I've seen some semi-related questions here, but nothing pertaining to uncertainty.
It has occurred to me (but I’m betting to others long before) is that a quantum state must be represented by a limited amount of information (i.e. bits, because Physics can be reduced to information theory).
Looking specifically at the uncertainty principle, the product of the precisions of position and momentum (or energy and time) must be greater than or equal to some lower limit (Planck’s constant over 2). Imagine that you took a bit of precision away from position (reducing its certainty by a factor of two) and gave it to momentum (doubling its certainty), then you’d get the same maximum precision. If you took into account Planck temperature (https://en.wikipedia.org/wiki/Absolute_hot), it might be possible to postulate a total number bits that could represent these quantities.
Do we know enough about physics to postulate some number of bits to represent this information?
If there is a limit on bits, does this imply some limits on maximum quantities? (I.e. can't have energy above some limit.)