## How big does a register ever need to be? (Time)

This article is the next in the series that started with Distance & Volume. As mentioned in that first article, these are back-of-the-napkin calculations that are based on our current understanding of physics. I make no claims to accuracy or even authority in this thought experiment, and I'd be happy to incorporate the advice and corrections of more expert minds.

If we take time as a quantity to be measured, how large does a CPU register ever need to be in order to accomodate any possible measurement?

If a Planck time as the smallest possible time scale that is meaningful, then the smallest unit of time is ~5.4x10-44 seconds.

What is the largest quantity of time that we can speak of? It would be from our current understanding of the beginning of time itself, the Big Bang, until the "end of the universe". Luckily for this line of questioning, but unfortunately for the universe itself, it is estimated that at some point in the very, very distant future the universe itself will reach a point of maximum entropy. After this point it is relatively meaningless to consider the ordering of events in the universe, and therefore time becomes meaningless.

There are many estimates for the fate of the universe based on different theories about the decay of fundamental particles, estimates of the mass of the universe, etc. As physics learns more about the universe these estimates may become more accurate, or there may be even more uncertainty and mystery discovered! For the sake of this thought experiment we'll put a stake in the ground and accept the estimated end of the "Black Hole Era" as the final moment of time as we know it. That is approximately 10100 years from now. This number so dominates the current age of the universe (13.75 billion years), we can neglect the current age as rounding error.

10100 years is 3x10107 seconds. Divide these seconds into tiny little Planck times and we get: 3.x10107 x 5.4x1044 =~ 1.7x152 Planck lengths, or 2508. Rounding 508 to the nearest power of two, we get 512 bits. That's cutting it close, so we may wish to bump that up to the next highest power of 2: 1024.

So there's our answer, 512 bits can probably hold any quantity of time that we could ever hope to measure, but maybe just barely. 1024 bits would definitely hold this number with more than double its resolution to spare, an important consideration given how uncertain some of the physics behind this estimate is!