Recently, I read two early papers of Penrose on spin networks (made available online by John Baez http://math.ucr.edu/home/baez/penrose/" [Broken]), familiar today of course because of their use in loop quantum gravity.(adsbygoogle = window.adsbygoogle || []).push({});

In their original form, however, they seem to me to have been quite different beasts: as far as I see, the idea was to let a quantum system define its own geometry, via interaction through the exchange of 'n-units', i.e. subsystems carryingnunits of spin 1/2. The spin networks then were just the representation of these exchanges.

Remarkably, it turned out that these spin networks reproduce the angles of Euclidean 3-space by the following procedure: you 'detach' a spin-1/2 unit from one large unit, and 'attach' it to another; the probability that the total spin of the second unit decreases then is given by the well-known [itex]p = \cos^2\frac{\theta}{2}[/itex]; this is taken to define the angle between both units.

This much, I was aware of abstractly -- as in 'spin networks reproduce the angles of 3-space' --, but two conclusions Penrose drew seemed very noteworthy to me. One, that the background geometry some quantum system is placed in doesn't matter -- from the system's point of view, it will always 'live' in 3-space -- the system defines its own geometry. Two, and I think this is more hypothesized about, this may pose an explanation for some quantum mechanical weirdness -- an electron 'going both ways' through a double slit experiment doesn't split in its own geometry; it simply doesn't live in quite the same geometry the two slits do, but brings its own geometry with it. These things, I hadn't heard about previously. So, my questions are:

1) Is what I said so far about right?

2) What's the modern view on these things -- quantum systems creating their own geometry, etc.?

3) Has the work in this way, i.e. apart from loop gravity, been continued? I'd especially like to know about elaborations on the idea that the particle and the slits in a double slit experiment don't share the same geometry; Penrose cites it as an idea of Aharonov, but the only source is 'private communication'.

Thanks in advance!

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# Penrose's original spin networks and 3-space

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