The modern quantum theory is a fascinating concept. It has been very successful since its introduction, although it seems to be common that nobody has a complete understanding of it yet. It poses strong contradictions to classical theories in physics. Below, there will be given an intuitive and very simplified version of the quantum theory, in order to give the reader the possibility to trace the author’s intuition towards an alternative approach to economic theory.
Mainzer (1996a) and Mainzer (1996b) provide a non-formal outline of what quantum physics is about. For a very easy access to quantum theory the internet1 provides a website which will be referred to in the following to sketch quantum theory. I will restrict myself not to use too many of the underlying technical terms to be found in any standard textbook on quantum physics.2
In figures A.1—A.4 a so-called Mach-Zehnder Interferometer is given. It is a simple apparatus that makes it possible to show the characteristics of both classical wave theory and quantum theory, and at the same time renders the implications of quantum theory.
The Mach-Zehnder Interferometer consists of four mirrors of which two are semipermeable. Besides, there is a source that emits waves or photons. Two detectors measure incoming waves or photons. In figure A.1 we see the scenario of a light wave as it flows through the apparatus. The first semipermeable mirror reflects only half of the wave. The two halves are each reflected by the top left mirror and the bottom right mirror, respectively. Successively, they meet at the second semipermeable mirror top right and, eventually, the wave is detected at detector 1. Notice that no wave is detected at detector 2.
In figure A.2 we add an obstacle, the black spot between the upper two mirrors. Now, the scenario looks a bit different: Again, the wave parts in the first semipermeable mirror and consequently, is reflected by the following mirrors. The obstacle, however, reflects one half of the wave, whereas the other half proceeds to the last semipermeable mirror. In contrast to the scenario above, we now measure incoming waves at both detectors, detector 1 and detector 2.
Wave theory gives us the explanation: The fact that the vertical wave reaches detector 2 in figure A.2 but does not reach detector 2 in figure A.1 shows the phenomenon of interference. Interference, in very simple words, denotes two waves that cancel each other out because of a phase difference. A wave consists of troughs and ridges. When a trough of a wave coincides with a ridge of another wave (given the same wave with just a difference in its phase), the wave vanishes and can no more be detected. This is what happens in figure A.1.
Figure A.1: Wave theory depicted in a Mach-Zehnder Interferometer without obstacle.
The same apparatus is used to illustrate the gist of quantum theory. Light waves consist of so-called photons. Photons are very small particles. Nowadays, it is even possible to produce a single photon in a laboratory.
Doing so, the source in our apparatus produces one photon and sends it through the arrangement of mirrors. In figure A.3, we have the same setting as in figure A.1, i.e. no obstacle. Similarly, we detect the incoming photon only at detector 1 and never at detector 2. Hence, the probability p=1. Notice that even though we only had one single photon, something prevented the photon from reaching detector 2; if we think in classical wave theory, we observe interference with a single photon. The question mark in the middle of the figure represents the puzzling explanatory deficit in quantum theory.
Suppose the photon takes the path from the source via the mirrors bottom right—top right to detector 2, how does the photon “know” that there is no obstacle in order to show interference?
In figure A.4, a Mach-Zehnder Interferometer with obstacle is shown. We emit a photon, and what we observe is again a paradoxical phenomenon. With probability p=0.5 the photon hits the obstacle and gets diverted, with probability p=0.25 the photon is detected either by detector 1 or by detector 2. And again, we cannot say anything about the path of the photon within the apparatus. The photon is a particle but it behaves like a wave. However, nothing can be said about the locality of the photon before it is measured in one of the detectors. If we added another detector, we would simply add another obstacle, which would change the setting of the apparatus but not the fact that nothing can be said about locality.
Figure A.2: Wave theory depicted in a Mach-Zehnder Interferometer with obstacle.
Now, what is the answer to one of the many questions: how can interference occur, when we only have one photon? Quantum theory interprets the wave property of the photon as the probability of photon’s locality. The light wave becomes a probability wave and the intensity of the light wave denotes the probability distribution of the photon’s locality.3 The photon apparently has two possible ways to take, the “upper” and the
Figure A.3: Quantum theory depicted in a Mach-Zehnder Interferometer without obstacle.
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When we repeat the experiment and use a bomb as an obstacle, the paradox of quantum logic become even more obvious. Suppose we have two options: a bomb with a highly sensitive fuze, sensitive to a single photon or a bomb unarmed which would equal the scenario of the no-obstacle case in A.1. In classical physics it is not possible to prove whether the bomb is armed or not without having the armed bomb exploded. In quantum physics, if the bomb is armed (i.e. the bomb is an obstacle as in figure A.4) and the photon is detected in detector 2, we know that the bomb is armed without having it exploded. Definitely, the photon could never have been there because then, the bomb was exploded. The conclusion is that the pure possibility of the photon hitting the fuze (what it obviously did not do) influenced the final position of the photon. This turns classical physics upside down; locality and causality become equivocal terms and possibilities that never occur influence physical procedures.
Quantum mechanics turns out to be less a new overwhelming insight into a better understanding of time and space and physical reality but rather questions contemporary commonly accepted philosophical, metaphysical and epistemological, concepts. It raises questions of ontology and rejects determinism. It questions a Newtonian world and it humbles scientists in their sophisticated claim towards a world of generally valid causalities. As the Cartesian system reduced nature to its alleged fundamentals, quantum theory reduces natural fundamentals to a pure possibility of indefinite states; it almost seems that nature itself is constrained ontologically, and from a philosophical perspective, epistemology becomes qualified by
Figure A.4: Quantum theory depicted
in a Mach-Zehnder Interferometer with
obstacle.
a subjective observer, a part of reality who reciprocally influences reality by observation.
Quantum theory leaves a lot of questions open but it supports the necessity of alternative explanations and approaches. Although quantum mechanics is hard to comprehend, if anybody at all has ever understood such phenomena. We are still far from speaking of a quantum theoretic paradigm or whatever, which can be transformed into a methodology of investigation. All the same, it provides us some analogies which are worth considering.
Notes
1<http://www.univie.ac.at/future.media/qu/quantentheorie.html> (03/26/2002).
2See for example Fink (1968).
3Only with a huge number of photons does the probability wave appear to be a light wave.
Appendix 134