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Classical and Quantum Mechanics via Lie algebras 
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#1
Apr1511, 04:54 AM

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I'd like to open a discussion thread for version 2 of the draft of my book ''Classical and Quantum Mechanics via Lie algebras'', available online at http://lanl.arxiv.org/abs/0810.1019 , and for the associated thermal interpretation of quantum mechanics, espoused in the book.
The goal of the thread is to obtain reader's feedback that helps me to improve the presentation while I work towards a version for publication. Abstract: The book fulfils the didactical purpose of showing that  quantum mechanics and classical mechanics are much more similar than can be seen from the usual presentations of the subject;  in a very significant sense, theoretical classical and quantum mechanics is nothing but applied Lie algebra;  quantum mechanics has a common sense interpretation once one takes the thermodynamical findings of statistical mechanics serious in the foundations. The content of the book is fully mainstream, covering hundreds of publications by others (301 references, too numerous to include them into this opening post), including many references to basic experiments. However, the selection and presentation of the material is very different from what one can find elsewhere. The importance of the topic is obvious. With exception of the thermal interpretation, nothing is new about the scientific content. The presentation of the book is in intelligible English, complemented by LaTeX (some of it only intelligible by intelligent readers). With exception of historical evidence (and perhaps oversights), everything is defined or derived with mathematical rigor. The empirical equivalence of the presented material to standard mechanics is manifest, and almost the whole body of experimental physics supports the theory presented. [If this paragraph sounds a bit crackpottish  I am required to state all these things in order to conform to the submission rules.] The thermal interpretation of quantum mechanics was presented first last year in a lecture whose slides (Slide 2334 define the interpretative core) are available at http://www.mat.univie.ac.at/~neum/ms/optslides.pdf , which in turn is based on insights from Sections 8.4 and 10.310.5 of version 2 (or Sections 5.4 and 7.37.5 of version 1) of the above book.A short exposition is given in the entry ''Foundations independent of measurements'' of Chapter of my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/ph...aq.html#found0 . See also the following PF posts: http://www.physicsforums.com/showthr...36#post3246436 http://www.physicsforums.com/showthr...39#post3187039 http://www.physicsforums.com/showthr...47#post3193747 


#2
Apr1811, 09:02 PM

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how does the thermal arise for a single electron.



#3
Apr2011, 10:38 AM

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I suggest that you begin by reading the slides http://www.mat.univie.ac.at/~neum/ms/optslides.pdf where the interpretation is explained for a single photon. The electron is essentially the same, except for the different state space. 


#4
Apr2011, 11:51 AM

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Classical and Quantum Mechanics via Lie algebras
This post contains replies to posts 17 from http://www.physicsforums.com/showthread.php?t=490677
I'll comment on the later posts at another time. then its quantum field oscillates in a wave manner. See Chapter 10.35 of version 2 of the draft of my book. No other interpretation can do that. where the interpretation is explained. They contain the material of a wellorganized lecture in which nothing is left vague. The thermal interpretation doesn't change anything in the theory. What is changed is _only_ the interpretation of measurements. All measurements are primarily measurements of the macroscopic object that is actually inspected when measuring something. To be valid, any inference about the value of some microscopic object must be (ideally) backed up by an argument that the microscopic object influences the macroscopic object in a way that the observed macroscopic behavior results. 


#5
Apr2111, 04:38 AM

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starting with an algebra of observables, then states and relying on a list of axiomatic (Whittlestyle) properties of expectations, I'm wondering whether one can indeed account for all features of QM that way... Consider the Cauchy (or BreitWigner) distribution that gives the probability distribution of the lifetime of unstable particles. The usual expectation, variance, etc, are undefined for that distribution but it's clearly an important part of quantum physics. How then do you get a BreitWigner distribution if you've started the theory from expectations? 


#6
Apr2111, 11:04 AM

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#7
Apr2111, 11:40 AM

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currents in a photodetector. We _infer_ from these raw measurements properties of systems that we cannot ''read'' directly, and the inference is as good or as bad as the causal link provided by quantum mechanical theory in the respective case. Instead, it gives the conditions under which an ensemble interpretation is valid. See Section 10.3 of my book. and give the quantum expectation a different interpretation. See Sections 10.310.5 of my book. 


#8
Apr2111, 12:36 PM

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#9
Apr2111, 11:44 PM

P: 789

Quote from chapter A5 section 1 
"Note that a measurement does not need a conscious observer. A measurement is any permanent record of an event, whether or not anyone has seen it. Thus the terabytes of collision data collected by CERN are measurements, although most of them have never been looked at by anybody." Consider a "Schroedinger's cat" scenario  the particles generating the tracks and the "permanent record" are inside an isolated box  How is the "permanent record" described by a scientist outside the box? I expect it would be a mixed state, but does this mixed state constitute a measurement? 


#10
Apr2611, 07:07 AM

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This makes the standard ontology quite weird. In the thermal interpretation (as in real life), many expectations are measurable (to some limited degree of accuracy), and so are many probabilities (as expectations of projectors). Thus these are real in the thermal interpretation, making things much more intelligible. 


#11
Apr2611, 07:11 AM

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Whether it constitutes a measurement depends on one's definition of a measurement. The thermal interpretation has the huge advantage that one doesn't need to know what a measurement is, and still has a perfectly valid interpretation. Measurement is a difficult subject, so it should not figure in the foundations. 


#12
Apr2611, 07:30 AM

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I hope this helps on the frontier of written communication. 


#13
Apr2611, 07:51 AM

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Poisson brackets define Lie algebras. Commutators define Lie algebras. But to appreciate how far this goes, you need to study the book, not the abstract. It will be worth your time. 


#14
May211, 09:09 AM

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The situation is similar as with a sphere of glass. If you throw it, you may regard it as a particle. But if it hits an obstacle and fragmentizes, it is no longer localized enogh to deserve the name of a particle. 


#15
May211, 09:29 AM

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#16
May211, 11:19 AM

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http://www.physicsforums.com/showthr...39#post3187039 and in the thread http://www.physicsforums.com/showthread.php?t=480072 


#17
May211, 05:32 PM

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#18
May211, 07:30 PM

P: 789




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