Note that "signal nonlocality" from direct back-reaction of the actual "beable" IT material hidden variables HV on their piloting BIT Bohm quantum potential Q (aka "sub-quantal non-equilibrium" Antony Valentini) violates the concept of locality given by Bell below. This requires a post-quantum theory that is to quantum theory as general relativity is to special relativity.
"Then the prohibition of superluminal signaling – signal locality – is the requirement that the empirical frequency for Alice’s outcome (A) shouldn’t depend on the spacelike
separated beables that Bob can control (ˆb)." -- Travis Norsen
“That is to say that, when averaged over the unknown [beables], manipulation of b has no effect on the statistics of A... “Do we then have to fall back on ‘no signaling faster than light’ as the expression of the fundamental causal structure of contemporary theoretical physics? That is hard for me to accept. ... Could ... no-superluminal-signaling ... be regarded as an adequate formulation of the fundamental causal structure of physical theory? I do not think so. For ... the concepts involved in relating it to causal structure are not very satisfactory. ... Suppose that we are finally obliged to accept [a theory which is not locally causal]. Can we
then signal faster than light? To answer this we need at least a schematic theory of what
we can do, a fragment of a theory of human beings. ... “...the ‘no signaling...’ notion rests on concepts which are desperately vague, or vaguely applicable. The assertion that ‘we cannot signal faster than light’ immediately provokes the question:
Who do we think we are?
We who can make ‘measurements’, we who can manipulate ‘external fields’, we who can
‘signal’ at all, even if not faster than light? Do we include chemists, or only physicists,
plants, or only animals, pocket calculators, or only mainframe computers? ... the consequences of events at one place propagate to other places faster than light. This happens in a way that we cannot use for signaling. Nevertheless it is a gross violation of relativisitic causality.” -- John S. Bell
Bell's quotes above as below are excerpted from the pedagogical review
http://arxiv.org/abs/0707.0401 (Travis Norsen)
“To avoid causal chains going backward in time in some frames of reference, we require them to go slower than light in any frame of reference.”
“simply showed that [Bohr, Heisenberg, and Jordan] had been hasty in dismissing the reality of the microscopic world. In particular, Jordan had been wrong in supposing that nothing was real or fixed in that world before observation. For after observing only one particle the result of subsequently observing the other (possibly at a very remote place) is immediately predictable. Could it be that the first observation somehow fixes what was unfixed, or makes real what was unreal, not
only for the near particle but also for the remote one? For EPR that would be an unthinkable ‘spooky action at a distance’. To
avoid such action at a distance [one has] to attribute, to the space-time regions in question, real properties in advance of observation, correlated properties, which predetermine the outcomes of these particular observations. Since these real properties, fixed in advance of observation, are not contained in quantum formalism, that formalism ... is in- complete. It may be correct, as far as it goes, but the usual quantum formalism cannot be the whole story.”
“For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and
fundamental relativity. That is to say, we have an apparent incompatibility, at the deepest level, between the two fundamental
pillars of contemporary theory...”
“It may well be that a relativistic version of [quantum] theory, while Lorentz invariant and local at the observational level, may
be necessarily non-local and with a preferred frame (or aether) at the fundamental level.”
“...I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincare thought that there was an aether – a preferred frame of reference – but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether. Now, in that way you can imagine that there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light. ....Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant...
[This] pre-Einstein position of Lorentz and Poincare, Larmor and Fitzgerald, was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether – that is a perfectly coherent point of view.”
“What does locality mean?”
“It’s the idea that what you do has consequences only nearby, and that any consequences at a distant place will be weaker
and will arrive there only after the time permitted by the velocity of light. Locality is the idea that consequences propagate continuously, that they don’t leap over distances.”
“The direct causes (and effects) of events are near by, and even the indirect causes (and effects) are no further away than permitted by the velocity of light.”
“Thus for events in a space-time region 1 ... we would look for causes in the backward light cone, and for effects in the future light cone. In a region like 2, space-like separated from 1, we would seek neither causes nor effects of events in 1.”
“A theory will be said to be locally causal if the probabilities attached to values of local beables in a space-time region 1 are unaltered by specification of values of local beables in a space-like separated region 2, when what happens in the backward light cone of 1 is already sufficiently specified, for example by a full specification of local beables in a spacetime region 3...”
“The beables of the theory are those elements which might correspond to elements of reality, to things which exist. Their existence does not depend on ‘observation’. Indeed observation and observers must be made out of beables.”
“The concept of ‘observable’ .... is a rather woolly concept. It is not easy to identify precisely which physical processes are to be given the status of ‘observations’ and which are to be relegated to the limbo between one observation and another. So it could be hoped that some increase in precision might be possible by concentration on the beables ... because they are there.”
“The concepts ‘system’, ‘apparatus’, ‘environment’, immediately imply an artificial division of the world, and an intention to neglect, or take only schematic account of, the interaction across the split. The notions of ‘microscopic’ and ‘macroscopic’ defy precise definition. So also do the notions of ‘reversible’ and ‘irreversible’. Einstein said that it is theory which decides what is ‘observable’. I think he was right – ‘observable’ is a complicated and theory-laden business. Then the notion should not appear in the formulation of fundamental theory. Information? Whose information? Information about what?”
“The terminology, be-able as against observable, is not designed to frighten with metaphysic those dedicated to realphysic. It is chosen rather to help in making explicit some notions already implicit in, and basic to, ordinary quantum theory. For, in the words of Bohr, ‘it is decisive to recognize that, however far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms.’ It is the ambition of the theory of local beables to bring these ‘classical terms’ into the equations, and not relegate them entirely to the surrounding talk.”
“The kinematics of the world, in [the] orthodox picture, is given by a wavefunction ... for the quantum part, and classical variables – variables which have values – for the classical part... [with the classical variables being] somehow macroscopic. This is not spelled out very explicitly. The dynamics is not very precisely formulated either. It includes a Schr¨odinger equation for the quantum part, and some sort of classical mechanics for the classical part, and ‘collapse’ recipes for their
interaction.”
“I think there are professional problems [with quantum mechanics]. That is to say, I’m a professional theoretical physicist and I would like to make a clean theory. And when I look at quantum mechanics I see that it’s a dirty theory. The formulations of quantum mechanics that you find in the books involve dividing the world into an observer and an
observed, and you are not told where that division comes... So you have a theory which is fundamentally ambiguous...”
“The word ‘beable’ will also be used here to carry another distinction, that familiar already in classical theory between ‘physical’ and ‘non-physical’ quantities. In Maxwell’s electromagnetic theory, for example, the fields E and H are ‘physical’ (beables, we will say) but the potentials A and are ‘nonphysical’. Because of gauge invariance the same physical situation can be described by very different potentials. It does not matter [i.e., it is not a violation of local causality] that in Coulomb gauge the scalar potential propagates with infinite velocity. It is not really supposed to be there. It is just a mathematical
convenience.”
“...there are things which do go faster than light. British sovereignty is the classical example. When the Queen dies in London (long may it be delayed) the Prince of Wales, lecturing on modern architecture in Australia, becomes instantaneously King.... And there are things like that in physics. In Maxwell’s theory, the electric and magnetic fields in free
space satisfy the wave equation ...corresponding to propagation with velocity c. But the scalar potential, if one chooses to work in ‘Coulomb gauge’, satisfies Laplace’s equation ...corresponding to propagation with infinite velocity. Because the potentials are only mathematical conveniences, and arbitrary to a high degree, made definite only by the imposition of one convention or another, this infinitely fast propagation of the Coulomb gauge scalar potential disturbs no one. Conventions can propagate as fast as may be convenient. But then we must distinguish in our theory between what is convention and what is not.”
However, see Yakir Aharonov's book "Quantum Paradoxes, A Guide for the Perplexed" - Bell's idea above is not adequate.
“you must identify in your theory ‘local beables’. The beables of the theory are those entities in it which are, at least tentatively, to be taken seriously, as corresponding to something real. The concept of ‘reality’ is now an embarrassing one for many physicists.... But if you are unable to give some special status to things like electric and magnetic fields
(in classical electromagnetism), as compared with the vector and scalar potentials, and British sovereignty, then we cannot begin a serious discussion.”
“Local beables are those which are definitely associated with particular space-time regions.
The electric and magnetic fields of classical electromagnetism ... are again examples.”
“it may well be that there just are no local beables in the most serious theories. When space-time itself is ‘quantized’, as is generally held to be necessary, the concept of locality becomes very obscure. And so it does also in presently fashionable ‘string theories’ of ‘everything’. So all our considerations are restricted to that level of approximation to serious theories in which space-time can be regarded as given, and localization becomes meaningful.”
“A theory will be said to be locally causal if the probabilities attached to values of local
beables in a space-time region 1 are unaltered by specification of values of local beables
in a space-like separated region 2, when what happens in the backward light cone of 1
is already sufficiently specified, for example by a full specification of local beables in a space-
time region 3...”
“it is important that events in 3 be specified completely. Otherwise the traces in region 2
of causes of events in 1 could well supplement whatever else was being used for calculating
probabilities about 1. The hypothesis is that any such information about 2 becomes redundant when 3 is specified completely.”
“Now my intuitive notion of local causality is that events in 2 should not be ‘causes’ of
events in 1, and vice versa. But this does not mean that the two sets of events should
be uncorrelated, for they could have common causes in the overlap of their backward light
cones [in a local theory]."
“Note, by the way, that our definition of locally causal theories, although motivated by talk of ‘cause’ and ‘effect’, does not in the end explicitly involve these rather vague notions.”
“I would insist here on the distinction between analyzing various physical theories, on
the one hand, and philosophising about the unique real world on the other hand. In this
matter of causality it is a great inconvenience that the real world is given to us once only.
We cannot know what would have happened if something had been different. We cannot
repeat an experiment changing just one variable; the hands of the clock will have moved,
and the moons of Jupiter. Physical theories are more amenable in this respect. We can
calculate the consequences of changing free elements in a theory, be they only initial conditions, and so can explore the causal structure of the theory. I insist that [the theory
of local beables, i.e., the local causality concept] is primarily an analysis of certain kinds
of physical theory.”
“Consider for example Maxwell’s equations, in the source-free case for simplicity. The
fields E and B in region 1 are completely determined by the fields in region 3, regardless
of those in 2. Thus this is a locally causal theory in the present sense. The deterministic
case is a limit of the probabilistic case, the probabilities becoming delta functions.”
“Of course, mere correlation between distant events does not by itself imply action at a distance, but only correlation between the signals reaching the two places.”
“It is important that region 3 completely shields off from 1 the overlap of the backward
light cones of 1 and 2.”
“suppose we can control variables like a and b above, but not those like A and B. I do
not quite know what ‘like’ means here, but suppose that beables somehow fall into two
classes, ‘controllables’ and ‘uncontrollables’. The latter are no use for sending signals, but
can be used for reception."
to be continued