Serious Units Fables: natural length and time units

Part 11 — The Strings of Distance, Time and Quickness

According to the Greeks, Apollo did indeed invent the lyre — which was originally made using a turtle shell to give resonance to the sound. The lyre would sometimes have passive strings strung inside the shell, underneath the ones you pluck and tuned to be resonant with them. In the story, the lyre's string of distance wasn't mentioned because it is one of the resonant strings.

Apollo is god of light and light's idea of distance is wavelength. Wavelength is related to frequency as a reciprocal — higher frequencies have shorter wavelengths. There is a wavelength associated with core frequency — I think of it as a tiny stitch in the fabric of space-time. This "stitch" provides an intrinsic length scale for the universe (and is called the Planck length).

Core frequency is extremely high — ten-to-forty times middle D! After all, it is the frequency associated with things like the top speed and main force and full power of the universe, so it should be high. And accordingly the world's intrinsic wavelet length, the "stitch," is very short. We are using practical scale-ups — our fingerwidth and mile are power-of-ten multiples of the intrinsic wavelet. A fingerwidth is equal to the basic stitch scaled up by a factor of ten-to-the-thirtythree. These scale-ups are decimal relatives of Apollo's lyre.

Also associated with core frequency is a tiny natural timelet of duration, which is how long it takes light to travel the length of a stitch. It is the "Planck time" and it's the time it takes one event to occur at core frequency. A natural minute is ten-to-fortyfive of these most-fleeting-of-all instants.

The universe also has a kind of upper limit on acceleration—an ideal quickness—in which the speed of light is acquired almost instanteously, in one Planck time interval. It is an inconceiveably swift acceleration. One might try to imagine it being briefly approached by two mite-sized black holes falling towards and into each other, in the last fraction of an instant before they merge. It's an absolute scale which the universe gives us, just as it does the speed of light, and we can use it to rate ordinary everyday accelerations: judging how quickly the speeds of things change compared with the ideal. All these quantities are strings of Apollo's lyre.