Light & very small distances - paradox??

Hi,
This is my first post to this group. I've always been intrested in
phsyics but tonight in particular I just can't sleep because I have a
thought that keeps running throught me head.

I just read a post about how the speed of time is the same as the speed
of light. That seems obvious -- the smallest unit of time would be the
time it takes for a photon to travel the shortest possible distance in
the universe. But then I thought "how big is the smallest distance in
the universe?" I would assume it would be infinitely small, right? It
would have to be because if it came in chunks, light would have to
travel between the chunks instantly.

Well the question becomes "how long does it take a photon to travel an
infinetesimally small distance?" It can't be instantly right?? That
would be impossible but on the other hand, how can it take any more
than zero seconds to travel an infinitely small distance? So if you
extend this out to infinity, light jumps between points instantly
meaning it will go an infinite distance in zero time???

Tell me what I'm missing - I doubt I'm smart enough to find something
every other physisyist in history overlooked. I need some sleep!

Thanks,
RC

.

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