Notes
[Sunday 20 January 2008 - Saturday 26 January 2008]
[Notebook: DB 62 Interpretation]
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Sunday 20 January 2008
From a physical point of view (which ignores meaning) communication is the exchange of energy. It nevertheless remains true that all information is encoded physically, so the exchange of energy is accompanied by the exchange of particles. In spacetime we measure energy as force times distance, but we may speculate that energy antecedes spacetime and is therefore a function of time alone, ie E = h nu where frequency nu is inverse time. With the advent of space we introduce momentum the spatial analogue of energy. The coupling between space and time is velocity and so in physics the relationships between space, time, momentum and energy are captured by the special theory of relativity. Since quantum mechanics is explicitly concerned only with energy and time, we find that special relativity is directly connected to quantum field theory that arises
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from quantum mechanics when we try to extend it to [space].
Our current standard explanation of our physical experiences of the world is expressed in two theories, general relativity and quantum field theory. The latter is the combination of special relativity and quantum mechanics. General relativity has yet to be satisfactorily explained in quantum mechanics
From the point of view espoused here, quantum mechanics may be understood as modelling the natural line along the lines first glimpsed by Cantor.
The physical line in our Universe is parametrized by time. Quantum mechanics is parametrized by energy, in the form of the Hamiltonian matrix which described the energy flow between the states of a system as time goes by. Even though we speak of time machines and time travel, all our experience point to time as something marked by an irreversible string of events that joins the moment of our birth to the moment of our death. It is this chain of events that quantum mechanics describes (not in detail, because the future is formally unpredictable) but as a set of probabilities which we interpret as a rate of traffic in the universal network. We may join [joined] this network with our scientific instruments and observed its behaviour as we developed the standard model.
Our study of physics is the study of timelines. While things live, their timelines have a sort of mathematical
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certainty that takes sudden jumps at moments of birth and death whose probability is expressed in creation and annihilation operators. In the fundamental particle world we have a relatively small number of fixed entities like the electron, photon, proton, neutrino etc each of which has a fixed personality and which interact in ways well specified by experiment and well matched by theory. The personalities of the particles, in other words, determine the way they act. Because they have such fixed personalities, the general structure of their nature and interactions becomes more and more precise as we learn to make subtler and more frequent observations.
Euclid first proposed a model for the geometric line.
Quantum field theory brings memory and meaning into the structure of the Universe, so that as well as a completely unconstrained flow of energy, as in the Hamiltonian of a one state system, we begin to develop 'historical' (spatial) constraints that introduce relativity, particularization due to stable communication and the world we experience now.
It is written, and to change it requires energy. Now that I have written it down (ie put it on the stack) I can safely go and do something else (respond to a telephone call) and then come back to where I was at a point in the future, Writing (ie space) in other words, establishes connections between various points in the time line.
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INVARIANCE
Claiming that quantum mechanics is indifferent to complexity shows it is indifferent to frequency, so that just as the formalism expressed by the equation psi = exp (i H t) is invariant with respect to H it is invariant with respect to H and t, where e and i are 'universal constants' something formally invariant.
We now introduce space, memory, frequency, cardinality ad constraint. A low frequency event may serve as memory for a high frequency event. We see space growing, so there is no doubt about the fact, just the explanations.
As energy splits, so frequency splits and space is automatically invented.
In a world with a time dimension alone, as described by quantum mechanics, no two things can really exist simultaneously, since some sort of space is needed to distinguish one from another. We shall take this to be our definition of space, so that a spacetime becomes by definition a space that can maintain two independent states simultaneously.
As Einstein noted, this definition immediately gets us into trouble because we cannot satisfactorily decide what simultaneous means and must accept the existence of two independent times, each corresponding to a given
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point in space.
phase space and time
pays 08 velocity, acceleration and gravitation.
The big problem in physics (see Veltman) is mapping from Hilbert space to real space and back, particularly when relativity is involved. Veltman
Monday 21 January 2008
Tuesday 22 January 2008
Memory, space, particles, velocity and relativity all come into existence at once by an act of universal insight analogous to human insight as described by Misner Thorne and Wheeler. Misner, Thorne and Wheeler Memory, that is space, endures through time, in other words it does not change while something else does. So an event with a period it acts as a memory relative to an event with period t.
We may accept on the grounds of observation that memory exists, and the relativity induced by velocity connect past to future using null geodesics. Without null geodesics we would have no knowledge of early states of the Universe, but the price we pay for photonic contact with ancient phenomena like the source of the cosmic background radiation is great distance. So the size of the Universe is a prerequisite for observing its history. Photons are in some way the first manifestations of memory [they are outside time] From an evolutionary point of view we guess that there must be some selective
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advantage of spacetime over pure time. Since complexification is meaningless without memory (since a system cannot be complex without some way of recording its details), and quantum mechanics is indifferent to complexity, quantum mechanics is our route from simplicity to complexity.
Quantum mechanics, like the Trinity, complexifies by observation or knowledge, since he Hilbert space of an observed / observer system is the tensor product of the Hilbert spaces of the observed and the observing systems. Given complete symmetry and the postulates of quantum mechanics, we can say that each observes the eigenvalues of the other. [(iii) immediate repetition of a measurement yields the same outcome; (iv) measurement outcomes are restricted to an orthonormal set { | si> } of eigenstates of the measured observable'] There is no limit to the complexity of this paradigm, but the logical starting point is a one state system ('the classical god') which observes itself and becomes a two state system (the procession of the Son from the Father).
We take such a two state system to be an embryonic spacetime, a fertilized spacetime egg which has two poles distinguished by the fact that one is not the other , something that we may model as a qubit with to equiprobable states, q = |0> + |1> / sqrt 2.
Since we now have an elementary spacetime, we should be able to find the velocity of light and special relativity in here, or do we have to wait till our egg grows to four cells, a two state electron and a two state photon? Special relativity us as indifferent to the velocity of light as quantum mechanics is indifferent to complexity, but, since we postulate delay in error free communication, we guess that the minimum delay is connected with the simplest communication, so the velocity of light is imprinted upon the Universe at some very early stage, when the thing is just complex enough to exchange photons.
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A bit later on it gets complex enough to exchange gravitons (in four space) which also travel at the maximum velocity but that is all. All subsequent particles are subsets of the Universe, having some sort of independent internal process (mass) and travelling at less that the velocity of light, beginning with neutrinos.
We can introduce the evolutionary paradigm at the two sell stage, since two one state systems place very few a priori constraints on their interactions and so the appropriate basis for their interaction can only be determined by 'experience', ie after sufficient efforts to communicate with one another, they develop a common language just as people (and everything else) do.
Uncertainty is introduced into a network of deterministic Turing machines by the fact that they are independent and so one cannot control the behaviour of another. If we imagine an electron as a two state machine (spin 'up' and spin 'down') while the transition from up to don may be deterministic, in the network context the electron may communicate its state at random points in the global process and so is described as probabilistic. In spatial terms, a 2D system does not carry enough information to determines its orientation in a 4D world and so its orientation (as decided by itself) is undetermined even though it may be determined by some more complex system (like a ferromagnet) (see notes 20? May? 1999. notesM06D27
We place our 1 state system at the origin. When this
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splits into two states, we put one at +- 1 (1 unit of space) and the other at +- i (one unit of time) so that the interval between the two states remains 0, although now their clocks are 90 degrees out of phase and they are 1 unit apart.
Why is probability | psi |2 and distance measured by a quadratic form ds 2 = (i dt )2 + dx2 ? Why is | z|2 = z zbar ?
A one state system is simply a clock represented by psi = exp (it ) When we move to more states, we get psi = exp (iHt ) where H is now a matrix of any size we like, subject only to normalization. The Hilbert space of two one state systems us two dimensional, the world of the qubit. A qubit then is two clocks observing one another. They may operate at different frequencies but we assume an event occurs only when they are at the same phase, so the observed frequencies are integral multiples of one another.
Is ordinary space four dimensional because a Turing machine is four dimensional or because we can wire all points in four dimensions together without our wires intersecting one another>
As we can see from Veltman and others, it is very hard to create a logically satisfactory combination of quantum mechanics and special relativity. The difficulty seems to lie in the union of Hilbert space and 4-space. On the approach we are taking here, we are in effect talking Hilbert space all the way, where the Hamiltonian is interpreted as a matrix of network traffic. To introduce space into this matrix is to introduce memory and delay, ie changes of phase which are linked to space-time distance between
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nodes in the network. The phase-distance relationship is encapsulated mathematically in the concept of momentum.
The problem with quantum field theory seems to be similar to the problem with the Christian god. In the first case we see ourselves as living in a four space which is somehow outside Hilbert space and so we need big complex transformation to map from one to the the and we cannot observe Hilbert space. In the Christian case, we are outside God,m so that god is a mystery to us and we need a tenacious and baroque fiction of revelation and Churches to couple us to the divinity. Here we see ourselves as inside the Hilbert space of the Universe and inside god, and we hope to exploit our insider status to get a much clearer and simple view of ourselves and our environment.
Every observation is within a Universe which includes the observer and the observed. The Hilbert space of this Universe is the tensor product of the spaces of the observing systems. This Universe (being isolated) evolves unitarily. Within it, however, the individual systems think they observe collapses of the wave function in eachother and receive signals from eachother as a result.
EROTIC LOVE vs PLATONIC LOVE
Trading in the market (and feeling the pleasures and pains) vs studying the market and observing other people's pleasures and pain. Australian Stock Exchange down 6% on about
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its tenth straight fall. A buyer's opportunity.
There are no outside observers in real life. The market watcher will have his or her own erotic connections.
The problem with field theory is that it takes fourspace as given (as its domain) and writes all its functions on this domain. Fourspace is treated as a continuum, a container for physics in exactly the same way as Newton used it. Einstein did not really change this picture with the special theory, he just introduced a new combined space-time metric to replace the independent metrics and space and time that Newton used. The general theory, on the other hand, made space a player in physics instead of just being the playing field. This insight must also hold for the 'flat' subsets of curved space defined by the Minkowski metric, which locally approaches the Einstein metric as we consider more and more diffuse systems of energy.
Among the functions mapped from the spacetime domain are potentials. We consider here that like the gravitational potential, these potentials are not in space, they are space.
Space is the theatre of observation so we expect it to manifest itself as an intrinsic part of the Hilbert space of observation, that is in the tensor product space of observer and observed, So how do we find a Minkowski metric inside the Hilbert space of observation?
Maybe the network interpretation of Hilbert space will show us how.
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Modern physics has achieved vast numerical agreements while fundamentally misunderstanding the world it studies.
We should be able to use the network to see how the path integral method is naturally relativistically invariant - because it does not map from spacetime?
Veltman physicist: 'He/she must know how Lorentz invariance, conservation of probability, renormalizability reflect themselves in the Feynman rules. In other words, even if there is no rigorous foundation for these rules, the physical principles at stake must be understood.' Veltman
Classical mechanics works in a space with six dimensions per particle, three for position, three for velocity. Time enters as an element of velocity, rather than in its won right. The Hamiltonian is a phase space where time appears explicitly as energy, E = t-1 where t is the lifetime of a state. What is the energy uncertainty of my 60 year lifetime?
A Lorentz transformation is a rotation (or reflection) in four-space. We can imagine a simplified form in 2-s[ace with a - + (or + -) metric, dS2 = +- (L2 - T2), S is an interval with dimensions of what? Action?
Space is a player whose shape encodes potential energy which guides the rate of communication between different points. So we can map a Hamiltonian straight onto space, attributing a different potential to every pair of points listed in the matrix,
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The metric in 4-space is the most abstract and 'continuous'. Reality is in no way continuous except at scales large enough to smear out all the detail, like the assumption that the Universe is homogeneous and isotropic. In fact it is an extraordinarily complex tree (at the level of the current leaves) but the root is very simple, and it is the root (the hardware) that physics studies. Theology, on the other hand, is primarily concerned with the upper branches and leaves of the cosmic tree,.
THE COSMIC TREE
Part of the tensor product is the straight product of the two subspaces and part is the entangled product. The separable part of the tensor products retains the independent specification of the spaces to be multiplies. This is the way two=space and 4=space remain visible and operative in all the more complex Hilbert spaces of the Universe.
All interactions occur by contact, that is in a local frame common to both interagents. This may not be the laboratory frame and so we have to transform what we see into what is going on in the interaction frame. Since the laboratory frame and the interaction frame, insofar as they are in contact are in the same Hilbert space, all this goes on in that space, which is a unitary Universe.
Lorentz rotates between space and time so that we can say that it converts space into time and vice versa, but not in
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the local frame, only between relatively moving frame.
So it opens up channels that might otherwise be closed, shifting the eigenfrequencies of a moving atom, for instance, so that it can interact with an atom of a different element in a different frame, - redshifted etc.
Wednesday 23 January 2008
Insofar as space is static memory, it is observable, like this writing. It serves as a sort of user interface for all commnication with the Universe.
A Universe is a closed system comprising a set of elemental Hilbert spaces communicating with one another (observing one another) in their mutual tensor product space. The observations are real to the participants, even though we model the Universe as a complex unitary evolution. The communication operators are Hermitean with real diagonals.
Systems communicate with one another sporadically. at a rate which measures their closeness. So lover may be in almost constant contact whereas some pairs of people never communicate. The rate of communication is a metric for the coupling between systems. Between communications (while they are thinking) physical systems are held to evolve deterministically and so maintain 'logical unitarity', ie become a logically continuous path through state space.
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A chain reaction is a many branched logical continuum, each step sending messages that initiate more tan one repetition of itself.
Interesting news passes by chain reaction, each hearer telling many.
The distinction between the quantum and classical world is false. There is one world, either keeping to itself or talking to others. The dichotomy was perhaps necessary because insofar as we communicate we live in the classical world, and it has been difficult to get a grip on what is going on, the meaning placed by sources in their communications.
But, we keep asking, if the global process is transfinitely complex, why is the interface so simple, $D, 4 serial channels. This is some sort of leftover from the first moment when the whose Universe was simply four dimensions (channels) of communication. Independent channels, ie degrees of freedom.
Structure of 4-space described by spinors, spin 2.
The tensor product spaces exist as long as the elemental spaces are interacting and deconstruct when the communication is over. A meeting. A party. The physical layer, represented by 4-space, never dies, except maybe in a black hole.
Lorentz transformations are equivalent to rotations of inertial frames in spacetime relative to one another. From
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this point if view, all inertial frames with the same velocity (ie zero relative velocity) have precisely the same orientation whereas frames with relative velocities are differently oriented.
These changes in orientation feed into quantum mechanics as changes of phase, which appear as changes in the superposition is we are superposing states with different relative velocities.
Thursday 24 January 2008
Light cone is a boundary on communication, and so events outside eachother's light cones are independent (or free) Universes.
Momentum, being a 3D vector, carries more information that energy, a 1D scalar. Between them they carry all the information that can be encoded (at a point) in 4D spacetime. [but not position]
Friday 25 January 2008
Let us say that a photon is of itself a one dimensional entity that can be parametrized simply by energy. We now introduce it into a 2D space-time so that it can have position as well as frequency. Then we put it into 3D spacetime, where it can have polarization. Finally we put it into 4D spacetime.
At the root space and time are formally identical, simply one is not the other?
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Each element in a two state system is a source from the point of view of the other, emitting a signal which reveals its internal state to the other as receiver. The probabilities of emission (as measured by the receiver) are normalized as we would expect from an information source, and this normalization applies to the message as seen by both transmitter and receiver, and so we say it is real, a real number expressing an integral or sum of probabilities.
Each transmission correlates the state of transmitter and [receiver].
