There are a large number of different approaches or formulations to the foundations of Quantum Mechanics. There is the Heisenberg’s Matrix Formulation, Schrödinger’s Wave-function Formulation, Feynman’s Path Integral Formulation, Second Quantization Formulation, Wigner’s Phase Space Formulation, Density Matrix Formulation, Schwinger’s Variational Formulation, de Broglie-Bohm’s Pilot Wave Formulation, Hamilton-Jacobi Formulation etc. There are several Quantum Mechanical pictures based on placement of time-dependence. There is the Schrödinger Picture: time-dependent Wave-functions, the Heisenberg Picture: time-dependent operators and the Interaction Picture: time-dependence split. The different approaches are in fact, modifications of the theory. Each one introduces some prominent new theoretical aspect with new equations, which needs to be interpreted or explained. Thus, there are many different interpretations of Quantum Mechanics, which are very difficult to characterize. Prominent among them are; the Realistic Interpretation: wave-function describes reality, the Positivistic Interpretation: wave-function contains only the information about reality, the famous Copenhagen Interpretation: which is the orthodox Interpretation. Then there is Bohm’s Causal Interpretation, Everett’s Many World’s Interpretation, Mermin’s Ithaca Interpretation, Brukner-Zeilinger interpretation, etc. Thus, QM is not one coherent theory.
The principle of mass-energy equivalence, which is treated as the corner-stone principle of all nuclear interactions, binding energies of atoms and nucleons, etc., enters physics only as a corollary of the transformation equations between frames of references in relative motion. Quantum Mechanics (QM) cannot justify this equivalence principle on its own, even though it is the theory concerned about the energy exchanges and interactions of fundamental particles. Quantum Field Theory (QFT) is the extension of QM (dealing with particles) over to fields. In spite of the reported advancements in QFT, there is very little back up experimental proof to validate many of its postulates including Higgs mechanism, bare mass/charge, infinite charge etc. It seems almost impossible to think of QFT without thinking of particles which are accelerated and scattered in colliders. But interestingly, the particle interpretation has the best arguments against QFT. Till recently, the Big Bang hypothesis held the center stage in cosmology. Now Loop Quantum Cosmology (LQC) with its postulates of the “Big Bounce” is taking over. Yet there are two distinctly divergent streams of thought on this subject also. The confusion surrounding interpretation of quantum physics is further compounded by the modern proponents, who often search historical documents of discarded theories and come up with new meanings or discard earlier theories to back up their own theories. For example, the cosmological constant, first proposed and subsequently rejected as the greatest blunder of his life by Einstein; has made a come back in cosmology. Bohr’s complementarity principle, originally central to his vision of quantum particles, has been reduced to a corollary and is often identified with the frameworks in Consistent Histories.