Notes
[Notebook: DB 59 Draughts]
[Sunday 18 June 2006 - Saturday 24 June 2006]
[page 22]
Sunday 18 June 2006
A symmetry is a path from a to b which can be expressed by a function much simpler than a random (maximum entropy) path from a to b. The path integral method is a way of picking certain paths out of all possible paths by adding up little arrows [ie complex numbers].
QED Feynman
Zee page 9: 'Feynman followed Newton and Leibniz. Take a path; approximate it by straight line segments and let the segments
[page 23]
go to zero.' Zee This works in any continuous space. Now what the physicists say is that what goes on in the complex continuous space of quantum mechanics determines the probabilities of the events we see, . . .
Weinberg vol I page 51: '. . . a symmetry transformation that is infinitesimally close to being trivial can be represented by a linear unitary operator that is infinitesimally close to the identity U = I + iet, with e a real infinitesimal. For this to be unitary and linear, t must be Hermitean and linear, so it is a candidate for an observable. Indeed most (and perhaps all) of the observables of physics, such as angular momentum arise in this way from symmetry transformations.' Weinberg
Fundamental of computing #1: a place for everything and everything in its place. Then the computer can compute addresses as well as operating on the materials that it finds at those addresses. Often the results of the latter computations are an input t calculating the next address.
Infinite (definition): you can always add another one. This does not mean that it is already big. This feature of infinity seems very helpful when it comes to understand the question of knowledge.
So we go via a well known network (the internet) through the transfinite numbers to a new look at gravitation.
Mine is a fides quaerens intellectum : I want my dream to be true.
[page 24]
Monday 19 June 2006
Veltman page xi: 'Perturbation means Feynman diagrams. Veltman Ie little fragments of a network, different nodes, . . . .
Veltman: 'There are formalisms that in the end produce the Feynman rules starting from the basic ideas of quantum mechanics. However, these formalisms have flaws and defects, and no derivation exists that can be called satisfactory'.
'Feynman rules have a true physics content and the physicist must understand that. 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.'
Weinberg: '. . . particle are introduced . . . as ingredients in the representation of the inhomogeneous Lorentz group in the Hilbert space of quantum mechanics.' In other words (perhaps) they are messages/messengers.
Shannon : Orthogonal = distinct, no mixing.
Tuesday 20 June 2006
We owe what we are at a certain level of probability to our ancestors, so respect for our ancestors is well placed.
[page 25]
Wednesday 21 June 2006
Let us guess that the succession of religions, like the succession of all other recursive (evolving) events, arises by giving new meaning to old symbols. Genes duplicate and evolve apart as their products catalyze some new process that confers added fitness (like being able to combat a wider range of infections).
Deo volente; in'sha Allah. At the moment I want to visit my sick daughter, but my car won't start. it is an intermittent fault that we have not been able to trace for six months, an apparently random event that occurs about only every ten starts. To start every prerequisite for starting must be fulfilled. In this case we have spark, fuel and timing.
Thursday 22 June 2006
Friday 23 June 2006
The official theology of the Roman Catholic Church serves as our classical or I might say Newtonian theology. Newton obtained his picture of the world by making certain simplifications. First the whole Universe is in the hands of God, who makes it move as it does. Our quest is to see and understand the harmonies in the works of God, helping ourselves by standing on he shoulders of giants.
[page 26]
..
The rest frame of light is the frame in which it is emitted ad that in which it absorbed, regardless of the relative motion of these frames.
Energy is conserved in the creation of structure, ie in the conversion from kinetic to potential energy. But what is the total energy of the Universe?
A convenient conclusion is that total energy = Potential Energy - Kinetic Energy (say) and that PE = KE so total energy is zero. What does this mean in communication terms. A message in motion has KE, dead in memory, it has PE [?]
Feynman and Hibbs page 23: in relativistic quantum mechanics 'the probability amplitude is a kind of hypercomplex number. Feynman and Hibbs
page 26: classical action, S, is minimized by the path actually taken by the particles, ie minimum cost [measured in action] So we say that action = money, energy = 'cash burn rate'
Classical Lagrangian: . . .
[page 27]
In words: the time rate of change f the difference between kinetic and potential energy (L) of a moving particle is equal to the rate of change of L with respect to position.
ie 'acceleration of Lagrangian = rate of change of L with position.
Lagrangian of the Universe has no position and so (?) no change in time, consistent with a value of zero.
. . .
