No Surprise Here
By Steven J. Grisafi, PhD.
Three theorists have shown mathematically, when using quantum mechanics to describe an infinite two dimensional crystal lattice, that an electron’s energy gap between its ground state and its first raised energy level, is indeterminate as to its existence. Read the news report here.
While some may see this as proof that a reductionist program for explaining all physical phenomena is doomed to failure, I see this as further evidence that practitioners of modern physics, while knowing much specialized knowledge, have lost contact with the basis of their craft. It does not surprise me that there are exist physical questions that can never be explained when applying mathematical methods to hypothetical situations. It is not that I suppose any such extrapolation of current mathematical models to physical situations that are unreachable through experimentation to be inappropriate. It is that I lament the apparent failure to recognize that quantum mechanics is only a mathematical model that was formulated entirely empirically from data that was within the reach of experimentation. A physical model becomes a physical truth, which we label as a law, only when there is an exhaustive body of empirical data which never deviates from the propositions of the model. Werner Heisenberg formed matrices of atomic spectra data, multiplying and transforming them into their canonical forms, to develop what he called his matrix mechanics. Erwin Schroedinger acted similarly when he postulated the form of a continuity equation whose eigenvalues yield the same energy states as did Heisenberg’s matrix mechanics. What modern physicists seem to forget is that this procedure was entirely empirical. They constructed their mathematical models to fit atomic spectra energy transitions. When these same methods were applied to other spectra, and other quantum phenomena, the mathematical models continued to predict energy level transitions consistent with the observations of experimentation. Thus, we have come to view quantum mechanics as a valid description of physical phenomena within our world.
However, quantum mechanics remains just a mathematical model. It possesses no explanatory mechanism for its operation. Neither the Copenhagen Interpretation, nor the Many Worlds Hypothesis, bears any reality. They are just explanations for laypersons who cannot understand the mathematics. There is no real collapsing of wave functions when measurements are taken. Wave functions are merely depictions of probability distributions. They have no real existence. There is no mechanism which operates to cause the collapse of possible states into the observed state when a measurement is taken. Nor are there many worlds in which each of the possible energy states exist until they become our realization. Quantum mechanics is just a mathematical model, which once established empirically, is tested and extrapolated to situations that we cannot yet reach experimentally. As such, it bears all of the faults and inadequacies that mathematics itself bears. No one should extrapolate any mathematical model far beyond its empirical basis and expect to get meaningful results. Unfortunately, some have come to view the mathematical models that comprise physical theory as having some sort of ecclesiastical validity or involuble truth. My approach to such matters is simple: If one cannot measure it, don’t worry about it.