As part of my not-very-successful quest to keep abreast of the latest developments in science, I just finished Einstein’s Relativity:The Special and the General Theory which was, as you’ll recall was a big hit when it came out around 1915. Right towards the end, you get the famous formula E=mc^2. Reading this, I recalled someone pointing out that, in a sensible system of units, c (the speed of light in a vacuum) would be set at 1, so the equation would just say Energy=Mass.
That got me thinking about how you would design units from scratch, in the light of our current knowledge of the universe. The designers of the metric system, at the time of the French Revolution, used the circumference of the earth as the basis for their measure of distance and volume, then used that, along with the density of water for the measure of mass. For time, they stuck with the Babylonian second ( there were, I think, some failed proposals to use a decimal system).
Given our understanding of the Big Bang, it seems to me that it would be more natural to base an absolute unit of time on the period elapsed since then. If we (arbitrarily) set the time from the Big Bang to the present equal to 1, then the current size of the universe would also be 1. It would obviously also make sense to make the total mass-energy of the universe equal to 1, which would then give us a tractable basis for talking about the uniformity or otherwise of its distribution.
At this point the limitations of my physical knowledge start to bite. I’m pretty sure we need additional constants to calibrate things like electrical charge, but I don’t know how many, or whether there is any prospect of deriving them all from a unified theory.
All of this would of course be totally impractical for everyday purposes, since we would have to multiply everything by 10^-15 or so to get down to human scale. But we manage OK with joules and pascals, which need to be multiplied up by many powers of ten to be of any use (I recall a letter in the paper from an Imperial fan saying something like “a joule is defined as the energy expended in a housefly’s dying breath”). Anyway, it would be a lot of fun (for appropriate values of “fun”).
fn1. That is, the furthest distance from which light could be received at any point.
Update Footnote 1 and the linked text are wrong. I should have checked Wikipedia first “The age of the universe is estimated to be 13.7 billion years. While it is commonly understood that nothing can accelerate to velocities equal to or greater than light, it is a common misconception that the radius of the observable universe must therefore amount to only 13.7 billion light-years. This reasoning makes sense only if the universe is the flat spacetime of special relativity; in the real universe, spacetime is highly curved on cosmological scales, which means that 3-space (which is roughly flat) is expanding, as evidenced by Hubble’s law. Distances obtained as the speed of light multiplied by a cosmological time interval have no direct physical significance.”