Through comparing Planck's trouble in the hypothesis of energy quantum with the first crisis of mathematics, the essence of them becomes much clearer. This shows the importance of the historical method in scientific research. This article also briefly illustrates that identity principle is the first principle of quantum mechanics.
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.
This chapter starts with the historical development of quantum mechanics and explanations of key concepts behind fundamental discoveries such as Planck's hypothesis, the photoelectric effect, Bohr's atomic model, Compton scattering, the de Broglie hypothesis, the Pauli exclusion principle, the Schrödinger equation, Heisenberg quantum mechanics and the uncertainty principle, the Born interpretation of wave function, the Davisson and Germer experiment, and Dirac relativistic quantum mechanics, which made important contributions to the foundation of modern quantum mechanics. Concepts like the particle properties of radiation, the wave properties of matter, quantized energy and momentum, and the idea that one can no longer know exactly where a single particle like an electron is at any instant of time are brought out clearly through this chapter. A list of important quantum mechanical parameters along with solved examples and unsolved exercises on the key concepts are included towards the end.
The history of the development of quantum theory since its discovery by Planck in 1900 is outlined. The great achievements of quantum mechanics and its contribution to science and mankind are summarized briefly. Judged by all possible criteria, namely, esthetics and scientific criteria and contribution to society in general, quantum mechanics can be ranked in as the highest one. It is stressed that our scientific efforts should be focused on eight to ten most important problems, which could benefit our economy or national defense.At the same time, we should also pay attention to some purely basic research topics that seems “useless” and devoid of any applications. The ongoing fourth breakthrough in physics is the one that deserves attention.
Intriguing questions from the early history of quantum theory (QT) raise serious doubts about the accepted theory of black body radiation. (The Planck theory builds on the apparently flawed Rayleigh-Jeans approach.) Furthermore, the validity of the theory of diffraction, the basis of the wave theory of radiation and matter, seems uncertain. Together, these raise fundamental questions about the foundations of QT and its current status. The apparently symbiotic relationship between QT and the theory of atomic and molecular structure, a key paradigm of modern scientific thought, may be a misleading indicator of the validity of QT. The protocols deriving from the Schrodinger equation lead to quantized states, but only along with certain assumptions. It is argued that QT applies uniquely to the interaction of electromagnetic radiation with matter, and that its scope is not universal: thus, it is best regarded as a quasi-empirical formalism. It is possible that the uncertainty surrounding QT is a legacy of the troubled historical period during which it was founded. This apparently has fascinating implications for the history and philosophy of science in general.
In this chapter, we present the basic principles of the quantum mechanics of particle systems from a modern mathematical perspective. The proper study of quantum mechanics brings together several interesting mathematical ideas, ranging from group representations to the spectral theory of unbounded self-adjoint operators in Hilbert spaces and the theory of C * algebras. The facts from analysis of operators in Hilbert spaces and C * algebras needed in this chapter are presented in detail in the appendices at the end of the book. More on the mathematical foundations of quantum mechanics can be found in the books by L. Fadeev and O. Yakubovskii [FY], G. Mackey [M], and F. Strocchi [Str] listed in the bibliography. The birth of quantum theory The origins of quantum theory can be traced back to M. Planck's study, published in 1900, of so-called black-body radiation. It is well known that matter glows when heated, going from red-hot to white-hot as the temperature rises. The color (or frequency of radiation) of the radiating body is independent of its surface, and for a black body it is found to be a function of temperature alone. The behavior of the radiation energy as a function of temperature seemed quite different at high temperatures and low temperatures. In a desperate attempt to fit these different behaviors into a single law, Planck introduced the hypothesis that energy was not continuous, but came in discrete packets or quanta . At the beginning of the twentieth century, a number of experiments pointed to a breakdown of the laws of classical mechanics at very small (subatomic) scales.
The first decades of the twentieth century were marked by two revolutionary scientific accomplishments, the theory of relativity and quantum mechanics, with repercussions still felt today. Relativity theory and quantum mechanics became the two most important branches of “Modern Physics” that emerged as an alternative to “Classical Physics” (a term often used interchangeably with that of “Newtonian” or “Galilean” physics). No field of science (from astronomy to the life sciences), no field of knowledge (from philosophy to sociology), and no artistic practice (from architecture to the fine arts) was left untouched by these investigations into the nature of our physical universe.