In note  a quantum paradox was stated. There are many others. Quantum theory is special in two ways. Firstly nobody really understands the ideas behind and the implications of quantum theory, even hundred years after its discovery. Secondly quantum theory is concerned with the microscopic nature of reality. In this sense it only reflects a level of reality which has become accessible to the human race due to its technological evolution. Luckily, in 1925, a mathematical formalism describing the quantum realm was developed, namely QM, which elevates quantum theory to the status of a mathematically exact theory. But at its foundation, quantum theory seems to blur the borders between science and philosophy. Indeed, also modern cosmology offers a philosophical approach to many problems, as seen in the anthropic principle of note . A full treatment of many of the problems of QM and their proposed solutions are given in [Om94]. Covering the philosophical aspects are [BH93], especially [Au95] and [CH01].
Basically the quantum realm seems to challenge the notion of object and subject. In some strange way observation (measurement) influences the observed. Hence the whole issue of perception re-emerges in an epistemological context. What can we know about the world outside of us? How do we perceive reality? A very cautious approach to the subject would only let one conclude that the reality which is perceived by ones consciousness is an image of the actual reality and does not allow any conclusions about its true nature to be drawn. This is a somewhat weaker statement along the line of thought proposed by the eighteenth century philosopher and bishop Berkeley who denied the very existence of a material world outside human consciousness. Although this seems to question the foundations of reality it is interesting to note that modern neurology is drawn to a similar conclusions: reality is generated in (by) the brain and what lies outside the brain cannot really be known; [Sp01]. Or in the words of Berkeley: the essence of the objects is to be perceived, the essence of the subject is to perceive. So one is to conclude that we only live with images or copies of reality without the possibility to directly access it. This is somewhat similar to the task performed by digital optical or audio appliances: physical reality is captured (translated) into a string of digital information. However, this technology can do more than just store information it can also reproduce the reality it copied. In a sense a string of 0 and 1 can be used to program reality (or what to our brain is seen to reflect reality). This is also close to the ideas encountered in the last section of appendix A.7 and note , concerning the information based notion of reality. However, quantum theory takes us a step further: by projecting an image of reality into the mind a link between the observer and the observed emerges. In measuring a property of a quantum one in effect makes that property manifest itself. This is true for the position of a particle in the two slit experiment as it is for the direction of polarization or spin of a quantum chosen by the experiment. It has also been experimentally verified in 1984 that the choice of the experimenter can in fact affect the past, in Wheeler's so-called delayed choice experiment (see reference at the end of the next paragraph). So although we will never experience what reality really is we are linked with its fundamental workings. In Frieden's approach to Fisher information this effect is also seen: observation gives rise to information and information gives rise to physics. The deep connection between mathematics and reality on one side and mathematics and intellect on the other side (seen in appendix B) also suggests the possibility of such a connection. Reality is a reflection of mathematics and mathematics is an image of reality and hence the human mind, being able to generate consciousness and intellect, which can discover and develop mathematics, is intimately linked to reality.
Another puzzling aspect of quantum theory was uncovered in 1982 by Aspect ([ADR82]) measuring Bell's inequalities ([Be65]). The notions of reality and locality seem to conflict each other. `Reality' means that the world exists when nobody is observing. This idea of the non-reality of the quantum world when no one is observing it is known as the Copenhagen interpretation of quantum theory proposed by Bohr and others in 1927 and takes the ideas of a subject-object relation even further. The issue of non-locality was raised by the Einstein-Podolsky-Rosen experiment ([EPR35]) and involves the instantaneous transmission of information regardless of the distance. Aspect's experiments showed: the quantum realm is not both local and real. Unfortunately there is no way to determine which notion should be abandoned. In the words of Feynman in 1965: `I think I can safely say that nobody understands quantum mechanics.' For a recent review by Wheeler -- who is a deep thinker on the foundations of physics -- of the last hundred years of quantum theory consult [TW01].
Whatever the implications of quantum theory turn out to be, the theory seems to indicate that the quantum realm is in fact at the boarder-line of reality, meaning that the obvious and clearly defined notions encountered at a macroscopic level break down and become `fuzzy'. If space-time really is discrete, as suggested in appendix A.7, then such a boarder should in fact exist and the quantum realm shields us from the void behind reality. Then it isn't very surprising that reality per se starts to break down at the quantum level. It is also interesting to note that life and consciousness are located well within these boundaries. This in effect creates the quantum paradoxes because the infant mind has no other frame of reality it can perceive and start to incorporate into a coherent perception of the world at an early stage of mental development. The effect of decoherence discovered in 1970 and which is still relevant today, seems to cut-off these strange effects arising at the fringes of reality and ensures that macroscopic reality manifests the stable and logical behavior we take for granted.
For controversial ideas on quantum theory and consciousness see Penrose's books; [Pen89-97]. His line of argument is however quite simple and in tune with this section: a fundamental insight and understanding of the mind is required before any fundamental insight and understanding of physics/reality can be achieved. Penrose seems to be one of the few physicists who can assert far-reaching ideas without loosing his scientific respectability. On the contrary, being not only a cosmologist but also a mathematician, he has developed new mathematical and geometrical tools which are believed to reflect fundamental workings of quantum gravity; see appendix A.5.
Being such a poorly understandable subject, quantum theory offers great opportunity for speculative proposals. E.g. [Pa00] where it is claimed that the whole of physics is explained using non-locality principles.