Notes
[Notebook: DB 62 Interpretation]
[Sunday 9 December 2007 - Saturday 15 December 2007]
[page 65]
Sunday 9 December 2007
So far in our imaginary Universe we have created time with the not operation. The question then arises how do we make space, and if we make it one dimension at time or go to 3-D space all at once.
We say that space is something that endures through time and so let us create a 2-D spacetime, one dimension of space and one of time. The space must have at least two points, a 'particle' and an anti-particle, which can revert back to pure time (energy) if they come into contact (annihilate). Let us measure the distance along the spatial dimension by how much energy is released on annihilation. So now we have a sort of one dimensional atom (even flatter than flatland) which can come into existence or annihilate. Abbott
Given the network heuristic, we seek a plausible description of this system n network terms so we imagine the particle and the antiparticle being attracted to one another by the exchange of energy, so something like a primitive graviton, eg a spin 0 graviton oscillating between and on and an anti-on. This is a step up from the not-oscillator, which annihilated one state to create another. Here we have two states existing 'simultaneously', each (and the exchange particle) carrying energy and so modelled by the not-operator. Can we map this little system onto a logical operation? Classical two input operators annihilate two states and emit one, as we see from their truth tables.
[page 66]
[diagram]
does this help? The answer is to keep going until we get to a dead end and then turn back and find a way around it.
Here we are trying to reconcile physics and classical logic: quantum logic is slightly different, in that we we require constant entropy (reversibility ) at each peer level.
We have begun with the classical not. What is we upgrade to the controlled not = c-not ?
A bit of meditation on the uncertainty relations might help here:
delta x . delta p = h
delta t. delta E = h
delta action , delta count = h.
Since action is quantized, this last relation introduces fractional numbers, since delta count = 1 / delta action. Similarly the first and second work if x, p, t and E are real even though we take h to be a [fixed] integer.
Does arithmetic antedate logic? Maybe yes, since it does not involve meaning as logic seems to do where we attribute truth and falsity to propositions depending on their
[page 67]
meaning whereas arithmetic (seen through the eyes of set theory) involves no meaning, units simply stand for themselves.
Messages correlate. So the message in the not operator correlates the 'next' state with the previous state, ie not-p follows (and precedes) p. In a two state system, not-not-p = p. But in bigger systems, this is not so. not-Alice may be Bob, but not-Bob maybe Carol and so on. What we can be sure about ]of] about the not operator is that the entity it is applied to will be annihilated but we cannot be sure of what will be created. So the future is not determined by the past, except in two state systems.
The identity operator wan be used to account for the energy in stable particles. However, the identity may be expanded (like the complex roots of ) I = not-not in a two state system. In an n state system we have a group of operations which may be strung together to get the identity.
Expanding the identity.
One of the fascinating features of complex numbers is that each has n nth roots, two square roots, three cube roots and so on. Looking at the Argand diagram, the roots of 1 lie on a circle of radius 1 spaces 2 pi / n radians apart. So the 4 4th roots of 1 are 1, i, -1, -i, and multiplying any two of them together gives another.
The upshot of all this is that a stable particle (an identity) like myself can be realized by a group of any number of operations.
[page 68]
Let us say that every complete communication in the symmetric network is an identity which may have any number of steps and be opened and closed at any peer level, equivalent to asking a question and ultimately answering it after searching (if necessary and possible) the whole Universe for an answer.
Turing machines are the hardware (deterministic) layer of the Universe. We use the relativity of transfinity (if a is (locally) infinite and b > a , then b is [locally] transfinite.
action is conserved in one space
energy in 2 space (potential/kinetic)
4-momentum in 4 space.
Field = Fourier transforms of creation and annihilation operators. Veltman page 20. Veltman
[equation, Veltman page 20]
[page 69]
phi(x) = A(x) + A+(x) is the field corresponding to the particles considered.
'The main property of the field is that it is local'
On the closure of operations: one abstract operator can account for a multitude of concrete operations. This is a bit like garbage collection (now called recycling) where we operator on a large variety of different recyclables with a single algorithm, ie pick out all the ferrous metal with a magnet, melt it down and refine it into the starting point for new products.
We have called this same idea knowledge and compression and it corresponds to the annihilation phase of the Hilbert operator.
phys07HilbertOperator (the abstract union of everything one can do in Hilbert space.
Monday 10 December 2007
We are constructing a Universe starting with the initial singularity. We make a 2 state Universe by using the not operator which creates two versions of the initial singularity, one of which is not the other. In other words . . . we start with the state vector |I> = initial singularity and decompose it into two orthogonal states |I> = a |0> + b |1>. At this point we allow a and b to take only two values, 0 and 1. Normalization then requires |I> = |0> + 0 |1> or |I> = 0 |0> + |1>. Now we use this little system as
[page 70]
hardware to build a 4-state system which serves as a context for the states o> and |1> so that both can exist simultaneously and so we can allow more values for a and b subject only to normalization requirements. Maybe the Pauli spin matrices come in here creating a little unit with one dimension of space and one dimension of time. Then we go to Dirac's equation and four dimensions. The idea of general covariance then becomes that we can assemble these parts in any order that we like, using any system of coordinates with sufficient variety (cardinality) to describe our structure. 4 dimensions of spacetime says that there are four real communication channels which may take independent values.
We ask for the statistics of the noton and notice first of all that it has no particular time scale because there is nothing to compare it to. Physicists are apt to construct coordinate systems. Let us establish a time coordinate and record the transitions of the noton. These might be a set of points n a line lying between zero frequency and the supremum of frequency measured as counts of events (eg 'passing phase 0' or |0> --> |1>). If the noton ticks like a clock, these points will be equally spaced. If not they might look like random events happening every now and then. The establishment of a timescale for the Universe is quantum mechanically called making an observation. Our timescale is the observer, and the coupling between the noton and the observer decides what the observer sees, In the case of the noton what the observer sees depends on the rate of some clock which serves as an affine parameter along the coordinate we are measuring. But the noton is itself a clock, or at least a ticker and it may have its
[page 71]
own representation of itself. What we are saying here is that a particle and an observation are identically real.
Now what do we see if we allow two notons to interact, that is to observe one another? Insofar as these notons are independent, each may observe that the other has a clock running at a different frequency (energy) that the other. The constraint we place here is conservation of energy, to that the sum of their frequencies is ℵ0 and (given transfinite arithmetic) each of their frequencies is ℵ0. So we say that they have equal and opposite energies. If energy is the power to of things, one in effect undoes everything that the other does. This is a fairy tale, but the intuitive way into the network model is to consider one;s actions in the simplest way possible. My life might be modelled by a noton of high cardinality.
We take birth, life (parametrized by time) and death as our fundamental universal facts and explain them as the transmission, passage and reception of a message in a transfinite network.
noton = message = string of transitions decoded by comparison (measurement) with a parameter (affine parameters).
The affine parameter of any noton is its proper time = phase.
So the coupling of notons distinguished by proper time might have some structure like the black body spectrum, which is the result of an electromagnetic field observing a set of oscillators and vice versa.
[page 72]
By superposition we mean phases can be constructed from phases by (in quantum mechanics) two dimensional addition. real + real, imaginary + imaginary. We can imagine the high frequencies as subprocesses within the lower frequencies, like the number of heartbeats in a life.
To get the proper black body spectrum, we must assume the existence of an oscillator with transitions corresponding to every mode of the field. All this does not need 3-D or 4-D to work. It functions in 1D, the time domain, parametrized either by intervals (eg between events) [or] frequencies (events per parametric unit).
Peacock page 66: 'To the relativist cosmology is the task of finding solutions to Einstein's field equations that are consistent with the large scale matter distribution of the Universe.' Peacock
page 66: '. . . the only allowed velocity field on a local scale is expansion (or contraction) with a velocity proportional to distance, V = Hr.'
page 67: 'The first point to note is that something suspiciously like universal time exists in an isotropic Universe, . . . t is the proper time measured by an observer at rest with respect to the local matter distribution/'
page 68: '. . . Robertson-Walker metric . . . applies in any number of dimensions,'
'Every fundamental observer with a sufficiently large ego will conclude that the Universe is centered on them.'
[page 73]
Robertson-Walker metric Misner, Thorne and Wheeler. Misner, Thorne and Wheeler
Since this applies to the whole Universe, we expect it to apply right back to somewhere near the noton.
Peacock page 71: 'In fact the Robertson-Walker metric turns out to be conformally flat for all values of K, ie a coordinate transformation can always be found that casts the metric in the form of a Minkowski metric multiplied by some spacetime function.'
page 72: 'Photon wavelengths therefore stretch with the Universe, as is instinctively reasonable.' [which makes us think that the photon is 'part' of spacetime]
page 77: 'A particular point to note is that the behaviour at early times is always the same: potential and kinetic energies greatly exceed total energy and we always have the K = 0 form R proportional to t 2/3. '
page 80: Positive vacuum energy = negative pressure.
'It would be more satisfying to have some mechanism that set the expansion in motion, and this is what is provided by vacuum repulsion. The tendency of models with positive Lambda to end up undergoing an exponential phase of expansion (and moreover one with Omega = 1) is exactly what is used in inflationary cosmology to generate initial conditions for the big bang.'
Tuesday 11 December 2007
Birth and death: One phase of the noton (Shiva-Kali)
[page 74]
undoes what the other phase does, ie it is reversible. Superimposed on this is the expansion and cooling of the Universe that has the overall effect of allowing more complex entities (like life bearing planets) to come into existence.
My life is one turn of phase, a quantum of action at a certain scale.
We can make stationary mass by confining a massless particle (which nevertheless has energy and moves at c) to going in a circle.
Peacock page 184: '. . . the general philosophy of quantum field theory . . . has been to sweep the big conceptual difficulties under the carpet and get on with calculating things.'
Our network picture is to be matched to the physical picture by giving algorithms for encoding and decoding the messages and showing what happens when a transmitter transmits a message and the receiver receives it.
Wednesday 12 December 2007
Thursday 13 December 2007
So we connect two notons together to make 2-D spacetime, ie two points that endure through time, ie last longer than 1 tick, or one long tick and one short tick. The network view of this is that we have a structure that can communicate without annihilating itself We can also start expressing all this in the quantum-operator formalism, since this formalism is invariant with
[page 75]
respect to energy-momentum. Once we have the 2-D spacetime we can introduce special relativity, on the grounds that enduring space requires error free communication.
Garret Lisi: 'An exceptionally simple theory of everything'.
Friday 14 December 2007
Lisi may have taken a step forward, but some of it seems to have been around for years, particularly the suspicion that E* has something to do with it. E8 (mathematics) - Wikipedia
Phys06Identity&Expansion
We have introduced dynamics into the initial singularity modelled by the not operator. Let us call this system the not-on or noton (on Greek = entity, being, etc eg proton, photon, electron etc) We now apply network ideas to the internal expansion of the noton.
Engineered networks grow [by adding hardware and then downloading software form the rest of the network].
