Notes
Sunday 31 July 2022 - Saturday 6 August 2022
[Notebook: DB 88: Salvation]
[page 131]
Sunday 31 July 2022
I can't join every dot. Reading is a creative process. Finish cc24_chromodynamics
Monday 1 August 2022
Revise cc23_quantum_field
[page 132]
Football as an analogue of the picture I tried to paint on page cc18_trans_minkowski. We have a lot of particles moving around in an analogue of Minkowski space where there are two realizations of the speed of light, the speed of a player and the speed of the ball. The players are the fermions and the ball is a boson. Both the players and the ball have minds of their own connected to each of them in an instance of Hilbert space. The players use their mental powers to work out their moves, largely assisted by their vision of the situation of the other players and the ball, trying to pass the ball to members of their own team around the members of the other team and thread the ball through the other team to the goal. The players, being fermions, are essentially only permitted to make contact with the ball and are fouled if they make contact with one another unless they are directly attempting to gain possession of the ball.
Tuesday 2 August 2022
Searching Greene for clues: a very irritating book [and very poorly bound], but I see that the fundamental problem with calculating probabilities in quantum field theory depends on maintaining complete sets of perfectly orthonormal basis states combined to form a vector which evolves unitarily so that the whole vector is normalized to probability 1 and the probabilities of the appearances of the basis states (the alphabet) add up to one as required for a communication source. Brian Greene (1999): The Elegant Universe: superstrings, hidden dimensions and the quest for the ultimate theoryGreen page 119; More waffle about the turbulent vacuum but how do we use the separation of Hilbert and Minkowski space to refute it? In the same way I argued that gravitation is nothing because a [n unmodulated] continuum does not carry information.
Why is the mnimum energy of the quantum harmonic oscillator ½ℏω when the energy of a pendulum can be zero?
For the first time I am feeling the pain of love. In previous attractions I was attracted and not committed and no investment was required. Now the lover wants a big investment up front and trust rather than attraction is required.
Wednesday 3 August 2022
Both mind and Hilbert space are outside Minkowski space and time in the sense that they extend across it, which is how the quantum of action appears in Minkowski space as ΔxΔp ≈ 1 quantum of action, pixellating space and time. See Veltman's description of Hilbert space, a formal picture
[page 133]
of serial events like a movie in a can. This to go in the page on the independence of Hilbert space, ie Hilbert space is present to regions of Minkowski space. Martinus Veltman (1994): Diagrammatica: The Path to the Feynman Rules, page 33
Thursday 4 August 2022
As I understand (or misunderstand) the SU(1) . . . SU(n) . . . SU(ℵ0) series of groups, they are all rotations in n dimensional spaces. Since the progress of field theory has so far run from group SU(1) to SU(3) all of which [have been identified as natural] group structures. I suppose that as complexification proceeds particles like myself are SU(n) groups and as groups become more complex so that a group like myself [all of whose activities may be mapped to rotations] is mortal, that is I die. The proton, as an example of an SU(3), is currently quasi eternal but (in current theory) even protons are not eternal so SU(3) can be imperfect so SU(3) can break. Some particles (hadrons) represented by SU(3) have exceedingly short lifetimes and are classified as 'resonances' rather than particles with a measurable lifetime, ie the minimal instances of such groups only last for one 'revolution' before they break down. Their representation by n × n unitary matrices of determinant 1 point to their operation on vectors of length n, which have n eigenvalues.
' The simplest group SU(1) is the trivial group having only a singe element and is diffeomorphic to the 3-sphere. Since unit quaternions can be used to represent rotations in 3 dimensional space there is a surjective homeomorphism to the rotation group SO(3) whose kernel is { +I, −I }. SU(2) is also identical to one of the symmetry groups of spinors, Spin(3), that enables a spinor representation of rotations.' Special unitary group - Wikipedia