Re: Quantum Interference and the Plentitude

From: Russell Standish <>
Date: Fri, 21 Dec 2007 16:39:01 +1100

I'm not sure how Wei Dai would answer this, but this is where it comes
from in my theory:

Interference, along with most of the other weird aspects of quantum
mechanics is a direct result of the measure of observer moments being

If quantum mechanics was done using a real-valued Hilbert space, you
simply don't get wavelike interference patterns.

So why is the OM measure complex and not positive real (like most
people assume). Because it can be - complex measures are more general
than real valued ones. A real valued measure would require an

Unfortunately, so does a complex valued one, as measures can be even
more general than complex valued - see the concept of spectral
measure. I suspect division has an important role in order to get real
probabilities as ratios of OM measures, and whilst there are still a
number of division algebras that can be deployed as measures, possibly
the division has to commutative, which would leave just the complex

Alternatively, perhaps the use of these more general spectral measures
give exactly the same result as using a complex-valued measure. It
would be interesting to develop alternative QM formulations using
modules over division rings rather than vector spaces to see if there
would be any physically measurable effect of (say) relaxing the
requirement of commutivity of multiplication. Alas, this is well out
of my comfort zone, so I'll have to pass the baton on to some other
foolhardy individual.


On Thu, Dec 20, 2007 at 08:18:59PM -0800, Jason wrote:
> Both Russell Standish's "Theory of Nothing" and Wei Dai's "really
> simple interpretation of quantum mechanics" suggest that the mere
> existence of all possible states is all that is needed to explain
> quantum mechanics. While I can understand how it would leads to
> unpredictability I was wondering how is quantum interference
> accommodated?
> Thanks,
> Jason
A/Prof Russell Standish                  Phone 0425 253119 (mobile)
UNSW SYDNEY 2052         
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Received on Fri Dec 21 2007 - 00:39:15 PST

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