Can You Fit the Entire Universe into a Nutshell?

An old math joke tells you how to catch a tiger: Build a cage in the interior of a perimeter and perform inversion.

Not only does Maxwell's constant $b^2=1/\epsilon_0\mu_0$ not coincide with the velocity of light, but different definitions of the speed of light turn out to be inverses of one another.

One definition used in the Kennedy-Thorndike (KT) interferometer uses a metric

$$c^2dt^2(1-\beta^2)=ds^2\pm2v\cos\omega dt,$$

When Ampere Meets Doppler

It has often been claimed that Ampere's force is equivalent to Grassmann's force, which is a precursor of the Lorentz force, when the force is integrated round a circuit, in which the current element forms a part, vanishes. This is taken to mean that a force exerted by a complex circuit element is a right angles to the element. As such it was taken to be equivalent to the earlier discovered Biot-Savart law. The Biot-Savart law, $$\vec{B}=\frac{\mu}{4\pi r^2}(\vec{v}\wedge\hat{r}),$$ is just the definition of the magnetic field.

Will the Real Speed of Light Please Make Itself Known

Never have two numbers been so similar, and, yet, so far apart. James Clerk-Maxwell—-not without understandable reservation—-proposed the equivalence of the speed of light, $c$, and his constant, $b$, which he found as the ratio of two completely and entirely stationary forces, the Coulomb force, $F_E$, and the magnetic force, F_M$, from the Biot-Savart law. 

Indistinguishability Between Electrodynamic and Gravitational Waves

According to Dennis Coyne, "The excitement surrounding gravitational wave astrophysical observation stems from the significant differences between electromagnetic waves and gravitational waves...." According to the conventionally accepted view that "a gravitational wave is a propagating distortion of spacetime which alternately produces out of phase elongations and contractions of space along two axes perpendicular to the propagation direction" would, indeed, make it different from electromagnetic wave propagation which is normal to the electric and magnetic fie

From Kepler's Second to Newton's Third: From Optics to Electrodynamics and Beyond

The conservation of angular momentum is always assumed in systems in which torques to not operate. Yet, non-central forces which depend on angles and velocities seem to challenge the conservation of energy. Angle dependent forces have been known since the time of Ampere, and velocity dependent force which invalidate Newton's third law of action-and-reaction are also well known since the work of Grassmann, and a half a decade later by Lorentz. 

It Takes Two to Tango: The Decline of Observer-Physics

The velocity $v$ seems innocuous enough. But, it has been the seat of many a misunderstanding. In fact, Einstein introduced his theory of special relativity to emphasize the fact that the ultimate velocity is the speed of light, $c$. The position of a body moving from point $x=0$ at $t=0$ along the $x$-axis is simply $x=vt$. That is, we measure $x$ and $t$ and obtain the velocity as $v=x/t$.

Does Gravity Need a Maxwellian Foundation?

The Ampere-Neumann-Weber theory of electrodynamics describes the mutual interaction of current elements or between moving charges that would account for phenomena like that of induction and radiation. Ampere's force is action-at-a-distance and is the antithesis of Maxwell's circuit equations that describe the propagation of electrodynamic fields. In order to apply the latter to material systems one needs an expression for the force that these fields exert on matter.

Weber's Electromagnetic Theory As an Optical Gravitational Theory

Weber's electrodynamics feel out of favor in the later half of the nineteenth century thanks to Maxwell's field theory. The distinction between the two is that the former predicts a pondermotive force between current elements whereas the later gives an electrodynamic force. The former produces a longitudinal force along the radius vector connecting the two elements while the latter produces a transverse force that acts normal to the direction of propagation.

What Clocks are Used to Measure General Relativistic "Effects"?

Relativistic effects, which supposedly support General Relativity, are considered as small appendices added on to Newtonian motion. Eddington, in fact, describes Einstein's 'correction' to the elliptical orbit of Mercury by saying:

"the equation of the orbit in the usual form of particle dynamics. It differs from the Newtonian orbit by the small term, $3mu^2$ [$m$ is gravitational mass, $u$ is the inverse radius, in units where the speed of light is unity], which is easily shown to give the motion of the perihelion."

Snell's Law for Rotational Motion

It has been burned into our minds that the index of refraction must be the inverse of the velocity in units where $c=1$. This has many ramifications like Snell's law here the ratio of the sine of the angle with respect to the normal and the velocity of the ray is constant. And in nonhomogeneous, but spherically symmetric, media where the index of refraction varies with the radial coordinate, the frequency of the wave remains constant making the velocity equal to the wavelength.