> 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

constraints.

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

cube.

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

description.)

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

'state'.

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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