vol VII: Notes
2012
Notes
[Sunday 5 August 2012 - Saturday 11 August 2012]
[Notebook: DB 73 Spring2012]
[page 1]
Sunday 5 August 2012
One can say that most of the mathematical complexity in physics arises from the use of coordinate systems. (Tomonaga pp 113 sqq). A coordinate system is a point of view from which we see and measure systems. The basic point of view of any particle in the Universe is its 'own' point of view. We can imagine trying to get a wider picture by learning to see things from other points of view, and then transform from one point of view to the other. How does the nucleus look to the electron? How does the electron look to the nucleus? General relativity gives us a global point of view by deising a coordinate system that effectively encompasses every point of view that involves communication at the speed of light, itself subject to variation with various points of view (eg watching the Schwartzchild surface of a massive body from a very large distance). The actual interaction between particles depends upon how they see one another. This applies universally from electrons to humans. In physics all transformations are species of Lorentz transformations, which depend on relative velocity, which suggests that velocity is a basic parameter in knowledge. From a Lorentz point of view, the faster something is moving relative to me, the more massive it looks. This holds for electrons too. Mass = number of units, rate of action, energy. Tomonaga
[page 2]
The transformation and its inverse that join two localities are a coder-decoder, implying the presence of a computer. The transformations express the content of the message in different alphabets or bases from sender to channel and from channel to receiver and back again [the channel code must be common to them both ]. In physics this means encoding information represented by fermions into information carried by bosons and back again. Wojciech Hubert Zurek
In physics transformations are a matter of converting the coefficients of each element of a multicomponent quantity into the coefficients appropriate to each element of the same multicomponent quantity in another basis. This process is made possible by a conserved element (the underlying reality) between the two representations. We may see the multitude of components as words in the sentence required to represent the reality and the transformation as translation into a different language, same reality, different words.
Scalar = cardinal of a set of units.
Mathematical transformations often treat the coordinate system as a rigid body (Newton), although Einstein showed how to make it soft (mollusc-like). The transformations in (Dirac's) quantum theory are deterministic (rigid) and the interpretation is stochastic.
Tomonaga page 118: '.. . it is not sufficient to say that a scalar is a quantity with one comonent, but it must be a quantity which does not change its value in any coordinate system, a count of units, a metric, ds2.
[page 3]
The Lorentz transformation is devised to make ds2 a scalar. Scalars are the only things we can measure and the fundamental unit is the quantum of action, a unit of motion, a logical step, an events, etc.
Algorithm is a pipeline that imposes certain constraints on the data flowing through it, the most fundamental of which (exemplified by leakless plumbing) is conserved flow. In general, the flow of signals is accompanied by a flow of meaning which is superposed on the signals by the terminals of the channel.
Tomonaga page 118: '. . . regardless of the rank of the tensor, the transformation of the components of the tensor and the rotation of coordinates always have a one to one correspondence . . . there is also a correspondence product to product. The existence of this type of correspondence is expressed by saying that the transformations of tensor components and the rotation of coordinate systems are covariant.
Natural religion: we worship one another as gods.
Tomonaga page 119: '. . . I mention in passing that A(n) is the 3n dimesnional representation of the rotation group, and a tesnor of the nth rank is a quantity with 3n components which are transformed by A(n).
multicomponent quantity (eg me) = dynamic and ordered set.
The fixed points are the elements of a dynamic ordered set, understood by flows of order (entropy, information).
[page 4]
We understand everything in terms of rotation, because we think of process in terms of phase [working day by day].
Tomonaga page 139: '. . . in quantum mechanics, only quantities of the form |φ|2 have physical meaning rather than φ itself.' So why do we map φ onto real space? It belongs only in Hilbert space.
Hilbert space is the space of quantum computation.
We conceive of action as rotation in infinite dimensional space [and note that the quantum of action has the dimensions of angular momentum].
Monday 6 August 2012
Non-commutation = communication (exchange of quantum).
Tomonaga 106: Interaction induces quantization.
It seems easy to see that a common theology and religion creates the trust that vastly improves human relationships.
Tomonaga page 108: '. . . all [Dirac] wanted to show was that a system of many bosons and the wave field in three-dimensional space are equivalent in three dimensional space. ' Does this give a clue to the structure of space, something created by bosons and fermions working together. In fact, (we suspect) bosons can exist in 1D space (ie line parametrized by discrete energies one quantum of action apart).
[page 5]
Aristotle: time is an ordered sequence of numbers [the natural numbers?]
We have placed an historical horizon behind Galileo, and have become blind to the very fundamental work done by the ancients whose theories workled for them as ours do for us
