[time 917] Re: [time 913] RE: [time 912] Re: [time 911] RE: [time 910] Re: [time 909] About your proof of unitarity

Sat, 9 Oct 1999 12:41:15 +0900

Dear Ben,

Ben Goertzel <ben@goertzel.org> wrote:

Subject: [time 913] RE: [time 912] Re: [time 911] RE: [time 910] Re: [time

> >
> > 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,

For 2D Dirac equations, it has also been treated without using analytic
continuation.

> but no one
> 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

Probably you are talking about Ito formula or Kac's one?

>
> 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.

If one can stop at a finite step, it is so of course...

>
> 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,

What is this "mind over matter" results? Could you explain?

> 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
>

Best wishes,
Hitoshi

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