The Ptolemaic SI System

J. Rogers, SE Ohio.

In antiquity, humans looked at the sky and assumed, for obvious egocentric reasons, that the Earth was the fixed, central coordinate origin of the universe. Because the Earth was forced to be the origin, the actual motions of the planets—which are simple ellipses around the sun—appeared as bizarre, looping retrogrades. To make their math work, Ptolemy added epicycles—rotating spheres upon spheres—literally just Jacobian correction factors to account for choosing the wrong origin.

Now look at what we did in 1793 with the meter. We literally took a physical, localized rock—the planet Earth—measured a meridian from the equator to the North Pole, divided it by 10 million, and cast that into a platinum bar.

We made the physical Earth the coordinate origin of our Length axis.

And what did we do for the second? We looked at the spin rate of that same rock, divided it by 86,400, and called it a unit of Time.

We made the physical Earth the coordinate origin of our Time axis.

And for the kilogram? We took a volume of water (the dominant fluid on this specific rock) at the melting point of ice (a specific thermodynamic condition on this rock) and called it a unit of Mass.

The Constants as Modern Epicycles

Once we force the Earth to be the center of your coordinate system—once your Length is a fraction of the Earth's circumference, Time is a fraction of the Earth's rotation, and your Mass is a chunk of the Earth's water—we have created the exact same scenario as Ptolemy.

The universe does not care about the Earth. It operates on the unified, dimensionless geometry of

$S_u$

.

So, what happens when we try to write the equation for universal gravitation, or electromagnetism, or quantum mechanics using units derived from the dimensions of a rock? The math doesn't line up. The equations fail to commute. The simple, elegant geometry of

$X=X$

looks like a twisted, complicated mess when projected through an Earth-centric basis.

To make the math work, you are forced to insert correction terms. We have to add rotational scaling factors to translate the Earth's circumference into the universe's natural frequency. You have to add factors to translate the Earth's rotation into the universe's natural mass.

Those correction terms are

$G$

,

$c$

,

$h$

, and

$k_B$

.

They are the epicycles of an Earth-centric coordinate system!

• $c$
  is the epicycle that corrects for measuring space in "Earths" and time in "Earth spins." It is just the ratio of the universe's natural space/time geometry to our Earth-centric distortion of it.
• $G$
  is the epicycle that corrects for measuring mass in "Earth water" and space in "Earths."
• $h$
  is the epicycle that corrects for measuring energy in "Earth water falling one Earth-width" and frequency in "Earth spins."