VII Notes
2010
Notes
[Sunday 6 June 2010 - Saturday 12 June 2010]
[Notebook: DB 69 Creation
Sunday 6 June 2010
[page 61]
Monday 7 June 2010
Pais page 372: Einstein : '"This discovery [ie the quantum theory] set science a fresh task: that of finding a new conceptual basis for all of physics. Despite remarkable partial gains, the problem is still far from a satisfactory solution. 1948. Pais
Tuesday 8 June 2010
Wednesday 9 June 2010
Photons 'travel' on null geodesics which, since their length is zero, does not amount to travel at all, because space is annulled at the cost of an interval of time. This is true of all travel when we substitute the relevant local 'communication velocity' for the physical velocity of light. In this way communication removes space and time, suggesting that the existence of space-time id more a matter of non-communication [orthogonality, adiabaticism] than communication.
Systems communicate when the interval between them is zero.
[page 62]
Quantum mechanics is independent both of the 'forces' involved and the scale of interactions. (S328:999). Bostwick et al
Inflationary period: the maximization of the entropy of the physical layer S328:989 Krauss et al
Gravitational waves = oscillating populations of gravitons. These are predicted by the classical theory, strongly supported by observation, so it is necessary for quantum mechanics to say something about them.
Philosophy is studied with pure reason? There is no pure reason; all information and information transformations are embodied.
Science: looking for signals from the world and decoding them.
Our taste for the esoteric (used by rulers to increase their power) leads us to overlook the continual daily existence of divinity.
Photon has two polarization states, ℵ0 entropy states.
What does it mean to say that the s state of the hydrogen atom has zero angular momentum?
Network signalling: forming and breaking H-bonds in water S 328:1003 Minbiao et al
Thursday 10 June 2010
Planck's constant is universal insofar as it applies to all interactions (like quantum mechanics) without regard to the nature or complexity of the force involved. It is a symmetry
[page 63]
of the universal alphabet of interactions.
Pais page 386: '. . . the enormous resistance to the light quanta found its roots in the particle-wave paradoxes.'
Brillouin developed the idea that information is negentropy, insofar as the information we can have about a state is equal to the entropy of the space in which the state exists. Brillouin
DIFFERENTIATION --> COMMUNICATION
The derivative of a function tells us something about the communication between points in the domain of the function, is the gradient of the range depends on communication between points in the domain. We use the domain as a reference frame against which to measure the range.
The essence of general relativity (which applies equally, symmetrically to all particle interactions (ie exchanges of energy)) is the notion of general covariance: locally the Universe is its own reference frame, since all references and relationships in the Universe are communications between communicating (interaction) particles. All communications take place 'outside' spacetime insofar as they are stationary points in the dynamics.
Weinberg: Wigner - particles, groups and symmetries. Weinberg
Hilbert space is a big pl;ace, and a large part of the development of quantum theory is finding our way around it. Perhaps the cardinal point is normalization. All the physically relevant vectors in Hilbert space can be represented on or in a multidimensional
[page 64]
sphere (starting with a circle in the complex plane.
Our basic clue is that the complex numbers fit the world so well.
All the physics is contained in
a) dimensions - Hilbert space - library - spaces and subspaces (books, letters)
b) complex numbers
c) normalization
d) inner product
e) probabilistic interpretation
f) communication source
g) communication theory
h) computers and network - all computation is computation of addresses = {address, contents} = name of a fixed point in the Universe.
The use of complex numbers in quantum mechanics reinforces the view that there is stuff going on that we cannot see because it is a process totally involving its participants with no spare capacity left over to communicate with the rest of the world.
Weinberg page xxi: 'The point of view of this book is that quantum field theory is the way it is because . . . it is the only way to reconcile the principles of quantum mechanics (including the cluster decomposition property) with those of special relativity.
[page 65]
Weinberg page 49: '. . . our first task is to study how symmetries like Lorentz invariance appear in a quantum setting.
Can we 'explain' the Lorenz transformation in computer terms? We light say that the velocity of light c is limited by the requirement that a photon has to 'process' itself along annihilating at one point and creating at another, a pixellated process that we ap[proximate with continuous motion. What we need to explain is the -1, 1,1, 1 (or vice-versa) signature of spacetime.
Null geodesic = touching = sharing some state (Aristotle: continuous have points in common)
Velocity lings space and time x = vt. Does this mean that v is prior to both, as suggested by the principle of inertia, Galileo's law (Newton's first).
Pais page 395: Sommerfeld: 'Degree of freedom must be weighed, not counted.'
Pais 397 '"As the temperature tends to absolute zero, the entropy of a system tends to a universal constant that is independent of chemical or physical composition or other parameters on which entropy may depend. This constant can be taken to be zero.
So initial singularity, T = 0, S = 0 because it is a single isolated system communicating with no other and with no countable internal states (a tautology, since counting breaks isolation).
The initial singularity is the physical layer of every process. Although in the beginning there is only one of them, the number increases
[page 66]
to the entropy of the Universe as higher layers exploit instances of the initial singularity in their own processes.
Have I just incorporated the third law of thermodynamics into the model?
The ubiquity of exponential structures in the Universe points to the implementation of position significant notation. The size of the numbers we can represent in such a system grows exponentially with the length of the numeral, its physical embodiment. The initial singularity is formally an atom, structureless and uncuttable.
GOD is COOL (absolute zero). How does entropy grow? By bonding. We make structures by binding parts together in every case exploiting natural atomic and molecular bonding forces (and their absence) as an alphabet for our constructions.
Nernst in Pais page 399: 'At this time the quantum theory is essentially a computational rule, one may well say a rules with the most curious, indeed grotesque properties. However, . . . it has borne such rich fruits in the hands of Planck and Einstein that there is now a scientific obligation to take a stand in its regard and to subject is to experimental test.
The Reagan and Bush administrations released a wave of corruption that is till sweeping the world.
A Einstein in Pais 399: '"The more success quantum theory has, the siller it looks."'
'the ordering of light around discrete points that move with light velocity.' Einstein in Pais page 403.
[page 67]
Pais page 410: '. . . if we leave aside the question of spin, we may say that Einstein abstracted not only the light quantum but also the more general photon concept from statistical mechanical considerations.
Statistical mechanics <==> communication theory embodied.
Eintein in Pais: 'it is "a weakness in the theory [of the atomic emission and absorption of photons] . . . that it leaves the time and direction of elementary processes to change." What decides when the photon is spontaneously emitted? What decides in which direction it will go?'
Nothing; symmetry is a 'level playing field'.
Pais 431: Bose-Einstein condensate and the third law of thermodynamics.
Pais 461: '[To find the new theory] -- and this was Einstein's main point -- one should start all over again, and endeavour to obtain the quantum theory as a by-product of a general relativistic theory of a generalization thereof.'
Quantum mechanics obeys general covariance wince all its computations involving the inner product are invariant with respect to the choice of basis for the Hilbert space used to model the interaction under study (the class of interactions). How do we derive quantum mechanics from a computer network? Each computer is an inertial space with but one time. Each particle may be assigned an inertial rest frame except the photon [whose rest frame (cage) is the initial singularity?]
Pais page 464: In electrodynamics and general relativity theory 'events are causally determined by differential equations combined with initial conditions on a spacelike surface.'
[page 68]
Einstein in Pais page 466: 'In my opinion there is the correct path . . . and it is in our power to find it. Our experience up to date justified us in feeling that in nature is actualized the ideal of mathematical simplicity. [from the inventor of general relativity!]
Friday 11 June 2010
What does God want? Supernatural selection. Rossano
God is a personality we have to get along with to survive.
You may think I am suffering from the same sort of senile megalomania that infects many of the worlds religious and political dictators from the Pope on down. I have to defense but a comparison of the quality of my product with theirs.
Peacock: 'This is a textbook on cosmology -- a subject that has the modest aim of understanding the entire Universe and its contents.' Peacock
We have monarchs like the Pope telling us that God does not want us to use condoms when we fuck. Why? Probably because much of the ideology of the Church derives from times and places where the rate of reproduction had to be maximized to cope with high mortality in primitive and dangerous living conditions. But while times have changed the Church remains essentially the same.
Peacock's cosmology is equivalent to theology given Universe = god.
Peacock page 3: the velocity of light is a property of 'empty space', ie no static (observable) objects (marks) [so how do we measure it?]
[page 69]
Peacock page 3: 'the way in which our everyday experience can be generalized to deduce the large scale structure of the Universe is one of the most magical parts of physics.'
'To reflect [the] interchangeability [symmetry] of space and time, and the absence of any preferred frame, we say that special relativity requires all true physical relations to be written in terms of 4-vectors.'
page 4: 'The whole ethos of special relativity is that, in the frame in which a particle is at rest, its intrinsic properties such as mass are always the same, independently of how fast it is moving. The general way in which quantities are calculated in relativity is to evaluate them in the rest frame where things are simple, and then transform them out into the lab frame.'
TRANSFORMATION = COMMUNICATION ALGORITHM
The fundamental computers in the universal network are quantum computers.
We see all things on the horizon separating self from the thing observed. This horizon is a screen carrying messages, as I look into the internet with my computer monitor.
The main principle of general relativity: the only valid physical laws are those that equate two quantities that transform in the same way under an arbitrary change of coordinates.
page 6: '. . . the prime characteristic of relativistic thought: we must be able to explain what we see from any point of view.'
In quantum mechanics, every new 'measurement' (interaction) is a new
[page 70] point of view.
Peacock page 6: '. . . gravitational effects are identical in nature to those arising through acceleration/'
page 7: '. . . the important aspects of gravitation are not so much to do with first order effects as second order tidal forces: these cannot be transformed away and are the true signature of gravitating mass. However, it is certainly true in one sense to say that gravity is not a real force" the gravitational acceleration is not derived from a 4-force Fμ and transforms differently.
page 10: 'The term gauge will occur often throughout this book: it always refers to some freedom within a theory that has no observable consequences . . . .'
'gravitational acceleration depends upon spatial change of the metric.'
What is the metric of a network? Bandwidth, transmission rate, acts per second - energy.
Peacock page 11: '. . . the metric tensor is the crucial object in general relativity: given it we know both the structure of spacetime and how particles will move.'
'The components of tensors have to change to compensate for the fact that the components of 4-vectors alter under a coordinate transformation.'
page 12: '. . . one can only construct an invariant quantity in general relativity (ie one that is the same for all observers) by contracting
[page 71]
vector or tensor indices in pairs: AμAμ is the invariant 'size' or 'norm' of the vector Aμ.
Saturday 12 June 2010
Thermodynamic equilibrium is equivalent to balanced creation and annihilation of states near the equilibrium point by fluctuation around that point. Brownian motion; S 328:1115.
'The work of Sun et al is an impressive demonstration of artificial multicomponent self-assembly similar to that observed in the self assembly of biological structures.' Stefankiewicz, page 1116. ie creation 328:1144 Sun
Value of theological intellectual property at cost - 50 yr @ $100k = $5M.
The Habitable Planet (www.learner.org/courses/envsci/) Annenburg Media Annenburg Media
What God Wants: All religions in the world appear to offer an explanation of the human place in the world and use this model to develop behavioural norms which people must obey if they are to fit in t with the world system.
S Schneps et al Science 328:1119 'All too often instruction assumes that students build knowledge sequentially from one prerequisite idea to the next in as linear, hierarchical manner that mirrors the design of traditional textbooks and lectures. In real life, however, we tend to advance our understanding through a process that is much more haphazard and stochastic. Our knowledge builds from conflicting ideas (often only partially formed) that we weigh against one another, so that the understanding that emerges is the weighed sum of probabilistic beliefs.' Schneps et al
[page 72]
The product of a quantum network.
The key point in religion seems to be that we maximize our fitness by doing what God (however conceptualized and defined) wants. The scientific basis of religion, [theology] is devoted to determining what God wants, which views are then disseminated through religious organizations to individual people. Religious education begins with birth, and is deeply ingrained (if not always visible) in every culture and very closely related to language. In the Roman Catholic Church, for instance, the primary language for theological opinion is a form of Latin, Church Latin.
We have two general classes of Gods, those that are in this World and those that are out of this World. In ancient times, the Greek theologians developed Gods that were more or less part of the World. The Hebrews, on the other hand, moved toward placing God outside the World. The fusion of the Israelite and Greek Gods gave us the Christian God whose development reached its peak in the thirteenth century work of Thomas Aquinas.
The Thomistic version of God remains central to the theology of the Roman Catholic Church, by far the largest and most powerful Christian orgaization on Earth.
Christian Churches maintain that they are the sole reliable channels of communication with the Thomistic God,m who is otherwise a complete mystery to us. This has the political consequence that the Christian Churches has built their great power through their claimed monopoly on God.
[page 73]
The situation might not be so bad if Christian theologians really were in communication with God and [could] keep us updated on God's changing moods. One has only to read the Old testament to see that God is a difficult Old man, prone to repetition, hubris and capricious behaviour. See God, a Biography. Miles
Yet, it turns out, we have no visible public connection with God but the Books of the Bible whose texts are fixed for all time. The best the Church can do to keep us in touch with its God is to reinterpret the Bible to suit changing times. the Catholic Church has restricted eve this channel by declaring itself infallible. In effect all we know about the living God is contained in one vague snapshot take thousands of years ago.
The New testament is the Word of God. when we read it we see that much of its advice is good even today, but the dramatic background to these words, the Fall, the Incarnation, the Crucifixion and the Redemption is difficult to associate with the Universe and the World as we now know them. And much of the advice given by the Church seems clearly in conflict with real life, like the ban on contraception and sex for fun.
At present the opposition to Catholicism is quite amorphous and not particularly characterized as non-religion or natural religion. the rising power and organization of fundamentalists, on the other hand deserves some response. The scientific approach is to show that the fundamentalism position is not compatible with the evolving and creative world that we experience. From a mathematical point of view, fundamentalism lacks the variety necessary to map the world of experience so it fails to know or
[page 74]
control the world of experience. The alternative in natural theology is to assume a space with no upper bound in complexity to model god.
General relativity: a moving world in a moving reference frame. We use the formalism of differential geometry to offset these motions against one another to arrive at the point of view of a freely falling observer.
Peacock page 23: 'The Riemann tensor in N dimensions has N4 components, but few are independent owing to various symmetries . . . For general relativity the symmetry of most importance is the Bianchi identity which says that the Einstein Tensor is covariantly conserved.
(
It is this property which makes the Einstein tensor such an immediately comp[elling candidate for the field equations in which it is proportional to the energy-momentum tensor.'
We cannot write coordinates without a basis. The basis defines the space in which the coordinates are written, so the information in the coordinates of an event is equal to the entropy of the basis. From an algorithmic point of view, this entropy is the entropy of the mathematical axioms used to define the basis.
Einstein use general covariance to express the symmetry of all possible bases.
The key to the creation of a network is its ability (through
[page 75]
its structure) to give different meanings to otherwise identical symbols.
The general theory of relativity is an epistemology of symbolism. We might be able to formulate it in terms of quanta of action as the atoms of the Universe, first seen as photons the atomic messengers with two states of polarization. Frequency comes later, since it is meaningless without space (?)
Peacock page 23: '. . . the metric tensor has zero covariant derivative
gμν;ν = 0.
Indeed this can be taken as the starting point of Riemannian geometry. It is a very easy equation to prove by working in a local inertial frame: the connection is zero there, and the first derivative of the metric also vanishes. This is just the equivalence principle again, saying that inertial frames are those in which the apparent gravitational force (as expressed by derivative of the metric) is transformed away.'
Peacock page 25: ' . . . a radiation-dominated fluid generates a gravitational attraction twice as strong as one would expect from Newtonian arguments.'
Energy density of the vacuum: If ρc2 + 3p < 0, we have gravitational repulsion, necessary for expansion.
We assume that the Universe (and the initial singularity) are isolated quantum systems.
The many worlds hypothesis becomes the one world hypothesis oif the many worlds are perfectly symmetrical, ie defined as far as they can ever be defined by the energy equation. Everett III
[page 76]
Gμν = Tμν = simplest version of Einstein equation.
Gμν = Rμν - 1/2 gμνR.
Cosmological constant 'represents curvature of empty space' or 'the energy-momentum tensor of the vacuum
Tμνvac = (Λc4/ 8πG) gμν'
These are all geometric concepts in which we map local 'force' top local length. The geometry is formal and symbolically static (since we can write down equations whose form is independent of time) but we bring these equations alive by matching their real variables to measurable phenomena, that is phenomena which can be effectively compared with one another.
We use general covariance to understand the ancients, decoding their words by trying to reestablish the intellectual, social, political and religious milieux in which they were committed to writing.
The Bible and religions derived from it are formalisms outside time that were stationary points in their own time but not in the transformed world 2000 years later. In other words we transform away the different environmental forces to see the underlying 'inertial' similarity.
Peacock page 26: '. . . we can be sure of one thing: the absence of a preferred frame means that Tμνvac must be the same for all observers in special relativity. Now apart from zero, there is one one isotropic tensor of rank 2 . . . : ημν. Thus in
[page 77]
order for Tμνvac to be unaltered by Lorentz transformations, the only requirement that we can have is that it must be proportional to the metric tensor. Therefore it is inevitable that the vacuum (at least in special relativity) will have a negative pressure equation of state
pvac = -ρvacc2.
'In this case ρvacc2 + 3p is indeed negative: a positive Λ will act to cause a large scale repulsion. The vacuum energy can thus play a crucial part on the dynamics of the early Universe. Since the vacuum energy is constant independent of time, there might seem to be a problem with conservation of energy in an expanding Universe: . . . what saves us is the peculiar equation of state of the vacuum: the work done by the pressure is just sufficient to ,maintain the energy density constant. In effect the vacuum acts as a reservoir of infinite energy. . . . '
Peacock page 29: 'The difference between Euclidian space and other manifolds is that a manifold need not possess a metric structure.
Manifold: 'a space where points can be parametrized continuously as a n-dimensional set of real numbers xi, which are the coordinates [address] of the point.'
page 30: Clearly the idea (which may seem surprising) that a dual structure of vectors and 1-forms can still be constructed in this restricted case [ie in the absence of a metric] is an important insight, which goes beyond the ideas of traditional tensor calculus. Let us see how this feat is accomplished. . . . '
Going ahead with the natural religion project is a foregone conclusion. Having come so far I cannot turn back (although i can change
[page 78]
course in the forward direction). It is like love and black holes, an irresistible attraction.
