Is the world made of loops?

I see no good reason to prefer (any version I know of) the `holonomy interpretation' to the `potential interpretation' of the Aharonov-Bohm effect. Everyone agrees that the inverse image $[A]=[A+d\lambda]_{\lambda}=d^{-1}F$ of the electromagnetic field $F$ is a class, full of individuals; and that the circulation $\small{\textsf{C}}$ of the electromagnetic potential $A$ around a loop $\sigma_0$ encircling the solenoid is common to the whole class $[A]$, and to the homotopy class or \emph{hoop} $[\sigma_0]$. If picking individuals out of classes is the problem, picking an individual potential out of $[A]$ should be no worse than picking an individual loop out of $[\sigma_0]$. The individuals of $[A]$ can moreover be transcended---punctually, without integration around loops---by an appropriate version of the electromagnetic connection.Comment: comments welcom

Logic of gauge

The logic of gauge theory is considered by tracing its development from general relativity to Yang-Mills theory, through Weyl's two gauge theories. A handful of elements---which for want of better terms can be called \emph{geometrical justice}, \emph{matter wave}, \emph{second clock effect}, \emph{twice too many energy levels}---are enough to produce Weyl's second theory; and from there, all that's needed to reach the Yang-Mills formalism is a \emph{non-Abelian structure group} (say $\mathbb{SU}\textrm{(}N\textrm{)}$).Comment: comments, corrections most welcom

How Weyl stumbled across electricity while pursuing mathematical justice

It is argued that Weyl's theory of gravitation and electricity came out of `mathematical justice': out of the equal rights direction and length. Such mathematical justice was manifestly at work in the context of discovery, and is enough (together with a couple of simple and natural operations) to derive all of source-free electromagnetism. Weyl's repeated references to coordinates and gauge are taken to express equal treatment of direction and length

Cartesian and Lagrangian momentum

Historical, physical and geometrical relations between two different momenta, characterized here as Cartesian and Lagrangian, are explored. Cartesian momentum is determined by the mass tensor, and gives rise to a kinematical geometry. Lagrangian momentum, which is more general, is given by the fiber derivative, and produces a dynamical geometry. This differs from the kinematical in the presence of a velocity-dependent potential. The relation between trajectories and level surfaces in Hamilton-Jacobi theory can also be Cartesian and kinematical or, more generally, Lagrangian and dynamical

Altering the remote past

An abstract treatment of Bell inequalities is proposed, in which the parameters characterizing Bell's observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that a property of a system can be changed by the timing of a distant measurement, which could take place in the future.Comment: 8 page

Franco Selleri and the rotating disk

I concentrate on the \emph{pars destruens}, rather than the \emph{pars construens}, of Selleri's work on the Sagnac effect. He speaks (2003) of the ``impossibilità di spiegare la fisica sulla piattaforma ruotante con la TRS,'' and may have a point. By confining our attention to the world-cylinder above a circle on the disk we avoid broader integrability issues that just cause confusion. A rate of rotation foliates the cylinder into timelike spirals, and also into the simultaneity spirals hyperbolically orthogonal to them; together the two foliations give rise to all sorts of temporal absurdities

The Aharonov-Bohm debate in 3D

Going from two dimensions (curl and circulation) to three (divergence and flux in electrostatics or `Newton-Poisson gravity') can shed light on the Aharonov-Bohm debate. The three-dimensional analogy is misleading if taken too literally; it makes sense on a more abstract, formal level (where, for instance, the electromagnetic field is viewed somewhat metaphorically as a `source'---of electromagnetic turbulence). A slight tweak is enough to produce (a fictitious) gauge freedom in three dimensions

Is the world made of loops?

I see no good reason to prefer (any version I know of) the `holonomy interpretation' to the `potential interpretation' of the Aharonov-Bohm effect. Everyone agrees that the inverse image $[A]=[A+d\lambda]_{\lambda}=d^{-1}F$ of the electromagnetic field $F$ is a class, full of individuals; and that the circulation $\small{\textsf{C}}$ of the electromagnetic potential $A$ around a loop $\sigma_0$ encircling the solenoid is common to the whole class $[A]$, and to the homotopy class or \emph{hoop} $[\sigma_0]$. If picking individuals out of classes is the problem, picking an individual potential out of $[A]$ should be no worse than picking an individual loop out of $[\sigma_0]$. The individuals of $[A]$ can moreover be transcended---punctually, without integration around loops---by an appropriate version of the electromagnetic connection

The Aharonov-Bohm debate in 3D

Going from two dimensions (curl and circulation) to three (divergence and flux in electrostatics or `Newton-Poisson gravity') can shed light on the Aharonov-Bohm debate. The three-dimensional analogy is misleading if taken too literally; it makes sense on a more abstract, formal level (where, for instance, the electromagnetic field is viewed somewhat metaphorically as a `source'---of electromagnetic turbulence). A slight tweak is enough to produce (a fictitious) gauge freedom in three dimensions

Franco Selleri and the rotating disk

I concentrate on the \emph{pars destruens}, rather than the \emph{pars construens}, of Selleri's work on the Sagnac effect. He speaks (2003) of the ``impossibilità di spiegare la fisica sulla piattaforma ruotante con la TRS,'' and may have a point. By confining our attention to the world-cylinder above a circle on the disk we avoid broader integrability issues that just cause confusion. A rate of rotation foliates the cylinder into timelike spirals, and also into the simultaneity spirals hyperbolically orthogonal to them; together the two foliations give rise to all sorts of temporal absurdities