[ Sunday 16 October 1983 - Saturday 22 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.
...
[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. ...
...
[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]
...
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]
...
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.
...
[page 95]
...
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.
...
[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 ...
...
[page 100]
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.
...
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.
...
[page 104]
Feynman page 16-10:
probability amplitude propagates continuously along x, even though
electron may move in a smeared and irregular manner.
...
[page 105]
...
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.
...
[page 108]
...
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.
...
[page 110]
...
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.
...
[page 111]
...
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.
...
[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.
...
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]
...
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.
...
[page 117]
...
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.
...
[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.
...
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.
...
[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.
Friday 21 October 1983
Saturday 22 October 1983