arXiv subjects

J. H. Field

Publications and source records attributed to J. H. Field.

At least 37 records · Page 2Linked to original sources

arXiv2009

Convergence and Gauge Dependence Properties of the Resummed One-loop Quark-Quark Scattering Amplitude in Perturbative QCD

The one-loop QCD effective charge $α_s^{eff}$ for quark-quark scattering is derived by diagrammatic resummation of the one-loop amplitude using an arbitary covariant gauge. Except for the particular choice of gauge parameter $ξ= -3$, $α_s^{eff}$ is found to {\it increase} with increasing physical scale, $Q$, as $\ln Q$ or $\ln^2 Q$. For $ξ= -3$, $α_s^{eff}$ decreases with increasing $Q$ and satisfies a renormalisation group equation. Also, except for the case $ξ= 19/9$, convergence radii of geometric series are found to impose upper limits on $Q$.

hep-ph↗

arXiv2009

The Space-Time Lorentz Transformation: Relativity of Simultaneity is Incompatible with Translational Invariance

Observations of the apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not spatial intervals, so breaking space time exchange symmetry and forbidding relativity of simultaneity and length contraction. A satellite cesium clock experiment to test these predictions is proposed.

physics.gen-ph↗

arXiv2009

Time and motion in physics: the Reciprocity Principle, relativistic invariance of the lengths of rulers and time dilatation

Ponderable objects moving in free space according to Newton's First Law constitute both rulers and clocks when one such object is viewed from the rest frame of another. Together with the Reciprocity Principle this is used to demonstrate, in both Galilean and special relativity, the invariance of the measured length of a ruler in motion. The different times: `proper', `improper' and `apparent' appearing in different formulations of the relativistic time dilatation relation are discussed and exemplified by experimental applications. A non-intuitive `length expansion' effect predicted by the Reciprocity Principle as a necessary consequence of time dilatation is pointed out

physics.gen-ph↗

arXiv2009

Relativistic velocity addition and the relativity of space and time intervals

A thought experiment first proposed by Sartori is analysed using the parallel velocity addition formula of special relativity. The distances and proper-time intervals between some similarly defined spatial coincidence events are found to be widely different in different inertial frames. This relativity of space and time intervals is quite distinct from the well-known time-dilatation and length contraction effects of special relativity. Sartori's claimed derivation of the parallel velocity addition formula, assuming relativistic time dilatation, based on the thought experiment, is shown to be fortuitous.

physics.gen-ph↗

arXiv2009

Muon decays in the Earth's atmosphere, differential aging and the paradox of the twins

Observation of the decay of muons produced in the Earth's atmosphere by cosmic ray interactions provides a graphic illustration of the counter-intuitive space-time predictions of special relativity theory. Muons at rest in the atmosphere, decaying simultaneously, are subject to a universal time-dilatation effect when viewed from a moving frame and so are also observed to decay simultaneously in all such frames. The analysis of this example reveals the underlying physics of the differential aging effect in Langevin's travelling-twin thought experiment.

physics.gen-ph↗

arXiv2009

Uniformly moving clocks in special relativity: Time dilatation, but no relativity of simultaneity or length contraction

Time-like and space-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances defined by two spatially-separated clocks. The time dilatation effect is confirmed, but not `relativity of simultaneity' or `relativistic length contraction'. How these latter, spurious, effects arise from misuse of the Lorentz transformation is also explained.

physics.gen-ph↗

arXiv2009

Muon decays in the Earth's atmosphere, time dilatation and relativity of simultaneity

Observation of the decay of muons produced in the Earth's atmosphere by cosmic ray interactions provides a graphic illustration of the counter-intuitive space-time predictions of special relativity theory. Muons at rest in the atmosphere decaying simultaneously are subject to a universal time-dilatation effect when viewed from a moving frame and so are also observed to decay simultaneously in all such frames, whereas the decays of muons with different proper frames show relativity of simultaneity when observed from different inertial frames.

physics.gen-ph↗

arXiv2009

The train/embankment thought experiment, Einstein's second postulate of special relativity and relativity of simultaneity

The relativistic time dilatation effect and Einstein's second postulate of special relativity are used to analyse train/embankment thought expriments, both Einstein's original one, and an extension where observers on two trains moving at different speeds, as well as on the embankment, are considered. Whereas the relativistic analysis of Einstein's experiment shows, in contradiction to Einstein's interpretation, no `relativity of simultaneity' effect, the latter is apparent for certain events in the two-train experiment. The importance of relativistic kinematics --embodied for photons in Einstein's second postulate-- for the correct interpretation of the experiments is pointed out and demonstrated by detailed calculation of a related example.

physics.gen-ph↗

arXiv2008

Invariant space-time intervals, clock synchronisation and correct application of Lorentz transformations in special relativity

Space-like and time-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances. The former are found to be Lorentz invariant --there is no `relativistic length contraction', whereas the latter exhibit the experimentally confirmed `time dilatation' effect, without, however, `relativity of simultaneity'. It is shown how the spurious predictions of length contraction and relativity of simultaneity arise from the use of inconsistent synchronisation procedures for spatially separated clocks.

physics.gen-ph↗

arXiv2008

Absolute simultaneity and invariant lengths: Special Relativity without light signals or synchronised clocks

It is demonstrated that the measured spatial separation of two objects, at rest in some inertial frame, is invariant under space-time transformations. This result holds in both Galilean and Special Relativity. A corollary is that there are no `length contraction' or associated 'relativity of simultaneity' effects in the latter theory. A thought experiment employing four unsynchronised clocks and a single measuring rod reveals that the physical basis of the time dilatation effect is a relative velocity transformation law, not `length contraction'. Time dilatation, which is universal and translation invariant for all synchronised clocks at rest in any inertial frame, is the unique space-time phenomenon discriminating Special from Galilean Relativity.

physics.gen-ph↗

arXiv2008

Space-time attributes of physical objects and the laws of space-time physics

Physical time intervals are attributes of single physical object whereas physical space intervals are a relational attribute of two physical objects. Some consequences of the breaking of the space-time exchange symmetry inherent in the Lorentz transformation following from the above distinction are investigated. In particular, it is shown that the relativity of simultaneity and length contraction effects which naively follow from space-time symmetry of the Lorentz transformation do not occur. Seven laws describing the relation between observations of space intervals, time intervals and velocities in different reference frames are given. Only two of these laws are respected by conventional special relativity theory.

physics.gen-ph↗

arXiv2008

A sign error in the Minkowski space-time plot and its consequences

A sign error in an angle while drawing the original Minkowski plot has persisted for a century in text books and the pedagogical literature. When it is corrected, the `length contraction' effect derived from the geometry of the plot disappears. It is also shown how the `relativity of simultaneity' effect that has been derived from the plot results from a lack of correspondence between certain geometrical projections on the plot and the properties of the physical system --two spatially separated and synchronised clocks in a common inertial frame-- that they are purported to describe.

physics.gen-ph↗

arXiv2008

Why Einstein, Podolsky and Rosen did not prove that quantum mechanics is `incomplete'

It is shown that the Einstein-Podolsky-Rosen conclusion concerning the `incompleteness' of Quantum Mechanics is invalidated by two logical errors in their argument. If it were possible to perform the proposed gedanken experiment it would, in fact, show that Quantum Mechanics is `complete' for the observables discussed. Because, however, of the non square-integrable nature of the wave function, the proposed experiment gives vanishing probabilities for measurements performed in finite intervals of configuration or momentum space. Hence no conclusion as to the `completeness', or otherwise, of Quantum Mechanics can be drawn from the experiment.

quant-ph↗

arXiv2008

Inter-charge forces in relativistic classical electrodynamics: electromagnetic induction in different reference frames

The force due to electromagnetic induction on a test charge is calculated in different reference frames. The Faraday-Lenz Law and different formulae for the fields of a uniformly moving charge are used. The classical Heaviside formula for the electric field of a moving charge predicts that, for the particular spatial configuration considered, the inductive force vanishes in the frame in which the magnet is in motion and the test charge at rest. In contrast, consistent results, in different frames, are given by the recently derived formulae of relativistic classical electrodynamics.

physics.class-ph↗

arXiv2008

Space-time transformation properties of inter-charge forces and dipole radiation: Breakdown of the classical field concept in relativistic electrodynamics

A detailed study is made of the space-time transformation properties of intercharge forces and the associated electric and magnetic force fields, both in classical electrodynamics and in a recently developed relativistic classical electrodynamical theory. Important differences are found and serious errors are found in the traditional treatment of special-relativistic effects in classical electromagnetism. Fields associated with radiation processes are also considered and classical and quantum mechanical predictions are compared. An important, though trivial, mathematical error in the derivation of the retarded Liénard-Wiechert retarded potentials is pointed out. It is also shown why electric and magnetic fields produced by moving source charges or current distributions are not `classical fields', and that they do not, in general, constitute an antisymmetic second-rank tensor, as is usually assumed.

physics.gen-ph↗

arXiv2008

Spatially-separated synchronised clocks in the same inertial frame: Time dilatation, but no relativity of simultaneity or length contraction

The Lorentz transformation is used to analyse space and time coordinates corresponding to two spatially-separated clocks in the same inertial frame. The time dilatation effect is confirmed, but not `relativity of simultaneity' or `relativistic length contraction'. How these latter, spurious, effects arise from misuse of the Lorentz transformation is also explained.

physics.gen-ph↗

arXiv2007

Clock rates, clock settings and the physics of the space-time Lorentz transformation

A careful study is made of the operational meaning of the time symbols appearing in the space-time Lorentz transformation. Four distinct symbols, with different physical meanings, are needed to describe reciprocal measurements involving stationary and uniformly-moving clocks. Physical predictions concern only the observed rate of a clock as a function of its relative speed, not its setting. How the failure to make this distinction leads to the conventional predictions of spurious `relativity of simultaneity' and `length contraction' effects in special relativity is explained.

physics.gen-ph↗

arXiv2007

On the Real and Apparent Positions of Moving Objects in Special Relativity: The Rockets-and-String and Pole-and-Barn Paradoxes Revisited and a New Paradox

The distinction between the real positions of moving objects in a single reference frame and the apparent positions of objects at rest in one inertial frame and viewed from another, as predicted by the space-time Lorentz Transformations, is discussed. It is found that in the Rockets-and-String paradox the string remains unstressed and does not break and that the pole in the Barn-and-Pole paradox never actually fits into the barn. The close relationship of the Lorentz-Fitzgerald Contraction and the relativity of simultaneity of Special Relativity is pointed out and an associated paradox, in which causality is apparently violated, is noted.

physics.gen-ph↗