Notes

[ Sunday 16 October 1983 - Saturday 22 October 1983 ]

Sunday 16 October 1983
Monday 17 October 1983
Tuesday 18 October 1983
Wednesday 19 October 1983
Thursday 20 October 1983

[Articles I DB25]

[page 79]

[Commentary on Feynman, Lectures on Physics Volume III Quantum Mechanics. Feynman.]

Feynman page 2-10: In classical mechanics, arbitrarily small errors (lack of information) in initial conditions lead to very rapid decay of information. In quantum mechanics, atoms last for billions of years - stable structure results from quantisation, eg Pauli exclusion principle.

...

Waves seem to act as a mathematical tool to get the right answer [in quantum mechanics], but they do not, as it were, appear in the end result. The ubiquity of periodic functions, however, is a constant characteristic of the Universe, and has a lot to do with its dynamic stability. Stationary in time = periodic. Fourier's theorem.

[page 80]

Conservation of information. In a Universe with no memory, to pass on a bit of information is to lose it, so once an electron has admitted to the world [in the two slit experiment] which slot it went through, that information is no longer available to make an interference pattern. Same with flipping [spin of] neutrons, etc.

periodic = nothing happening = stable = rhythm = energy

Feynman page 3-9: There is more to wave mechanics than waves, eg spin states, boundary conditions in general.

Waves are characteristic of a state and show how closely that state can be defined in space and time. Perhaps Fourier transformations and superposition are misleading mathematical artifacts when it comes as an attempt to define events by waves. Although they are properties of waves, eg transients in music etc. So we have fundamental frequencies, harmonics and transients. It is in the transients that change, information and intelligibility lie.

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[page 86]

Feynman page 5-10: ...

The information obtained by an observation is equal to the entropy of the observed space before observation less the entropy after observation. This is recognised explicitly by nature in quantum mechanics. So to extract information [about which slit the electron went through] from a two slit experiment is to 'collapse the wave function' thus preventing interference phenomena further on. If the system is to be stable, the information obtained must be fed back in. At the atomic level, the world has no memory. Chaos can be created by absorbing information and not passing it on.

In the Stern Gerlach thought experiment, the beam is put together again after it has been taken apart - the information separated out is fed back in again. We postulate that this is the basis of the stability of the Universe - there are structures that set themselves up so that there is a stable dialogue (polylogue) within itself, without errors - hence the importance of coding, and that is how a structure as amazingly complex as ourselves could be made out of n, p and e [neutron, proton and electron]

page 5-11: A complete set of base states transmits all the information. it is a channel whose entropy (variety, capacity) is sufficient for/equal to the entropy of the source driving the channel. ...

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[page 88]

All explanation is setting the context for the next sentence, a is b, which in turn becomes the context for c is d and so on. We are trying to find it in science, so we beat around the bush looking, but we are creating it ourselves as we do it ourselves. Meaning relates to the nesting binary, nesting perhaps of context after context. The broader define the finer, but have something added to them in the process. So each word in a

[page 89]

is like each digit in a binary number, adding entropy and precision at the same time. As you define each thing, you increase the possibilities [since possibilities] are defined by actualities, each showing the size of the other. An actuality with 2n possibilities represents information of entropy n; even though the 2n - 1 things did not happen, they are the matrix out of which what has happened has come, and in this sense non being defines being, as white space defines the written word. No yin without yang. Yin is female is entropy, the sea of possibility, mother of all, and yang is male, the realised one, the form out of the sea of possibility which by its being defines that possibility and stands poised to take another leap into more precise definition, or better, greater complexity, thus defining an even greater sea of undefined space. A hydrogen is one of a small number of arrangements of nuclear particles. A human being is one of a very much smaller number of arrangements of 1025 or so atoms. 1025 binary choices can define 2 raised to the power of 1025 + 1 possible binary numbers, an exceedingly great quantity. The sort of number we find in statistical mechanics ...

[page 90]

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What is it happens to a child as the words that look just like weird scribbles on a surface to a baby slowly become an instantly meaningful and engaging stimulus after a long enough apprenticeship. We crave communication, above all from our own kind, although we dig trying to get to know the things before us because we are only setting out on the voyage of conscious discovery of ourselves. Everything we learn is a little bit of self. I feel quantum mechanics in my bones as I feel the universal cosmology. Microcosms is what we are, and we're right into ourselves as some sort of pinnacle, not of size or of power, but of density of information.

Cuddle each other, communicate, that is what makes us one, differentiates us into a new superorganism that could be made in 2 to the tenth to the tenth factorial different ways, maybe.

Feynman page 5-11: 'In a certain representation". Ie base states are arbitrary, the structure lies in the relationships between them, just as spatial structure depends on the spatial relationships of its components. .

[page 91]

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Friday 21 October 1983

Feynman page 5-11: 'If you have a base state, then the future is independent of the past.'

Page 5-12: 'One of the great games of quantum mechanics is to make use of the fact that things can be calculated in more than one way.

[page 92]

Feynman page 6-2 cultural excursion:

'Only when we try to make specific models of the internal machinery of the fundamental particles and their interactions are we unable to find a theory that agrees with experiment.'

[page 93]

Feynman Chapter 7: Dependence of Amplitudes upon Time.

Feynman page 7-1: 'An atom does not stay excited forever because it manages to dissipate the energy by interaction with the electromagnetic field.'

Radiation and absorption go in the direction of increasing entropy.

page 7-2: for an atom at rest, the quantum mechanical amplitude to find an atom at a place is the same everywhere, but depends on time. ...

definite energy => definite momentum=> infinite positional uncertainty, or putting it another way, to be anywhere in the Universe requires a definite rest mass.

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[page 95]

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Quantum mechanics talks about the matrices of probabilities to go from state to state. The size of these matrices depends on the number of base states, 'Communication mechanics' will concern itself with the information flow involved in a given transition, and will see the base states as the context, defining the entropy for a particular situation. The amplitudes for a system to be in its base states defines an entropy for the state of the system.

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[page 96]

Feynman page 8-6: 'The main problem in the study of fundamental particles today is to discover what are the correct representations for the description of nature.

In low energy interactions, we do not have to look inside things - they can be specified by such things as momentum and spin ...

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[page 100]

Saturday 22 October 1983

Universe is rather like a set of nested pinball machines. All the pins and flippers etc define a set of expectations for a particle moving in the machine. Each of them in turn is defined by a set of expectations of a previous context, and so on.

[page 101]

Feynman page 16-3: 'If we consider any two states | phi > and | psi >, the amplitude that the state | psi > will also be in the state | phi > can be found by projecting the state | phi > into the base states and then projecting from each base state into the state | phi > ...

No time here, just a superposition of states whose structure is in some way exposed over time, as are the properties of a source, or a person, or anything else. There is a lot more stored there than is available at a given time. A source must be observed over time to see its whole structure. It can be thought of as a memory full of stuff which takes a certain time to go through its act. So source has an entropy per character given by total entropy/total characters, ie entropy per character may be one bit, memory capacity 64 kilobytes.

A superposition of states may be thought of as a sort of story that is told letter by letter as each state is realised. Thus a superposition of different energies defines a group velocity which behaves like a classical particle. The story is - something is moving along here with a velocity proportional to momentum/mass.

[page 102]

Each Hamiltonian, with its statistical properties, is like a language, with its statistical properties, which is recognisable to a given listener. Physicist studying a language without understanding it could give all the transition probabilities without realising what the sequence of actual transitions (as in this writing) mean.

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page 103: 'amplitude per unit time for a jump' ...

in the limit, ... the amplitude for a jump, multiplied by the length of the jump, becomes the constant h/2m. ...

Schroedinger's wave equation. Represents propagation of a probability amplitude from one point to the next along a line. Each point on the line is a state, a basis vector so to speak, so communication from point to point is like communication between states.

The concept of distance is explained by amplitude and not vice versa. Coonabarabran is far away because I never go there.

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[page 104]

Feynman page 16-10:

probability amplitude propagates continuously along x, even though electron may move in a smeared and irregular manner.

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[page 105]

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Feynman page 16-13: Birth of quantum mechanics dates from Schroedinger's equation, 1926 ... . In principle this equation can describe all phenomena except those involving magnetism and relativity.

[page 106]

Feynman chapter 17: Symmetry and Conservation Laws.

In quantum mechanics conservation laws are closely related to the superposition of amplitudes - theorems about conservation of all kinds of things are related to the symmetries of the system.

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[page 108]

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Bonding comes from swapping electrons. The swapping state has lower energy than the electron at either of the actual atoms. Here it is exactly communication that lowers the energy.

Energy difference comes through as bandwidth which in turn defines precision with which things can be located in space and time.

A given set of base states is continually being occupied - this is commonly expressed as oscillation in two state systems. It is this process which at once defines the two states and connects them together and defines also their context.

[page 109]

Simplification in physical studies usually results by ignoring a large selection of states as either being lower or higher energy than we are interested in.

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[page 110]

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From the world's point of view everything matters, and it is arrogant of us to abstract from detail for physical purposes and then to act in practical situations as though this information was not important. We must take care of the consequences of our deliberate pullback.

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[page 111]

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To understand is to remember.

What are the actual constraints imposed by quantum theory, and are they any greater or less than might be imposed by information theory? Can it be shown that these two theories are isomorphic?

A stationary state may be thought of as a stationary source, which in the course of a long message will approximate to its statistical entropy, which is given by the piei or some other characteristic. Energy, momentum, spin etc are representations with their basis vectors, with operators operating on the bases to give different results.

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[page 112]

So we go to Quantum Mechanics and Path Integrals by Feynman. Feynman.

Feynman page 2: Probability in quantum mechanics - new laws of combining probabilities; the concept of probability is not altered.

page 9: Uncertainty principle: Any determination of the alternative taken by a process capable of following more than one alternative destroys the interference between alternatives. ... [This] says something about the calculation of amplitudes by different paths, which carry on just like waves, hence the concept of carrier fields. But the wave equations are quite deterministic. It is in the interpretation of the results that the trouble comes, and it is here that Everett comes in with his information theory as an interpretative device, showing that to an observer the Universe is uncertain. But each system is an observer of every other. Communication is what it is all about, and bandwidth limitations must be intrinsic to the whole thing. Also, if the same rules go all the way in, this will be the situation right back to nothing, so to speak.

The uncertainty principle preserves the probability wave approach by making it impossible to get better observations that the theory, so to speak, and thus contributes to consistency.

[page 113]

One cannot determine where a source is at in any better detail than the information which the source is emitting. Ie the most you can learn from me writing is limited (as you watch over my shoulder) by the rate at which I am writing. You can have no certainty about aspects of my dynamics which I am still getting round to describing. A complex system like me has so many superposed internal states that it will take a long time for me to put out the full entropy through such a narrow bandwidth. It is no use knowing more than you can write down in a lifetime, or, the more you know the more need you have of coding to get it across efficiently. Each particle is presumably going on with its internal life between words to the outside, and its internal bandwidth, responsible for its structure, will be very much wider than what it has got to say to the outside but coding will make it possible to expose it all in the right context.

page 14: Interfering = interacting = communicating = relating alternatives require wave functions = indistinguishable = same code = same quantum numbers etc.

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page 16 All particles are either bosons or fermions.

Identity of particles is sharply defined in quantum mechanics, not in classical mechanics, and is clearly determined by their interactions. All electrons are as same as it is possible to be [yet they are distinct]

180 degrees out of phase = opposite, 1, 0.

[page 114]

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Feynman page 21: Path integral concept generalised from holes in screens.

A communication theory of quantum mechanics will be applicable to everything else, and vice versa. So we can freely use analogies from people, telephones, computers, communication theory and anywhere else we can find it.

We have two things: 1 specifications of channels etc; 2 meaning to be sent through them.

In the search for 2 we are looking in a way for a theory of meaning and its generation in this Universe, so what we are dealing with is more in the nature of metaphysics than specific scientific theory, but it, hopefully, a metaphysics that will plug directly into science and put the whole intelligent Universe in perspective.

[page 115]

Feynman page 56: Event, like passing through a slit, causes loss of memory for particle. We postulate that the Universe has no memory, but must do so by communicating with itself, which process is compromised by interacting with the slit, etc.

[page 116]

Because mathematics is logical and deterministic, it inputs nothing new, and we can go round and round in circles arriving at the same results by different roots and going from one point to another in logical space (relationship space). We continue to postulate an isomorphism between mathematics and the Universe, but are not too happy about the widespread prevalence of infinite processes, yet. The wider the slit, the more information can get through.

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[page 117]

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Different mathematical approaches to the same physics may have different transparency and ease of calculation. A lot of this has to do with choice of representation. I suppose that what we are doing is saying that of we look at the world from the right point of view it will look simpler than from any other point of view, and the fact of this simplicity will confer a wider grasp. The hypothesis is that the Universe is above all an information processor, not an energy processor, and that an information theoretical representation will fit the facts far more happily than any other approach to date.

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[page 118]

Feynman page 76: Schroedinger description of quantum mechanics: 'In almost every case it is easier to solve the differential equation than it is to evaluate the path integral directly.

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page 82: In all cases of quantum mechanics, the Hamiltonian is Hermitean.

page 84: Periodic solutions of wave equation are independent of time and have a definite energy. ...

page 86: Two (n) states of definite energy are orthogonal, and may be used as basis vectors for linear combination solution of wave equation.

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[page 119]

Chapter 5: Measurement and Operators

Feynman page 96: What is the ultimate measure in the Universe? Energy, momentum, entropy, information, complexity, being? [action?] The only legitimate system must take the whole into account. it must be relative., it must be intelligibility if Lonergan is right. Lonergan. So our hierarchy must be energy, information, complexity, programming, ... intelligibility.

page 105: Transform from one representation to another is just the Fourier Transform.

page 230: 'Almost all the effort in quantum field theory is devoted to solving the classical equations of motion, an activity completely within the realm of classical physics.'

page 231: crystal vibrations = phonons; electromagnetic vibrations = photons; meson field theory = mesons.

Fields quantised as modes of harmonic oscillators are called Bose particles.

page 232: Excitation or deexcitation of harmonic oscillators corresponds to creation or annihilation of particles, and this is the way particles are represented in relativistic quantum field theory.

[page 120]

Feynman page 244: ground state = lowest possible energy = vacuum state, is that in which thee are no photons in any mode.

page 245: cutoff rule h/Mc (M = mass of proton) = 2 x 10-14 cm = 1024 Hz. Given this, the mass of the vacuum state is 2 x 1015 grams per cubic centimetre.