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Peter Morgan

Publications and source records attributed to Peter Morgan.

At least 19 recordsLinked to original sources
arXiv2022

Classical and Quantum Measurement Theory

Classical and quantum measurement theories are usually held to be different because the algebra of classical measurements is commutative, however the Poisson bracket allows noncommutativity to be added naturally. After we introduce noncommutativity into classical measurement theory, we can also add quantum noise, differentiated from thermal noise by Poincar\'e invariance. With these two changes, the extended classical and quantum measurement theories are equally capable, so we may speak of a single "measurement theory". The reconciliation of general relativity and quantum theory has been long delayed because classical and quantum systems have been thought to be very different, however this unification allows us to discuss a unified measurement theory for geometry in physics.

quant-ph↗
arXiv2021

A source fragmentation approach to interacting quantum field theory

A corollary to the Reeh-Schlieder theorem is proved: that the time-ordered Vacuum Expectation Values and the S-matrix of a regularized Lagrangian quantum theory can be approximated by a local operator that uses nonlinear functionals of a locally supported source function. For the Wightman axioms, this suggests a modification that takes the algebra of measurement operators not to be generated by an operator-valued distribution. The use of operator-valued nonlinear functionals of a source function introduces many abstract fragments of the source to give a well-defined top-down construction of interacting quantum fields, in contrast to a bottom-up blocking and scaling construction or to analyzing response to changing renormalization scales. The construction can also be thought of as solving a localized inverse problem for the interacting dynamics or as a generating function for multi-point bound state fields.

hep-th↗
arXiv2021

The collapse of a quantum state as a joint probability construction

The collapse of a quantum state can be understood as a mathematical way to construct a joint probability density even for operators that do not commute. We can formalize that construction as a non-commutative, non-associative collapse product that is nonlinear in its left operand as a model for joint measurements at timelike separation, in part inspired by the sequential product for positive semi-definite operators. The familiar collapse picture, in which a quantum state collapses after each measurement as a way to construct a joint probability density for consecutive measurements, is equivalent to a no-collapse picture in which L\"uders transformers applied to subsequent measurements construct a Quantum-Mechanics--Free-Subsystem of Quantum Non-Demolition operators, not as a dynamical process but as an alternative mathematical model for the same consecutive measurements. The no-collapse picture is particularly simpler when we apply signal analysis to millions or billions of consecutive measurements.

quant-ph↗
arXiv2019

Nondynamical modeling of resonances in a Quantum Field formalism

Well-defined nonlinear deformations of free quantum fields are introduced as manifestly Poincar\'e invariant scaling and resonance properties of non-dynamical scale models in Minkowski space, instead of introducing nonlinear dynamical deformations of free quantum fields that require the various truncations and scaling corrections of regularization and renormalization. With the given algebraic construction, energy and momentum operators can be constructed \emph{ex post facto} as the generators of translations. A weakened version of microcausality emerges naturally, "convex hull microcausality" ---that operators associated with two regions of space--time must commute if \emph{the convex hulls of} those regions are space-like separated---, which is enough for us to be able to construct an abundant class of interacting quantum fields.

quant-ph↗
arXiv2019

An Algebraic Approach to Koopman Classical Mechanics

Classical mechanics is presented here in a unary operator form, constructed using the binary multiplication and Poisson bracket operations that are given in a phase space formalism, then a Gibbs equilibrium state over this unary operator algebra is introduced, which allows the construction of a Hilbert space as a representation space of a Heisenberg algebra, giving a noncommutative operator algebraic variant of the Koopman-von Neumann approach. In this form, the measurement theory for unary classical mechanics can be the same as and inform that for quantum mechanics, expanding classical mechanics to include noncommutative operators so that it is close to quantum mechanics, instead of attempting to squeeze quantum mechanics into a classical mechanics mold. The measurement problem as it appears in unary classical mechanics suggests a classical signal analysis approach that can also be successfully applied to the measurement problem of quantum mechanics. The development offers elementary mathematics that allows a formal reconciliation of "collapse" and "no-collapse" interpretations of quantum mechanics.

quant-ph↗
arXiv2017

Classical states, quantum field measurement

Classical Koopman--von Neumann Hilbert spaces of states are constructed here by the action of classical random fields on a vacuum state in ways that support an action of the quantized electromagnetic field and of the $U(1)$--invariant observables of the quantized Dirac spinor field, allowing a manifestly Lorentz invariant classical understanding of the state spaces of the two field theories, generalizing the Quantum--Mechanics--Free Systems of Tsang&Caves and Quantum Non-Demolition measurements. The algebra of functions on a classical phase space is commutative but the algebra of classical observables associated with coordinate transformations is noncommutative, so that, for example, we can as much ask whether a classical state is an eigenstate of a rotation as we can in quantum mechanics and so that entangled states can be distinguished from mixed states, making classical random fields as weird as quantum fields.

quant-ph↗
arXiv2015

Multi-particle quantum fields for bound states and interactions

The Fock-Hilbert space generated by a single-particle interaction-free Wightman field is augmented by introducing non-trivial multi-particle (that is, multi-point, multilinear) quantum fields, which is justified insofar as Haag's theorem establishes that free field Fock-Hilbert spaces cannot model bound or interacting states. Two Gaussian constructions are given: one that modifies the combinatoric factors and masses associated with products of propagators and a second for which locality is determined by the center of mass of the n-particles and relative separations of the n-particles determine the strength of resonance; it is shown how the two constructions may also be used together. Finally, a method is given for generating non-Gaussian n-particle quantum fields that quite closely tracks familiar interacting quantum fields but that is significantly better-defined and that offers a much richer algebraic structure for future use.

hep-th↗
arXiv2014

Regularization by Test Function

Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by properties of test functions, in a way that preserves Poincar\'e invariance, microcausality, and the Fock-Hilbert space structure of the free field. The construction can be taken to be a physically comprehensible regularization because we can introduce a sequence that has a limit that is a conventional interacting quantum field, with the usual informal dependence of the effective dynamics on properties of the experimental apparatus made formally explicit as a dependence on the test functions that are used to model the experimental apparatus.

quant-ph↗
arXiv2013

Nonlinear dependence of the renormalization scale on test functions

Quantum electrodynamics exhibits an informal nonlinear dependence on Lorentz invariant test function properties that determine the renormalization scale, such as Mandelstam variables, contrary to the linear dependence on test functions that is required by the Wightman axioms. A first example of an alternative interacting quantum field formalism that has a comparable weakly nonlinear dependence on Dirac spinor test functions is constructed, using U(1)-gauge connections and U(1)-gauge invariant Dirac spinor test functions.

quant-ph↗
arXiv2012

Nonlinear Wightman fields

A nonlinear Wightman field is taken to be a nonlinear map from a linear space of test functions to a linear space of Hilbert space operators, with inessential modifications to other axioms only to the extent dictated by the introduction of nonlinearity. Two approaches to nonlinear quantum fields are constructed and discussed, the first of which, starting from Lagrangian QFT, offers a fresh perspective on renormalization, while the second, starting from linear Wightman fields, provides an extensive range of well-defined nonlinear theories.

math-ph↗
arXiv2012

A graphical presentation of signal delays in the datasets of Weihs et al

A graphical presentation of the timing of avalanche photodiode events in the datasets from the experiment of Weihs et al. [Phys. Rev. Lett. 81, 5039 (1998)] makes manifest the existence of two types of signal delay: (1) The introduction of rapid switching of the input to a pair of transverse electro-optical modulators causes a delay of approximately 20 nanoseconds for a proportion of coincident avalanche photodiode events; this effect has been previously noted, but a different cause is suggested by the data as considered here. (2) There are delays that depend on in which avalanche photodiode an event occurs; this effect has also been previously noted even though it is only strongly apparent when the relative time difference between avalanche photodiode events is near the stated 0.5 nanosecond accuracy of the timestamps (but it is identifiable because of 75 picosecond resolution). The cause of the second effect is a difference between signal delays for the four avalanche photodiodes, for which correction can be made by straightforward local adjustments (with almost no effect on the degree of violation of Bell-CHSH inequalities).

quant-ph↗
arXiv2010

Comment on "A glance beyond the quantum model" [arXiv:0907.0372]

The aim of "A glance beyond the quantum model" [arXiv:0907.0372] to modernize the Correspondence Principle is compromised by an assumption that a classical model must start with the idea of particles, whereas in empirical terms particles are secondary to events. The discussion also proposes, contradictorily, that observers who wish to model the macroscopic world classically should do so in terms of classical fields, whereas, if we are to use fields, it would more appropriate to adopt the mathematics of random fields. Finally, the formalism used for discussion of Bell inequalities introduces two assumptions that are not necessary for a random field model, locality of initial conditions and non-contextuality, even though these assumptions are, in contrast, very natural for a classical particle model. Whether we discuss physics in terms of particles or in terms of events and (random) fields leads to differences that a glance would be well to notice.

quant-ph↗
arXiv2009

Equivalence of the Klein-Gordon random field and the complex Klein-Gordon quantum field

The difference between a Klein-Gordon random field and the complex Klein-Gordon quantum field is characterized, explicitly comparing the roles played by negative frequency modes of test functions in creation and annihilation operator presentations of the two theories. The random field and the complex quantum field can both be constructed from the same creation and annihilation operator algebra, making them equivalent in that sense.

quant-ph↗
arXiv2009

An empirically equivalent random field for the quantized electromagnetic field

A random field that is empirically equivalent to the quantized electromagnetic field is constructed. A mapping between the creation and annihilation operator algebras of a random field and of the quantized electromagnetic field provides a functor between the algebras and the Hilbert spaces generated by the vacuum states over those algebras. The functor inevitably does not extend to a functorial relationship between the local algebras generated by the random field and by the quantized electromagnetic field, but the empirical content provided by the vacuum state restores an empirical equivalence through the Hilbert spaces. The isomorphism from one creation and annihilation algebra to the other is not translation invariant because it depends on mapping positive frequency modes of one helicity to equivalent negative frequency modes, but the two theories taken independently are presented in equally well-defined and manifestly Lorentz and translation covariant ways.

quant-ph↗
arXiv2009

Lie random fields

The algebras of interacting "Lie random fields" that were introduced in J. Math. Phys. 48, 122302 (2007) are developed further. The conjecture that the vacuum vector defines a state over a Lie random field algebra is proved. The difference between Lie random field algebras and quantum field algebras is the triviality of the field commutator at time-like separation, the field commutator being trivial at space-like separation in both cases. Many properties that are usually taken to be specific to quantum theory, such as the superposition of states, entanglement, quantum fluctuations, and the violation of Bell inequalities, are also properties of Lie random fields.

quant-ph↗
arXiv2008

The direction of time in quantum field theory

The algebra of observables associated with a quantum field theory is invariant under the connected component of the Lorentz group and under parity reversal, but it is not invariant under time reversal. If we take general covariance seriously as a long-term goal, the algebra of observables should be time-reversal invariant, and any breaking of time-reversal symmetry will have to be described by the state over the algebra. In consequence, the modified algebra of observables is a presentation of a classical continuous random field.

quant-ph↗
arXiv2008

The straw man of quantum physics

The violation of Bell inequalities by experiment has convinced physicists that we cannot maintain a classical view of the world. When we argue against the possibility of local realist hidden-variable models, however, the ubiquitous requirement of realism, that "measurement results depend on pre-existing properties of objects that are independent of the measurement", reduces classical theory to a straw man. When our most successful physical theories have been field theories for well over a century, and probabilistic for almost as long, the proper comparison is between quantum fields and random fields, for which there are no sharply defined objects and no properties, so that realism is inapplicable. If we model quantum fluctuations explicitly, we can construct random field models as alternatives to quantum field models.

quant-ph↗