To be able to discuss why I find the assumptions of Bell far too strong, let me distinguish two kinds of causality: extended causality and separable causality. Both kinds of causality are manifestly local Lorentz invariant and imply a signal speed bounded by the speed of light. Here a signal is defined as a dependence of measured results at one spacetime point caused by a preparation at another spacetime point.
Separable causality is what is assumed in Bell-type theorems, and is thereby excluded by the standard experiments (assuming that all other conditions used in the derivation of such theorems hold in Nature). On the other hand, extended causality is far less demanding, and therefore is not excluded by the standard arguments.
To define these two kinds of causality I use the following terminology. A
point object has, at any given time in any observer's frame, properties only at a single point, namely the point in the intersection of its world line and the spacelike hyperplane orthogonal to the observer's 4-momentum at the time (in the observer frame) under discussion. An
extended object has properties that, in some observer frames at some time depend on more than one space-time position. A joint property is a property that explicitly depends on more than one space-time location within the space-time region swept out by the extended object in the course of time.
Both kinds of causality agree on the causality properties of point objects (''point causality'') but differ on the causality properties of extended objects. Extended causality takes into account what was known almost from the outset of modern quantum mechanics - that
quantum objects are intrinsically extended and must be treated as whole. This is explicitly expressed in Bohr's writing (N. Bohr, On the notions of causality and complementarity, Dialectica 2 (1948), 312. Reprinted in
Science, New Ser. 111 (1950), 51-54.):
(Thanks to
Danu for locating this quote!)
Here are the definitions:
- Point causality: Properties of a point object depend only on its closed past cones, and can influence only its closed future cones.
- Extended causality: Joint properties of an extended object depend only on the union of the closed past cones of their constituent parts, and can influence only the union of the closed future cones of their constituent parts.
- Separable causality: Joint properties of an extended object consist of the combination of properties of their constituent points.
I believe that only extended causality is realized in Nature. It can probably be derived from relativistic quantum field theory. If this is true, there is nothing acausal in Nature. In any case, causality in this weaker, much more natural form is not ruled out by current experiments.