With regard to the problem of making physical sense of the mathematical formalism of quantum mechanics, the physics community appears to be divided into three factions.

This faction is split into numerous warring sects. Here is how Chris Fuchs describes the situation:

"Go to any meeting devoted to some aspect of the quantum foundations, and it is like being in a holy city in great tumult. You will find all the religions with all their priests pitted in holy war—the Bohmians, the Consistent Historians, the Transactionalists, the Spontaneous Collapseans, the Einselectionists, the Contextual Objectivists, the outright Everettics, and many more beyond that... They all declare to see the light, the ultimate light..."

At the heart of the quantum formalism is the amplitude (a.k.a. propagator)

< x_f , t_f | x_i , t_i > .

In the case of a single particle, x_i and x_f are points in "ordinary" 3-space. In general, they are points in the system's configuration space, which has as many dimensions as the system has degrees of freedom. (The absolute square of this amplitude, integrated with respect to x_f over a region R of the configuration space, gives the conditional probability of finding the system in R if the appropriate measurement is made at the time t_f, the condition being that the particle was last "seen" at x_i at the time t_i.)

It is customary to introduce the so-called "wave function" Ψ(x,t) by requiring that it satisfy the equation

Ψ(x_f,t_f) = ∫ dx_i < x_f , t_f | x_i , t_i > Ψ(x_i,t_i) .

Wave functions and propagators provide the same information. Knowing either one can calculate the other. Yet some proposed quantum ontologies (most notably, Everett's "many-worlds interpretation") transmogrify the wave function into a representation of "what ultimately exists" and treat the propagator as nothing more than a computational tool.

Whence this partiality? I should have thought that if the propagator is nothing more than a computational tool, then so is the wave function.

If we want to make sense of the physical world, we need to realize that the origin of these notions is psychological — they concern our way of experiencing the world rather than the world itself.

It is obvious why we are more interested in assigning probabilities to later outcomes on the basis of earlier outcomes than in assigning probabilities to earlier outcomes on the basis of later outcomes, but quantum mechanics allows us to do both. It is indifferent to our preference for predictions over retrodictions. It even allows us to assign probabilities on the basis of both earlier and later outcomes, with intriguing consequences.

An algorithm that serves to assign probabilities to possible measurement outcomes on the basis of actual outcomes has two perfectly normal dependences:

Misinterpret the algorithm's dependence on the time of measurement as the time dependence of an evolving state of affairs of some kind, and you have to explain why

As far as physics is concerned, this is the mother of all pseudo-problems.

Most of the time we think and behave as if the visual world — the world as we see it — were a more or less faithful reproduction of the real world "out there," if at all we make the distinction. Apart from the many well-known philosophical objections to this naive attitude, psychological and neurobiological studies in the 1980s and 1990s have uncovered a radically different story: the visual world is a creation (by the mind and/or brain) that is guided by a surprisingly sparse stream of clues from "outside." The way in which this world is created conforms to the cookie cutter paradigm (CCP). It is therefore only natural that we should try to construct our model of the physical world along lines laid down by the CCP, and that we should be perplexed beyond measure by Nature's refusal to follow suit.

As the previous article has shown, the visual world is constructed in conformity with the cookie cutter paradigm (CCP). Here we examine how the CCP tends to lead us down the garden path.

The following table highlights some of the differences between the world according to quantum mechanics (QM) and a world that is constructed along the lines laid down by the CCP. You may smile or scoff at the naivety of some or even most of the items in the second column, which aren't even mutually consistent. (For example, the notion that the ultimate constituents of matter are pointlike objects is at odds with the view that forms are bounding surfaces). All the same, at least some of the items in this column are all but universally accepted, for instance the representation of physical space as an intrinsically and completely differentiated "manifold."

Recall those "spooky actions at a distance": Bell's theorem, the experiment of Greenberger, Horne, and Zeilinger, and a follow-up. What is so unsettling is not that we cannot explain them.

As we have seen, no fundamental theory can be explained by a "more fundamental" theory; if there is a "more fundamental" theory, then the "less fundamental" theory isn't fundamental at all. Nor does the classical sleight-of-hand, which consists in the transmogrification of a mathematical algorithm into a physical mechanism or process, produce anything but nonsense.

What is so unsettling is that these spooky actions at a distance do not seem possible at all.