Ben Goertzel (ben@goertzel.org)
Tue, 8 Oct 2019 12:36:17 -0400
>
> In a few cases... I had been studying Feynman integral myself. It
> is hard to
> say that it has been given a definition mathematically.
>
In 2D it has been dealt with nicely using analytic continuation, but no one
has made this work
for real 4D space as far as I know
Some people have dealt with the Feynman integral using some nice Hilbert
space mathematics, but I forget
the references
My inclination is to discretize everything, and then everything becomes
automatically definable, i.e. it becomes
a finite sum over a large number of combinations rather than a divergent
integral.
The measure underlying the Feynman integral is not clear. Here I would like
to introduce a notion of subjective
simplicity, whereby e.g. the weight of a path in the measure is the a priori
simplicity of the path. As a first
approximation algorithmic information could be used for a simplicity
measure. But I have never pursued this idea
mathematically, althought it makes sense to me intuitively.
Also, if you believe the "mind over matter" results from the Princeton labs,
these could be explained by the mind altering
the simplicity measure underlying the Feynman integrals governing particle
motion. But this is raw speculation
of course!!
ben
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