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.
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.
As we know the main results of quantum physics in 1900 Planck began to obtain mainly because of the need to describe the experimental data. Therefore, it further became necessary to obtain theoretical justifications for these results. This means to obtain proofs of these results on the basis of the basic equations of theoretical physics, i.e. equations that are obtained on the way where the right choice of results is made performing the role of the basis of the theory of thought. As is known, these problems began to be solved, taking as a basis the possibilities of the following new ideas of Bohr. That quantum physics should be considered as a generalization of classical physics. But as we know, this path led to the results of matrix mechanics. Results for which such contradiction as non-commutativity of multiplication is inherent. In this paper for obtaining proofs for the results of Planck's quantum physics the fundamental ideas in the field of scientific philosophy were taken as a basis. That is philosophy where from the very beginning for the basis of the theory of thinking the possibilities of equations of algebra and arithmetic are accepted.
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.”
[概要] 量子なる概念は, プランクの放射公式によって議論に俎上した. しかし, それは未だ単なる関数的関係にすぎず, リアルで現実的な物理的実体ではなかった. プランクの量子は現実存在ではないのである. これに対してアインシュタインは, 光量子仮説を導入することで, 量子をリアルでビビッドな存在とし, 量子は実体となった. これは, 量子を粒子として実体化することでもあった. われわれは, 本論において, このアインシュタインのアイデアと実体化の過程を詳細に追跡し, 幾ばくかの哲学的側面についての考察も行う. また, 考察の過程で波動一粒子の二重性の根源についての議論も行うこととなる. [Abstract] The concept of quantum came up in the discussions by the Planck's formula for radiation. However, it was a merely a functional relation, but not physical substance that is the reality. Planck's quantum does not have a real existence at all. In contrast with this, Einstein proposed the hypothesis of the light quanta as a real and with a vivid existence. Thus the quantum becomes a physical substance. This is also a substantiation of quantum as particles. We will see the process of this substantiation and the developments of the Einstein's idea in this article in details and have a few philosophical discussions about this process. We will see and also argue about the roots of the wave-particle duality.
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.
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.