FrediFizzx wrote:Gordon Watson wrote:FrediFizzx wrote:Gordon Watson wrote:The n different a

xb

are cross-products.

Where did the cross products come from? Because as far as I can tell, those cross products don't physically exist. They are mathematical artifacts.

For example, see this comment -- after the reduction of eqn (8) to (12) -- in your 5 June 2019 essay with Joy and Jay:

" ... where we have used the Pauli identities, and the cross products terms reduce to zero because of the rotational invariance of the singlet state. It is easy to see from the cross product terms that we indeed have left and right handed components as they are pointing in opposite directions." [My emphasis.]

NB: in my thought-experiment, no two cross-products are the same. So, in addition to seeking an explanation of my experiment in your latest terms, the further question arises: How do you "reduce them -- my cross-products -- to zero".

Thanks.

Oh, because it is a singlet state. So a x b = c and any individual observable is zero. See eq. (3). What you actually have is

. If you do the following calculation by hand, you will see that the cross product components cancel out anyways in the step from (A2) to (A3).

Thanks for this, Fred. And though the above calculation is now included in v.3 of the Joy, Fred, Jay paper: it does not, in my view, remove the difficulty.

In my view you should have no reference to cross-products at all: which means, I suppose, no need for chirality??

nb: a constant in my experiment is the angle (a,b) between the detector settings: but with no two detector settings [Alice

with

, Bob

with

, etc.] being the same.

So your use of identical settings is not allowed in analyzing my experiment: its whole point being that cross-products have no place in such analysis.

Instead, let's use that constant angle (a,b). Then, in a fairly conventional notation, we can use the Probability Law that applies. That is, the extension of Malus' Law -- c.1810 -- the extension we find by analyzing the experiment*** in accord with Einstein-classicality and true-local realism:

So

So

Thus a straight-forward result in line with the classicality that Einstein argued for -- according to Bell (2004:86) -- a classicality that I support.

*** The same Law is confirmed experimentally in Aspect (2004) with spin

s = 1.

Thanks again; Gordon