On Sun, Jun 17, 2018 at 07:20:10AM -0500, Jason Resch wrote: > > > > > > 6. Most of all, theories of everything that assume a reality containing > > all possible observers and observations lead directly to laws/postulates of > > quantum mechanics (see Russell Standish's Theory of Nothing > > <http://www.hpcoders.com.au/theory-of-nothing.pdf>, Chapter 7 and > > Appendix D). > > > > > > Unfortunately, Russell's attempt to derive quantum mechanics from the > > plenum of all possible bit strings failed at the first step. So you don't > > have much support from this. > > > > I would be very interested to see this, do you recall the subject or time > frame of this discussion?
The subject thread was "Do Observer Moments form a Vecor Space?". The misspelling of Vector might help find the thread. Actually, "failing at the first step" was not my recollection of the discussion. Bruce had some important critiques, the most important of which is that the linear span of projected states L(ψₐ) that is used for defining the inner product (D.9) is, well, as arbitrary as the originally chosen observable A. My first cut at an answer to this tried to identify the everything with the origin of the vector space - which had a nice property that a complex field was required in order for some non-everything states not to collapse to the origin. However, that approach ultimately ran into a problem with non-orthonormalisability of the basis states. So I tried an alternate approach with the everything being a primitive direction in the vector space, and all subsets of the everything being orthogonal to it. This had some very nice properties, including the subset measure being given by the square of the vector norm, and that the vector space is a vector (or spectral) measure, the most general kind of measure there is. But lost was the nice requirement for the field to be complex, which was always a bit of a problem with the original derivation. I've been meaning to get this in publishable form, but time and other commitments have gotten in my way. In the meantime, Bruce thought he had a proof this was impossible to do (ie a vector space representation of the powerset of bitstrings that gives rise to the Born rule). However, he has yet to present his proof. My work mentioned above, appears to be a counterexample. In the meantime, another problem came to my attention from Markus Mueller (arxiv:1712.0181), where he points out that it is an open question whether transition probability for process on strings is naturally Markovian. The latter portion of my proof, in particular (D.13) is assuming a Markovian process. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow hpco...@hpcoders.com.au Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
