Mikko wrote:Gordon Watson wrote:Mikko wrote:It doesn't make much sense to introduce new terms and definitions and then to not use them for anything. As long as the new concepts and definitions are not used there is no demonstration that they could be useful. A simple example to get started could be the toy theory by Bell in section III "Illustration" of http://cds.cern.ch/record/111654/files/ ... 00_001.pdf , with equation (9) as its main postulate; and the variants of this theory discussed in the same section. Which of the definitions do these theories satisfy, or how close they come?

Do you mean something like this, in my terms? (9) satisfies true local realism.

Basically yes, though if there is something else in the theory that does not satisfy it, that would be significant, too. But in this theory there is not much more. How about the variant presented in the last paragraph of the section?

However, I didn't limit my question to "true local realism". You have also used the name "pseudo-realism". Does the equation (9) and the theory using it satisfy that, too?(10) is a valid conclusion from the interactions/projections in (9).

Equation (9) does not represent interactions. They may be called projections in some mathematical sense that hardly is useful for physics.An experiment based on (9) will confirm (10). QED.

What do you mean by "based"? Equation (9) is an assumption about the relation of the hidden variable and the result of a measurement. How can an experiment be based on a particular assumption about that?

Whether an experiment confirms (10) or not is not part of a theory. The theory predicts that no experiment, whether "based on (9)" or not, will refute (9) but an experiment might refute it anyway. But the usual meaning of "realism" and its variants is that it is an intrinsic property of theory that does not depend on any experiments or results of experiments.(EPRB-style experiments are not represented by (9), so (10) does not hold in such.)

This doesn't really make sense but somehow seems to contradict what you already said. In what sense EPRB-style experiments are not represented by (9) are not represented? Are some other experiments represented? Equation of (9) is a statement about measurement of spin, so it applies equally to all experiments where a spin is measured. Equation (10) is a consequence of equation (9), so it is true at least whenever (9) is.

I take (9) to be a toy model that can be experimentally replicated on paper by means of unit-vectors a, b and random λ. I take the signs to reflect the rotation ("via interaction" as I envisage the experiment) of λs onto a and b (i.e., ± = UP/DOWN). I take a, b and λ to be truly realistic and well-defined variables in the toy experiment which is an experiment that can be done to validate (10).

Since the correct results are derived, I see no pseudo-realism here: unless Bell is trying to replicate EPRB. To be clear: imho, Bell uses pseudo-realism in his analyses of EPRB +++; that's why he gets the wrong answers -- which, coming full circle -- is how I DEFINE pseudo-realism: it gives wrong answers.

We agree: Equation (10) is a consequence of equation (9), so it is true whenever (9) is true.