Laboratory-Space and Configuration-Space Formulations of Quantum Mechanics, Versus Bell–Clauser–Horne–Shimony Local Realism, Versus Born’s Ambiguity

A survey of more than thirty quantum mechanics and quantum field theory textbooks and review articles reveals two distinctly different schools of thought regarding what quantum mechanics is. Indeed, these books are found to promote two very different formulations of quantum mechanics. One is formulated in laboratory space, while the other is formulated in configuration space. Max Born (1933, 1935, 1969) appears to have been the founder and earliest promoter of the lab-space formulation. His textbook also acknowledges the two different possible formulations and pronounces them to be equivalent. He does so via what is herein called Born’s argument-space ambiguity. His pronouncement is shown here to be false. The two formulations are, in fact, very different, and are herein shown to be incompatible. This article thus compares and contrasts these two formulations with each other, and with competing formulations from quantum field theory and with Bell-Clauser–Horne–Shimony Local Realism. Born’s ambiguity is found to be embedded in quantum field theory also. Textbooks that promote the laboratory-space formulation are definitely easier to understand and visualize, in that they attempt to provide a “clean story line” that appears to explain many experiments. Born found the lab-space formulation preferable, because it is less mathematically abstract. Unfortunately, a lab-space formulation, a.k.a. a space–time formulation, is found to suffer from several serious fatal deficiencies. Paramount among these is that it can only describe single particle systems and cannot describe entanglement. Moreover, there does not appear to be any rigorous method to allow it to be extended to N ≥ 2 particle systems, and thence to describe entanglement. Attempts in various books to do so are examined and found wanting. It is also noted that all charged particles in the world interact with each other, at least weakly, and are thus are always slightly entangled. Born’s associated important construct, his “conserved probability current” is also examined. It is noted here that it may be constructed only in lab space, although various textbooks erroneously claim otherwise. Finally, it is noted that the lab-space formulation of quantum mechanics is really a form of Bell-Clauser–Horne–Shimony Local Realism, whereupon any successful attempt at a generalization to cover N ≥ 2 particle systems will also violate experimental evidence that has been amassed against Local Realism. Alas, the conceptual model that lab-space formulations promote and use is found to be untenable. It is commonly, but incorrectly, suggested that a lab-space formulation is justified because it provides an approximation to a better theory, that is, to a formulation that is formulated in configuration space. That suggestion is unfounded. Unfortunately, the configuration-space formulation requires a highly abstract mathematical formalism that is difficult to understand and that provides no conceptual model to allow its inner workings to be visualized.