The Quantum Wave Function as a Psychological Barrier
Today’s columnist, Erich Joos, received his doctorate in 1983 in theoretical physics from the University of Heidelberg, working on the Quantum Zeno effect. Not to be confused with the Quantum Zero effect or point fluctuations (although both may give technologists pause when the time comes to go beyond the notion of brain death as cessation of electrical activity to brain death as cessation of quantum activity), the Quantum Zeno effect is the observation that constant monitoring of a quantum subsystem perceptibly slows down its dynamics. Joos did research with John Wheeler at TheUniversity of Texas at Austin before Wheeler moved to Princeton. He also worked at the University of Hamburg. Currently, Joos is living with his family in Schenefeld near Hamburg, and thinking about quantum foundations as a freelance/independent physicist a la Julian Barbour.
Remember, as Joos cautions on his website: WARNING: All answers given here representmy current views. These may change without notice.
What are the proper concepts to describe Nature at a fundamental level? Favored approaches have changed over the centuries from epicycles modelling planetary motion to mass points of Newton’s mechanics controlled by forcesacting at a distance, fields obeying Maxwell’s equations, non-euclidian dynamic spacetime geometry in general relativity, and so on. At present, the most general and successful fundamental description is given by quantum theory. Despite its formidable achievements there is no consensus what it tells us about Nature.
In pre-quantum times concepts used to describe physical objects were chosen close to everyday experience, so that they are often viewed as natural or non-abstract (usually, however, only after getting used to them).
Objects that we can see or touch seem to have a position in space. This leads to the notion of a mass point. This successful concept is in a sense already abstract: nobody has ever seen a mass point. Using such a model we can, for example, predict the motion of planets with extraordinary accuracy. Even the inclusion of relativity or curved spacetime posed no insurmountable difficulties. For small velocities relativity smoothly reduces to Newtonian mechanics.
With the advent of quantum theory this rather calm situation changed dramatically. The idea of viewing an atom as miniature planetary system with electrons orbiting a nucleus failed. It turned out that microscopic objects rather behave like waves in many situations. When quantum mechanics was formulated in the 1920s, the mathematical structure of the final theory (up to the present day) was essentially found.
Strangely enough, this most successful theory is still faced with agonizing interpretation problems. What is the meaning of the wave function and related concepts used in quantum theory? Why do microscopic objects behave like waves in some situations, while in others—in particular when interacting with a measurement device—they look like particles? Why are composite systems so strange? A somewhat desperate way out of these problems soon became orthodoxy: The main purpose of the wave function is to calculate results of measurements we happen to make on these strange microscopic objects like electrons. Measurements are described by observables (mathematically similar to wave functions), measurement results by values (borrowed from classical physics). This dichotomy between micro- and macroworld overshadowed the quest for understanding from the beginning until today . Since classical values could still be used, albeit with some uncertainty, a certain degree of common-sense intuition (Anschaulichkeit) could be maintained at the price of using a language, which to many appears ambiguous, imprecise or even inconsistent. This fault was then turned on its head and corroborated by the success of the mathematical formalism.
For generations students were told (look in any textbook on quantum mechanics) that quantum theory is just a tool to calculate probabilities for the occurrence of phenomena, or clicks in a counter, or other facts in the macroscopic world, triggered by quantum objects in the hidden world of atoms. All these classical phenomena, as well as the micro-objects which produce them, are certainly part of the physical world—if exploring Nature has any meaning at all.
Then, what is the difference between a single atom (which nowadays I can see in the lab) and the tree I see in my garden? In a fundamental description one may expect that there should be no difference in principle (only in scale).
The apparent conceptual wall that seems to separate microscopic and macroscopic objects is demolished more and more every day by clever experimentalists. Remember that atoms were considered as non-existent, unobservable, or at least hypothetical at Boltzmann’s times—an obvious misjudgement of the skills of experimentalists.
Since classical concepts proved wrong long ago, it seems unavoidable that we use quantum (kinematical) concepts as building block of our world model. After all, we believe that macro-objects are made of atoms, don’t we?
But many people hesitate to take this step. There is a strong psychological barrier to overcome, since the properties of wave functions appear so strange to our classically biased mind. In particular, the (holistic) features of composite systems defy any classical explanation. Therefore, one often encounters the view that quantum concepts are abstract and therefore purely formal. In earlier times it was perhaps as difficult to accept that the earth is not flat or at center of the universe (despite appearance), as it is nowadays to accept a description of the world in terms of wave functions. But wishful thinking does not help. The correctness of a description in terms of wave functions has been proven by so many experiments, in particular those invalidating classical preconceptions such as locality (recall the famous EPR-Bell-experiments). Even states resembling the infamous Schroedinger cat (resisting any classical interpretation) can now be produced in the lab. The quantum wave function evidently characterizes properties of Nature in a quite direct way. A thorough quantum description seems unavoidable to maintain consistency. In the last two decades decoherence theory  has shown us how to explain the appearance of a classical world entirely in quantum terms.
Nevertheless, classical notions are extremely attractive because they are so familiar. So it is not surprising that all sorts of contraptions were invented in order to keep up with classical notions. Quantum particles are said to go through two slots at once. A particle cannot do that: this would be a contradiction in terms. The correct description for a quantum particle is exactly the wave function. Sometimes it appears less fuzzy, on a screen, for example. But all this can be described and explained in quantum terms. Modern decoherence theory  accounts for the appearance of a macroscopic world in terms of wave functions—not particles. In short, it turns out that the difference between micro- and macro-objects lies essentially in their different degree of isolation from their natural environment. No widgets such as dualism or complementarity are needed any more. To be sure, several fundamental questions (such as the precise location of observers in a holistic quantum world, or the role of gravity) remain open. The inconsistency introduced by using quantum and classical notions in parallel, however, has dissolved.
A description of Nature which is more than an accumulation of incompatible pieces is not only aesthetically pleasing, but also seems to be essential for doing science at all: It is a good idea to re-read the dialogue between Einstein and Heisenberg , culminating in Einstein’s admonition that “only the theory can decide what we observe. … On the entire long path from a process up to conscious perception, we need to know the workings of Nature in order to claim that we have observed anything at all.”
In the absence of new hints from experiments, the insistence on conceptual consistency has to be of utmost importance. The quantum wave function should be considered one of the prime candidates for a coherent world view.
 M. Tegmark, M. and J.A. Wheeler: 100 Years of Quantum Mysteries.Scientific American 284, 54 (Febr. 2001) .
 more on www.decoherence.de
 W. Heisenberg, Der Teil und das Ganze, dtv