Nature as quantum computer

Set theory reduces all processes to assembly and disassembly. A similar architecture is proposed for nature as quantum computer. It resolves the classical space-time underlying Feynman diagrams into a quantum network of creation and annihilation processes, reducing kinematics to quantum statistics, and regularizing the Lie algebra of the Einstein diffeomorphism group. The usually separate and singular Lie algebras of kinematics, statistics, and conserved currents merge into one regular statistics Lie algebra.Comment: 16 pages. Paper contributed to a memorial volume for Jack Schwartz edited by E. Schonber

MELENCOLIA I: The physics of Albrecht Duerer

Duerer's engraving ``MELENCOLIA I'' was circulated in two versions not previously distinguished. Besides their conspicuous early Renaissance scientific instruments and tools, they contain numerous apparently unreported concealments whose detection reveals heresies expressed in the work. The main one is encoded in the motto {\em MELENCOLIA I} itself: Natural Philosophy, not Mathematical Philosophy or Theological Philosophy, is the way to knowledge. Unusual optical illusions and subliminal images, differing between the two versions, declare the relativity and ambiguity of perception, and indicate that the work was a Humanist document intended for a Humanist viewership.Comment: 38 pages. Corrects and extends an earlier versio

Homotopy approach to quantum gravity

I construct a finite-dimensional quantum theory from general relativity by a homotopy method. Its quantum history is made up of at least two levels of fermionic elements. Its unitary group has the diffeomorphism group as singular limit. Its gravitational metrical form is the algebraic square. Its spinors are multivectors.Comment: For International Journal of Theoretical Physics, Oberwolfach 2006 issu

Quantum field theory in quantum set algebra

A modular quantum architecture is given for the space-time, particles, and fields of the Standard Model and General Relativity. It assumes a right-handed neutrino, so that based on their multiplet structure all fundamental fermions have isospin 1/2. This opens the possibility that the Higgs field can be identified with the Yang $i$-field of 1947. The quantum gravitational metric form proposed is a quantification of the Killing form of the quantum space-time cell. There is no trace of the black hole phenomenon at the one-cell quantum level.Comment: 19 page

General quantization

Segal's hypothesis that physical theories drift toward simple groups follows from a general quantum principle and suggests a general quantization process. I general-quantize the scalar meson field in Minkowski space-time to illustrate the process. The result is a finite quantum field theory over a finite quantum space-time with higher symmetry than the singular theory. Multiple quantification connects the levels of the theory.Comment: 25 pages. Edited to 21 pages. References added. Typos remove

Palev Statistics and the Chronon

A finite relativistic quantum space-time is constructed. Its unit cell has Palev statistics defined by a spin representation of an orthogonal group. When the Standard Model and general relativity are physically regularized by such space-time quantization, their gauges are fixed by nature; the cell groups remain.Comment: 14 pages. For the proceedings of IX International Workshop on Lie Theory and its Applications in Physics. Bulgarian Academy of Sciences 2011. Ed. V. K. Dobre

Interpretation of the topological terms in gauge system

We provide an alternative interpretation for the topological terms in physics by investigating the low-energy gauge interacting system. The asymptotic behavior of the gauge field at infinity indicates that it traces out a closed loop in the infinite time interval: -infinity, + infinity. Adopting Berry's argument of geometric phase, we show that the adiabatic evolution of the gauge system around the loop results in an additional term to the effective action: the Chern-Simons term for three-dimensional spacetime, and the Pontrjagin term for the four-dimensional spacetime.Comment: 12 pages, RevTeX; submitted to Phys. Rev. Let

Quantum-Statistical Computation

Systems of spin 1, such as triplet pairs of spin-1/2 fermions (like orthohydrogen nuclei) make useful three-terminal elements for quantum computation, and when interconnected by qubit equality relations are universal for quantum computation. This is an instance of quantum-statistical computation: some of the logical relations of the problem are satisfied identically in virtue of quantum statistics, which takes no time. We show heuristically that quantum-statistical ground-mode computation is substantially faster than pure ground-mode computation when the ground mode is reached by annealing.Comment: 12 pages, LaTeX Minor changes for journa

Quantum ground-state computation with static gates

We develop a computation model for solving Boolean networks that implements wires through quantum ground-state computation and implements gates through identities following from angular momentum algebra and statistics. The gates are static in the sense that they contribute Hamiltonian 0 and hold as constants of the motion; only the wires are dynamic. Just as a spin 1/2 makes an ideal 1-bit memory element, a spin 1 makes an ideal 3-bit gate. Such gates cost no computation time: relaxing the wires alone solves the network. We compare computation time with that of an easier Boolean network where all the gate constraints are simply removed. This computation model is robust with respect to decoherence and yields a generalized quantum speed-up for all NP problems.Comment: 10 pages, LaTeX, 1 PS figur

Finite Quantum Kinematics of the Harmonic Oscillator

Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we apply general quantization to the time-independent linear harmonic oscillator. The unstable Heisenberg group becomes the stable group SO(3). This freezes out the zero-point energy of very soft or very hard oscillators, like those responsible for the infrared or ultraviolet divergencies of usual field theories, without much changing the medium oscillators. It produces pronounced violations of equipartition and of the usual uncertainty relations for soft or hard oscillators,and interactions between the previously uncoupled excitation quanta of the oscillator, weakly attractive for medium quanta, strongly repulsive for soft or hard quanta.Comment: Based on Ph.D. thesis of Mohsen Shiri-Garakan