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As far as I understand, the universe is not divided into discrete units, but rather its continuous.

This seems backed up by a quick search:

Does the Planck scale imply that spacetime is discrete?

I have also heard, however, that there is a finite amount of information in the universe. There is a finite "density" to which information can be stored.

If this is correct I am having trouble reconciling these two things in my head.

Surely in any continuous line, even in a single dimension, a single point can express any number to any precision? Is this not infinite information...at least some type of infinite.

Now I am not saying we can ever store or extract information of course - merely if a objects position doesn't have discrete units then its position akin to a point on that line. So even one object needs infinite information to express its location, thus infinite information is "stored" in its position - and in fact in the positions of every particle in the universe.

I've been racking my head as to what I am missing but I cant see it. :?

Any help?

Thanks,

Notes; I am aware that on small scales there is a certain "noise" to things. That..I think...we can only get "probability maps" not precise locations of any subatomic particle. But is not the centre of such probability maps also a non-discrete position? Even if its changing constantly?

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  • A universe can be continuous and infinite and yet empty. There's (alomst) no information then, and certainly a finite amount, and these things are not contradictory. – ACuriousMind Mar 09 '15 at 16:20
  • Note that uncertainty principle is some systems quantize the energy spectra. Energy is not discrete however. The spacetime could be doing the same thing, actually this is a consequence of norm in hilbert space + locality. – Nogueira Mar 09 '15 at 17:11
  • @ACuriousMind Good point with a hypothetical there. In fact, would not in that scenario an infinite empty universe in fact have less information then a finite empty one? (which at least has its size itself as a value) – darkflame Dec 09 '15 at 16:14

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