The Gödel Hurdle

The latest issue of The Quantum Times was just e-mailed around and should appear on the website soon. In it I give a summary of the APS March Meeting from Denver. One thing that I’ve been thinking about (in relation to this) lately is the fact that so many folks are attempting to axiomatize physics (which I wholeheartedly support). However, it gets me wondering what this all means in relation to Gödel’s Incompleteness Theorems (yes, there were two). I have a hunch that Rob Spekkens’ view that quantum states are states of incomplete knowledge will rectify this problem. In fact I have an idea brewing in my head concerning probability theories and meta-descriptions of the type discussed by Douglas Hofstadter nearly thirty years ago in his Pulitzer Prize-winning book Gödel, Escher, Bach: An Eternal Golden Braid. Stay tuned as I put together something for the arXiv on it.

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3 Responses to “The Gödel Hurdle”

  1. serafino Says:

    As David Finkelstein wrote many years ago … ‘There is, to be sure, a genuine problem in the phenomenon of quantum measurement,
    but I will not discuss it here. It concerns ‘introspective’ systems,
    where subject = object so that
    the basic conception of a single subject observing an ensemble of objects must be modified.’
    -David Finkelstein, in the paper ‘The Physics of Logic’
    (in ‘Paradigms and Paradoxes’, editor R.G. Colodny, 1971, p.60).

    There are many references here …
    http://egregium.wordpress.com/2006/11/25/theorema-egregium/#comments

    -serafino

  2. serafino Says:

    As David Finkelstein wrote many years ago … ‘There is, to be sure, a genuine problem in the phenomenon of quantum measurement,
    but I will not discuss it here. It concerns ‘introspective’ systems,
    where subject = object so that
    the basic conception of a single subject observing an ensemble of objects must be modified.’
    -David Finkelstein, in the paper ‘The Physics of Logic’
    (in ‘Paradigms and Paradoxes’, editor R.G. Colodny, 1971, p.60).

    There are many references here …
    http://egregium.wordpress.com/2006/11/25/theorema-egregium/#comments

    -serafino

  3. Quantum Moxie Says:

    I’ve started looking at Breuer’s PhD thesis, notably the section on self-measurements. I am intrigued by his idea (?) that experiments, at least partially, constitute the semantics of physical systems. It shows just how deeply theory is pounded into me since I always think in terms of the mathematics being the semantics. But, in a sense, I suppose the mathematics are simply a way to describe the experiments, a translation of sorts.

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