Which Quantum Theory do you favor?

[Dr Alain L Fymat]

Classical physics had its defects, experiments it could not explain, that eventually led to its downfall. There is no experiment that quantum theory does not explain, at least in principle. Quantum theory is a perfect match for the quantum facts. Whereas classical physics considered the entire physical world as consisting of nothing but ordinary objects, quantum theory, on the other hand, suggests that the world is not made of ordinary objects. For example, the electron possesses static attributes (mass, charge, spin) whereas its dynamic attributes (position, momentum) seem to be created in part by the electron’s measurement context. Nobody knows how an electron or any other quantum entity possesses its dynamic attributes, and this is the subject of the quantum reality question. When you take away the measuring device, the electron undoubtedly still exists, but it possesses no dynamic attributes at all, in particular it has no definite place or motion.

Quantum theory is a method of representing quantumstuff mathematically: a model of the world executed in symbols. In the pre-quantic (called “paleoquantic” or “stone age” quantum) area, 1920-1925, fragments of classical physics were pieced together with certain quantum notions (notably the wave-particle attributes) in clever but essentially haphazard ways. The high-water stage was Bohr’s model of the hydrogen atom, which was largely a matter of inspired guesswork. Physicists yearned for a quantum theory to lead them out of Stone Age ignorance. There are currently four quantum theories (QT).

QT # 1: Matrix mechanics (Heisenberg): Each Heisenberg matrix represents a different attribute, such as energy or moment; the matrix diagonal entries represent the probability that the system has that particular attribute value, and the off-diagonal elements represent the strength of non-classical connections between possible values of that attribute.

QT # 2: Wave mechanics (Schrodinger): Quantumstuff is represented as a waveform. The Schrodinger’s equation describes the wave’s law of motion. At first, Schrodinger believed his waves to be classical waves as real as Maxwell’s electromagnetic waves, but their reality status is extremely dubious.

QT # 3: Transformation theory (Dirac): Quantumstuff is symbolized as an arrow (or vector) pointing in a certain direction in an abstract space of many dimensions. Dirac was able to show that both Heisenberg’s and Schrodinger’s theories were special cases of his own rotating-arrow version of quantum theory. Whereas Schroedinger’s equation applies to slow quons, Dirac’s equation applies for quons moving near the speed of light.

QT # 4: Sum of Possibilities (Feynman): It is a fundamentally new way of looking at quantum theory that cannot be reached by a Dirac transformation. It has been inspired by the work of Huyghens who analyzed light waves by breaking them into simple sums of spherical wavelets. Feynman assumes that the unmeasured world works according to two rules: (1) A single quon takes all possible paths; and (2) No path is better than any other. These paths, unlike classical trajectories, possess phases which add wavewise to produce the system’s proxy wave – a representation of the probability pattern of a large number of quons prepared in the same state. Adding up possible paths has much in common with classical statistical reasoning. Feynman’s possibilities are different from classical probabilities. Classically, the more ways an event can happen, the more probable its occurrence. In quantum theory, possibilities have a wavelike nature that allow them to cancel, so increasing the number of quantum possibilities does not always make an event more probable. To calculate an electron’s fate, Feynman adds up all possible histories, some histories cancel, whatever remains represents what will actually happen – expressed as a pattern of possibilities. Feynman also introduced the celebrated “Feynman diagrams” for carrying out complex quantum calculations; each diagram is shorthand for an entire class of possible histories.

So, which quantum theory (QT # 1or # 2 or # 3, or QT # 4) do you favor?