What is the smallest unit of time? What is the largest unit of time? Is it possible for time to actually stand still?
The smallest known unit of time is the Planck Interval, approximately 10^-44 of a second.
The largest known unit is the age of the known universe…anywhere between 12 and 20 billion years.
And that can be extended to about 100 billion years into the furure if we extrapolate from physics the possibility of the universe expanding forever and all matter decays into nothingness.
And just as relativity prevents matter from achieving precicely the speed of light, so does it also prevent time from slowing down to precicely zero.
FYI the Planck Time is derived from the time it takes light to traverse the Planck Distance which is 10[sup]-35[/sup]m. It is worth noting however that the Planck Distance is not the smallest you can get. Presumably you can get even smaller. However, our notions of how physics works breaks down completely at the Planck Distance so we can’t really speculate what happens below this threshold.
Also, I think the maximum age of the universe will be a LOT longer than 100 billion years. I thought the number was on the order of several trillion years till the universe can be considered completely ‘ended’ in the sense that everything has decayed to basic particles, spread out roughly evenly through space and cooled to some temperature arbitrarily close to absolute zero (the Heat Death of the universe…totally depressing to my mind). Even then I don’t know that you could say time has ended…someone with a bigger clue than I will have to answer that.
That’s actually one of the side-effects of matter reaching light speed (time stopping). It’s funny when people suggest a ship that travels the speed of light even as a hypothetical because among a bevy of other issues with doing this is one often overlooked issue.
Say you get in your new super duper light speed ship. As soon as you hit a button your ship reaches light speed. However, you’re worried what will happen so you just want to test it for a second by hitting the button on and then hitting it again as fast as you can to shut it off. So…you hit the button and accelerate to light speed. You will never ever turn it off because the universe will cease to exist before you can hit the button a second time (either that or you will spend eternity trying to hit the button to stop your ship if you assume the universe never ends).
[sub]Sorry for the multiple posts but I kept having additional thoughts about this after I previously posted.[/sub]
whack: Time will only stop in that frame of reference though, right?
Yes…time only stops for the thing moving at the speed of light. However, an object with mass that reached the speed of light would essentially have infinite mass and be everywhere in the universe at once. I’m not certain what implications that would have for the universe as a whole were such a thing to happen but I doubt it would be anything good. It might likely be the end of everything for all of us and maybe the whole universe to boot thus ending time for everyone but that’s just a WAG on my part. Thankfully it is impossible (e.g. how could you accelerate something approaching infinite mass?) so we needn’t worry about this.