On 1 August 2014 14:45, meekerdb <[email protected]> wrote: > On 7/31/2014 5:03 PM, LizR wrote: > > On 1 August 2014 11:25, meekerdb <[email protected]> wrote: > >> On 7/31/2014 3:52 PM, LizR wrote: >> >> On 1 August 2014 09:05, meekerdb <[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]> 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. >> > > Yes, it's awlays possible to claim a granularity smaller than our best > measurements. How does this connect with QM and it being impossible to > measure anything smaller than the Planck length? (Or does it?) > > >> 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. >> > > I can see that unitarity would be undermined, and hence Everett (I > think), but how come time-reversibility? > > It would mean that interference terms between different "worlds" could not > become arbitrarily small. There would be a least quantum of probability > and when something became more improbable than that, its probability would > drop to zero. Then the time evolution couldn't be reversed. >
Ah, yes, I see what you mean. I suspect that if it worked like that, the minimum probability would have to be the bottom limit - that is, it couldn't drop to zero but would always have a finite probability. However this looks (well, to me) like the obverse of the observer collapsing the wavefunction - placing an arbitrary limit on what is and isn't "quantum mechanical". Interesting. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
