23 January 2024

Metric Meters And Seconds

The speed of light is, by the current definition of the meter, 299,792,458 m/s. The second, in turn, is currently defined in terms of the rate of radioactive decay of a certain isotope of an unstable atom. Specifically:
The second [...] is defined by taking the fixed numerical value of the caesium frequency, ΔνCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1.

The second was originally based upon 60 seconds per minute, 60 minutes per hour, 24 hours per day on Earth. The new definitions, however, are independent of the properties of planet Earth.

Meanwhile

The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's polar circumference is approximately 40000 km. . . . today Earth's polar circumference measures 40007.863 km, a change of 0.022% from the original value of exactly 40000 km, which also includes improvements in the accuracy of measuring the circumference.

If the original definition of the meter from 1791 had been carried through to the currently accurately measured distance from the North Pole to the Equator, then the speed of light would have been: 299,858,412.340 76 m/s, about 0.05% less than the nice round number of 300,000,000 m/s.

It would have be nice if the definition of the meter could have been changed to make the speed of light 300,000,000 m/s (which would be a meter that is is 0.0691806666667% longer than the current definition), or better yet, 100,000,000 new meters/s which would be 33333.3333 old mm per per new meter (about 13.12 Imperial inches). But the speed of light wasn't possible to measure until the length of the meter had been established to high precision, and the slight adjustments to precision metric measurements weren't deemed worth the numerological convenience by the time that the speed of light started to be used to define the meter.

A 300,000,000 m/s speed of light would slightly increase the size of the kilogram (by a fraction of a gram) which was originally based upon the mass of 1000 cubic centimeters of water at room temperature at sea level air pressure.

It would also slightly tweak the electromagnetic units that were originally based upon interactions that are a function of the meter.

Incidentally, the Imperial system of length measurement is defined in terms of the metric system, with one Imperial inch equal to exactly 25.4 mm, and all other Imperial length measurements flowing from that definition.

2 comments:

Dave Barnes said...

Next you will advocate for the metric 10-hour day.
Commie

andrew said...

Hey, this is all about capitalism. I already sell my time in units of tenths of an hour.