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From: Archimedes Plutonium on 27 Mar 2010 16:47


Archimedes Plutonium wrote:
(snipped)
>
> Do I have any confirmation of Symmetry-Breaking as defined as this:
>
> Eucl geom = Elliptic geom unioned Hyperbolic geom
>
> Is there any sort of confirmation in Physics that such a formula is
> Symmetry
> Breaking in Quantum Mechanics?
>
> I suspect so. Notice that the formula is truly unlike any other math
> formula because
> it has a "union" rather than it has addition, for which no other math
> formula has
> a union rather than the operator addition.
>
> But if you look in Physics there is a formula that sticks out like a
> sore thumb which has
> a set-theory-operator union rather than that of math operators of add,
> subtract, multiply
> and divide. I am speaking of the Uncertainty Principle in its
> "uncertainty operator"
>
> del_x * del_P > h
>
> where x is position, P is momentum, and h is Planck's constant, and
> where del stands
> for Uncertainty operator.
>
>
> So, here, all I have to do is show that
>
> Eucl = Ellipt unioned Hyperb
>
> is the same as
>
> del_x * del_P > h
>
> The literal translation is easier than the mathematical manipulations.
> Literally, it
> means that the Uncertainty Principle gets to a "smallness in size"
> that where
> the physics can no longer tell whether the geometry is Elliptic,
> Hyperbolic or
> Euclidean. The Uncertainty Principle for Mathematics, means that at
> some small
> size we cannot convert Euclidean geometry into its component
> NonEuclidean
> geometries.
>
> In this book, I covered the idea of the limits of concavity of
> triangles in that a
> equilateral triangle of 60 degree arc longitude is the upper limit of
> reversing the
> concavity in forming the hyperbolic triangle.
>
> Well, the Uncertainty Principle in Math means that the conversion of
> Ellipt and
> Hyperbolic geometries into forming Euclidean is also limited or
> restricted by
> Planck's constant, and where reversing concavity is one limiting
> factor amoungst
> many limiting factors.
>
> So I would have to show, mathematically that these two equations are
> the same
>
> A = B union C
> B' * C' = A'
>
> First I would have to show that set theory "union" is turned into a
> set-theory
> multiplication. Then I would have to show that position/momentum are
> geometries.
> But if I simply showed that the above two equations are "in general,
> the same"
> will be sufficient proof.
>
> P.S. the fact that Planck's constant comes in so many different
> "flavors and stripes"
> is a sign or indicator that the above is true, because the many
> flavors of Planck's
> constant is a sign that it is Euclidean geometry with Elliptic and
> Hyperbolic bursting
> out the seams of trying to come alive.
>

Now I vaguely remember that in set theory, the complimentary set, that
multiplication
of complimentary sets is equivalent to the union of specified other
sets relative
to the complimentary sets. What I am trying to say, without refreshing
my memory
is that the union of sets is an additive relationship but that the
complimentary set in
multiplication is this union of sets.

So that I am on the right path in saying that the Uncertainty
Principle is another form
of the formula Eucl geom = Ellipt unioned Hyperbolic geometries.

That the Uncertainty Principle is multiplication of complimentary sets
while the geometry
formula I give is the union of NonEuclidean geometry sets.

So let me refresh my memory, but I sense I am on the correct path of
truth.
And also, one on reflection, it makes sense that Uncertainty in
physics would be
akin to complimentary set in set-theory, where a complimentary set is
a set outside
the set that is in question. So we begin to sense that set theory and
uncertainty and
geometries are all melding together into a coherent and comprehensive
picture.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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