On 29 Apr 2011, at 04:03, Stephen Paul King wrote:


    Hi Bruno,

But are machine semantics restricted to a position basis mode of expression?

That was the question I as asking. Probably not, but I am not sure. Even pure spin computations needs the use of position, at least for reading and writing memories. But this might be a human limitation, not a machine limitation.



I can see how this would do damage claims of universality!

Why? I don't see this at all. Remember that with comp the numbers are only dreaming space and position. Such notion are secondary and emerging from the numbers points of view.



This is a open problem for me as well as my toy model is only framed in the position basis at the moment and I do not know how to generalize it at the moment, but I have seen hints in the C* algebra duality of Gel’fand. arxiv.org/pdf/0812.3601 and www.mathstat.dal.ca/~p.l.lumsdaine/research/Lumsdaine-2009-Duality.pdf

QM seems to demand that all possible basis be treated equally, there can be no preferred basis (via the linearity of the tensor product of Hilbert spaces?!); just as there can be no preferred reference frame in GR. http://www.physicsforums.com/showthread.php?t=362959 and http://plato.stanford.edu/entries/qm-everett/


Yes. I agree. There are no preferres basis, like they are no preferred universal system. That is why I take the numbers.



“The preferred basis problem is arguably a more serious problem for a splitting-worlds reading of Everett. In order to explain our determinate measurement records, the theory requires one to choose a preferred basis so that observers have determinate records (or determinate experiences) in each term of the quantum-mechanical state as expressed in this basis. The problem is that not just any basis will do this. Making the total angular momentum of all the sheep in Austria determinate by choosing such a preferred basis to tell us when worlds split, would presumably do little to account for the determinate memory I have concerning what I just typed. But this is the problem, we do not really know what basis would make our most immediately accessible physical records, those records that determine our experiences and beliefs, determinate in every world. The problem of choosing which observable to make determinate is known as the preferred-basis problem.”

There is no splitting, both with Everett and comp. Only relative states. The 3-states are defined relatively to universal numbers., and the 1-states are defined relatively to infinities of universal numbers (the infinitely many competing below our substitution level).






That we humans have a bias toward the position basis may very well be an artifact of our physical senses. It is interesting to note that bases exists that are combinations of other bases. Some research by Aharonov et al in the so called Weak Measurement area shows some unusual implications of this: http://en.wikipedia.org/wiki/Weak_measurement I suspect that the “basis problem” is just another version of the measure problem.

I think there is no basis problem. All versions of it comes from a too much literal understanding of the notion of world or universe (which makes no sense with comp). Also, I think that the measure problem in QM is mainly solved by Gleason theorem. And the measurement problem is solved by Everett MW. I might be wrong (if Weinstein is correct, for example). Comp is far from being as clean as QM, though, but it should lead to QM, with perhaps some modification, which might solve the remaining problems.

Bruno

http://iridia.ulb.ac.be/~marchal/



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