Random thoughts at 2 a.m.: I have been playing poker all night and it’s 2 a.m., so this post may make no sense when I wake up in the morning…
\nIf we take a single spin 1\/2 particle, and put it in a magnetic field, the spin precesses. We can use this to form a sort of clock by preparing the spin in a particular state and then measuring the spin along a particular direction. Of course this clock only has two value 0 or 1. So a universe with a single spin has a single bit clock. But this clearly doesn’t approximate our univerese. What do we need? More spins! So add more spins. Now we get clocks that count in some binary fashion. So we can more accurately measure a time with more spins. Look: if we add more spins we gain accuracy in keeping track of time.
\nNow look at relativity. If our clock has a very small mass, and it is all that exists in the universe, we will read a time which is nearly that of clocks which are infinitely distant. But add more clocks and the mass increases. Now we have a clock with a larger mass. And the larger mass will cause the clock to run slow compared to a clock at infinity. But this means that such a clock can be used to measure the time at infinity much more accurately.
\nAre these two effects really one and the same?
\n**Update** Yep, it’s morning and this makes no sense. Although the two effects scale similarly in the non-relativistic regime.<\/p>\n","protected":false},"excerpt":{"rendered":"
Random thoughts at 2 a.m.: I have been playing poker all night and it’s 2 a.m., so this post may make no sense when I wake up in the morning… If we take a single spin 1\/2 particle, and put it in a magnetic field, the spin precesses. We can use this to form a … <\/p>\n