When you mention time, are you asking what's the smallest measure of time we can express or what's the smallet amount of time we can measure?
I think you are just picking an argument that for any unit of time i can name you can name one smaller, so I won't argue any about how we can express an infinate range of numbers, meaning there's no defined end of how small they can go.
If you keep halving time, eventually you will get to the point where nothing in the universe changes state. At that point, time is no longer measurable.
What is the shortest measurable time in existance? Depends on what method you are using to measure it.
There are a lot smaller measurements I could use in my woodworking, but my tape measures are limited in what they show on their index, so the smallest unit of measure I can use is limited to the index of the tape measures I use.
Mike
Lakota's Dad
If at first you don't succeed, deny you were trying in the first place.
If time is the fourth dimension, then it is a distance and therefore is infinitely variable, and not limited to discrete quanta. Therefore there is not a smallest amount of time, any more than there is a smallest number.
I think what may be confusing is that temperature has a lower limit, absolute zero. But this is not because it is a quantum function, but because by definition temperature is a measurement of the movement of atoms in a material and therefore when there is no movement (which is impossible) then you have reached absolute zero. As far as we know, there is no upper limit.
Now you're getting into calculus - infinity is not a number. You would have to take a limit as you approach infinity. You will not reach infinity - you could try, but it would take you an infinite amount of time, but that's another discussion...
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