From Statistical Mechanics to Quantum Statistics

Boltzmann was not easy to argue with.

The development of modern physics follows a path from statistical mechanics (Boltzmann 1866) over statistics of energy quanta of blackbody radiation (Planck 1900) to quantum mechanics statistics (Born 1926). In each case there was a pressing demand from empire power politics on theoretical physicists to assist in advancement of new technologies, from steam engines to atomic energy:

1. Boltzmann took on the challenge to give the 2nd Law of Thermodynamics a rational mathematical physical meaning as the outstanding problem of the mid 19th century.  
2. Planck took on the challenge to give blackbody radiation a rational mathematical physical analysis, as the outstanding problem of classical physics at the end of the 19th century. 
3. Born took on the challenge to give the wave function of the new quantum physics a scientific meaning.       

Boltzmann failed and so invented statistical mechanics based on an idea of macro-states supported by micro-states with probability increasing with number of micro-states. 

Planck failed and inspired by Boltzmann invented a way of computing energy quanta with probability decreasing with increasing frequency. 

Born inspired by Planck resorted to statistics by giving the wave function a meaning as probability of electron configuration. 

 

The use of statistics is fundamentally different in all three cases, but Boltzmann started it all.

This means that modern physics largely is statistical physics. Is this a problem? It means giving up the essence of classical physics as rational deterministic physics based on cause-effect. In statistical physics things happen by chance and rationality is lost. It may be a high price to pay, in particular if it is not really necessary.  

Real Quantum Mechanics offers an new approach to quantum mechanics without statistics.

Crisis of Modern Statistical Physics vs Classical Deterministic Physics

This is a further comment on Leibniz Principle of Identity of Indiscernibles seemingly in conflict with the modern physics main-stream idea of electrons all alike like equal probabilities of outcomes of tossing a fair coin. 

That modern physics is in a state of deep crisis is acknowledged by leading physicists and also largely understood by the general public. Buzz words like dark energy, dark matter, inflation, Big Bang, multiversa, entanglement, collapse of the wave function,  particles and quarks, are floating around as elements of relativity theory on cosmological scales and quantum mechanics on atomic scales, both formed 100 years ago but still today harbouring toxic unresolved foundational problems, and on top of that being incompatible. A veritable mess. 

The root of the seemingly unresolvable problems of quantum mechanics can be traced back to the statistical interpretation of the multi-dimensional Schrödinger wave function as solution to the multi-dimensional Schrödinger equation serving as foundation. 

While classical physics is ontology about what reality is, modern physics is epistemology about what can be said. While classical physics is deterministic physics independent of human observer, modern physics in the form of quantum mechanics is statistical physics depending on human observers acting as mathematical statisticians in an insurance company busy computing insurance premiums. 

The departure from classical into modern physics was initiated by Boltzmann in the late 19th century seeking an ontological realistic explanation of the 2nd Law of Thermodynamics as the main unresolved problem of classical physics giving time a direction, which had to be resolved to save physics from disbelief. When Boltzmann understood that he could not reach this main goal of his scientific life, he made a Faustian deal in the form of an explanation based on statistical mechanics. This served to save the life of physics, but not Boltzmann's own life, and opened the door into the heaven of modern physics as quantum mechanics as statistical mechanics, which is now in a state of crisis. 

The step from deterministic physics to statistical physics, was taken in order to save classical physics from credibility collapse in front of the 2nd Law. The medication worked for the moment but the patient as classical physics died and so was replaced by modern physics, which however showed to be quite sick without any cure in sight still today. 

The first step in coming to grips with the crisis of modern physics, is to ask if it is impossible to explain the 2nd Law within classical deterministic physics? If not, then the step to statistics is not necessary and much trouble can be avoided. More precisely, it appears to be possible to replace statistics by a concept of finite precision physics as presented in Computational Thermodynamics and in popular form in The Clock and the Arrow with follow up into a realistic deterministic form of quantum mechanics as Real Quantum Mechanics. 

This means a return to deterministic physics with a new element of finite precision computational physics coming with resolutions of problems of classical physics making it possible to avoid paying the very high price of taking the drug of statistical physics. 

Real physics is what it is and is given to us for free. Statistical physics is man-made physics, which needs massive data and human interference. Real physics seeks to describe the World as it is, while modern physicists have the reduced goal of statistical prediction outcomes of man-made experiments. Schrödinger and Einstein could not accept physics as man-made statistics, but were cancelled. Maybe the present crisis can open to restart following their spirit?  

We may view real physics as a form of engineering or professional soccer game with basic questions: What is the basic mechanism/principle? How to improve it? On the other hand, a statistical physicist simply watches the game on TV and finds meaning in betting.  

Computational vs Statistical Physics

Statistical physics was created by Boltzmann (1844-1906) in an attempt to explain observed irreversibility of thermodynamic processes as a necessary evolution from more ordered/less probable to less ordered/more probable states in a microscopic particle-collision model of a gas. This was captured in Boltzmann's macroscopic equations derived from an assumption of molecular chaos (StossAnzahlAnsatz) stating that particle velocities prior to collision are uncorrelated. Boltzmann's H-theorem states that a gas left alone will approach a uniform rest state with a Maxwellian velocity distribution. 

Statistical physics is based on some assumption of statistical nature, such as molecular chaos, to be compared with computational physics where the evolution of a gas as a collection of colliding particles is simulated simply by computing the trajectories of all particles subject to collision with chaos/unordered motion as an emergent phenomenon without any assumption. 

One can argue that computational physics is real physics because particle trajectories subject to Newton's laws of motion = real physics,  are computed. On the other hand, statistical physics is not real physics in the sense that real physics cannot do statistics and decide to evolve according to an assumption of molecular chaos.  

On the other hand it is possible for human beings to do statistics by computing mean values and standard deviations in particle-collision models. 

Statistical physics was developed before the computer when computational physics could not deliver. Today with the computer computational physics can answer the questions posed in statistical physics, see Euler Right! showing physics emerging in a discrete finite element model by computation. 

PS The classical approach is to derive a continuum model in the form of a partial differential equation from a particle model. A computational model can then be derived by discretising the differential equation using the finite element method, which can be viewed as a form of particle method, in a way closing the circle with the particle model as the real model and the continuum model as a fictional model.