What's Wrong With The Robertson-Walker Metric, and Why a Critical Mass Has No Meaning

The Robertson-Walker metric supposedly describes a homogeneous and isotropic universe.It supposedly gives the criterion of a critical mass of the universe whose deficiency has led to the supposition of "dark matter."

It is commendable that the same criterion also follows from an elementary, nonrelativistic, derivation where the total kinetic and gravitational energies of the universe are conserved at two different times

$$\frac{1}{2}v^2-\frac{GM}{R}=\frac{1}{2}v_0^2-\frac{GM}{R_0},$$

Why Do Apples Fall and Non-Radiative Electric Fields Don't Aberrate?

Newton could tells us, but Einstein can't. According to his "general" theory of relativity, all particles follow what are known as 'geodesics'. These are paths of the shortest distance between any two points. In flat space, these paths are straight lines, but in non-euclidean spaces, these are curves where a point moving along such a segment moves at constant velocity with zero acceleration. How can Newton's apple be reconciled with such behavior?

Beyond the Confines of Relativity: The Breakdown of Symmetry in Past and Future

There is a deep connection between the formula for aberration,

$$\cos\omega=\frac{\cos\omega'-\beta}{1-\beta\cos\omega'},$$

and the Mobius automorphism that swaps the relative state of motion, $\beta$, with one at rest, $0$,

$$\mathcal{M}(\cos\omega')=\frac{\cos\omega'-\beta}{\beta\cos\omega'-1},$$

except for the negative sign. If $\cos\omega'=\beta$, then $\mathcal{M}(\beta)=0$, while if $\omega'$ is a right-angle, then $\mathcal{M}(0)=\beta$. But, there is more to this than what meets the eye.

The Limited Scope of Special Relativity

In his first paper on special relativity, Einstein wrote (in our notation)

$$\cos\omega=\frac{\cos\omega'-\beta}{1-\beta\cos\omega'},$$

for "the law of aberration in its most general form. If $\omega'=\pi/2$, the equation takes the simple form

$$\cos\omega=-\beta$$. In the annotated version of this paper, the angle $\omega$ is formed from "light source-observer" was changed to "direction of motion."

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

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

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.