Einstein wrote: Then, however, we must also give up by principle, the space-time continuum.

AFAIK he's referring to the space-time continuum of GR, so the quote is more-or-less about gravity. If I'm wrong, I'll happily concede the nit.

Thomas Ray wrote: Here's what Christian defines as measure space: "It is also crucial to appreciate that the spin angular momenta L(s, λ) (i.e., the bivectors) trace out an su(2) 2-sphere within the group manifold SU(2) ∼ S3, not a round S2 within IR3 as Gill has incorrectly assumed."

Two possibilities: he means this theoretically, or practically.

Theoretically he defined his bivectors as quaternions that square to -1. So theoretically, he's right.

But practically he's using them to represent directions in real space (the spins of the exploding ball halves). In real space you can use quaternions for this purpose, but must (according to normal thinking) consider any unit vector equal to its negative. Thus removing the double cover and "collapsing" to SO(3). But he claims the "normal thinking" is false, and it's possible to distinguish between 2 pi and 4 pi rotations. That's the whole point of the paper, as you can tell from the title. Following normal thinking I don't buy this, without some proof or at least justification.

[EDIT] reading Christian's response to Gill, I see the bivectors are angular momenta, pseudo-vectors, and not equal to their negatives, as I said. I have to think about that. Still it doesn't seem to affect Gill's point which, after all, is simple algebra ...

secur wrote previously: Gill assumes (as I do) that those measurements take place in an SO(3) world, while Christian assumes SU(2), quaternionic or spin space.

Gill wrote: I don't assume anything.

Hard to believe. Everyone assumes that if they turn in a circle, they're back where they started. You don't think you need to turn once again to restore initial state, do you? So, you assume real space is SO(3) not SU(2). With the appropriate caveats: local tangent space, whatever.

Gill wrote: I read Christian's instructions to the experimenters. They are completely explicit. The actual numbers which result from the experiment will generate correlations which, with absolute certainty, will satisfy the CHSH inequality, whatever kind of world we live in. Hence the desired "singlet correlations" will certainly not be obtained.

Ok, that's not nit-picking. Your point is that no matter what the N values of lambda are, no matter how they're obtained, the Script-E correlation function must satisfy CHSH, by simple algebra. You've said this before, and I admit it's been hard to wrap my head around this apparent fact. It's such an egregious mistake on his part, I keep thinking I'm missing something. I'll read his response and see if it makes any sense.

AFAIK he's referring to the space-time continuum of GR, so the quote is more-or-less about gravity. If I'm wrong, I'll happily concede the nit.

Thomas Ray wrote: Here's what Christian defines as measure space: "It is also crucial to appreciate that the spin angular momenta L(s, λ) (i.e., the bivectors) trace out an su(2) 2-sphere within the group manifold SU(2) ∼ S3, not a round S2 within IR3 as Gill has incorrectly assumed."

Two possibilities: he means this theoretically, or practically.

Theoretically he defined his bivectors as quaternions that square to -1. So theoretically, he's right.

But practically he's using them to represent directions in real space (the spins of the exploding ball halves). In real space you can use quaternions for this purpose, but must (according to normal thinking) consider any unit vector equal to its negative. Thus removing the double cover and "collapsing" to SO(3). But he claims the "normal thinking" is false, and it's possible to distinguish between 2 pi and 4 pi rotations. That's the whole point of the paper, as you can tell from the title. Following normal thinking I don't buy this, without some proof or at least justification.

[EDIT] reading Christian's response to Gill, I see the bivectors are angular momenta, pseudo-vectors, and not equal to their negatives, as I said. I have to think about that. Still it doesn't seem to affect Gill's point which, after all, is simple algebra ...

secur wrote previously: Gill assumes (as I do) that those measurements take place in an SO(3) world, while Christian assumes SU(2), quaternionic or spin space.

Gill wrote: I don't assume anything.

Hard to believe. Everyone assumes that if they turn in a circle, they're back where they started. You don't think you need to turn once again to restore initial state, do you? So, you assume real space is SO(3) not SU(2). With the appropriate caveats: local tangent space, whatever.

Gill wrote: I read Christian's instructions to the experimenters. They are completely explicit. The actual numbers which result from the experiment will generate correlations which, with absolute certainty, will satisfy the CHSH inequality, whatever kind of world we live in. Hence the desired "singlet correlations" will certainly not be obtained.

Ok, that's not nit-picking. Your point is that no matter what the N values of lambda are, no matter how they're obtained, the Script-E correlation function must satisfy CHSH, by simple algebra. You've said this before, and I admit it's been hard to wrap my head around this apparent fact. It's such an egregious mistake on his part, I keep thinking I'm missing something. I'll read his response and see if it makes any sense.