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1) ordinary classical physics is non-deterministic without infinite precision; this isnt observed 2) these "60 or 70" digit -type reasoning omit iterative prob

1) ordinary classical physics is non-deterministic without infinite precision; this isnt observed 2) these "60 or 70" digit -type reasoning omit iterative problems, such as the number of digits required to specify the behaviour of a gas of 10^{big} particles over 10^{big} nanoseconds 3) QM is the most dependent on infinite precision out of all the theories of physics, requiring infinite-dim hilbert space to be linear. QM is linear, so we have infinite dimensions. Reality aint computable. This seems fairly obvious if you're not a csci zealot. QM only limits conjugate precision in conjugate varaiables. The Un-P' says absolutey nothing about whether reality is computable; and as far as QM weighs in, it is overwhelmingly against a computable universe. The formalism uses hilbert spaces indispensibly. ie., whilst expectations of conjugates may, via UP, have a "conjugate precision" the underlying wavefn requires infinite

naasking 3y ago
Only an HNer would so boldly and unironically contradict Peter Shor. Infinite dimensions aren't needed for any real interaction because the number of particles are bounded, and the precision of any real measurement is itself necessarily bounded, ergo infinite Hilbert spaces simply aren't relevant for any actual measurement. They are as unreal as a Turing machine's infinite tape, which is why quantum computers provide only polynomial speedup over Turing machines.
- mjburgess 3y ago
  > Infinite dimensions aren't needed for any real interaction because the number of particles are bounded, The number of particles in an interaction is irrelevant to the property of linearity requiring infinite dimensions. It is straightforward to show QM isnt a linear theory in anything other than an inf-dim space. The question, "are real numbers eliminable in physics?" is an extremely well-discussed on by more people than Mr Shor. There is overwhelming evidence they are not, and no evidence they are. All these local arguments do is show approximations work in some cases. They don't deal with the big issues. The UP does not constrain the value of physical constants, this is just a misunderstanding on Shor's part. It's only relevant to pairs of conjugates; not even to singles, since a single is not constrained by the UP at all. Many physicists are not well-positioned to answer questions in the philosophy of physics.
  - naasking 3y ago
    > It is straightforward to show QM isnt a linear theory in anything other than an inf-dim space. Even if this were strictly true, which it's not for any real purpose, it's completely irrelevant because reality is non-linear. This non-linearity is how we get probabilities out of QM. Unless of course you're merely assuming a particular interpretation of QM that says otherwise, like MWI, but then I have no reason to accept this premise so your argument is still unconvincing. > There is overwhelming evidence they are not, and no evidence they are. In fact, the opposite is the case, and we don't even need any fancy arguments to demonstrate this: if what you say were true then a trivial proof refuting the Mathematical Universe hypothesis would have been published years ago. No such proof exists.

naasking 3y ago

Only an HNer would so boldly and unironically contradict Peter Shor. Infinite dimensions aren't needed for any real interaction because the number of particles are bounded, and the precision of any real measurement is itself necessarily bounded, ergo infinite Hilbert spaces simply aren't relevant for any actual measurement. They are as unreal as a Turing machine's infinite tape, which is why quantum computers provide only polynomial speedup over Turing machines.

mjburgess 3y ago
> Infinite dimensions aren't needed for any real interaction because the number of particles are bounded, The number of particles in an interaction is irrelevant to the property of linearity requiring infinite dimensions. It is straightforward to show QM isnt a linear theory in anything other than an inf-dim space. The question, "are real numbers eliminable in physics?" is an extremely well-discussed on by more people than Mr Shor. There is overwhelming evidence they are not, and no evidence they are. All these local arguments do is show approximations work in some cases. They don't deal with the big issues. The UP does not constrain the value of physical constants, this is just a misunderstanding on Shor's part. It's only relevant to pairs of conjugates; not even to singles, since a single is not constrained by the UP at all. Many physicists are not well-positioned to answer questions in the philosophy of physics.
- naasking 3y ago
  > It is straightforward to show QM isnt a linear theory in anything other than an inf-dim space. Even if this were strictly true, which it's not for any real purpose, it's completely irrelevant because reality is non-linear. This non-linearity is how we get probabilities out of QM. Unless of course you're merely assuming a particular interpretation of QM that says otherwise, like MWI, but then I have no reason to accept this premise so your argument is still unconvincing. > There is overwhelming evidence they are not, and no evidence they are. In fact, the opposite is the case, and we don't even need any fancy arguments to demonstrate this: if what you say were true then a trivial proof refuting the Mathematical Universe hypothesis would have been published years ago. No such proof exists.