CELL THEORY OF NATURE Work in process David Ritz Finkelstein1 October 17, 2008 1Physics, Georgia Institute of Technology, Atlanta, Georgia. fi[email protected] 2 Time is the number of motion with regard to before and after. Aristotle, Physics I would indeed admit these infinitely small spaces and times in geometry, for the sake of invention, even if they are imaginary. But I am not sure whether they can be admitted in nature. G. W. Leibniz [3] It is, for example, true that the result of two successive acts is unaffected by the order in which they are performed; and there are at least two other laws which will be pointed out in the proper place. These will perhaps to some appear so obvious as to be ranked among necessary truths, and so little important as to be undeserving of special notice. And probably they are noticed for the first time in this Essay. Yet it may with confidence be asserted, that if they were other than they are, the entire mechanism of reasoning, nay the very laws and constitution of the human intellect, would be vitally changed. A Logic might indeed exist, but it would no longer be the Logic we possess. G. Boole [14] To be sure, it has been pointed out that the introduction of a space-time contin- uum may be considered as contrary to nature in view of the molecular structure of everything which happens on a small scale. It is maintained that perhaps the success of the Heisenberg method points to a purely algebraical method of description of nature, that is, to the elimination of continuous functions from physics. Then, however, we must also give up, by principle, the space-time continuum. It is not unimaginable that human ingenuity will some day find methods which will make it possible to proceed along such a path. At the present time, however, such a program looks like an attempt to breathe in empty space. A. Einstein [29] And so I suggested to myself that electrons cannot act on themselves; they can only act on other electrons. This means that there is no field at all. R. P. Feynman [34] Contents 1 Strata of actuality 5 1.1 Atoms of atoms. 5 1.1.1 Simplicity and stability . 7 1.1.2 Locality . 8 1.1.3 Swaps . 10 1.1.4 Beneath geometry . 11 1.1.5 The cosmic crystal film . 13 1.1.6 Praxics . 15 1.1.7 Indefinite probability forms . 17 1.1.8 Probability vector spaces and algebras . 17 1.1.9 The need for full quantization . 18 1.1.10 A cellular hypothesis . 19 1.1.11 Quantum time . 23 1.2 The idea of the queue . 26 1.2.1 Strata . 29 1.2.2 The Clifford algebras of Fermi and Dirac . 36 1.2.3 The origins of i .............................. 37 1.2.4 The origins of H ............................. 38 1.2.5 Notation . 40 1.2.6 Q terminology . 41 1.2.7 The origins of g ............................. 42 1.2.8 Fields and queues . 44 1.2.9 Dynamical law of the queue . 45 1.2.10 The vacuum queue . 48 1.2.11 The cosmic crystal . 49 1.3 Quantization . 51 1.3.1 Canonical quantization . 53 1.3.2 Full quantization strategy . 55 1.3.3 Regularization . 58 1.3.4 Quantification . 59 3 4 CONTENTS 1.3.5 Cellularization . 59 1.3.6 The choice of statistics . 60 1.3.7 Internal structure of the photon and graviton . 62 1.3.8 Indefinite forms . 63 1.3.9 The representation of symmetry . 64 1.3.10 Finiteness . 64 1.4 The groups of nature . 66 1.4.1 Canonical strata . 68 1.4.2 Metric forms . 69 1.4.3 Fully quantum strata . 69 1.4.4 Fully quantum self-organization . 70 1.4.5 Full quantization tactics . 71 1.5 Fully quantum regularization . 74 1.5.1 Fully quantum dynamics . 74 1.5.2 Gauge . 74 1.5.3 Spin . 78 1.5.4 Real quantum theory . 79 1.5.5 Root vectors and quanta . 80 1.5.6 Full Fermi quantization . 81 1.5.7 Physical Lie algebras . 82 1.6 Gravity and other gauge fields . 83 1.6.1 History as quantum variable . 84 1.6.2 Fully quantum equivalence principle . 85 1.6.3 Weyl gauge strategy . 88 1.6.4 Kaluza gauge strategy . 89 1.6.5 Queue gauge strategy . 90 1.6.6 Fully quantum gauge group . 91 1.6.7 The space-time truss . 92 1.6.8 The gravitational and gauge potentials . 93 1.6.9 Vacuum . 94 1.7 Unifications . 95 1.7.1 Being and becoming . 95 1.7.2 Gravity and quantum theory . 96 1.7.3 Products . 96 1.7.4 Non-commutativity and granularity . 97 1.7.5 System and metasystem . 98 1.8 Outline . 99 CONTENTS 5 2 Linear praxics 101 2.1 Praxics in general . 101 2.2 Heisenberg and von Neumann praxics . 102 2.2.1 The system itself . 105 2.2.2 The equatorial bulge in Hilbert space . 106 2.2.3 Commutative reduction . 107 2.3 Standard semantics . 107 2.3.1 The orthogonal group . 108 2.3.2 Probability vectors . 108 2.3.3 The probability form . 110 2.3.4 The linear operators . 110 2.3.5 The projectors . 111 2.4 Change is a quantum effect . 112 2.5 Simple systems . 112 2.6 Probabilities . 113 2.7 Mixtures . 113 2.8 Transformations . 114 2.9 States, proper and coordinate . 115 2.9.0.1 Proper state . 116 2.9.0.2 Coordinate state . 116 2.10 Praxiology and its singular limit . 116 2.10.1 Ritz combination rule. 122 2.10.2 Probability Principle. 122 2.10.3 System catenation . 123 2.10.4 Relation to probability . 123 2.10.5 The von Neumann ambiguity . 124 2.10.6 Schr¨odinger's frozen cat . 132 2.10.7 Fundamental law . 134 3 Polynomial quantum logic 137 3.1 Set algebras . 137 3.1.1 The random set . 137 3.1.2 The queue . 138 3.1.3 Input-output processes . 139 3.2 Clifford algebra . 141 3.2.1 Clifford semantics . 142 3.2.2 Fermi Clifford algebra . 142 3.2.3 Fermi vectors . 143 3.2.4 Grade operator . ..