## Saturday, August 03, 2019

### [fwuecmvk] Light second

Consider dropping the meter as the SI unit of length and replacing it with the light second (with various SI prefixes).  Because it's obviously the right thing to do.

light nanosecond = nano light second = 0.299792458 m = 0.98 ft. People accustomed to US customary units will have an easier time converting, at least from feet; miles and inches are another matter.

Create a (joke) ruler marked in light picoseconds.  Easiest is to glue a new printed scale onto an existing ruler.  10 light picosecond ~= 1/8 inch, but we often want to measure to slightly higher precision.  1 light picosecond = 0.3 mm, which is probably too fine for people to see.  Here the customary units tradition of powers of 2 is superior to metric's powers of 10.  Probably best is markings of 5 light picosecond, 10 c ps, and 50 c ps, and numbers on n*100 c ps.

Astronomy:

light year = 31.557 light megasecond (exact)
parsec = 103 light megasecond

The age of the universe is 440 petasecond.  1 peta light second = 9.7 megaparsec, a convenient unit for cosmology.

Previously: distances within the solar system.

A human-scale unit of speed is a light nanosecond per second, or equivalently, nano lightspeed or nano c.  1 nano c = 1.08 km/h, so here the metric people will have an easier time converting.

Acceleration: Earth's gravity g = 33 nano light second per second per second = 33 nano c per second.

Area:

acre = 45 femto square light second
1 m^2 = 11 atto square light second
1 ft^2 = 1 atto square light second

For very small areas, we run out of metric prefixes, so we double (and triple) them:

1 mm^2 = 11 yocto square light second
1 micrometer^2 = 11 micro yocto square light second
1 barn = 1.1 zepto yocto square light second
1 femtobarn = 1.1 pico yocto yocto square light second
1 shed = 1.1 zepto yocto yocto square light second

You could put the prefix inside the square, e.g., 1 ft^2 = 1 square light nanosecond, but then the prefixes start denoting powers of a million instead of a thousand, so this is not recommended (but is currently commonly done in SI for units like mm^2 = 1 micro square meter).

For volume, we also run out of standardized metric prefixes, so we double (and triple) them.

1 yocto cubic light second = 7118 gallon
1 liter = 37 micro yocto cubic light second
1 fluid ounce = 1.1 micro yocto cubic light second
1 ml = 37 nano yocto cubic light second
volume of proton = 110 yocto yocto yocto cubic light second

We just miss needing quadruple prefixes.  The three consecutive yocto means the length scale of the proton, equivalently the length scale of the strong nuclear force, is about 1 light yoctosecond.  We used proton radius = 0.88 fm = 2.9 light yocto second to calculate spherical volume.

Using the light second as the base unit, the length scales of the universe conveniently range over the defined metric prefixes, from light yoctosecond to light petasecond, though the same can be said about the meter (880 attometer - 130 yottameter).  The universe keeps growing, so we're in danger of soon running out of large prefixes for the meter.  For the cgs system, we do run out of prefixes for lengths, so we combine them: the farthest light we can see has traveled 13 kilo yotta centimeter (kiloyottacentimeter, kYcm).  Relatedly, 1 cm/year = 1.06 atto c.

1 mile per gallon = 38 zetta per square light second
30 miles per gallon = 1.1 yotta per square light second

"yotta per light second squared" would have ambiguity in parenthesization: yotta per (light second squared) versus (yotta per light second)squared.  The former is what we want.

"yotta inverse square light second" is possible.

Another way to do all of this is to keep the meter as the standard unit of length, but make the meter per lightspeed (m/c) the standard unit of time.

giga meter per lightspeed = 3.3 second
1 second = 299.792458 mega meter per lightspeed (exact)
1 hour = 1.1 tera meter per lightspeed
age of the universe = 130 yotta meter per lightspeed

Earth's gravity g = 109 atto meter per square (meter per lightspeed).  Not sure how to write or speak this without parentheses.  Maybe 109 atto lightspeed squared per meter.

lightspeed per meter (c/m) would be the standard unit of frequency, replacing the hertz.

299.792458 MHz = 1 lightspeed per meter (exact)
440 Hz = 1468 nano lightspeed per meter
Hubble constant H0 = 7 milli yocto lightspeed per meter

More things like ampere or coulomb would also be replaced.  If we keep the coulomb, then the standard unit of current would become 1 coulomb lightspeed per meter = 299.792458 megaampere (exact).  If we keep the ampere, then the standard unit of charge would become 1 ampere meter per lightspeed = 3.3 nanocoulomb.