Tuesday, May 10, 2016

sci.physics.research › A Better Interpretation of Quantum Mechanics?

> time T will Have a different probability
> at T', think of radioactive decay,
> which is contextuality.
> The goal of MWI, which is similar
> with Bohm's QM formalism, is that
> QM is unitary "all the way down,"
> including during measurements. This more
> generally also means decoherence of
> the density matrix. Observers and apparatus
> are ultimately quantum mechanical, but we
> have still this "gap" in our descriptions.
> This is particularly if we are to follow
> Bohr's dictum that experimental outcomes
> must be classical.
> LC

One way to hold with this Bohr dictum
and also earnestly face, I guess it is
the paradox or conflict arising with  
the Kochen-Specker theorem, as you write
above, Lawrence, of, among other
requirements,  needing or expecting
an odd nine whereas the standard or
accepted mathematical formulation
only provides an even eight, is
summarized below.

Hopefully, readers can pardon  my
non-standard notation which
I will claim here today are
largely required by both

1. The solution, let's say, begins with
eight unit vectors pointing outward
from a center point to the vertices
of a cube.

2. The next step is to sequentially,
perhaps imaginatively,
one-half rotate, oscillate or
re-orient each of the eight
unit vectors, end-for-end, so as
to form the nine, let's call them,
'states', of this eight-unit-vector

3. If it's possible, for now please
assume the vectors are held somewhat
loosely just these eight in-out, or
out-in radial orientations, by, say,
tension members or a rigid
frame work, akin to axes of a
coordinate system. (Please pardon
my incomplete and non-standard

4. To hold closer with the Bohr
dictum, replace each unit vector
with a magnet where the north
poles are placed at the arrow-ends
of the eight unit vectors in each

5. Adopting a notation for
the count of north and south
poles at the centers, of the nine
'(primary) states' -- (s8,s7n,s6n2,
s5n3,s4n4,s3n5,s2n6,sn7,n8), the
s8 and n8 states both would, or
could have a bit of repulsion at
their centers and under some
conditions could exhibit, besides
'multiple states', also 'variable
mass density', or convey,
somewhat in accord with Bohr's
dictum, physical intuition on
multiple states AND variable
mass density  to most
experimenters who do the exercise.

6. A general ~rule for having
"an even eight also be an odd nine,
is incremental:

       N + 1

7. Vaguely, this says something like
"the number of (primary) states
of this type of N-hedron is at
least equal to N plus one". For
a cube having eight vertices,
8 + 1 = 9.

For other instances:

Tetrahedron     4+1 =  5
Octahedron      6+1 =  7
Cube            8+1 =  9
icosahedron    12+1 = 13
dodecahedron   20+1 = 21

8. If one considers many of
the images shown when Googling
"octahedron circumscribed
inside of cube", one may
notice that  the coordinate
axes in the "standard" Cartesian
xyz mathematical system (origin at
center with three axes, split
into positive and negative
halves, exiting the center of
each of the cube's
six faces) is ~also the same as
or ~coincident with the six
center-to-vertex "non-standard
math formulation" vectors
as outlined above for the
inscribed octahedron. That is,
there seems to be use of the
"non-standard octagon's axes"
as the "standard axes of
the cube"

9. In #8, I attempt  
to point out that in the
non-standard math formulation
by giving center-to-vertex
vectors one-half spin, one
gets multiple states (and variable
mass density) directly, whereas
beginning with the standard xyz
math formulation, applying a
factor of -1 to halves
of the three axes, one does not
get as direct a model of
multiple-states (and variable
mass density).  

Instead, the standard math
formulation has 'complex numbers'
having real and imaginary parts.  
The imaginary numbers involve
factors of the square root
of -1.

The point here is  
utilizing a different
conceptual modeling
or handling of
halving and also how
duality or differences
are incorporated
influences representations
of multiple states.

The "non-standard" way summarized
crudely and very imperfectly above
provides one alternative. I would
expect there would be  many other,
better representations that
would fit with the same two
constraints you gave.

Best regards,

Ralph Frost

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