torsdag 8 maj 2014

Quantum Statistics as Salvation from Catastrophe?

Planck awarding the Planck Medal to Einstein in 1929 for his elaboration of Planck's idea of discrete of quanta of energy into quanta of light, an idea which Planck viewed as a "hypothetical attempt" resulting from an "act of desperation".

To understand a theory of physics it is helpful to seek the reason the theory was developed. In The Conceptual Development of Quantum Mechanics by Max Jammer we read:
  • Quantum theory had its origin in the inability of classical physics to account for the experimentally observed distribution in the continuous spectrum of black-body.
  • It is convenient to define the first phase in the development of quantum theory the period in which all quantum conceptions and principles proposed referred exclusively to black-body radiation or harmonic vibrations.  
  • …the study of the single physical phenomenon of blackbody radiation led to the conceptions of quanta and to quantum statistics of the harmonic oscillator, and thus to results which defied the principles of classical mechanics and, in particular, the equipartition theorem.
  • It was generally agreed that classical physics was incapable of accounting for atomic and molecular processes.
  • Planck obviously regarded the use of the law of chance… merely as a provisional device… in his own opinion his new theory was but a "hypothetical attempt" to reconcile the law of radiation with foundations of Maxwell's doctrine, and not a final solution to the problem.
Quantum mechanics thus developed from Planck's hypothetical attempt to save Wien's classical radiation law with radiance of frequency $\nu$ scaling like $T\nu^2$ with $T$ temperature, from an ultraviolet catastrophe with the radiance apparently tending to infinity without any bound on the frequency $\nu$.

To save the world from this catastrophe, Planck against his basic convictions as scientist seeing no way other out, then gave up causality as the essence of science by corrupting his deterministic harmonic oscillators by statistics. And on this shaky ground quantum mechanics was formed. No wonder that quantum mechanics in its present form is a catastrophe (with uncomputable wave-functions without physical meaning), although depicted as an imposing intellectual structure of great beauty. 

But can statistics really save us from catastrophe? Catastrophe may be the result an unfortunate throw of dice by fate, but you don't avoid a catastrophe by letting dice throw decide how to steer your car.  

Computational Blackbody Radiation describes a different way of avoiding the ultraviolet catastrophe with statistics replaced by a constructive version of classical mechanics based on finite precision computation. From this starting point a quantum mechanics without statistics may be possible to formulate. If so the present catastrophe of quantum mechanics can (perhaps) be avoided.


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