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Simple question (I think).

Is time infinitely divisible?

I heard that it was, although not from a particularly explanatory source. If so, are we sure that it is, without a shadow of a doubt?

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  • $\begingroup$ Time is what a clock measures. Can you make an infinite number of measurements using any clock you have ever seen? Me neither. So we are, without a shadow of a doubt, sure that time is not "infinitely divisible". Now, are we glossing over this fact when we define a time variable in our theories? Yes, totally. But that's what physics is: the use of approximations to describe reality. In this case we have decided to approximate finite measurements with a fairly easy to deal with mathematical fiction called "the real numbers". The good news is that it works for a lot of purposes just fine. $\endgroup$ – CuriousOne Dec 28 '14 at 4:49
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/9720/2451 , physics.stackexchange.com/q/35674/2451 , and links therein. $\endgroup$ – Qmechanic Dec 28 '14 at 6:44
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https://en.wikipedia.org/wiki/Chronon

In most of physics we treat it like it's continuous, but treating it as quantized might have important implications for quantum gravity, etc. etc. etc.

(Even though the Planck time is the smallest meaningful amount of time that can exist between two events, that doesn't mean time is quantized into Planck times.)

TLDR; no one knows... yet.

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You are asking if time is a continuous variable. This is on par with asking if space is a continuous variable.

Time we measure with clocks is as quantized as space we measure with meter sticks, the accuracy of our measurements.

In the past hundred years we have explored the microcosm and have found that it is quantized, from the existence of countable atoms to the existence of quarks we have found matter to be quantized and have been studying it with elegant theories which assume continuous variables for both space and time.

At present the whole construct of particle physics is well described in this manner, and theories with quantized space and time violate Lorenz invariance which is a well validated part of the theory, so quantization of either space or time is contradicted by data. What the case is for regions of space and time not explorable with our instruments yet is an open research question for the future.

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  • $\begingroup$ That time and space are quantized are assumptions. We don't have any experimental evidence for either and we are still lacking a useful theoretical description for quantized spacetime. There are ideas that spacetime might actually require a thermodynamic approximation rather than a quantized one. Don't tell that to the string folks, though, they think their little pet theory is already the bottom of the turtle stack rather than just a medium sized turtle in the middle. $\endgroup$ – CuriousOne Dec 28 '14 at 5:56

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