```X-Message-Number: 14210
From: "Yvan Bozzonetti" < var s1 = "totara"; var s2 = "free.fr"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>"); >
References: < var s1 = "200007290900.FAA08490"; var s2 = "rho.pair.com"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>"); >
Subject: Multiuniverse.
Date: Sun, 30 Jul 2000 19:54:33 +0200

Here has been some messages lately on the Everett's multiuniverse
interpretation of quantum mechanics (QM). Here I would get to the basic
roots of that idea:

I have said before aboout distinguishability, how QM works on a space of
functions, or 0-forms, or dual point or hyperplane in p-1 dimensions in a p
dimensional space (On ordinary 3 dim. space, the hyperplane reduces to a
surface).

So, assume we have a flat surface (the identity function) pinned to a point
A in euclidean space. If we move it to a point B, we have an arrow from A to
B, its dual is a differential 1-form, or a stack of flat parallel surfaces.
These surfaces may be tilted with respect to the arrow orthogonal surface,
so we must cancel that tilt (definned as the imaginary part of the function)
by  the product with the same function endowed with the opposite tilt (we
call this the conjugate function)

The problem is when A and B are the same. There is no arrow giving a
privilegied direction. We may then tilt the function surface along two
angles a and b in 3 dimensions and 3 angles: a, b, c in four.

We know that tilting the 3 dim. space along the time fourth direction is
what we feel as velocity in special relativity, so we know what the angle c
is about. By analogy, the angle b could be termed "static relativity" or
"point relativity", because the problem arises when there is no
displacement.

What is this? For each function, such the identity one, we have now an
infinite set of functions, each characterized by its own value of the b
angle. The total number of functions in the Hilbert's space is not only
infinite, it is uncountable. This is the so called nonseparable Hilbert's
space.

Now, in special relativity, space tilt in the time direction is related to
velocity by the hyperbolic tangent transform. Using on angle b the analogous
tangent function of euclidean space, we turn the angle b into a scale
factor.

To get access to nonseparable Hilbert's space, we must so have a quantum
system in a quantum system, a fractal property.

Doing that, we have induced a new tilt in angle a (recall the Euler's
angles: move an angle a, then b, then a anew). To cancel that new tilt, we
must anew introduce a product of the function by its conjugate. We are now
in a space where the metric (what define distance) rests on the 4th power of
the coordinate-function.

I have conduced that reasonning in the function formalism, it could have
been done in the operator one with full tangent space. In that case, the
second tilt cancelling on angle a seems define a displacement along a new
dimension in a parallel universe. This is Everett's multiuniverse. In fact,
the second tilt of angle a applies to the other quantum scale, not another
dimension.

Making some small drawings help a lot to follow that recipe. To summarize:
sorry but there is no other universe. Without cryonics you live one time in
one world with no hope or help from elsewhere.

Yvan Bozzonetti.

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