Theoretical Considerations

The phenomena that Metaclassical Physics is trying to describe and/or explain are several orders of magnitude more distant from the physical reality of everyday experience than those of Classical Physics. In addition, the experiments that could provide critical data which would validate or falsify physical theories need extremely high energies and therefore are very costly.
This had led to an emphasis to the development of the mathematical aspect of physical theories, which was the only way open to physicists in the absence of experimental evidence. As a consequence, today physics could be arguably more accurately described as "physical mathematics" than as "mathematical physics".
This trend is inevitable to some extend, on the other hand though it also has acquired its own momentum, leading to an ever increasing "hypermathematization" of physics, a phenomenon that reached its extreme in string theory. The danger lurking in this approach is of course that physical theory goes off at a mathematical tangent, loosing contact with the physical reality it tries to describe. Now, especially after the publication of Lee Smolin's and Peter Woit's books, string theory may conceivably enter a crisis period as defined by Kuhn. It is an interesting fact that in this case the "anomalies" that may lead to the crisis are not experimental evidence that cannot be explained by the theory, but mainly the fact that the theory can explain anything, and therefore nothing.
This "hypermathematization" of physics may also have a further sideeffect that has been described by Hubert Goenner in his paper On the History of Unified Field Theories in Living Reviews in Relativity, in which he says the following referring to Einstein himself:
If there is an enigma left in the scientific part of Einstein’s life, then it occurs here, in the area of unified field theory.... [where] not only did [his] endeavors... lead nowhere, but sometimes they were also quite behind what others knew already... Unlike in his previous scientific career where he was most ingenious and prolific in devising (thought) experiments, now Einstein’s physical intuition seems to have been buried under formal structural thinking (italics added).
This sideeffect, which is also amusingly described by John Baez as "mathematical rigor mortis" in his Oz tale, means that the current trend develops the mathematical intuition of physicists, but hampers their physical intuition.
Here we will try to follow a different approach, giving emphasis to mathematically sound but also physically meaningful solutions. A physically meaningful description or theory is one that connects back to the reality that it is supposed to describe or explain, and can answer, in physical terms, questions such as "What does really happen?" or "What does this mean?", as opposed to a "mathematical black box approach" of using a mathematical formula that can take as input some parameters of the phenomenon and give correct predictions about its outcomes (or wrong predictions, or no predictions at all, as the case may be), without us having any idea of how or why this happens, or what the formula does, or which physical reality it describes, if any. Mathematics obviously will be used, but hopefully in an "open box model", in the sense of knowing what parts of physical reality our mathematics describe.
See also