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From: Russell Standish <lists.domain.name.hidden>

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

complex.

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

explanation.

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

numbers.

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.

Cheers

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
*

*>
*

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

complex.

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

explanation.

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

numbers.

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.

Cheers

On Thu, Dec 20, 2007 at 08:18:59PM -0800, Jason wrote:

-- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 hpcoder.domain.name.hidden Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list.domain.name.hidden To unsubscribe from this group, send email to everything-list-unsubscribe.domain.name.hidden For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---Received on Fri Dec 21 2007 - 00:39:15 PST

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