Originally Posted by MacM
Thye implications of Bell's inequality in your link can be narrowed in scope as it does have a possible dynamic implied by the following:
Here are three simple statements describing spin-1 particle transitions through Stern-Gerlach filters.
+S -> xT-> +S ---- 
+S -> xT+ B ->xT ---- [1/3]
+S -> +S+B ->+S ---- 
The symbols represent various "spin states", motion indicatiors is a more proper description, (I borrowed the word "spin" from another model), of the particles which I simplify by stating that the S and T states may be in any one of three states, +S ,+/-S aor -S and similalry for T. However, +S is not the same as +T. The "S" and "T" are merely designations for the Z-axis of the respective segments, and the +, +/- and - are merely the directions of motion of the partuicle observed along the S or T line, i(the Z direction) after entering the segment from a field free region. the [#] are the fraction of the input beam, surviving the transition through the T segment.
The 1st statement says: An S state particle is transformed into an xT state particle (polarized) when entering the T segment, (S segment is different from the T segment only by its (the T segment) rotation about the motion of travel of the particle along the Y-axis and then the xT state is transformed back into the S state.
The second says:A +S state particle is transformed into an xT state where the T segment has two of the possible 3 channels physically blocked, and the particle exits the T segment in the xT state.
The third is physically the same as the 2nd: An S state particle enters an S segment (returns to the segment of its original polarizing segment) that has two channels blocked and exits in the state S.
The numbers to the right of the statements are the fraction of the input beam that survive the transition through the segment. Also, the "x" in the T statement means "any of the three possible directions", where +(S) not equal to +(T), or The + of S is not the same as the + of T. T is rotated around the y-axis, remember?
Comparing 1 and 2 we see the difference in the final result is dependent only on the "wide open" versus "obstructed" arangement. As the "+S", for instance describes the particle as moving "up" in the postive Z-axis. By inspection we can say that the "+S" does not adequately describe those elements intrinsic to the +S state that guarantees the reformation of the +S state upon exit from the segment so I will add a simple reminder that these elements that are not observed are, 00[+S], to be arbitrary. So we also have to do the same for T, so I give T, or 00[+T] the same kind of elements, unobserved of course. So we then say that Y(+S) = Y(1 00[+S]) and Y(xT) = Y (x 00[xT]), where the "1" refers to + which we arbitrarily choose (with no loss of generality, trust me).
Logically we must, we have to assume that the elements guaranteeing the reformation of the original +S state are imposed on the xT state when the particle is polarized when entering the T segment, therefore the three statements look like (I assume the +T state in th T segment):,
Y(1 00[+S]) -> Y(1 00[+S] 00[+T]) -> Y(_ 00[+S] _ _ ) -> Y(1 00[+S]) (1)
where I have added the extra term (3rd) to emphacise the fact that Mother Nature abhors "instantaneous activity" during transition processes when al the xT state undergoes alteration.
The second statement then is
Y(1 00[+S]) -> Y(1 00[+S] 00[+T]) -> (B)Y(1 00[+S]) -> Y(1 _ _ _ _) -> Y(1 00[+T]) -> Y(_ 00[+T]]) -> Y(1 00[+T]) (2)
and the third,
Y(1 00[+S]) -> Y(1 00[+S] 00[+S]) -> (B)Y(1 00[+S]) ->Y(_1 _ _ _ _ ) -> Y(1 00[+S)) -> Y(_ 00[+S]) -> Y(1 00[+S]) (3)
and for clarity I put them together, adding the physical polarization (P)and depolarization, (P') operators,(the underscoe are temporary 'null' positions) :
Where the (B) is the physical "blocking operator", and (P) and (P') the polarization and depolarization operators respectively, physical operators that is.
(P)Y(1 00[+S]) -> Y(1 00[+S] 00[+T]) -> (P')Y(1 00[+S] 00[+T]) -> Y(_ 00[+S] _ _ ) -> Y(1 00[+S]) (1)
(P)Y(1 00[+S]) -> Y(1 00[+S] 00[+T]) -> (B)Y(1 00[+S]) -> Y(1 _ _ _ _) -> (P')Y(1 00[+T]) -> Y(_ 00[+T]]) ->Y(1 00[xT]) (2)
(P) Y(1 00[+S]) -> Y(1 00[+S] 00[+S]) -> (B)Y(1 00[+S]) ->Y(_1 _ _ _ _ ) -> (P')Y(1 00[+S)) -> Y(_ 00[+S]) -> Y(1 00[+S]) (3)
The 2nd and 3rd expressions are identical physically and they say: The state of the particle that enters a segment (polarized) that has two of the channels blocked is the eventual surviving state of the particle. The 1st and 2nd tell us that up to the instant the particle reaches the plane of the location of the obstructions (in the 2nd) the state of the transition states are identical, which means that the obstructions, which are observed , physical, local, must absolutely be a collision point for nonlocal elements of the +S state state and after perturbing the unobserved elements 00[+S] and the 00[+T], only the 00[+T] survives to reform with the "1" (of the +T state), while in the 1st transition the unperturbed 00[+S] is proved to be necessary and sufficient to reform the S state, which means the magnetic polarization vector of the unstable (hybrid) T state is physically reoriented to the original +S direction in the same sense that a perturbed magnetic compass needle returns to the direction of north by virtue of the force of he earth's magnetic field. (The nonlocal elements are the motion and orientation records of the particles.)
The only difference here is that the +S state is reformed in the absence of any forces.
There are two polarization events: entrance, polarization and exit, depolarization, both effetivley ignored by some standard models.
The 2nd and third expression tell of the incomapatibility of the perturbed 00[+S] reforming with the *xT" which is a momentarily unsupported xT state, or direction when the particle os inside the T segment. In the 3rd, only 00[+S] unobserved elements (two sets just like the 2nd) are available to reform with the momentarily unsupported *+S*direction vector, which isn't much here.
As an aside observation, the above is not a quantum mechanical structure, is it? The 'randomly oriented , rigidlty attached ' magentic polarization vector was summarily discarded on the 1920s, and also assumed is that the various particle states are generated in the "heat of the tungsten filament" from which they boil off, instead of assuming the particle itself generating its own states dynamically. This process is seen in a time history as
... 100 010 001 100 010 001 100 010 001 100 010 001 ...
whre the states are not generated "randomly", and the observed state (the "1' ) is the once virgin unpolarized state (+, or +/- or -), the default polarized state when effectivley entering the Stern-Gerlach segment. Simply assume the virgin state to be an undistorted spherical magnetic configuration until distorted by the SG field/gradient in the SG segment.
All of this resolves to a few simple statements:
- The spin-1 particle exhibits "inertial platform" attributes, not unlike a gyroscopic inertial guidance device, where the original magnetic polarization vector is restored, necessarily by a force not external to the particle but by forces "nonlocally internal" to the particle (a necessary revison to Newton's law of motion) and
- in the case of the 2nd and 3rd transitions the physical host particle is , relatively speaking, solar system distances away from the obstructions as it crosses through the plane of the obstructions (real distance being a millimeter or two), and
- In the 1st 'wide open' arrangement the unobserved elements are not sufficient by themselves to quarantee the reformation of the +S state, they are absolutely necessary for the reformation of the original +S state (in all cases actually)
- Action at a distance has been proved, unambiguously, and
- Bell's requirement for the inclusion of nonlocal forces in constructing the model of the particle state, as a minimum condition for "completeness" has been satisfied.
See the post here regarding the QM James R challenge to Geistkiesel.
A self-serving graphics rich, math poor description is here.
All of this is more Aristotelian than anything.