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[The following passage, which deals with the significance of Bell’s theorem, is from chapter twelve of Nick Herbert’s excellent book, Quantum Reality, Beyond the New Physics, 1985. An actual proof of Bell’s Theorem can be found earlier in the chapter, which is entitled “Bell’s Interconnectedness Theorem.” Though many proofs of Bell’s theorem have been formulated, Herbert’s version is quite accessible to the determined layman (or women).]

Impossible Worlds

Bell’s theorem is an important tool for reality research because it enables folks who create imaginary worlds confidently to reject millions of impossible worlds at a single glance. Bell’s theorem tells you right away: “If it’s local, it’s hokum.”

One of the worlds soundly obliterated by Bell’s proof is the “disturbance model” of quantum reality. In this model—a species of neorealism—quantum entities actually possess attributes of their own whether measured or not, but the measuring device changes these attributes in an unpredictable and uncontrollable way. The inevitable disturbance of the quantum system by the device which measures it gives rise, in this model of reality, to quantum randomness, to the uncertainty principle and all the other quantum oddities.

As a picture of how the quantum world might actually operate, many physicists who have not given much thought to the matter take refuge in some vague disturbance model of reality. For several years I avoided thinking about the quantum reality question by supposing that a disturbance model of some kind was sufficient to account for the strange quantum facts... Bell’s theorem shows than any such local mechanism, no matter how ingenious, simply fails to fit the quantum facts: Bell’s proof knocks out the disturbance model because it’s local.

Facile popular expositions often invoke the disturbance model of measurement to justify Heisenberg’s uncertainty principle: we cannot know a quantum entity as it is because we must inevitably disturb whatever we observe. Bell’s result shows this notion of quantum measurement as local disturbance to be as outdated as the obsolete picture of the atom as miniature solar system.

Another type of impossible world is the “classical style” reality symbolized by Newton’s apple. Apples, and everything else in such a world, are truly ordinary objects which possess attributes all their own even when not being measured. When measured, whether by man, woman, or machine, a classical apple merely reveals some attributes which it previously possessed.

Such an apple world (which experts call a “local non-contextual reality”) is not inconceivable or illogical. But, according to Bell’s theorem, apple world is impossible because it can’t possibly fit the facts. As a model for the world we actually live in, apple world and all its local non-contextual cousins are, by virtue of their locality, sheer fantasy worlds.

We obviously need to be more sophisticated in our choice of possible worlds. Let’s imagine, for instance, a relational reality patterned after the notions of Niels Bohr. The entities that make up such a world are like rainbows: they do not possess definite attributes except under definite measurement conditions. Upon measurement, attributes do emerge but they are a joint possession of entity and M (measurement) device. In such a rainbow reality (called “local contextual”), attributes are not innate to an entity but change when the conditions of observation change. The only restriction we place upon such observer-induced changes is that distant M devices cannot change an entity’s condition if such an influence would require a faster-than-light signal. In such a contextual, but local, reality, only nearby observers take part in the determination of an entity’s apparent attributes.

Like apple world, rainbow world is neither inconceivable nor illogical. It is simply, on account of its locality, not the sort of world we happen to live in.

Bell’s theorem rejects apple worlds; it also rejects rainbow worlds. What kinds of worlds does Bell’s theorem allow?

A Possible World

Imagine Joe Green, an inhabitant of a non-local contextual world. Up in his sky, Joe sees a rainbow made up of a glistening pattern of coloured dots. Unlike the regular dots in a photographic halftone, Joe’s rainbow’s dots form a random array.

On the other side of the same sun lies a counter-Earth, where Suzie Blue watches another rainbow in her counter-sky. Susie’s rainbow is likewise composed of a random array of coloured dots. When Joe Green moves his chair, his rainbow moves too (a rainbow’s position attribute is contextual, not innate), but Suzie’s rainbow stands still. However, when Joe moves his chair Suzie’s random array 200 million miles away instantly changes into a different (but equally random) array of coloured dots. Suzie is not aware of this change—one random array looks pretty much like any other—but this change actually happens whether she notices it or not.

The phenomenon in this hypothetical world, whether the rainbow moves or not, is completely local: Suzie’s rainbow doesn’t move when Joe changes places. However, this world’s reality—the array of little dots that make up both rainbows—is non-local: Suzie’s dots change instantly whenever Joe moves his chair.

Such a non-local contextual world, in which stable rainbows are woven upon a faster-than-light fabric, is an example of the kind of world permitted by Bell’s theorem. A universe that displays local phenomena built upon a non-local reality is the only sort of world consistent with known facts and Bell’s proof. Superluminal rainbow world could be the kind of world we live in.

During the past twenty years Bell’s theorem has been proved in many ways, some of which refer to photon attributes and some which don’t. My version of Bell’s proof makes no essential use of the concept of a photon or its attributes. Although Green and Blue photons and their polarization attributes are mentioned to familiarize you with the details of the EPR experiment, when it comes to the proof of Bell’s theorem my argument is formulated entirely in terms of a pair of binary messages printed by particular macroscopic objects. I prove Bell’s theorem here in terms of moves (orientations of calcite crystals) and marks (ups and downs on a data tape).

Bell’s theorem as a relation between move and marks takes non-locality out of the inaccessible microworld and situates it squarely in the familiar world of cats and bathtubs. Expressed in thoroughly macroscopic language, Bell’s theorem says: In reality, Green’s move must change Blue’s mark non-locally. From arguments based on phenomena alone (no appeal to hidden attributes) we conclude that clicks in a certain counter must be instantly connected to the movement of a distant crystal of calcite.

For anyone interested in reality, Bell’s theorem is a remarkable intellectual achievement. Starting with fact plus a bit of arithmetic, Bell goes beyond the facts to describe the contours of reality itself. Although no one has ever seen or suspected a single non-local phenomenon, Bell proves conclusively that the world behind phenomena must be non-local.

If all the world’s phenomena are strictly local, what need is there to support local phenomena with a non-local fabric? Here we confront an alien design sense bizarre by human standards: the world seems strangely overbuilt. In addition the world’s superluminal underpinning is almost completely concealed—non-locality would have been discovered long ago if it were more evident; it leaves its mark only indirectly through the impossibly strong correlations of certain obscure quantum systems.

In his celebrated theorem, Bell does not merely suggest or hint that reality is non-local, he actually proves it, invoking the clarity and power of mathematical reasoning. This compulsory feature of Bell’s proof particularly irks physicists whose taste in realities is strictly local.

Bell’s important proof has caused a furor in reality research comparable to the Einstein-Podolsky-Rosen scandal of 1935. On the other hand, Bell’s theorem proves the existence of an invisible non-local reality. Those who prefer their realities to be local have so far not been able to refute Bell’s argument. The fact that Bell’s proof is remarkably clear and brief has not hastened its refutation.

On the other hand, although Bell’s theorem indirectly necessitates a deep non-locality, no one has come up with a way to directly display this purported non-locality, such as a faster-than-light communication scheme based on these deep quantum connections. If reality research’s bottom line is “Reality has consequences,” then this Bell-mandated deep reality has so far failed to make a showing. What the future holds for Bell’s instantly connected but as yet inaccessible deep reality is anyone’s guess.

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