2004/2005 Topic for Criticism, Comment, Discussion, Debate and Proposals for
Papers at ANPA’s 25th Birthday Meeting in Cambridge UK – July 31st to August 5th please use cybergroup@bcs.org.uk and the previewed BCSCMsG International Symposium at CASYS ’05 in Liege, Belgium

Nilpotence provides Creation of 3+1 space-time, Standard Model Elementary Particle Physics & an Irreversible Second Law Thermodynamic Evolution in a Single Quantum Cosmology Compatible with Einstein’s General Relativity, see below.
“ Is it the unique key to the antechamber of the universe?”

Dear Colleague,

• We would like to draw to your attention, two recently discovered possibilities in theoretical physics, which are natural “extensions” of the currently described standard models of physics:-

where E, p, m, t and r are respectively energy, momentum, mass, time, space and the symbols ± 1, ± i, ± i, ± j, ± k, ± i, ± j, ± k, are used to represent the respective units required by the scalar, pseudoscalar, quaternion and multivariate vector groups, such that both amplitude and phase are uniquely and simultaneously determined by a single nilpotent state vector (in the form of a differential operator). This equation combines both Heisenberg and Schrodinger descriptions, and is necessarily non-local [1].

The spontaneous symmetry breaking, it defines, results in the simultaneous creation of 3+1 space-time and complementary elementary particle matter as currently experimentally understood in relation to the known quantizations of the strong, electro-magnetic and weak charges, including their spin, where the four vector nature of (1) ensures compatibility with Einstein’s general relativity. That is to say, it can be postulated, see B below, that it is this (description of the) nilpotent quantum vacuum as phase, from which the sought-for quantum universe would then evolve; i.e. equation (1) maybe envisaged computationally as defining “the order code” of the Universe in the subsequent evolution.

B) is the publication last year in Science in 2003 [2] of the description of the Quantum Carnot Engine (QCE). This is an extension of the classical description of the well known thermo-dynamic Carnot engine, such that the Second Law of Thermodynamics continues to hold since any quantum system must be quantum mechanically prepared prior to measurement, and where such a measurement would then (it is proposed) constitute the quantum mechanical preparation for the next cycle of the QCE, etc (so as to define an autonomous evolution in accordance with Second Law from the initial vacuum phase) see [3] and the appendix below for further mathematical support for this proposal.

In such QCE, quantum coherence alone fundamentally alters Carnot heat engine operation (ie the Carnot efficiency h for converting heat into work) from what is thermodynamically possible classically

where T_c, and T_h are the temperatures of the low temperature entropy sink and the high temperature source respectively, and is the quantum coherent phase, such that by the proper choice of , work is obtained even when T_h = T_c i.e. even when there is only one thermal bath.

Thus it is only necessary to proscribe the quantum mechanical preparation of the QCE such that it concerns the nilpotent quantum vacuum as phase, in accordance with R&C’s discovery (A) to have what is a highly satisfactory quantum (& global!) process model of the evolving Universe as a single quantum mechanical system/whole, to define a true quantum cosmology. The proposed QCE may again be envisaged from a computational perspective as constituting functionally the autonomous “operating system” of the postulated evolving Universe of which (1) is the basic order code. That is, an evolution of which 3+1 space time and elementary particle matter are the entire basic quantum material constituents (as currently experimentally known) and where ‘dark energy’ would be defined as quantum coherence [3]. See appendix.

This nilpotent QCE evolution :- explains the dichotomy between matter and anti-matter; resolves any potential renormalization problem; determines all the dimensionless physical constants, which are global (ie hold everywhere in the universe); and is irreversibly without end ie will be essentially Euclidean not Elliptic/Hyperbolic.
°° See for example, Science, 303, 5th of March, 2004, Perspectives, Physics, “The Cup of the Hand” R.B. Laughlin. rbl@large.stanford.edu, 1475-1476

References.
1. Rowlands P. and Cullerne J.P. 1999 A derivation of particle structures and the Dirac Equation from fundamental symmetries, Proceeding of the 20th annual meeting of the Alternative Natural Philosophy Association (ANPA), Wesley House, Cambridge, editor K.Bowden,155-191.contact is via anpa-discussions-subscribe@yahoogroups.com
Rowlands P. and Cullerne J.P. 2001, Nilpotent Representations of the Dirac Algebra, Proceeding of the 22th annual meeting of the Alternative Natural Philosophy Association (ANPA), Wesley House, Cambridge, editor K.Bowden, 99-106.
See also at xxx.lanl.gov
the Dirac algebra and its physical interpretation, with J. P. Cullerne
arXiv:quant-ph/00010094
Applications of the nilpotent Dirac state vector, with J. P. Cullerne
arXiv:quant-ph/0103036
A foundational approach to physics
arXiv:physics/0106054
The Dirac algebra and grand unification with J. P. Cullerne
arXiv:quant-ph/0106111
QED using the nilpotent formalism, with J. P. Cullerne
arXiv:quant-ph/0109069
The group structure bases of a foundational approach to physics, with J. P.
Cullerne and Brian D. Koberlein
arXiv:physics/0110092
2. Scully M.O. et al 2003, Extracting Work fro a Single Heat Bath via Vanishing Quantum Coherence, Science, 299, 7th February, 862-864. 10.1126/science.1078955.
3. Zenergy : The “Phaseonium” of Dark Energy That Fuels the Natural Structures of the Universe. 2004, Peter Marcer, Edgar Mitchell, Peter Rowlands, Walter Schempp, present at CASYS ’03, August 11-16, 2003, International Journal of Computing Anticipatory systems, editor, Dubois D. (in press) can be requested by email as an attached file.

Appendix. General mathematical support.
The body of work known as the (functional, non standard) analysis over the surreal number fields (derived from the highly original work of the mathematician John Conway), see references below, shows that a universal model of any theory described in a language of sets, must have a unique birthorder field automorphism or birthordering (of the mathematical field of all its morphisms/mappings). And clearly the formalism of quantum mechanics defines the existence of such a theory and universal model, since Deutsch has proved the functional universality in the sense of quantum computation. This birthordering of quantum mechanics (as described by the quantum formalism) is therefore by definition irreversible and uniquely so, and can be identified with the physics of the Quantum Carnot Engine (QCE). (As is supported by the fact that this quantum mechanical extension of the classical thermodynamic Carnot Engine, retains the irreversibility demanded by the Second Law of Thermodyanmics, due to the fact that any quantum system must be prepared prior to the quantum measurement that the QCE then describes) It is then simply necessary to chose a quantum mechanical preparation that corresponds to the mathematical condition known as nilpotence (meaning can be derived from the empty set), ie the initial vacuum as a phase, as in the above.

Furthermore such a unique quantum birth order field automorphism must of necessity in physical terms in this case imply quantum non locality, so defining the “quantum non local event ” from which the basic constituents, those of space, time and matter of the above cosmology, emerge.

In Conway’s initial demonstration of such birthordering - that of the generation from the empty set, of all the numbers great and small [including the infinitesimals and the transfinite and by implication of all the mathematical functional relationships between them, which leads to the analysis over all the numbers generated this way (called surreal by Knuth)] - the half integers play a unique role!! see J.H. Conway’s book “On numbers and Games” Academic Press, London 1976 and Alling N. Foundations of Analysis over Surreal Number Fields, North Holland, Amsterdam, 1988, mathematical studies 141.

It thus becomes clear that the empty set /the vacuum as phase is the unique constituent ensuring that both mathematics & theoretical physics are both single bodies of knowledge and are essentially one and the same, as postulated by Chapline, 1999, Elsevier Physics Reports, 315, 95-105, in relation to Langlands’ programme for the unification of mathematics, which is now nearly complete [Science, 4 February, 2000, vol. 287, 792-793, D. Mackenzie]