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.
An examination of the limitations placed by the conceptual structure of quantum mechanics on the simultaneous measurement of two or more observables leads, for the case of an even number
m=2k of observables, to a quantitative estimate, depending only on the mean values of their commutators in the state in question, of the least value which the product of their
m uncertanties may assume. This indeterminacy relation is interpreted classically to mean that, by measurement of these observables alone, a point (
p,q) in phase space can be determined only to within a certain channel whose normal cross section, as measured by the value of the
kth integral invariant taken over it, must be at least of order
hk.
Existing derivations of uncertainty for single-particle interactions violate complementarity because they require that the photon exhibit wave and particle behavior simultaneously, and thus singularly. In order to restore physical consistency to quantum theory, a model of the photon is proposed with spatial extension equal to the wavelength. As a result, uncertainty and indeterminacy must be assigned independent meanings. Uncertainty describes the limit in measurability for instantaneous exchanges of momentum and is due to a photon’s particle properties. It is causal in origin and provides a model for the kinematics of quantum theory. Indeterminacy, however, is statistical in nature and is attributed to the exchange of momentum by time-averaged fields. The need for two limitations on measurability is seen as an extension of the duality principle to measurement theory.