ca314159 (ca314159@bestweb.net)
Sat, 20 Mar 1999 16:41:29 -0800
Hitoshi Kitada wrote:
> Yes, it can be seen as one of the standard Kaluza-Klein arguments. My point
> that R^6 is more fundamental than R^4 is in that space and momentum are more
> fundamental than space and time in the point that space configurations
> x=(x_1,x_2,x_3) and momenta p=(p_1,p_2,p_3) are the basic quantities, from
> which one can define time t of the system of particles as a kind of quotients:
>
> t ~ |x| / |p|
>
> where |x|, |p| are "approximate" absolute values of quantum mechanical
> quantities x, p, "approximate" being understood as a kind of average of
> quantum mechanical obscure values. Here is a kind of contraction procedure of
> R^6 to R^4 by some compactification of a small region into a point, in the
> expectation that the region would be quite small compared to the classically
> recognizable region. (In some of my papers, I described this "smallness" as an
> uncertainty of time.)
This seems to make perfect sense from the point of view of spatial
clipping. If a spectrum is cropped or windowed, the resulting
time-domain representation for that window is the local time for
that spatial segment. The |x|/|p| is a segment of a spatial spectrum
for points x and associated energy from the p.
I think it must be hard for people to realize that the spectrum
is not necessarily something parametrized on statistical "frequency"
or temporal "frequency", but is much more general. But I would hesitate
to say this is more "fundemental" than space and time. I would
say it is more "complete".
For example, if I take *any* histogram it has spatial positions (states)
for each magnitude(intensity), which we might map onto with x and p respectively.
Then transforming these into the time domain yeilds a time based
function which might seem like a silly idea if the spectrum is the
intensities of ingredients in breaskfast cereal. But we can do this
mathematically, the rest is a matter of interpretation (Quines'
translation indeterminacy).
The spatial "center of mass" of a culture is the window of geographical
positions in which the culture is localized. If a histogram is built
up of relative intensities for particular cultural activities, some
cultures will have more activity in specific activities than others.
If we spatially isolate one culture's spectrum (histogram), it's
"center of mass", from all the other cultures we can obtain a time-domain
function of that activity as separate from all other cultures
(it's local time).
But these histograms are taken to be established "instantaneously"
which is not possible in practise, so seems where the uncertainty
comes in.
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