See that little guy on the bridge, suspended halfway between all the way down and all the way up? That’s us on the cosmic size scale.

I suspect there’s a lesson there on how to think about electrons and quantum mechanics.

Let’s start at the big end. The physicists tell us that light travels at 300,000 km/s, and the astronomers tell us that the Universe is about 13.7 billion years old. Allowing for leap years, the oldest photons must have taken about 4.3×10^{17} seconds to reach us, during which time they must have covered 1.3×10^{26} meters. Double that to get the diameter of the visible Universe, 2.6×10^{26} meters. The Universe probably is even bigger than that, but far as I can see that’s as far as we can see.

At the small end there’s the Planck length, which takes a little explaining. Back in 1899, Max Planck published his epochal paper showing that light happens piecewise (we now call them photons). In that paper, he combined several “universal constants” to derive a convenient (for him) universal unit of length: 1.6×10^{-35} meters. It’s certainly an inconvenient number for day-to-day measurements (“Gracious, Junior, how you’ve grown! You’re now 8×10^{34} Planck-lengths tall.”). However, theoretical physicists have saved barrels of ink and hours of keyboarding by using Planck-lengths and other such “natural units” in their work instead of explicitly writing down all the constants.

Furthermore, there are theoretical reasons to believe that the smallest possible events in the Universe occur at the scale of Planck lengths. For instance, some theories suggest that it’s impossible to measure the distance between two points that are closer than a Planck-length apart. In a sense, then, the resolution limit of the Universe, the ultimate pixel size, is a Planck length.

So that’s the size range of the Universe, from 1.6×10^{-35} up to 2.6×10^{26} meters. What’s a reasonable way to fix a half-way mark between them?

It makes no sense to just add the two numbers together and divide by two the way we’d do for an arithmetic average. That’d be like adding together the dime I owe my grandson and the US national debt — I could owe him 10*¢* or $10, but either number just disappears into the trillions.

The best way is to take the geometrical average — multiply the two numbers and take the square root. I did that. It’s the **X** in the sizeline, at 6.5×10^{-5} meters, or about the diameter of a fairly large bacterium. (In the diagram, **VSC** is the Vega Super Cluster, **AG** is the Andromeda Galaxy, and the numbers are those exponents of 10.)

That’s worth marveling at. Sixty orders of magnitude between the size of the Universe and the size of the ultimate pixel. Yet from blue whales to bacteria, Earth’s life just happens to occupy the half-dozen orders right in the middle of the range. We think that’s it.

Could this be another case of the geocentric fallacy? Humans were *so* certain that Earth was the center of the Universe, before Brahe and Galileo and Newton proved otherwise. Is there life out there at scales much larger or much smaller than we imagine?

Who knows? But here’s an intriguing physics/quantum angle I’d like to promote. We know a lot about structures bigger than us — solar systems and binary stars and galaxy clusters on up. We know a few sizes and structures a bit smaller — viruses and molecules and atoms. We’re aware of quarks and gluons that reside inside protons and atomic nuclei, but we don’t know their size or structure.

Even a proton is huge on the Planck-length scale. At 1.8×10^{-15} meters the proton measures some 10^{20} Planck-lengths. There’s as much scale-space between the Planck-length and the proton as there is between the Earth (1.3×10^{7} meters) and the Universe.

It’s hard to believe that *Terra infravita’s* area has no structure whereas *Terra supravita* is so … busy. The Standard Model’s “ultimate particles,” the electrons and photons and neutrinos and quarks and gluons, all operate down there somewhere. It’s reasonable to suppose that they reflect a deeper architecture somewhere on the way down to the Planck-length foam.

Newton wrote (in Latin), “I do not make hypotheses.” But golly, it’s tempting.

~~ Rich Olcott