The three decoupled quantum field theories (with similar "symmetry" characterisics), the plasma dynamics theories, as well as the two theories of relativity operate with different mathematical concepts. Those concepts were developed by a step by step approach, which started 1900, when Max Planck introduced the theory of „quanta with specific energies“ to explain „radiation“ effects. The consequences of this step-by-step development process resulted into

- paradoxes (from a natural science and common sense perspective) with respect to contradicting predictions (e.g. the wave-particle dualism)

- paradoxes (from a mathematics perspective) having two different mathematical models explaining the same phenomenon by different physical causes (e.g. linear and nonlinear Landau damping) 

The step-by-step development process of physical theories generated the following paradigm of physics, (DeP) p. 551:


                    Physics is scale dependent and decoupling


1. Physics is scale dependent and at each scale

there are different degrees of freedom and different dynamics. Therefore, at each scale level to be studied, there is the need for a different theory (e.g. classical continuum mechanics, theory of granular structure, nucleus + electronic cloud, nuclear physics, QED, free-electron theory, modelling, e.g. the properties of metals, semiconductors, and insulators) to describe the behavior of the considered physical system depending on a scale (of energies, distances, momenta, etc.). For example, in quantum field theory, the dependence of the behavior on the scale is often expressed mathematically by the fact that in order to regularize (i.e. render finite) Feynman diagram integrals one must introduce auxiliary scales, cutoffs, etc. The effect of these choices on the physics is encoded into the renormalization group equation. This equation then becomes an important tool for the study of physical theories. 

2. Physics at large scale decouples from the physics at a smaller scale

 when passing from a smaller scale to a larger scale irrelevant degrees of freedom are averaged over. Mathematically this means that they become integration variables and thus disappear. 


3. The different scales

- In classical mechanics one deals with three scales according to its three basic measurements: distance D, time T, mass M

- in non-relativistic quantum theory and classical relativity it has two scales: D & T resp. D & M (mass M can be expressed through T & D using the Planck constant resp. T can be expressed via D using the speed of light) 

- in relativistic quantum theory there is only one scale: distance D.   

                                              Supporting data

Braun, K., Current physical and mathematical realities regarding an unified field theory

  

Braun, K., A Krein space based quanta energy field model, supporting mathematics

                                             

                               

Braun K., UFT related list of papers