[ Sunday 21 August 1983 - Saturday 26 August 1983 ]
[notebook Creation - The Metaphysics of Peace = CMP I: DB20]
[page 117]
We must start with the most primitive thing of all that can be said to exist (what about a singularity [, God]) and give it there and then intelligence (an indivisible quality) which will enable it to build itself up into the sort of Universe we have.
[page 118]
Mathematical objects are hierarchically nested from the simplest to the most complex.
And what do we see to be the simplest: mathematical logic maybe, so as Wheeler says, pregeometry must be dynamic logic = digital computer.
Elkana page 12: Kant a great believer in the great unifying principles of nature. Elkana
The basic requirement: no contradictions is the equivalent of the pragmatic principle: it works.
[notebook: Creation - The Metaphysics of Peace II = CMP II: DB31]
[page 60]
Misner Chapter 15 page 364: Bianchi Identities and the Boundary of a Boundary. Misner, Thorne and Wheeler
Einstein was not for a long time aware of these identities and they caused him much trouble (by their absence from his consciousness). Here is an example of a physical idea whose expression was to some extent hindered by lack of mathematical insight. A case for publishing the idea piecemeal. Bianchi identities were obviously well known in parts of the mathematical establishment.
'Look for a coupling machinery between gravitation (spacetime curvature) and source (matter, stress energy tensor, T) that will guarantee the automatic conservation of the source (∇ . T = 0
[page 61]
What tensor like feature of geometry is automatically conserved? The Einstein tensor.
Misner page 365: Ten potentials (metric coefficients gμν) in metric tensor g = gμνdxμdxν
Boundary of a boundary = 0, ie differentiate something enough times and you get a constant. F = md2x / dx2, ∂∂ = 0
page 368: Source primary, field secondary or vice versa?
'classical electric charge is nothing but electric lines of force trapped in the topology of multiply connected space.'
Mathematicians might be getting a bit carried away by their art.
page 372: 'The sum of the curvature induced rotations associated with the six faces of any elementary cube us zero.'
. . .
[page 62]
. . .
One cannot expect the actual mechanism of the Universe to 'show' on the macroscopic.
Misner page 386: Equivalence principle breaks down at extreme curvature: what you should say is that it does not exist yet.
. . .
page 399: There is no noise in the Universe, only lack of precision, which is sometimes very high, as consider non-collapse of electrons in iron atom through maintenance of their identity and the Pauli exclusion principle.
[page 63]
Misner page 399: Nothing has been called gravitational field. A whole set of different functions are involved in the structure of gravitation. It itself is the concatenation of a number of more primitive ideas abut gravitation which now show through since we have a clear perception of what gravitation is. In other words, gravitational field is already an organism composed of simpler organisms. Atoms and so on must be more complex and be composed, in some intelligible sense, of the more primitive organism just as we are composed of cells, mitochondria, proteins, atoms, electrons, positron, quarks, gravity, something prior. This image of the world in a way completes the idea that it is both intelligent and intelligible all the way up.
Many different mathematical entities are associated with gravitation.
page 404: Automatic conservation of source.
page 409: Einstein's ten field equations include four conservation laws - local conservation of energy and momentum.
Einstein disturbed to discover that geometrodynamic law
[page 64]
predicts a dynamic Universe.
At last a method dawns. Look through existing mathematical physics and enumerate mathematical structures that are to be found there. One of the major predictions of the theory is that there is not a unified field theory but a whole multitude of hierarchically arranged mathematical structures that have built on one another solely on the basis that they are not incompatible. The variety of earlier structures may not allow for any evolution within them, but by the time we come to a structure as complex as the atom we have a gradual evolution of heavier structures as the appropriate substrates and techniques become available.
page 411: The expansion of the Universe could have been the most impressive proof of he theory of gravity.
TVAC is the stress energy tensor of the vacuum arising from quantum considerations. Weinberg: The cosmological constant problem
page 416: Einstein's equations have stood unchanged while derivations and axiomatisations have multiplied.
. . .
[page 65]
Misner page 419: The quantum of angular momentum expressed in geometrized units is the Planck length.
There need not be any fundamental derivation of electric force, but merely a non-contradictory relationship between it and all else, ie quantum electrodynamics stands alone [like a language].
. . .
page 429: Every theory contains elements of complexity for which there is no experimental motivation.
-no prior, non-dynamic geometry.
page 434: Hilbert: 'From the knowledge of all 14 physical potentials gμν, Aσ in the present, all predictions about the same quantities in the future follow necessarily and uniquely insofar as they have physical meaning.'
[page 66]
Misner page 435: [Chapter 18] Weak gravitational fields: Linearised theory of gravitation
Misner page 457: closed Universe has no energy or angular momentum.Quantities conserved cannot be measured for the whole universe from outside. Must be estimated from inside.
page 467: Local gravitational energy momentum is not observable. It does not have weight and does not curve space. Is this consistent, making such a sharp distinction between geometric curvature and source, in matter. [Yes]. Because a [n inerttial] frame can always be found in which all local gravitational fields disappear. Equivalence of relativity. Gravitational energy exists but is not localisable.
. . .
Electromagnetism: I see all charge
Gravitation: I see all
[page 67]
Does gravitation in fact affect all forms of matter, or are there particles which are immune to both gravitation and inertia, and presumably therefore do not have energy or momentum, but may nevertheless carry information?
Misner page 476: Attempt to devise point particles from continuous fields seems perverted.
The evolutionary approach, favouring complexity, does away with the classical einstinian presumption that the ultimate laws of the universe nerd to be very simple, or to be all subsumable under one guise. In fact as we go to higher energies (which is back in time) we come to times when the universe is simpler and simpler. (higher energies will not necessarily lead to more structure, but less, in line with evolutionary hypothesis) [more energy per state implied reduced entropy for given amount of energy]. In other words particle physics is discovering more and more possible but in some way unstable states of matter. Becsue rates of communication in very high energy particles are so high, contradictions are revealed very quickly and particle decay in consequence. Coding is very inefficient.
In a sense, there is a unified field theory, but it tells us almost nothing. It is the theory of intelligence, the basic tautology of evolutionary existence.
[page 68]
Misner page 479: No object with finite rest mass follows geodesic world line.
Maybe, for instance, neutrinos are outside the influence of gravity.
page 480: System of uncharged black holes moves according to geometrodynamics pure and simple.
Local curvatures associated quantum mechanical fluctuations at Planck scale of distance are intense.
page 484: Things are as they are because they were as they were (yes and no).
page 485: 4of 10 components of Einstein's law connect the curvature of space here and now with distribution of mass-energy and the other six determine how the geometry thus determined proceeds to evolve.
Hilbert's variational principle based on Lagrange function.
. . .
page 489: Feynman's 'democracy of paths'.
probability amplitude to transfer from (x', t') to (x", t") propagator <x", t"|x', t'>. Destructive interference wipes out all but classical history.
This is a mathematical artefact, surely?
[page 69]
'Is there not an inner contradiction in trying to apply to a 'particle' (implying idealization to a point) a field equation that deals with the continuum? Answer: There is a contradiction in dealing with a point. Therefore do not deal with a point. Do not deal with internal structure at all. Analyze the motion by looking at the geometry outside the point. That geometry provides all the handle one needs to follow the motion.'
All this [Misner Box 21.1] 'Rate of change of Action with dynamic coordinate (= 'momentum') and with time, and the dispersion relation (= 'Hamiltonian') that connects them in particle mechanics and electrodynamics] looks like low grade and pretty complex ad hocery, but this, after all, is what one might expect the Universe to be! [from the point of view of entities which took 13 billion years to evolve= us]
. . .
Pais page 543: Mach's principle and the origin of inertia
E: 'In my opinion the general theory of relativity can only solve this problem satisfactorily if it regards the world as spatially self closed.'
What is is a function of what can be known. Mach's principle.
page 546: Geon, bound gravitational particle.
page 547: Geometry is influenced by the presence of matter to an extent proportional to the factor G / c2 = 0.742 x 10-28 cm/g.
page 529: Mack's idea that mass there determines inertia here has its complete mathematical account in Einstein's geometrodynamic law.
'Ratio of mass to radius remains unchanged.'
Discontinuity in curvature tensor may be propagated with the speed of light.
Quantum mechanics - commuting observables may be examined simultaneously.
[page 70]
Misner page 557: Thermodynamics, Hydrodynamic, Electrodynamics, Geometric Optics and Kinetic Theory
page 558: n = baryon number density;
S = entropy per baryon.
The fundamental law of thermodynamics is baryon conservation.
page 559: Entropy can be generated but not destroyed.
Number of states available tends to increase. More states = more
markers. Planck's constant represents absolute maximum number of
states = minimum conserved quantity of energy-time per marker.
Fundamental laws of geometric optics:
1. light rays are null geodesics;
2. polarization is transported;
3. amplitude is governed by adiabatic invariant which, in quantum language states that the number of photons is conserved. [?]
. . .
[page 71]
Pressure rises faster than Newtonian in relativistic star, ie GR predicts stronger gravitational forces in stationary body than Newton.
Only intelligence can tell the difference between meaningful and meaningless entropy. Better read Brillouin after this. Brillouin
. . .
Misner page 639: There comes a point where centrifugal force cannot save an object from gravitational collapse.
. . .
How does principle of superposition relate to coding?[page 72]
Some codings:
superposition
fermi-dirac
bose-einstein
Pauli exclusion
Misner page 703: The Universe
Homogeneous and isotropic on scales 108 light years and larger. Universe about 1010 light years in diameter, so we have 106 elementary volumes.
Misner page 705: 'The amount of mass energy in the Universe changes in accordance with the work done by pressure in expansion.'
Total mass energy of closed Universe has no well-defined meaning.
To a first approximation, assume that matter is not created, just coding improved.
page 710: To initial singularity must give infinite redshift.
[page 73]
Misner page 713: Universe considered completely homogeneous and isotropic.
page 14: at a given moment in time, on a given spacelike hypersurface.
do you think that a universe in which nothing happens after the evolution of relativity would carry on like this one?
functioning of the scientific establishment . . .
page 717: as he keeps saying, four velocity always has unit length.
page 718: Universe is expanding but meter rods are not - or vice versa, etc.
page 79: Intergalactic spacing 106 light years, ie 1012 in universe, 1012 stars in each.
Universe may go from point set to Riemann manifold in a series of steps, ie via affine connection.
page 725: Metric does not define topology.
page 726: First law for the universe: It is considered that radiation once dominated the Universe - for the first few seconds - hint hint photon is simplest and most primordial particle [algorithm] Neutrino, graviton, Rest mass comes later. You want tp start with pure quantum gravitons?
[page 74]
. . .Misner page 736: Particles created out of vacuum at exceedingly high temperatures.
page 740: Causal isolation of parts of the universe cannot be from the beginning otherwise there is no ground for similarity of physical laws throughout the Universe [maybe parallel evolution, fundamental laws are so simple there is no other choice?]
page 742: In early days photons etc have not gone far enough to find out whether the Universe is open or closed.
745: De Sitter model of the universe.
page 749; 'Only the genius of Riemann, solitary and uncomprehended, had already won its way by the middle of the [nineteenth] century, to a new conception of space, in which space was deprived of its rigidity, and in which power to take part in physical events was recognized as possible. [2014 quantum mechanics deals with action/energy/time and is prior to space]
[page 75]
. . .
page 763: Standard hot big bang model.
Crucial assumption: the universe began in a state of rapid expansions from a very nearly homgeneous isotropic condition of infinite (or near infinite) density and temperature.'
page 764: initial thermal equilibrium between all particles,
few secs old, T = 1010 K. density = 105 gram per cc.
. . .
page 769: What preceded initial singularity - here comes the discussion of intelligence.
page 780: Photon and particle wavelengths all redshifted in proportion to size of the universe.
. . .