Planck units

(synonym Planck-Wheeler units, after John Archibald Wheeler who developed the precise system described here, inspired by a similar system by Max Planck)

What units to use when measuring things is always a subject of heated debate. In the United States of America, the so-called imperial system is in use, creating problems for visiting tourists. The more rational France attempted to solve this by creating the metric system, as a part of the same process that created the ten-day week. Even the metric system has ugly quirks, though, so the SI Units were invented.

But throughout this progression, there is is a disturbing feeling of arbitrarity. Why is a kilogram a kilogram? Because that's the mass of a little iridium cylinder in Paris, which at one time was thought to weigh as much as a cube of water whith a side equal to 1/400,000,000 of the circumference of the Earth. We cannot expect the Americans to switch system on so arbitrary grounds, can we? Is there no way to create a truly universal system of units? One that even aliens from outer space could agree upon?

As a matter of fact there is! There are certain physical universal constants, which could in principle take any value, but were given a particular one by God. These are: the gravitational constant G(as used in general relativity), the speed of light c, Boltzmann's Constant k (thermodynamics) and planck's constant divided by 2pi h-(quantum mechanics). (Yes, divided by 2pi. Arbitrary, why do you say that?).

Now, each of these constants has a dimension, in the sense of mass, time, etc. If we use braces for "dimension of", and M, L, T, t for mass, length, time, and temperature, then:

{G} = force/mass = M^-1L³T
{c} = velocity = LT^-1
{k} = energy/temperature = ML²T^-2t^-1
{h-} = ML²T^-1

So by simple multiplying, dividing, and taking roots of fundamental constants, we can form quantities of any dimension we wish. These quantities can then be used as universal units. Here we go:

• Planck length: (h- c^-3 G)^1/2 = 1.6 × 10^-35 metres.
• Planck time: (h- c^-5 G)^1/2 = 5.4 × 10^-44 seconds.
• Planck temperature: k^-1(h- c⁵ G^-1)^1/2 = 1.4 × 10³² kelvins
• Planck density: c⁵ h-^-1 G^-2 = 5.2 × 10⁹⁶ kilograms per cubic metre.

...And so on. The Planck velocity becomes plain c, which for once does not seem terribly huge by comparison. The Planck density, according to my physics book, corresponds to the entire visible universe compressed to the size of a proton.

So we finally have a rational unit system. Now go lobby your politicians to implement the switch!