arXiv subjects

L. Polley

Publications and source records attributed to L. Polley.

12 recordsLinked to original sources

arXiv2012

Modelling an observer's branch of extremal consciousness

Extreme-order statistics is applied to the branches of an observer in a many-worlds framework. A unitary evolution operator for a step of time is constructed, generating pseudostochastic behaviour with a power-law distribution when applied repeatedly to a particular initial state. The operator models the generation of records, their dating, the splitting of the wavefunction at quantum events, and the recalling of records by the observer. Due to the huge ensemble near an observer's end, the branch with the largest number of records recalled contains almost all "conscious dimension".

quant-ph↗

arXiv2005

"Measurement" by neuronal tunneling: Implications of Born's rule

A non-collapse scenario for ``conscious'' selection of a term from a superposition was proposed in quant-ph/0309166: thermally assisted tunneling of neuronal pore molecules. But ``observers'' consisting of only two neurons appear to be at odds with Born's rule. In the present paper, an observer is assumed to possess a large number of auxilliary properties irrelevant for the result of the measurement. Born's rule then reduces to postulating that, prior to the result becoming conscious, irrelevant properties are in an entangled state with maximum likelihood, in the sense that phase-equivalent entanglements cover a maximal fraction of the unit sphere (leading to equal-amplitude superpositions).

quant-ph↗

arXiv2005

"Measurement" as a neurophysical process: a hypothetical linear and deterministic scenario

Tunnel amplitudes of molecular configurations (like neuronal channel pores) may be very sensitive to thermal vibrations of the barrier width (vibration-assisted tunneling) resulting in pseudo-random spikes of widely varying sizes. An observer who ``lives'' behind the barrier would experience as an ``event'' an accidental minimum of the barrier width, the timing being determined by the microstate of the neuron's heat bath. In two neurons, set to detect a ``left'' or ``right'' state of an object, firing amplitudes typically differ so much as to produce a quasi-selection of one option.

quant-ph↗

arXiv2001

Spin 1/2 as propagation on a lattice with symmetries modulo gauge transformations

Relativistic spin 1/2, as represented by Susskind's 1977 discretization of the Dirac equation on a spatial lattice, is shown to follow from basic, not typically relativistic but essentially quantum theoretic assumptions: that position eigenstates propagate to nearest neighbours while respecting lattice symmetries modulo gauge transformations.

quant-ph↗

arXiv2001

Position eigenstates and the Statistical Axiom of Quantum Mechanics

Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the time evolution to obey the Schroedinger equation, and it can be used to complete a truely basic derivation of the statistical axiom as recently proposed by Deutsch.

quant-ph↗

arXiv2000

Position eigenstates, symmetries, and the redundant hermiticity of free-particle Hamiltonians

The quantum state of a particle can be completely specified by a position at one instant of time. This implies a lack of information, hence a symmetry, as to where the particle will move. We here study the consequences for free particles of spin 0 and spin 1/2. On a cubic spatial lattice a hopping equation is derived, and the continuum limit taken. Spin 0 leads to the Schroedinger equation, and spin 1/2 to the Weyl equation. Both Hamiltonians are hermitian automatically, if time-reversal symmetry is assumed. Hopping amplitudes with a "slight" inhomogeneity lead to the Weyl equation in a metric-affine space-time.

quant-ph↗

arXiv2000

Quantization via hopping amplitudes: Schroedinger equation and free QED

Schroedinger's equation with scalar and vector potentials is shown to describe "nothing but" hopping of a quantum particle on a lattice; any spatial variation of the hopping amplitudes acts like an external electric and/or magnetic field. The main point of the argument is the superposition principle for state vectors; Lagrangians, path integrals, or classical Hamiltonians are not (!) required. Analogously, the Hamiltonian of the free electromagnetic field is obtained as a twofold continuum limit of unitary hopping in Z(N) link configuration space, if gauge invariance and C and P symmetries are imposed.

quant-ph↗

arXiv2000

Quantum-mechanical probability from the symmetries of two-state systems

In 1989, Deutsch gave a basic physical explanation of why quantum-mechanical probabilities are squares of amplitudes. Essentially, a general state vector is transformed into a highly symmetric equal-amplitude superposition. The argument was recently elaborated and publicised by DeWitt. It has remained incomplete, however, inasmuch as both authors anticipate the usual normalization (sum of amplitudes squared) of state vectors. In the present paper, a thought experiment is devised in which Deutsch's idea is demonstrated independently of the normalization, exploiting further symmetries instead.

quant-ph↗

arXiv1995

QCD AT FINITE BARYON DENSITY WITH t-ASYMMETRIC FERMIONS

Susskind's continuous-time fermions, with two flavours, can be latticized using a one-sided time derivative. We are presently investigating the interacting case, where we hope to find the onset at finite $μ$ at the right place due to the reduced number of flavours. As for these fermions there is only a discrete chiral symmetry left over, the lightness of pions in the broken phase has to be investigated.

hep-lat↗

arXiv1994

Negative-Energy Spinors and the Fock Space of Lattice Fermions at Finite Chemical Potential

Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial ``energy'' in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We consider Kogut-Susskind fermions and, for comparison, fermions with an asymmetric one-step time derivative.

hep-lat↗

arXiv1993

C-Periodicity and the Physical Mass in the 3-State Potts Model

The standard infinite-volume definition of connected correlation function and particle mass in the 3-state Potts model can be implemented in Monte Carlo simulations by using C-periodic spatial boundary conditions. This avoids both the breaking of translation invariance (cold wall b.c.) and the phase-dependent and thus possibly biased evaluation of data (periodic boundary cconditions). The numerical feasibility of the standard definitions is demonstrated by sample computations on a 24*24*48 lattice.

hep-lat↗

arXiv1992

Cosmic Strings on the Lattice

We develop a formalism for the quantization of topologically stable excitations in the 4-dimensional abelian lattice gauge theory. The excitations are global and local (Abrikosov-Nielsen-Olesen) strings and monopoles. The operators of creation and annihilation of string states are constructed; the string Green functions are represented as a path integral over random surfaces. Topological excitations play an important role in the early universe. In the broken symmetry phase of the $U(1)$ spin model, closed global cosmic strings arise, while in the Higgs phase of the noncompact gauge-Higgs model, local cosmic strings are present. The compact gauge-Higgs model also involves monopoles. Then the strings can break if their ends are capped by monopoles. The topology of the Euclidean string world sheets are studied by numerical simulations.

hep-lat↗