Relativity and quantum dynamics : Einstein-Planck

Theodore P. Jorgensen

Tapan Kumar Ghosh

It is established that special relativity and quantum mechanics are two very wide apart theories of measurements in modern physics in terms of determinism versus indeterminism. Modern physics accepts indeterminism against classical determinism. But it is remarkable that Einstein's special relativity in its present form alone contains the basic ingredients of quantum theory. Einstein's theory can give a simple theoretical proof of the Planck's quantum hypothesis and can explain the origin of mass out of zero rest mass of photon. This article at the first place shows how to proceed in this path from relativistic energy momentum relations and at the second place it shows the reason of energy and momentum indeterminacy from the framework of relativity. At the last phase the article puts a question on the sustainability of special relativity itself before oscillation of any kind. This paper deals with the matter to the extent special relativity containing quantum theory. Index Terms— Special relativity, simultaneity of events, Planck's quantum theory, energy momentum 4 vector, Heisenberg's indeterminacy principle, concept of mass, ensemble of photon. —————————— a —————————— 1 I NTRODUCTION t is a common belief that the jurisdiction of special relativi- ty and quantum theory are mutually exclusive. In 1900 Max Planck gave his famous quantum hypothesis of light together with the energy- frequency relation . Eh Q In 1905 Einstein gave special relativity. Both the regime went their own way and ultimately clashed each other with the arrival of Heisenberg's indeterminacy principle in 1926. Einstein con- ceded defeat to Bohr ultimately but still believed that quan- tum theory lacks something very serious. But modern physics points clearly to the triumph of Heisenberg's indeterminacy principle in every context. Nonetheless it is worthwhile to mention that the very genesis of quantum theory of light pre- scribed by Eh Q and the very essence of mass can be de- rived even in the frame work of special relativity. Even Ein- stein could get it using his own energy momentum relation. Planck's quantum relation of photon and the construction of mass from an ensemble of photons are indeed inbuilt in Ein- stein's theory. We can even reconcile Heisenberg's principle of indeterminacy with the framework built by Einstein.

Christian Bracco

In the absence of any reliable document, from which Einsteins ideas on relativity prior to 1905 could uniquely be drawn, we are forced to make assumptions. If many historians (J. Norton, O. Darrigol, ) have privileged an electromagnetic origin, others like A. Miller have emphasized the role of light quanta. Ill come back on some evidences that the March quanta have played a role in the June and September 1905 relativity papers and reciprocally that the relativity principle may have influenced Einsteins reflexions on free moving quanta. From both a scientific and an historical perspective, the association of quanta and relativity is indeed natural if one has in mind Plancks work on the black body radiation and Poincarés contribution Lorentz theory and the reaction principle to the Lorentz Jubilee, which both occurred in mid-December 1900. As well known, the former introduced fixed energy quanta and the latter (quoted by Einstein in 1906) opened the way to a dynamical and relativistic (at first order in v/c) account of the electromagnetic field behaviour. But unknown, Poincarés paper also exhibited at this order the same transformation law for the energy and the frequency of an electromagnetic plane wave of finite length. If Einstein remarked this before 1906 (which is not proved), it may have encouraged his thinking of moving quanta. We would then meet the point of view expressed by R. Penrose in his preface of J. Stachels book Einsteins miraculous year, that it is virtually inconceivable that [Einstein] would have put forward two papers [March/June] in the same year which depended upon hypothetical views [particle/wave] of Nature that he felt were in contradiction with each other. March, June and September 1905 Einstein's papers would constitute a remarkable synthesis, in a fully original and new epistemological view, of Planck's 1900 work on the interaction between matter and radiation and Poincarés 1900 paper on the relativistic dynamics of charges and the electromagnetic field.

Gianrocco Guerriero

We present a heuristic derivation of the Planck–Einstein relation E = hν and the de Broglie relation p = h/λ starting from a single hypothesis: the existence of an absolute minimum action h. From dimensional considerations alone, both relations follow immediately, with h identified a posteriori with Planck’s constant on the basis of experimental data. The work complements a previous paper in which special relativity is derived from a correspondence principle, suggesting a unified heuristic framework for the foundations of modern physics. Correspondence: gianroccoguerriero@libero.it or gwriterekphrasis@gmail.com