Kaplan’s Rule of Universal Constants

The Speed of Light Isn’t 299 Million Everywhere

Some constants are woven into the structure of reality itself, and others are human inventions.
π is of the first type. c is of the latter.

π emerges from pure geometry—the ratio of a circle’s circumference to its diameter.
It’s unit-free. It never changes. And any civilization, anywhere in the universe, that studies circles will discover the exact same number.

That’s what it means for a constant to be baked into reality.

But not all constants meet that standard.
Some only seem universal because we forget to check where their numbers come from.

The Test

Here’s the rule:

If the value of a constant changes when you change the units, it’s not baked into the universe.
It’s an artifact of human measurement.

That’s the essence of Kaplan’s Rule of Universal Constants: it asks whether the number we assign to a constant reflects something cosmic, or something based on an arbitrary unit of measurement.

Essentially: “Would aliens from another galaxy be using the exact same number?”

Case Study: The Speed of Light

We’re all taught Einstein’s famous equation:

E = mc²

But the definition of c is intimately tied to the physical lengths of meters and seconds:

• A meter was originally defined as 1⁄10,000,000 of the distance from the equator to the North Pole along a meridian—based on Earth’s size.

• A second was defined as 1⁄86,400 of a day—based on Earth’s rotation.

These definitions are tied to Earth itself.

Aliens on another planet—with different geography and clocks—would never come up with the number 299,792,458 m/s to describe the speed of light.

There is a universal speed of light. But the number we use to describe it is not universal.
It’s a projection of a cosmic truth onto a local measuring stick.

But What About Natural Units?

Some argue that by using the natural units version of E = mc², written simply as E = m, we’ve eliminated the constant and therefore made the formula universal.

But this overlooks a critical fact: in natural units, we’re not removing c²—we’re building it into the units themselves.
Specifically, we’re redefining the unit of energy so that one unit of mass automatically equals one unit of energy.
To do that, we have to scale our original energy values by c².

The constant is still there. It’s just been moved into the conversion.

The formula looks simpler, but the conversion is still doing the work—just behind the scenes.

The Dollar-Euro Analogy

To illustrate how this sleight of hand works, imagine:

• You start with a real exchange rate:
  1 dollar = 2 euros

• You define a new unit:
  1 natural euro = 2 regular euros

• Now you say:
  1 dollar = 1 natural euro

That’s technically fine. But if you then claim dollars and euros are now the same thing, you’ve made a basic mistake.

This is exactly the error made when people take E = m and treat it as more universal than E = mc².
The conversion didn’t vanish—it was just absorbed into the new unit.

Historical Sidebar: How Modern Units Still Encode Earth

Even though today’s official definitions are more precise, they still encode Earth:

• The modern meter is defined as the distance light travels in 1⁄299,792,458 seconds.

• The modern second is defined as 9,192,631,770 oscillations of a cesium-133 atom.

But these definitions were deliberately calibrated to match the old Earth-based values:

• The length of the modern meter was tuned to preserve the meridian-based standard.

• The cesium second was chosen to match the rotational second based on Earth’s day.

So even with atomic precision, the value of c in meters per second still carries Earth in its bones.

The Difference Between Calculation and Measurement

There’s another crucial distinction that reinforces Kaplan’s Rule: some constants can be calculated purely through mathematics, while others must be measured.

Take π. We can estimate π by physically measuring a circle—but we don’t have to. There are countless ways to calculate π using pure logic: infinite series, integrals, geometric constructions, or algorithmic methods. Computers routinely calculate millions of digits of π without ever referencing the physical world. No rulers, no clocks, no units. Just math.

This makes π a different kind of constant. It emerges from the structure of mathematics itself, independent of any measuring tools or physical reference points.

Now consider c, the speed of light. You can’t calculate c from first principles the way you can calculate π. To assign it a number, you need to measure a distance and a time. Even if those measurements are incredibly precise—down to atomic transitions—they’re still measurements. They still rely on definitions like the meter and the second, which were created by humans.

Even when we say c = 1 in natural units, we’ve simply baked that measurement into the unit system. We didn’t remove the measurement—we relocated it.

π is tool-free.
c is tool-dependent.

That’s a key part of what separates constants that emerge from pure structure from those whose values depend on how we’ve chosen to measure the world.

Conclusion

This isn’t a critique of natural units. They’re incredibly useful. They make equations elegant.
But usefulness doesn’t mean universality.

Changing the ruler doesn’t erase the conversion—it just hides it.

Kaplan’s Rule of Universal Constants offers a simple test:

Does the value of the constant stay the same across all unit systems?

If yes: it’s woven into the structure of the universe.
If no: it’s a human construct—carefully designed, but not fundamental.

That doesn’t make the constant less real.
But it does mean the number belongs to us—not the cosmos.