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What's smaller than a nanosecond? And if there isn't anything smaller, aren't we technically frozen in time between nanoseconds?

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1 nanosecond = 1000 picoseconds.
It takes about 84 picoseconds for light to travel one inch.

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I just learned on wiki that one picosecond equals one trillion yoctoseconds.
Wow.
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.01 of a nanosecond

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A picosecond is smaller.

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A picosecond, but no we aren't frozen in time between nanoseconds or picoseconds for that matter because all such measurements are arbitrary. If we wanted to we could infinitely divide any amount of time and it will still be an un broken amount of time. As long as we are existing time must be passing because without it the algorithms which set the world in motion won't work. Time won't stop until our universe either freezes or rips apart. So no, technically between nanoseconds we do as we do during nanoseconds, we pass through time.

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Surely we must be dropped into pockets of time, though? I mean, yes. 1 can be infinitely divided. As any number can, but... After a while it just starts to repeat, correct? So time loops... And every loop has a hiccup in it...
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and there are femto seconds and atto seconds...

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femto and atto... Lots of eastern type names and bases...
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And lets not forget zepto (10^(-21)) and yocto (10^(-24))
I dont know if there's anything naming convetion beyond that..
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There's always a smaller unit. The answers above are good enough so I won't go into that much detail, but just remember that time is man-made. BTW, no, at the smallest of time increments, you wouldn't be frozen.

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Well I mean wehn crossing over from, say, 2:00 to 2:01 in between those picto or femto or whatevers we are crossing into the next patch of time... so... we are in limbo for that small increment of time, right?
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It's good that you are thinking along these lines- it shows that you are using your brain rather than just going along with what everyone else things- good job!

The ticks on a clock- no matter how small we make them, are just made-up divisions so we can talk about how long a certain thing takes to happen- time is not actually divided into those units, only our conversations about time are dividing into those units :-)
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(typo- sorry - meant 'thinks' not 'things')
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when you get a little better at math, you can Google 'Planck Time' and find out that there really might be a 'smallest unit of time', but this is a very, (VERY) complicated thing to understand..
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Well, for one, I'm in 9th grade, and understand math as well as I can for now.. Another thing, while time does have to do with math, it still doesn't mean you need to be Einstein (although he couldn't do simple math) to understand time increments. But what I'm saying is that there has to be a point where it is neither 3 picoseconds or 4 pico seconds, or whatever our smallest unit of time is, where it's right in between, so we are passing from time A to time B without realising or truly understanding it... For all we know, we're actually moving very slowly, just not realising it, like how we thought the sun orbitted earth (not sure if I spelled that right).
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Actually- yes it does. Our current understanding of time DID require Einstein- who, by the way was a superb mathematician- he may not have enjoyed simple math, but don't for a second (or picosecond!) think he 'could not do math'!! His formulations of special and general relativity cannot be understood in their entirety without a deep understanding of the mathematics behind them.

When you say 'there has to be a point...' all we are telling you is NO- there does not- as counterintuitive (against common sense) as that seems.

It turns out there may be a smallest time (called the Planck Interval), but you need to understand how closely time and space are related before this will even make sense to you.

Keep thinking about this. unfortunately, I don't know of any books that deal with time that are not probably beyond your current mathematical capabilities (though if you keep pondering things like this, maybe one day we'll all be reading YOUR paper on the nature of time!)- Stephen Hawkings book 'A brief History of Time' is pretty non-mathematical but still may be more they you can bite off at the moment.