5 ms·

As far as we know the universe isn't discrete like a cellular automata. So it's state contains infinite information for starters. I'm not sure what the current

As far as we know the universe isn't discrete like a cellular automata. So it's state contains infinite information for starters. I'm not sure what the current theories of physics say, but I don't believe the universe is finite in time or space either. And who knows what new discoveries physics might make in the future and what weird math it might require. There's no a priori reason to expect the universe to be modelled by finitist math. But even if we knew for sure it was, so what? Theorems about real numbers apply perfectly well to finite approximations. You don't gain anything by restricting yourself to finite math, and you lose quite a bit and make a lot of things much harder.

pbhjpbhj 9y ago
Current theories AFAIAA are that the universe is finite in all dimensions. If it had finite particles, with finite (quantised) states, with finitely many discernible locations, to be found at finitely many discernible times, then the states overall are finite. Time and space are effectively discretised, Planck scale and time. Even aside from that: for considerations of physical measure we always use something with an explicit size, a wavelength of light say, as our rod which limits our precision.
- gus_massa 9y ago
  There may be finite real particles, but there are infinite virtual particles (and some times, the difference between a real and a virtual particle is not too clear). For example, a proton has three real quarks. But the mass of the three quarks is only the 1% of the mass of the proton https://en.wikipedia.org/wiki/Quark#Mass https://en.wikipedia.org/wiki/Quark#Mass the rest is crap, or in more technical terms https://physics.stackexchange.com/a/81284 https://physics.stackexchange.com/a/81284 . When you measure with more energy, you see more and more virtual particles, infinite virtual particles.
  - sgregnt 9y ago
    But if the energy is finite, soesnt it mean that you can only produce so much virtual particles?
    - gus_massa 9y ago
      That's the nice part of virtual particles. If they are short lived enough they can be so many or so massive as you wish. Well, not as you wish because there are a lot of rules that relate the amount of particles, the mas and momentum of each one and the available energy. At low energy the effect of the virtual particles is negligible (except in a very few weird cases like the https://en.wikipedia.org/wiki/Lamb_shift https://en.wikipedia.org/wiki/Lamb_shift ). At high energy the probability of the virtual particles is bigger, so their effect is easier to measure. I like this drawing of that shows the firs three steps of diagrams with virtual particles that are necessary to calculate the magnetic moment of the electron: http://www.strings.ph.qmul.ac.uk/~bigdraw/feynman/slide3.html http://www.strings.ph.qmul.ac.uk/~bigdraw/feynman/slide3.htm...

pbhjpbhj 9y ago

Current theories AFAIAA are that the universe is finite in all dimensions. If it had finite particles, with finite (quantised) states, with finitely many discernible locations, to be found at finitely many discernible times, then the states overall are finite. Time and space are effectively discretised, Planck scale and time. Even aside from that: for considerations of physical measure we always use something with an explicit size, a wavelength of light say, as our rod which limits our precision.

gus_massa 9y ago
There may be finite real particles, but there are infinite virtual particles (and some times, the difference between a real and a virtual particle is not too clear). For example, a proton has three real quarks. But the mass of the three quarks is only the 1% of the mass of the proton https://en.wikipedia.org/wiki/Quark#Mass https://en.wikipedia.org/wiki/Quark#Mass the rest is crap, or in more technical terms https://physics.stackexchange.com/a/81284 https://physics.stackexchange.com/a/81284 . When you measure with more energy, you see more and more virtual particles, infinite virtual particles.
- sgregnt 9y ago
  But if the energy is finite, soesnt it mean that you can only produce so much virtual particles?
  - gus_massa 9y ago
    That's the nice part of virtual particles. If they are short lived enough they can be so many or so massive as you wish. Well, not as you wish because there are a lot of rules that relate the amount of particles, the mas and momentum of each one and the available energy. At low energy the effect of the virtual particles is negligible (except in a very few weird cases like the https://en.wikipedia.org/wiki/Lamb_shift https://en.wikipedia.org/wiki/Lamb_shift ). At high energy the probability of the virtual particles is bigger, so their effect is easier to measure. I like this drawing of that shows the firs three steps of diagrams with virtual particles that are necessary to calculate the magnetic moment of the electron: http://www.strings.ph.qmul.ac.uk/~bigdraw/feynman/slide3.html http://www.strings.ph.qmul.ac.uk/~bigdraw/feynman/slide3.htm...