This is a work in progress.

Copyright © 2026 Barry Schwartz. This essay is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License. It is available as a webpage at https://bell-multivectors.crudfactory.com/ and in source form at https://github.com/chemoelectric/michelson-morley

Introduction

Transmission antennas emit a substance radially at a velocity \(c\). The substance then moves inertially along with the antenna. Therefore the transmissions exhibit the Michelson-Morley effect. Special Relativity incorrectly introduces time dilation and length contraction, without bothering to explain the Michelson-Morley effect. Here we have an explanation, and there is no time dilation nor length contraction.

Thus this new theory supplies a mechanical explanation for the Michelson-Morley phenomenon: the waves themselves, instead of a luminiferous ether, are the inertial material. An antenna does not vibrate a medium. It emits vibrating electromagnetism.

Special Relativity, on the other hand, supplies no reasonable explanation for the Michelson-Morley phenomenon. It is merely descriptive. And it veers into error when it introduces time dilation and length contraction.[1]

Below I will derive the Doppler shifts formerly known as “relativistic” but henceforth to be known as “electromagnetic.” The reason for the renaming is I do not employ “Observer and Frame-of-Reference” methods and therefore the kinematics is not a “relativity.”

All calculations formerly delegated to Special Relativity should now be doable instead using the Doppler shifts. An exception is for problems usually solved incorrectly with Special Relativity, such as the “Twin Paradox.” That the usual solution must be wrong should be obvious. Physics teachers often cleverly attribute the asymmetric aging to the acceleration at the pivot, but this is not so. The amount of asymmetric aging is controlled by the amount of inertial motion. Thus it is inertial motion that is responsible for asymmetric aging, and this simply must be impossible.

Anyone who is just blows off such a situation ought to reconsider their role in the sciences, and perhaps should not be teaching physics. I imagine Einstein blew it off because he was very young and already an international celebrity for it! Often it is better to be rejected and search for the truth alone, over a lifetime.

The transverse electromagnetic Doppler shift

This is the simpler of the two, for the motion is orthogonal to the radial direction, and the Doppler shift is entirely due to the inertial motion of the emitted substance.

diagram of the transverse Doppler shift

In the figure above, the transmission antenna is depicted as motionless, and an object is moving leftwards with respect to it.[2] If the object had stayed stationary, transmission wavelengths would have been proportional to \(\lambda_2'\). On account of the leftward motion at speed \(v\), the actual wavelengths are proportional to \(\lambda_1'\). Thus the Doppler shift is

\[ \begin{equation*} \lambda_1' / \lambda_2' = \frac{1}{\sqrt{ { 1 - (v/c) ^ 2 } }} \end{equation*} \]

Special Relativity gives the same prediction.

The longitudinal electromagnetic Doppler shift

Suppose we have a stationary object, from which a transmission antenna is receding at velocity \(v\). For “ordinary” Doppler shift in a stationary medium, this would result in each wavelength increasing by an amount due simply to the recession of the source. For electromagnetic Doppler shift, however, the wavefronts themselves also are receding. Thus the situation is more complicated.

The speed of a wavefront is now not \(c\) but \(c-v\). The speed of light is not \(c\) except relative to the light source.

Similarly, if the transmission antenna is moving towards the stationary object, the speed of the wavefront is \(c+v\) instead of \(c\).[3]

We are going to want to deal with wavefronts themselves, which means spherical surfaces. Let us compute the surface area of a sphere. In a spherical coordinate system, the differential of surface area for a sphere of radius \(r\) is \( dA = r^2 \sin\varphi \, d\varphi \, d\vartheta \), and the area is the double integral

\[ \begin{equation*} A = r^2 \mkern-1mu \int_0^{2\pi} \mkern-10mu \int_0^\pi \mkern-5mu \sin\varphi \, d\varphi \, d\vartheta = 4\pi r^2 \end{equation*} \]

Now suppose a receding antenna. You are on the surface of a sphere of area \( ( 1+v/c )^2 \), representing that the antenna is receding at speed \(v\). That, however, is in ordinary units of measurement. We should adjust for the wavefront speed, and will do so by using an areal scale of \( ( ( 1+v/c )( 1-v/c ) )^{-1} \). This scale is the square of a factor familiar from Special Relativity:

\[ \begin{equation*} \gamma = \sqrt{\frac{1}{ ( 1+v/c ) ( 1-v/c ) }} = \frac{1}{\sqrt{1-(v/c)^2}} \end{equation*} \]

It also shows up above as solution to the transverse Doppler shift. Its appropriateness as the radial scale factor can be guessed from the following diagram, although I need to prove it:[4]

right triangle depicting the radial scale equivalence

The scaled sphere area is thus

\[ \begin{equation*} A' = 4\pi \, \frac{ ( 1+v/c )^2 }{ ( 1+v/c ) ( 1-v/c ) } = 4\pi \, \frac{ 1+v/c }{ 1-v/c } \end{equation*} \]

and the sphere’s radius is

\[ \begin{equation*} r' = \sqrt{\frac{ 1+v/c }{ 1-v/c }} \end{equation*} \]

This radius is the longitudinal Doppler shift for a receding antenna. You can convince yourself of this. I chose the sphere so it would be so.

If the sign of \(v\) reverses the Doppler shift becomes that for an approaching antenna. For \(v=0\) there is no Doppler shift.

1. I will later supply references to the work of A.F. Kracklauer, who shows how to interpret a Minkowski diagram so you do not get time dilation and length contraction. A Minkowski diagram read that way might give the same results as my theory. I once used Einstein’s tensor notation to describe the difference between Einstein’s and Kracklauer’s approaches. There appeared to be only a different constant tensor factor, with the notation favoring Einstein’s version of the theory by making that constant an identity, and thus leading to General Relativity. However, I have lost those notes, and also did not put in an effort to retain skill in that kind of mathematics. Needless to say I would not seek a gravitational or unified field theory by Einstein’s methods, but instead would go back to doing it the way Maxwell and Heaviside did. However, I would favor geometric algebra over vector analysis, if I knew Maxwell’s theory in geometric algebra form. In Euclidean geometric algebra it cannot be too different, but I would especially like to know Maxwell’s theory in conformal geometric algebra or something similar.
2. Of course, an alternative interpretation is that the transmission antenna and its wavefronts are moving rightwards, relative to a stationary object. It is this motion of the wavefronts that would not happen if there were a luminiferous ether. Instead they would move with the ether.
3. Though this is a “speed” greater than \(c\), it is not a license for Star Trek. A starship would have to overtake its own electromagnetic substance, and thus would crush itself. Furthermore, \(v\lt c\) always. People who extrapolate to \(c\le v\), thus obtaining singularities, imaginary numbers, etc., are called “ding-a-lings.”
4. PROVE IT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I am not a Ramanujan who can just whip up a proof that is right half the time. I do not yet know how to prove this, though it must be correct and so there is a proof.