On 7/31/2014 5:03 PM, LizR wrote:
On 1 August 2014 11:25, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
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.
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.
Brent
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