The basic laws of classical physics relied upon the principle ”Natura non facit saltus” (nature does not make jumps), transmitted from ancient philosophy. The underlying assumption was the existence of a space-time continuum and all changes in nature should occur continuously within this space-time continuum. Starting towards the end of the 17’th century, the classical laws governing these changes were expressed in form of differential equations or variational principles, where infinitesimally small changes of various physical variables are related to each other. Typically these differential equations of classical physics possessed exact solutions for given initial and boundary conditions, at least in principle. This led to the general conclusion that nature is deterministic; the state of nature at any given time was believed to be related in a unique way to its state at any past or future time. Even if the development of statistical thermodynamics related probabilities to thermodynamic variables, these probabilities were meant to describe insufficient knowledge of details due to the large numbers of microscopic particles involved, but deterministic behavior of all individual processes was not questioned. ...No, this is a very strange statement of the QM basic principles.
Born, Werner Heisenberg and Pascual Jordan in 1925, are contained in:
The basic principles of Quantum physics:
- On the microscopic level all elementary changes in nature are discontinuous,
consisting of quantized steps: ”quantum transitions”.
- The occurrence of these quantum transitions is not deterministic, but governed by probability laws.
(He means atomic level, not microscopic level.)
Position, momentum, time, frequency, energy, etc. are not necessarily discrete. The wave function for an electron is typically a continuous function of space and time, and progresses smoothly according to a differential equation. So it is just wrong to say everything is discontinuous.
The emphasis on probabilities is also misleading, as he concedes that other physics theories also hinge on probabilities. He distinguishes QM by whether "insufficient knowledge" is involved, but that is just a philosophical issue.
The path towards the future Quantum Theory is defined asSome problems have a discrete spectrum, but all this talk about a discrete manifold is misleading.
”the systematic transformation of classical mechanics into a discontinuous atomic mechanics..... the new mechanics replaces the continuous manifold of (classical) states by discrete manifold, which is described by ”quantum numbers”....
quantum transitions between different states are determined by probabilities...
the theoretical determination of these probabilities is one of the profound tasks of Quantum Theory....”.
The essence of QM is that the observables are represented by non-commuting linear operators.
The core of the theory is continuous, with continuous spacetime, continous wave functions, etc. For all we know, light is continuous, but only shows properties at discrete frequencies sometimes because some continuous problem has a discrete spectrum. Even then, that spectrum can often be perturbed by applying an electric or magnetic field.