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Why is Planck time the shortest possible duration ever? It's defined as the duration needed by light to travel Planck's length, but surely, give me any number, I can give you a lower number than that? So what's so special about Planck's time? Is the universe discrete, in the sense that time moves through discrete $N$ Planck units of time?

In the same way, when you say Planck length is the smallest possible distance ever, does that mean every particle( or it's constituents) jumps from one point to another where distance between the points is Planck's length, kinda like strip lighting, where bulbs lit in a sequence give the illusion that the glowing section is moving along the strip?

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It's a commonly repeated myth in popular science articles, including Wikipedia, that Planck units represent the quanta of the quantity they measure in quantum mechanics. This simply untrue -- the Planck length, Planck time, etc. are just combinations of $h$, $c$ and $G$ obtained via dimensional analysis. You could as well scale them by some amount, their physical significance wouldn't change -- much like the Planck mass isn't the smallest unit of mass (which would be hilarious), none of these are the smallest unit of anything.

Space and time are continuous in quantum mechanics, and this is also essential in relativity for Lorentz transforms to work out. However, discretisation is treated as an assumption in loop quantum gravity and some related theories -- the breaking of Lorentz invariance has odd consequences, like violet light having to travel than red light, which is not observed in nature.

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    $\begingroup$ From the Planck Units Wiki page: In fact, 1 Planck unit is often the largest or smallest value of a physical quantity that makes sense according to our current understanding. Your thoughts are correct. $\endgroup$
    – Kyle Kanos
    Commented Sep 8, 2013 at 2:32
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    $\begingroup$ Personally, I like the Planck units regardless of their usefulness because of the fact that they are derived from universal constants. $\endgroup$
    – Kyle Kanos
    Commented Sep 8, 2013 at 2:33

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