On 7/31/2014 3:52 PM, LizR wrote:
On 1 August 2014 09:05, meekerdb <[email protected] <mailto:[email protected]>> wrote:On 7/31/2014 11:27 AM, John Clark wrote:On Wed, Jul 30, 2014 at 7:57 PM, LizR <[email protected] <mailto:[email protected]>> wrote: > if space-time isn't an infinitely divisible continuum, it presumably has some sort of granularity, Our quantum theories may need work. Quantum theories of Physics insist that space is quantized just like everything else,I don't think that's true. In fact all quantum field theories assume a continous spacetime. I would think that at the very least they assume a continuous Hilbert space.
That too. But the spacetime is a kind of background to the Hilbert space. The vectors in Hilbert space are square-integrable functions of positions or momenta in a continuous spacetime. Of course it's impossible empirically to prove the spacetime is continuous; computationalist can just say they need more digits and hypothesize as many digits as they need. Similarly the complex field for Hilbert space could be just the rational complex field; but that would imply a smallest non-zero probability which in turn would undermine unitarity, Everett, and time-reversibiity.
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