The history of the particle concept is briefly reviewed, with particular emphasis on the `foliation dependence' of many particle creation models, and the possible connection between our notion of particle and our notion of simultaneity. It is argued that the concept of `radar time' (originally introduced by Sir Hermann Bondi in his work on k-calculus) provides a satisfactory concept of `simultaneity' for observers in curved spacetimes. This is used to propose an observer-dependent particle interpretation, applicable to an arbitrary observer, depending solely on that observers motion and not on a choice of coordinates or gauge. This definition is illustrated with application to non-inertial observers and simple cosmologies, demonstrating its generality and its consistency with known cases.
The history of the particle concept is briefly reviewed, with particular emphasis on the foliation dependence' of many particle creation models, and the possible connection between our notion of particle and our notion of simultaneity. It is argued that the concept of radar time' (originally introduced by Sir Hermann Bondi in his work on k-calculus) provides a satisfactory concept of `simultaneity' for observers in curved spacetimes. This is used to propose an observer-dependent particle interpretation, applicable to an arbitrary observer, depending solely on that observers motion and not on a choice of coordinates or gauge. This definition is illustrated with application to non-inertial observers and simple cosmologies, demonstrating its generality and its consistency with known cases.
The nature of time has long been debated in human history and nowadays is considered of central importance for understanding quantum gravity. We focus on and advocate the relational concept of time, which was put forward in the 17th century in opposition to Newton's absolute time, and only in 1990 explored in a quantum mechanical framework by Carlo Rovelli. After a historical introduction the mathematical models of time are carefully analyzed in chapter 1, followed by a discussion of the role of time played in fundamental theories. Using as an example nonrelativistic mechanics, the process of parametrization is explained, leading to a separation of a 'canonical time coordinate' from an arbitrary evolution parameter. The discussion of the role of time in special and general relativity as well as in quantum mechanics shows that more fundamental theories use less structure of time. This is followed by an exposition of the history of the relational concept of time, which negates the existence of an absolute duration and therefore often is called "timeless". Next it is shown how fundamental theories can be formulated and re-interpreted using this concept. We put emphasis on the hitherto neglected connection between relationalism and non-extensibility, while absolute time is shown to be unproblematic in classical mechanics just because of the possibility to extend the system without changing its nature. We conclude chapter 1 with a new axiomatic basis for the construction of time observables based on a simultaneity relation between 'observations', which are treated as a primitive concept and intuitively correspond to measurement events, but without knowing 'when' these events occur. There is no fundamental time observable; any observable qualifies as a time observable, if it allows to separate all instants. Chapter 2 gives a brief account of three main problems connected with time: a) The problem of the arrow of time. This has to be disentangled from the problem of irreversibility: a solution of the latter essentially excludes cyclic motions and is required for a solution of the former, which consists in showing that a fundamental direction between any two non-identical instants is physically meaningful. We give a formal definition of the arrow of time. This classical analysis is followed by a review of the problem of the arrow of time in quantum theory, where the situation becomes more complicated because of indeterminism. The discussion shows that there is no experimental evidence for a fundamental arrow of time, so that no contradiction with the relational concept of time arises. b) The problem of time measurement, which is of particular importance for the relational approach, in which time has no reality except if measured by a clock. In quantum theory useful time operators seem to be possible only within the more general formalism of positive operator valued measures (POVM). Clocks based on an oscillation mechanism do however require phase measurements; quantum phase operators can be defined as certain POVMs. Phase difference operators do also exist in the traditional Hilbert space formalism, if another quantization is used, as is done with relational quantization. c) The problem of quantum gravity is sketched only briefly. Chapter 3 introduces and discusses a model of Rovelli consisting of two oscillators with no external time. In this model one oscillator is considered as a clock and defines a relational time for the other one. In the first section we introduce this model and generalize it to a free massless scalar field in one dimension. We establish the relation between a single field mode and the infrared behaviour of the field through constants of motion. In the second section after a short review of canonical quantization we review Rovelli's quantization and generalize it to the free field. We could not prove the existence of the quantization map, but calculations using computer algebra indicate that the quantization does exist. For an enlarged algebra we are able to prove the nonexistence of a quantization map similar to a proof by Groenewold and van Hove. In chapter 4 we observe that a clock time always requires infinitely many degrees of freedom, and we make the hypothesis that a time observable is given by the infrared behaviour of quantum fields, leading to a classical notion of time when using algebraic quantum mechanics. This does however not solve the main problem of quantum relationalism: Which conditions determine a particular evolution?
Despite its name, Quantum Field Theory (QFT) has been built to describe interactions between localizable particles. For this reason the actual formalism of QFT is partly based on a suitable generalization of the one already used for systems of point particles. This circumstance gives rise to a number of conceptual problems, stemming essentially from the fact that the existence within QFT of non-equivalent representations implies the existence of field theories allowing, within the same theory, different, inequivalent, descriptions of particles. This led some authors to claim that in QFT the concept itself of particle should be abandoned. In this paper we will shortly discuss the validity of this claim, as well as the possibilities, so far existing, of building alternative versions of QFT, not designed in advance to allow some kind of particle representation. We will also spend some words about the generalizations of the concept itself of particle which could grant for a better cohabitation of particles and fields within a wider formulation of QFT. The latter is indispensable if we want to extend the range of application of QFT from particle physics or simple condensed matter physics to other domains of scientific research.
The development of modern quantum theory has superseded the classical theory of particles. Nevertheless, the imagery and terminology of the classical theory still surivive, both in intuitive understanding and mathematical formulation. This paper shows that although the classical concept of a particle may be useful for some purposes of intuition, it is useless for others, and it is never necessary. In microphysics, particles are usually; assigned a cherge e and a mass m. we discuss the meaning of these quantities in terms of laboratory; experience.
Abstract The temporal parameter t ∈ ℝ carries three properties that no experiment has confirmed as features of physical reality: negative extension, loop-admitting topology, and reversal symmetry. We identify these as surplus structure in the sense of Weatherall, applying Gisin's observation on ℝ-modelling to the temporal parameter specifically. Its operational content is N_ref: the accumulated state-transition count of a reference system, non-negative and monotonically non-decreasing. The caesium-133 hyperfine oscillator is one realisation; the framework is characterised axiomatically (N1–N4, Section 4) and is independent of the choice of clock. We establish two theorems. Theorem 1: restricting the Wheeler–DeWitt scalar-field clock to its operationally grounded domain φ ∈ [0, ∞) halves the minisuperspace solution space, excluding independently contracting universes. Theorem 2: within the Page–Wootters framework, the process-accumulation arrow (a spectral property of the clock operator) and the thermodynamic arrow (a boundary condition on the constraint surface) are formally independent. The Bondi k-calculus then derives the full Lorentz transformation — including the relativity of simultaneity — from three operational inputs: transition-count ratios between inertial observers, the relativity principle, and a finite signal speed c. No prior notion of time, metric, or spacetime is assumed; 1/γ is a theorem rather than an input. Closed timelike curves, parameter reversal in T-symmetry, and the block universe as the default interpretation of the formalism are shown to depend on the surplus structure of ℝ and to lack independent empirical support.
The analysis of geometric phases is briefly reviewed by emphasizing various gauge symmetries involved. The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry becomes explicit in this formulation and specifies physical observables; the choice of a basis set which specifies the coordinates in the functional space is arbitrary in the second quantization, and a sub-class of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. It is shown that the hidden local symmetry provides a basic concept which replaces the notions of parallel transport and holonomy. We also point out that our hidden local gauge symmetry is quite different from a gauge symmetry used by Aharonov and Anandan in their definition of non-adiabatic phases.
A literature review of related articles, either by affinity or by contrast, to a fundamental theory of time and space - time previously developed. It shows how from a primitive concept of preparticle and membership relation of set theory, and four postulates that refer to simple concepts, derived concepts of time, space-time, reference frame, particle, fields, and interaction between fields are obtained. The problem of the "direction " of time is analyzed and a paradox whose solution goes against the idea that this direction is fixed by the increase of entropy prescribed by the second law of thermodynamics is examined. In our theory this direction is unique to each reference frame, and is an intrinsic property of time. Two kinds of particles are described as derived concepts, and it is shown that one of them fullfills the Bose-Einstein statistics, and the other one fullfills the Fermi-Dirac statistics. We also consider the analysis of the wave function concepts and particle detector as concepts derived from the mentioned theory. Using these concepts, the process of locating both a macroscopic body (typical location) as well as one of a microscopic scale (quantum localization) is analyzed, and the significance of the location is examined in both cases.