the colour force field stretches between the quark and its neighbours. In so doing, more and more energy is added to the colour force field. At some point, it is energetically cheaper [?] for the color force to 'snap' into a new quark-anti-quark pair. In so doing energy is conserved because the energy of the
[page 51]
color-force field is converted into the mass of the new quarks, and the color force field can relax back to its original state.'
The jump from energy to matter / antimatter seems to be the candidate for the first bifurcation. How does it relate to 2-D space-time, an earlier candidate?
We distinguish processes and frequencies of processes. A forbidden [impossible] process has frequency 0.
Feynman II 28-4: 'Poincare stresses' in an electron If everything has to be held together by something else we get an infinite regress. Better to hold together by being in a loop, a Lonergan 'scheme of recurrence' or computational recursion. Lonergan page 141
Processes are bound when one follows the other; ie they are seen to be connected. Binding and differentiation are closely related.
An interpretation of quantum mechanics.
At the heart of classical physics is the mapping of the algebra of vectors onto spacetime. Quantum mechanics has added the algebra of vectors in Hilbert space, and the trick is to couple these two systems and we hope to do it by showing that they both describe network structures of stationary action. (I can say the words but not yet do the deeds).
Residual strong interaction.
Weak force: [Particleadventure ] 'There are six kinds of quarks and six kinds of leptons. But all the stable matter in the Universe appears to
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be made of just the two least massive quarks (the up quark and the down quark), the least massive charged lepton (the electron) and the neutrinos.
'Weak interactions are responsible for the decay of massive quarks and leptons into lighter quarks and leptons'. [code optimization?]
In decay '. . . the resulting particles always have less mass than the original particle that decayed.'
'The only matter around us that is stable is made up of the smallest quarks and leptons, which cannot decay any further.'
'When a quark or lepton changes type . . . it is said to change flavour. All flavour changed are due to the weak interaction.'
Weak interaction = mass reduction [= less internal processing]
'The difference between the observed strengths [of the electromagnetic and weak interactions] is due to the mass difference between W and Z (80 GeV) and gamma [photon] (nil).'
Fermion vs Boson.
'If it can happen it will happen': the quantum mechanical tautology.
'When a fundamental particle decays it turns into a less massive particle and a force carrier particle (always a w boson for fundamental particle decays)' W boson then decays into quarks.
[page 53]
{become lighter, send message}
'Most particle processes are mediated by virtual-carrier particles.'
'Only the weak interaction . . . can change flavour and allow the decay of a truly fundamental particle.'
Annihilation --> force carrier --> new particles.
. . .
Particle accelerators produce snippets of code or process which are tiny parts if the continuing ongoing interactions of the Universe.
'Standard model lacks any explanation for a possible pattern of particle masses.'
'Why are there exactly three generations of quarks and leptons?' Because a fourth generation would be so massive and unstable as to be unobservable, ie so unfit that it cannot exist.
'We will need to extend the Standard Model with something totally new in order to thoroughly explain mass, gravity and other phenomena.'
Mass/ Higgs; Supersymmetry; String theory.
end of particle adventure.
[page 54]
Friday 20 March 2009
'. . . the law of motion in a gravitational fields can . . . be stated: An object always moves from one place to another so that a clock carried on it gives a longer time that any other possible trajectory -- with of course the same starting and finishing conditions. Feynman II 42-8
We have assumed a) that the space of quantum mechanics is 'logical' and outside space-time' and b) that particles emitted by quantum processes corresponding to the halting of a computation exist in space-time and have spent a week or two trying to understand how these two pictures fit together, ie what is the relationship between
LOGICAL SPACE and REAL SPACE (MTW). Misner, Thorne & Wheeler
Both spaces are self consistent, but there is long standing trouble when we try to combine them.
Feynman II 28-1: 'In bringing together relativity and Maxwell's equations, we have finished our main work on the theory of electromagnetism. But we want to stop for a moment to show you that this tremendous edifice, which is such a beautiful success in explaining so many phenomena, ultimately falls on its face.'
'. . . the classical theory of electromagnetism is an unsatisfactory theory all by itself.'
ie self contradictory, inconsistent or absurd.
[page 55]
'The concepts of simple charged particles and the electromagnetic field are in some way inconsistent.'
Aristotle and his contemporaries saw the future as attractive, the final cause that provides the psychological motivation for events along with the other causes, material (what it is made of) formal (its design, intended to achieve the end) and efficient (the maker, armed with materials, plans and motivation (either the final cause itself or payment from someone motivated by the final cause).
Statistical mechanics explains the attraction. There are more states in the future (since it is some permutation or combination of present events) so a thing changing state at random is biassed toward being in a future state.
3 SPACE is STATIC, FORMAL, MEMORY
(three dimensions are required so the netwok can be fully connected without interference [without one connection being noise for another].
4 SPACE is DYNAMIC and a binary Lorentz transformation can convert a pure timelike vector into a pure spacelike vector via the velocity of light, a 90 degree rotation in the {x, y, z } t plane. From pure energy to pure momentum.
All the trouble arises at the interface between quantum mechanics and 3-space (4-space). No, 3-space. An electron is a point in 3-space, a line (geodesic if free) in 4-space. A photon is a point in 4-space, ds2 = 0.
[page 56]
We meet at a point in space and time, the hall, 4.30 pm etc.
We can apply logic to the geometry of 3D space, which has given us 3D Newtonian vector calculus. But we cannot apply the geometry of 3D space to logic, which has its full implementation in infinite-D Hilbert (function) space.
4-D space is the cosmic communication interface between infinite dimensional Hilbert spaces like my own mind, the mind of an atom and so on. Ie spacetime is the serial link between large parallel memories.
Can we take literally the statement that the 'field is purely imaginary' (in the sense of complex) and must always be multiplied by its own complex conjugate to get real value?
There is no way I can expect other people to understand my story if I do not understand it myself. On the other hand, my partly digested ideas might give hints to others on the same track and together we will get there.
FAITH -- PAST
CHARITY -- PRESENT
HOPE -- FUTURE
Ie charitable action on past faith gives hope for the future.
The present is no more a point than a point in spacetime. I and my activities occupy a considerable volume of space and many of my tasks (like this one) take years and (like the houses I build) affect people for many decades.
Saturday 21 March 2009
What we may say is that it requires a significant volume of spacetime to represent a logical process like my life and this volume is necessary to maintain the signal to noise ratio that makes my life possible.
The point of contact between logic and spacetime is the event, and we have characterized an event as something observable in space-time which corresponds to the halting of a computation, ie completion of a computation of collapse of a wave function. An event, of its nature, is durable, ie exists through time or is a line in spacetime joining two points, like my life or the life of a proton. An event may be composed of sub-events and can ultimately be broken down to elementary events. All events mimic the creation of the world from pure energy in their own way. So underlying all elementary events is pure energy, the quantum mechanical representation of the initial singularity.
Always looking for the utterly convincing 'statement in a nutshell' or 'sound bite' that will turn the tide in my direction. Basically my starting point is the hypothesis that the human act we call insight and the quantum mechanical 'collapse of the wave function' are isomorphic events, and that observed events are the fundamental input both to our science and the whole management of our lives.
This article is an informal proof justification for this hypothesis based on modelling and observation. If
[page 58]
we assume the isomorphism we can conclude from the anatomy of the human brain that since network structure of the brain is the physical foundation for human insight [the network structure of the Universe is the source of its creative power].
The transfinite theory establishes an infinite hierarchy of complexity, the space between each integer being undetermined in line with the observation that aleph(n) + aleph(n) = aleph(n) = aleph(n).aleph(n).
The only function with the power to transcend the transfinite divide is the exponential, so we surmise that it is through exponentials that the dynamic Universe populates the formal transfinite tree. Why is it a 3D tree. Constrained by 4-D dynamics: time can fully express in three spatial dimensions (meaning?). First we write the sentence and then we explore to see why it makes sense [and if it is unfit (meaningless) , delete it].
. . .
Wigner: 'It is often said that the objective of physics is the explanation of nature, or at least inanimate nature. What do we man by explanation? It is the establishment of a few simple principles which describe the properties of what is to be explained. If we understand something the behaviour -- that is the events which it presents -- should not produce any surprises for us.' Wigner page 38
Maybe nature is so complex that it is incomplete and incomputable, and so will always be providing surprises for us.
[page 59]
To be overall incomplete and incomputable does not exclude the presence of complete and computable elements whose interactions are nevertheless so complex as to be incomplete and incomputable.
So physics sticks to the complete and computable.
Wigner page 39: '. . . the great success of physics is due to a restriction of its objectives: it only endeavours to explain the regularities in the behaviour of objects.'
And maybe rule out the possibility of certain irregularities.
Wigner page 39: '. . . the specification of the explainable may have been the greatest discovery of physics so far.'
Crombie Augustine to Galileo Crombie
Another succinct slogan that requires explication is 'the Universe is divine', which implies that we and all other observable events are subprocesses in the divinity.
Wigner page 39: 'The elements of behaviour which are not specified by the laws of nature are called initial conditions. These, then, together with the laws of nature specify the behaviour as far as it can be specified at all: . . . '
Wigner page 40: 'The surprising discovery of Newton;s age is just the clear separation of the laws of nature on the one hand and the initial conditions on the other.
[page 60]
The initial conditions are the messages which set the system evolving, either unitarily, as in quantum mechanics, or longest time / fastest clock as in gravitation.
'the rate at which field energy moves around in space' = the rate at which processing bandwidth moves around in space = the dynamic geography of action. Feynman II 27-5.
Wigner page 47: 'In quantum theory invariance principles permit even further reaching conclusions than in classical mechanics. . . . The reason for this increased effectiveness of invariance principles in quantum theory is due, essentially, to the linear nature of the underlying Hilbert space. As a result from any two state vectors psi1 and psi2 and infinity of new state vectors
can be formed.
Back to Streater and Wightman Streater & Wightman
page 1: '. . . the quantum theory of fields never reached a stage where one could say with confidence that it was free from internal contradictions -- nor the converse. In fact the Main Problem of quantum field theory turned out to be kill it or cure it: either to show that the idealizations involved in the fundamental notions of the theory (relativistic invariance, quantum mechanics, local fields etc) are incompatible in some physical sense, or to recast the theory in such a form that it provides a practical language for the
[page 61]
description of elementary particle dynamics.'
Streater and Wightman page 4: 'In the Heisenberg picture, each state of the system under consideration corresponds to a unit vector, say phi, in a Hilbert space H. The vector does not change with time, whereas the observables represented by Hermitian linear operators acting on H in general do.'
'. . . states of a physical system are represented by unit rays.'
Super selection rules: 'Any statement that singles out a certain unit rays as not physically realizable is called a super-selection rule. If there are super selection rules in a theory then not all Hermitean operators are observables.'
A room of one's own. This book is a record of a motion toward trying to understand motion, so the theory will be good when it can explain its own genesis, which is all that we need for creation.
Physics is in crisis and theology is dead and it may be that the resuscitation of theology and the consequent new understanding of physics may resolve the critical problems of physics.
The world is quantized at the physical level because logic is quantized at the deterministic level.
We act out our fantasies to see if they are qualified to become real, that is to be build upon invariant foundations in the physical world, like the strength of materials.
[page 62]
Streater and Wightman page 9: Among the most important symmetries of relativistic quantum mechanic are those which arise from the Lorentz transformations.
Slowly reaching critical mass, that s a self sustaining reaction whose gains scale as volume and losses as surface area.
From an observer's point of view, the Universe is quantized. Why? Error correction is inherent in every observation which transfers information.
In the days before gravitation (?) all motion was inertial. This is the 2D stage. So how does energy couple to itself? A by product of quantization, when space and mass enter the picture.
Wikipedia Stress-energy tensor: 'The stress-energy tensor is the conserved Noether current associated with spacetime translations.' Stress-energy tensor - Wikipedia, Noether's theorem - Wikipedia
'. . . in general relativity there is not a unique way to define densities of gravitational field energy and field momentum. Any pseudo-tensor purporting to define them can be made to vanish locally by a coordinate transformation,'
Zero 4-momentum = pure formalism? ie no change. The whole aim of physics is to explain motion and change, as Aristotle saw.
[page 63]
Noether's first theorem: 'To every differentiable symmetry generated by local actions, there corresponds a conserved current.'
We study motion by finding what does not move, the fixed points of the motion. Only those (as we say again and again) can be written down and remain true forever, or at least for a useful period.
Zero divergence of the stress-energy tensor in special relativity corresponds to conservation of 4 momentum in the special theory.
Noether's Theorem -- Ward Takahashi identities. Ward-Takahashi Identity - Wikipedia
Lorentz transformation works because communication delay is linearly proportional to distance, and in physics the constant of proportionality, c, is the same for all observers.
We attribute communication delay to coding delay so we cannot think of time (duration) existing without coding. We may still think of time in terms of order even if the delay is of zero duration.
Delay is duration, but Lorentz transformations are concerned with velocity, the ration of 'duration of space' to 'duration of time', so the minimal substrate for a Lorentz transformation is a 2D space-time.
Why does it take time to move through space? The logical notion is that space is memory and it takes much processing to change memory to mediate the progress of an object through space,
[page 64]
like moving a heap of bricks from a to b one by one.
Light, corresponding to a massless brick, moves fastest, with an infinite ratio of momentum to mass.
The formal constraints define the mechanism of the Universe, like bearings etc in physical machinery. Since information is represented physically, we expect to see the physical constraints that make the world like a computer network formally expressed.
Causality a) time ordered, any effect at all
b) size ordered: effect depends on energy and momentum seen by the
interagents.
space -- exclusion principle, resulting from antisymmetric wave function? Explained by antisymmetric wave function |2 fermion's in same state |2 = 0
States are differentiated logically which includes spatially.
Thinking time has no relationship to space outside my head, but the spatial relationships of my central neural network certainly control the speed of my thought from inside.
I am writing, hoping for more insight. But like collapses of wave functions, insights appear to be random events that cannot be forced by 'trying hard' or exerting greater force -- the response of insight to force is decidedly non-linear.
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