New Metric Fables: universality

Laotzu and I watch the sunset

Today Laotzu was a different kind of creature on a different planet from me. But we were both ten-users and that gave our minds a point of tangency. So together we watched our stars setting—I watched the sun set with Laotzu's eyes and he watched with mine. I don't know the color of his star or how far from it he was or what he breathed or what temperature he liked or what pressure, but the constants of nature present in that situation were the same for both of us.

For us here on Earth, our star's a surface temperature is 40 grade. (That's approximate, in terms Laotzu would recognize as natural for ten-users, it's 40.8 grade.) You know I set store by the fact that the numerical values of five of the most fundamental and accessible physical constants are a millionth, a billion, a trillion, a quadrillionth, and a quintillionth. Well, because of the trillion in that series, the keynote frequency in the light coming from the sun was 40 trillion per trice.

On the other hand Laotzu's star's temperature might be 50 grade and then the keynote frequency in the light coming from it would be 50 trillion per trice. He and I may see different stars but we see the same fundamental ratios.

In a generic hot thing's glow, the average quantum's frequency is 2.7 times the keynote frequency. That includes stars and it's true whatever units you use, being a ratio between frequencies that's built into nature. Since the keynote in the light I saw was 40 trillion per trice, the average had to be 110 trillion per trice. And by the way, the red was around 150, the green 200, and the blue 250 trillion per trice. That's just a fact about human eyes: what frequencies tickle the cone cells in our retinas. Laotzu's eyes may have been sensitive to other colors and other frequencies but those were the ones I saw.

What about the energies of quanta that stimulate cells in my retina? To find the photon energy from each frequency I simply multiply it by a quadrillionth, or divide it by a quadrillion, which comes to the same thing. That tells me the voltage barrier which one individual tingle of the light can make an electron overcome. It's the most convenient handle on energies at that level. For the average sunlight frequency of 110 trillion, you can see this voltage has to be 0.110 tao. Dividing by a quadrillion is not hard in this case. For red it is 0.150 tao, for green 0.200, and for blue 0.250 tao.

Laotzu and I have come to an agreement about the values of the five fundamental constants. For us both, the values of the gravitational constant, the speed of light, the frequency coefficient of temperature, the voltage coefficient of frequency, and the elementary charge are a millionth, a billion, a trillion, a quadrillionth and a quintillionth. That means all our units are the same, although presumably they have different names—it's natural to assume they are called differently on different planets. In particular, aside from the different names, Laotzu and I use the same voltage unit. I hope he appreciates my calling it tao.

About our natural Planck measure of voltage you may remember that a tao is about 12 conventional volts so that 0.25 tao is about 3 volts. In conventional Earth terms I am saying that the photoelectric voltage for blue light is about 3 volts and that a blue photon carries around 3 "electronvolts"—common knowledge among physicists of my acquaintance.

In conventional terms the work it takes to raise one electron up a step of twelve conventional volts is called 12 electronvolts. For Laotzu and me the energy it takes to raise an electron up a 1 tao step of voltage is called an "electrontao". Just different ways of saying the same thing. We have microscopic and macroscopic units of energy—one is the energy it takes to raise one electron up by tao voltage and the other is what it takes to raise a quintillion electrons (the macroscopic unit of electric charge) up by the same voltage. The macroscopic unit of charge is appropriate for household appliances and everyday electric matters like that. The microscopic unit is more appropriate for nerve cells and chemistry and what goes on inside a transistor. Laotzu and I use the number quintillion (10¹⁸) to relate microscopic and macroscopic realms. By analogy, unfortunate metric-users have 6.24151...× 10¹⁸, and its reciprocal 1.602176...× 10^-19, if they can remember those two numbers.

I set store by being able to tell the voltage simply from dividing the frequency by a quadrillion, which happens when you use tao but not when you use conventional volts. The blue frequency is 250 trillion per trice—I divide by quadrillion, and get 0.250 tao. So I think of the blue voltage as a quarter tao. And the energy carried by a blue photon is, for me, a quarter of an electrontao.

As I watch the sunset with Laotzu I think that the red photons coming to my eye carry 1/7 electrontao, the green ones carry 1/5 electrontao, and the blue ones 1/4. And although his eyes may be sensitive to different frequencies, Laotzu understands and approves. He is a ten-user and witness to the same phsical constants, upon which he bases his everyday units just as I do. His star may be a different color from our sun but the light from it comes at the same speed. For Laotzu, just as for me, that speed is a billion. Whatever its surface temperture he, like I, multiplies by a trillion to get the keynote frequency in the light. Whatever the frequencies he sees, he divides by a quadrillion just as I do to get the photoelectric voltages and the quantum energies. And whatever he happens to call his macroscopic unit of energy, the microscopic unit is one quintillionth of it, just as with me.