Notes
[ Sunday 7 August 1983 - Saturday 13 August 1983 ]
[notebook Creation - The Metaphysics of Peace II = CMP II : DB31]
[page 8]
Sunday 7 August 1983
Invariance - relativity - communication. What we understand is what is constant, although ephemera are just as important for the process.
Pais page 131: 'Invention is not the product of logical thought, even though the final product is tied to a logical structure.' [the logically consistent consequences of any situation are infinite, but each one, once realised, is logically connected to its antecedents.] Abraham Pais: 'Subtle is the Lord. . .': The Science and Life of Albert Einstein
page 133: E believed in aether till 1901.
. . .
page 139: '. . . special relativity was born after a decade of gestation.'
page 140: 'E was driven to the special theory of relativity mainly by aesthetic arguments, that is arguments of simplicity.'
page 141: 2 principles:
1. the laws of physics take the same form in all inertial frames
2. In any given inertial frame, the velocity of light, c is the same whether the light be emitted by a body at rest or a body in uniform motion.
This constancy of c must say the same thing about space-time resolution as the dimensions of Planck's constant. Is this the clincher?
'there are as many times as there are inertial frames.'
page 147: 'Not just in 1905 but throughout his life, Einstein considered quantum theory as a preliminary to a true theory and relativity as the royal road to such a theory.'
[page 9]
. . .
Pais page 148: 'The law of conservation of mass is a special case of the law of tranformation of energy.' Einstein,
page 150: 'The publication of his paper was met by an icy silence.
page 151: 'Planck deduced that the constant h is a relativistic invariant.'
page 152: Minkowski's tensor expression of relativity theory "superfluous learnedness". '
Minkowski: 'The views of space and time which I wish to lay before you have sprung from the soil of experimental physics and therein lies their strength, They are radical. Henceforth space by itself and time by itself are to fade into mere shadows, and only a kind of union of the two will preserve an independent reality.'
'Hilbert called Minkowski "a gift of heaven" when he spoke in his memory.
page 153" '[It took] the real pros a reasonably short time to realise that the special theory of relativity constituted a major advance.'
His work on the consequences of the special theory over by 1909.
Intelligence is what produces insight.
page 155: Self energy of the electron [Self communication].
One should get stuck into this question of rest mass etc. Quantum electrodynamics looks like the best place to let communication theory into physics.
[page 10]
Pais page 163: Bergson : 'I see [in this work] not only a new physics, but also, in certain respects, a new way of thinking.
page 170: Harold Bloom: 'Strong poets make . . . history by misreading one another so as to clear imaginative space for themselves.'
page 177: 'The happiest thought of my life.'
page 188: 'for an observer falling freely from the roof of a house there exists - at least in his immediate surroundings - no gravitational field.'
If the communication theory can be applied to QED (quantum electrodynamics) and to gravitation, do we at last have a GUT (grand unified theory)?
General relativity depends upon the local application of special relativity. Make this how it actually works. Messages are passed on step by step, being modified as they go by local conditions - this must be a consequence of the general equivalence principle between mind and matter - this one has to be ridden hard. The Universe discovers mathematics and puts it into action. The mind discovers mathematics, and uses it to understand the Universe, and then to branch out on its own.
Outline of philosophy article:
[page 11]
1. Lonergan on Insight
2. Empirical metaphysics
3. Lonergan's proof for the existence of God
4. The nature of Intelligence
5. The general equivalence principle - no God
6. Physical applications: Uncertainty - bandwidth
7. Mental applications - mental waves, time uncertainties of brain function / processes
8. An hypothesis on mathematics
9. Physical creation - evolutionary tautology
10. Creativity
11. Some consequences of the general equivalence principle
The special thing about mind is the uncertainty to be found in time sharing systems operating under interrupts and multi processors - parallel processors.
Pais page 184: 28/2/1908 E became a member of the academic community.
page 187: Generalisation from invariance under uniform motion to invariance under general motion.
page 188: 1908-1911 E preoccupied with quantum theory, not gravitation.
page 189: 'You can hardly imagine how much trouble I have taken to invent a satisfactory mathematical treatment of quantum theory.'
page 197: 'It was Einstein's style forever to avoid the quantum theory.'
page 198: Velocity of light is no longer a constant in accelerated frames.
Time depends on intensity of gravitation.[page 12]
page 200: Einstein: 'Just now I am teaching the foundations of the poor deceased mechanics, which is so beautiful. What will her successor look like? With that question I torment myself incessantly.'
page 206: '1912: he understood that the sources of the gravitational field were not just ponderable matter, but also field energy. He realised that gravitational field energy had to be included as a source, and that the gravitational field equations were therefore bound to be nonlinear.
The physical treatment of particle interactions may in fact be overlooking a major proportion of the communicative content in the world. Rather like trying to understand the way books behave in a library (which is determined by their inertial and information content) by simple kinematic and dynamic considerations. How does physics fit at all into a dynamic Universe, except as a series of rather vacuous constraints. The conservation of energy tells us nothing about the evolution of life. [?]
page 208: Einstein's theories depend on differential geometry and tensors. Communication theory is happier with statistics and an area of mathematics which I have not yet worked out - possibly all. This is a matter for research and the area in which progress must be made. [from a pure energy (geometrodynamic) point of view, the transfinite network looks like the large scale spacetime structure of the Universe?]
[page 13]
Mathematical laws have very little content. What it of interest are the boundary conditions. These, in general, are a matter of programming. We can model the Universe as an infinite partly random computing machine - particularly of interest is parallel processing and the uncertainties it introduces.
Pais page 210: Between 10 and 16 August 1912 Einstein understood that Riemannian geometry was the stuff of relativity. 'The impact of this abrupt realisation was to change his outlook on physical theory for the rest of his life.
page 211: 'If all accelerated systems are equivalent, then Euclidian geometry cannot hold in all of them. To throw out geometry and keep physical laws is equivalent to describing thoughts without words. We must search for words before we can express thoughts.'
Gauss's theory of surfaces holds the key to unlocking this mystery.
The theory being that the universal system has discovered and implemented much mathematics and that human physical theory is just the discovery and application of the same mathematics.
page 212: "Einstein: 'I realised that the foundations of geometry had physical significance.'
[page 14]
Pais page 212: 'I posed to Grossman the problem of looking for generally covariant tensors whose components depend only on the derivatives of the coefficient gμνdxμdxν '
ds2 = gμνdxμdxν
page 217: Gravitation = Gauss, Riemann, Chritoffel, Rici, Levi Civita. History by Christian Felix Klein.
page 228: 'The fundamental role of the metric tensor as the carrier of gravitation became clear.'
Minimum energy criterion is equivalent to eliminating redundancy in communication a la Chaitin.. Electric and gravitational fields have a potential which reduces energy as particles get closer together. Gregory Chaitin: Randomness and Mathematical Proof
page 235: Einstein: 'Nature shows us only the tail of the lion. But I do not doubt that the lion belongs to it even though he cannot at once reveal himself because of his enormous size.'
page 239: Planck: 'As an older friend I must advise you against [the general theory] for in the first place you will not succeed; and even if you succeed, no one will believe you.
[page 15]
Pais page 242: 'Planck notes, natural laws always imply certain restrictions on infinitely many possibilities.'
page 243: 'According to our theories there do not exist independent qualities of space.'
page 252: 'The apparently compelling nature of [my old causality objection] disappears at once if one realises that . . . no reality can be ascribed to the reference system.
page 266: General relativity deprived Lorentz invariance of its global valididty but left it as a local principle.
. . .
page 273: Einstein: 'I do not consider the main significance of the general theory of relativity to be the prediction of some tiny observable effects, but rather the simplicity of its foundations and its consistency.page 275: In general relativity energy and momentum conservation are an almost immediate consequence of general covariance.
If we are to find out why data rate is conserved, we had better look around [in the telephone book]. Misner, Thorne &Wheeler; Gravitation. . ..
page 276: Einstein: In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius since the higher education of women began.' Emmy Noether - Wikipedia, Dwight Neuenschwander: Emmy Noether's Wonderful Theorem
Monday 8 August 1983
Tuesday 9 August 1983
[page 16]
Wednesday 10 August 1983
A major advantage of this hypothesis, if it gains empirical respectability, is that it will be in a position to undo the enormous damage done to human morale by Plato's fear of human consciousness. In his attempts to justify the fascist monarchic principles of government that he had inherited from his family, he was forced to reduce the Universe and its inhabitants to mere shadows of a transcendent reality. This opened the way for religions and kings based on authority and the immense harvest of human misery that these have brought and continue to bring in the non-democratic countries of the world. Devotees of pure science might decry the humanitarian notions that I express but I feel that I am in the company of giants such as Einstein and Grossman. Science, with its ultimate appeal to the facts is the only sure antidote to the counter-factual assertions of the mystery religions that bring so much suffering to the planet by disenfranchising man. Any woman (in particular) who doubts this assertion should endeavour to trace the inferior position of women in the west to the Platonising tendencies of Paul the Apostle, Augustine and the bulk of the early and influential fathers of the Catholic church. Jesus himself, it might be noted, seemed to prefer the company of women.
[page 17]
The Platonists, on the other hand feared and belittled women, perhaps because of their stronger intuitive/biological grasp of the reality of this world. I have no less a program, then, than a plan to restore the self-assurance of the Universe by constructively doing away with the need for gods and creators, our ultimate self induced oppressors.
Pais page 283: Einstein's precursors: Newton, Lorentz, Planck, Mack and Maxwell.
'Einstein said he had always believed that the invention of scientific concepts and the building of theories upon them was one of the creative properties of the human mind. His view was opposed to Mach, because Mach assumed that the laws of science were only an economical way of describing a large collection of facts.
. . .
page 285: 'Mach's bold idea that inertia originates in the interaction of a given mass point with all other masses.'
Thursday 11 August 1983
[notebook: Creation, the Metaphysics of Peace I CMP I: DB 20]
[page 108]
Intelligence, guesswork and language, H B Barlow, Nature 21 July 1983 p 207. H. B. Barlow: Intelligence, guesswork, language.
Barlow pointed out that intelligence is what intelligence tests test for. A circle. What objective criteria are there?
' Is intelligence after all simply a matter of mental speed?' YES.
McPhail: 'first, there are no differences, either quantitative or qualitative, among the mechanisms of intelligence of non-human vertebrates; second that man's intellect is distinguished from that of non human vertebrates by his possession of the capacity for language.
Barlow page 209: 'In other words intelligence implies versatile and creative guessing as well as correct and efficient guessing.'
[page 109]
'Intelligence is not just a matter of detecting this association or that association, but requires a knowledge of the associative structure of a large body of information, and that is a formidable task.'
'A new look at the problem suggests a simple role for intelligence: it is the capacity to guess right by discovering new order'.
Conceptual continuity - NO - Conceptual discontinuity is the order of the day. We are always making leaps.
. . . Computer information is logarithmic [exponential] based on our position significant notation, Nature uses a simple 'additional' number system, 10 = 1111111111.
[notesbook: Creation, the Metaphysics of Peace II: CMP II DB 31]
[page 18]
Pais page 285: E: 'I have . . . again perpetuated something about gravitation theory which somewhat exposes me to the danger of being confined in a madhouse.'
Most primitive physical system has no coding. It uses the highest possible energy per bit, ie E = hf. Improved codings give more structure for less energy. Therefore, when we find the number of states (ie entropy) increasing though the energy becomes less or remains constant, we can recognise the existence of higher coding efficiencies - more entropy per energy. Thus at the beginning we can say much energy but no entropy, E/S = ∞. This is the initial singularity. The physical manifestation of this system should be very subtle change of energy where there is a relatively large increase in entropy, an indication of more efficient coding. This at last seems to be a route to a physics of information. Leon Brillouin: Science and Information Theory
page 288: 'It must be said that the origin of inertia is and remains the most obscure subject in the theory of particles and fields. Mach's principle may therefore have a future, but not without quantum theory. Mach's principle - Wikipedia
How can expansion and differentiation of universe be the result of more efficient coding? Let us say that spatial grainings
[page 19]
remain contant, and therefore as coding becomes efficient a greater volume of space can be specified with the same number of bits. We move from linear to logarithmic energy for a given amount of specification, ie exponential information oer unit energy.
Measure variety not in bits but in total number of states. With absolute minimal coding we can distinguish only two states of the Universe, existent and non-existent, With improved coding, number of distinguishable states increases with enormous [exponential] rapidity.
Pais page 289: Einstein"s desiderata:
1. To unify gravitation and electromagnetism
2. To derive quantum physics from underlying casual theory [2014: Turing machines]
3. To descibe particles as singularity free solutions of continuous fields.
[page 20]
Pais page 290: Gravitation alone constrains its own systems to obey energy-momentum conservation laws [ie 'resolution' conservation].
page 299: The later journey. The suddenly famous Dr Einstein.
Creation of a particle - a better coding [ordering] of an energy field.
Period of illness began 1917 and lasted several years.
page 300: 'completed a fundamental paper on the pseudotensor of energy-momentum.
page 301: 'tragic marriage'
page 302: E: ' "My aim lies in smoking, but as a result things tend to get clogged up, I'm afraid. Life too, is like smoking, especially marriage" . '
Pages 302-305: experimental proof of the bending of light.
page 308: ' "I was in accord with the hight and general principles of English science that English scientific men should have given their time and labour . . . to test a theory that had been completed and published in the country of their enemies in the middle of war".'
page 310: [Eyewitness to Einstein's first visit to the US] ' "People were in a curious state of excitement in which it no longer matters what one understands, but only that one is in the immediate neighbourhood of a place where miracles happen".'
page 313: Haldane: E: "A man distinguished by his desire, if possible to efface himself, and yet impelled by the power of genius which would not allow the individual of which it had taken possession to rest for one moment."
[page 21]
Pais page 319: E: ' "Since Maxwell's time, physical reality has been thought of as represented by continuous fields. . . . This change in the conception of reality is the most fruitful that physics has experienced since the tie of Newton".'
An information type world is not continuous - has uncertainties and conceptual jumps - improvement in coding.
page 320: 'Creative period ceased abruptly after 1924, though scientific effort continues unremittingly for another thirty years.
In the 1920s had a strong attachment to a younger woman. This ended in 1924 when he wrote that he had to seek in the stars what was denied him on earth.
1928: 'I believe less than ever in the statistical nature of events and have decided to use the little energy still given to me in ways that are independent of the current bustle.'
page 325: 'I believe that this process of deepening the theory has no limits.' Unified field theory strongly dependent on formalism.
Does the intelligibility of the Universe lie in the mathematical equations of physics?
What, physically, is the marker? - a bit of mass energy, momentum?
[page 22]
The real interest of the Universe lies in the arrangement of the markers.
ANGEL: We start with a lot of markers, all unrelated. The number of markers is conserved. This is the conservation of energy. But then the markers begin to arrange themselves in more and more efficient codings - entropy is increasing. More and more states can be described with the same amount of energy. The energy per state decreases.
Release of binding energy = improvement in coding [two can live as cheaply as one]
Pais page 328: '. . . [Einstein's] hope of a new dynamics, based on a generalisation of general relativity, in which quantum mechanics would be explained rather than postulated.'
'Ultimately it must turn out that action densities must not be glued together additively. I too, concocted various things, but time and again I sank my head in resignation.'
E: 'I believe that in order to make real progress one must ferret out some general principle from nature.' - yes, more efficient coding is where its at. That's what I say, and lets see if Khinchin agrees. [in 2014, the general principle is that nature is a layered communication network.]
[page 23]
Pais page 329: His work on unification was probably all in vain.
Kaluza-Klein theory. Klein believed that the fifth dimension was something to do with quantization.
page 333; 'In what follows we shall see time and time again Einstein kept insisting on the existence of singularity free solutions of source free equations as a condition that must be met by any theory acceptable to him.'
. . .
The evolution of the Universe is a transformation from one for one correspondences to position dependent notation 10 = 10 or ||||||||||.
If all space equally defined, expansion of universe is a result of increase in entropy, ie more efficient coding.
. . .
page 343: Einstein: 'Above stands the marble smile of implacable Nature, which has endowed us more with longing than intellectual capacity.'
[page 24]
Thus, romantically, began Einstein's adventures with general connections, adventures which were to continue until his final hours.
Pais page 347: Spencer lecture: pure mathematical construction enables us tp discover the physical concepts and the laws connecting them.
page 358: From 1926 till his death, he was the only one to resist quantum theory.
page 362: Quantisation is really a discussion of atomic stability. Either it gets the message or not. A change of angular momentum (such as happens to an electron) of h can cause a large change Δνh in frequency and energy. The problem for my conceptualisation lies in the meeting of space, time, momentum and energy.
page 363: 'I do not believe that Einstein presented valid arguments for the incompleteness of quantum theory, but neither do I think that the times are ripe to answer the question of whether the quantum mechanical description is indeed complete, since to this day the physics of particles and fields is a subject beset with many unsolved fundamental problems.'
page 369: Planck's derivation of quantum theory should also be an important theoretical step for the application of information theory.
[page 25]
Pais page 370: 'Planck's statistical step was wild' Planck: '. . . an act of desperation. I had to obtain a positive result under any circumstances and at whatever cost.'
'The electromagnetic theory of radiation does not provide us with any starting point whatever to speak of such a probability
.page 371: Planck counted partitions of indistinguishable objects (Bose-Einstein statistics)
Indistinguishable means not related to one another (and therefore differentiated and distinguishable) [not ordered].
Pais: 'His reasoning was mad, but his madness had that divine quality that only the greatest traditional figures can bring to science.'
Continuous functions gave way to discontinuities, limited resolution and catastrophes. The Universe is not analogue but digital [both].
page 372: 'From the very start Planck's results were a source of inspiration and bewilderment to Einstein.'
Einstein on Planck: 'This discover 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.'
page 377: Einstein used volume dependence of entropy for his derivation of the light quantum hypothesis.
'Einstein's introduction of light quanta in the Wien regime is the first step toward the concept of radiation as a Bose gas of photons.
[page 26]
Pais page 382: In 1951 Einstein wrote: 'All these fifty years of pondering have not brought me any closer to answering the question: what are light quanta?' [messages, stationary points in the Universe]
page 383: Einstein felt great tensions between the wave picture of electromagnetic radiation and the light quantum hypothesis.
Energy theorists speak of the heat death of the Universe and make it sound like a bad thing. Information theories must see the increase in entropy as a godsend (excuse the phrase) which makes the enormous intelligent beauty of the whole thing possible.
'Resistance to light quantum idea was so strong that Einstein's caution was almost hopefully mistaken for vacillation.'
. . . quantum field theory, when the concepts of particle creation and annihilation were formulated.
page 386: Rutherford 1918: 'There is at present no physical explanation to this remarkable connection and frequency.'
Particles combining eliminate redundant markers, thereby reducing the overall mass-energy of the bound particles while at the same time increasing the complexity of the bound system.
[page 27]
Pais page 393: degrees of freedom = degrees of non-communication = non-correlation. Communication reduces degrees of freedom which (for instance) reduced heat capacity. Correlation = communication.
page 395: Sommerfeld: Degrees of freedom must be weighed, not counted. [like communication source letter probabilities]
page 396: Quantum rules have no particular dependence on electromagnetism.
page 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 upon which entropy might depend. The constant can be taken to be zero.'
page 399: Nernst (1910): At this time the quantum theory is essentially a computational rule, one may well say a rule with 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 it to experimental test.'
page 402: The Photon:
page 406: A and B coefficients
page 407: photon momentum hν / c
page 409: 'Particle' does not imply a high degree of spatial localisation.
By 1917 E convinced photons are real.
[page 28]
Pais page 411: No one before Einstein in 1917 saw as clearly the depth of the conceptual crisis generated by the occurrence of spontaneous processes with a well defined lifetime. The chance character of spontaneous processes meant that something was amiss with classical causality.
Einstein 1917: 'I feel that the real joke that the eternal inventor of enigmas has presented us with has absolutely not been understood yet.
Discovery of the Compton effect 'created a sensation among the physicists of that time.'
Sommerfeld: 'Probably the most important discovery which could have been made in the current state of physics.
page 416: E to Bohr: 'Not often in life has a human being caused such joy by his mere presence as you did.'
E of B: 'He writes his opinions like one perpetually groping and never like one who believes to be in possession of definite truth. ' 'Never express yourself more clearly than you think, he used to admonish himself and others.'
[page 29]
. . .
Pais page 423: The birth of quantum statistics.. . .
page 425: Bose devised thermal equilibrium law for massless particles with two states of polarization, not conserved, which obey new statistics.page 427: 'Planck's law follows from Bose statistics with energy held fixed as the only consrtaint.
page 428: 1. Photon non-conservation; 2. Particles indistinguishable; 3. particles not statistically independent.
. . .
'If it is justified to conceive of radiation as a quantum gas, then the analogy between the quantum gas and the molecular gas must be a complete one.'
[page 30]
Pais page 432: Fermi-Dirac statistis discovered in 1926.
page 435: The birth of wave mechanics.
page 436: De Broglie on matter waves: "After long reflection in solitude and meditation, I suddenly had the idea during 1923, that the discovery made by Einstein in 1905 should be generalized by extending it to all material particles, and notably electrons."
page 441: E thought of wavefields as Fuhringsfelder - guiding fields. Schroedinger introduced on guiding field - the S wave function. E: "I have troube with Dirac. This balancing on the dizying path between genius and madness is aweful." 1926
"Dirac, to whom in my opinion we owe the most logically perfect representation of [quantum mechanics]".
442: Born: "I myself am inclined to renounce determinism in the atomic world, but that is a philosophical question for which philosophical arguments alone do not set standards."
page 443: E "Quantum mechanics is very impressive but an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that he does not play dice."
page 444: March 1927: Heisenberg states the uncertainty principle.
page 445: E: "I must apologise for not having penetrated quantum mechanics deeply enough.
'From 1931 on the issue for him was no longer the consistency of quantum mechanics, but rather its completeness.' Pais on E.
