In 1900, Planck presented an equation that became fundamental to quantum physics and paved the way for interpreting the nature of radiation. However, in a 1911 article where he attempted to theoretically justify this equation, some errors might have been introduced. In this paper, Planck proposed that the central concept in quantum physics is the quantum of action, which diminished the significance of the energy quantum. Many researchers argue that this approach was flawed, as it contradicted the foundational ideas he introduced in 1900, termed the “quantum hypothesis.”
In 1900, Planck presented an equation that became fundamental to quantum physics and paved the way for interpreting the nature of radiation. However, in a 1911 article where he attempted to theoretically justify this equation, some errors might have been introduced. In this paper, Planck proposed that the central concept in quantum physics is the quantum of action, which diminished the significance of the energy quantum. Many researchers argue that this approach was flawed, as it contradicted the foundational ideas he introduced in 1900, termed the “quantum hypothesis.”
It is well known that in 1900, after Planck obtained the basic equation of quantum theory, there came a moment when it became necessary to obtain a theoretical justification of this equation. In 1911, based on the possibility of Gibbs' canonical distribution function (CDF), he solved this problem partially: he obtained a justification for the second multiplier of his equation. Then on the basis of the analysis of these results he stated that henceforth in the role of the basic concept of quantum theory there is a necessity to accept the possibility of the concept of the quantum of action. However, Poincaré at the same congress criticized these new ideas. For he recognized the value of the idea of the quantum of action in solving only frequent problems. Therefore, he further, in his article entitled "On the Theory of Quanta", made the following conclusion: in his opinion, the main essence of quantum theory is connected with the concept of the quantum of energy [1]. Thus, he wanted to say that in the future the main results of Planck's quantum theory have the possibility to substantiate only if the possibility of the concept of energy quantum is taken as more general. In this paper an attempt is made to prove that it is really so.
The origin of the relativity theories was closely bound up with the development of electromagnetic concepts, a development that approached a coherent fieldtheoretical formulation, according to which all actions may vary in a continuous manner. In contrast, quantum theory arose out of the development of atomic concepts, a development that was characterized by the acknowledgment of a fundamental limitation to classical physical ideas when applied to atomic phenomena. This restriction was expressed in the so-called quantum postulate, which attributed to any atomic process an essential discontinuity that was symbolized by Planck's quantum of action. Quantum field theory (QFT) is a later phase of the conceptual developments of quantum theory, and has the old quantum theory and non-relativistic quantum mechanics, essentially the preliminary analyses of the interactions between atoms and radiation, as its predecessors. This chapter will review some features of quantum physics that are relevant to the rise of QFT. The quantization of motion In solving the problem of the equilibrium between matter and radiation, Max Planck (1900) showed that the laws of heat radiation demanded an element of discontinuity in the description of atomic processes. In the statistical behavior of atoms represented, in Planck's description, by linear resonators in their interactions with radiation, only states of vibration should be taken into account whose energy was an integral multiple of a quantum, hv , where h is Planck's constant and v is the frequency of the resonator. Planck himself believed that the discontinuity of energy was only a property of atoms, and was not ready to apply the idea of energy quantization to radiation itself.
Planck's introduction of the quantum of action in 1900 was followed by 25 years of trial and error in quest of the understanding of the quantum world; different ideas and directions had to be pursued until the path leading to the elementary quantum theory was discovered. Radical changes away from traditional perceptions about natural phenomena were necessary, the entire system of basic concepts in classical physics had to be abandoned and replaced by a new mode of thought. Continuity and determinism of classical laws were no longer applicable on the quantum scale, where dynamical behaviour proceeds by discontinuous and statistical quantum transitions. Albert Einstein laid the essential foundations for the new concept; Max Born made the decisive step further leading to the breakthrough in 1925. The development of the ideas, which eventually resulted in the elementary quantum theory in 1925/26, will be described, relying on original publications and letters written during that period in time by the major contributors. The fundamental laws of Quantum Theory derived by Max Born and Pascual Jordan may mathematically be represented in many different ways, and particular emphasis is given to the distinction between physical content and mathematical representation.
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.
A century ago, the energy quantization hypothesis required to derive Planck's formula has been proposed as the foundations of the quantum theory. So far, this quantization hypothesis still lacks complete theoretical proof and interpretation, even no answer for why the quantization occurs. Here Planck's quantization hypothesis has been proved completely in pure theoretical methods, and accompanied by a full interpretation of the related physical laws. A new physical and mathematical expression of Planck's law has been achieved. From now on, the energy quantum presumption is no longer the premise hypothesis of quantum theory, but the credible conclusion.
Beginning in 1900 with 1-iax Planck's hypothesis of quanta, physics has been embarked on a course which has raised serious questions about the true nature of physical reality, about the foundational assumptions and structures of science, and about the relationships between physical reality and physical theory. In particular, attempts to give a physical interpretation to quantum theory seem to result in "pictures" of nature which are paradoxical. A subatomic entity is described by the theory as exhibiting the properties and behavior of both particle-like phenomena and wavelike phenomena. Since it seems unreasonable that a single entity could be both a point-like mass and a wave spread out through a region of space, quantum theory would seem to be less than satisfactory or less than complete at the interpretational level. The purpose of this dissertation is to investigate the underlying causes of this paradox. The dissertation proceeds by reviewing the development of quantum theory and the emergence of the paradox. Next, the problem of physical interpretation is examined and several of the more significant existing interpretations are discussed and analyzed. Finally, the foundations of science and the general structure of scientific theory are examined in a search for the origins of the paradox. As a result of these investigations and analyses, it is concluded that the paradoxical nature of the physical interpretation of quantum theory is the consequence of certain paradigms and preconceptualizations about physical reality which have been incorporated into the theory at the foundational level. These fundamental assU14ptions produce, within quantum theory, a forced marriage of the plenum and atomic views of physical reality. They also produce an ambiguity with respect to the nature of causality which is charaeteristic of the theory. These problems are reflected in the mathematical formalisms and physical concepts of the theory as well as in its metaphysical foundations. Lastly, methods of resoling the paradox are discussed. It is argued that a successful solution is possible, but that it would involve the creation of a new metaphor-an extension of the present language--which would lead science to a deeper, subquantum level in terms of which the present paradox would vanish.