Author(s)

Takahisa Okino

Applied Mathematics Department, Faculty of Science & Technology, Oita University, Oita, Japan.

The relation of matter wave, which is well-known as a hypothesis proposed by de Broglie in 1923, gave basis for establishing the quantum mechanics. After that, experimental results revealed that a micro particle has a wave nature. However, the theoretical validity of the relation itself has never been revealed since his proposal. Theoretical basis that a micro particle has a wave nature has been thus disregarded in the unsolved state. The diffusion equation having been accepted as Fick’s second law was derived from the theory of Markov process in mathematics. It was then revealed that the diffusivity D depends on an angular momentum of a micro particle in a local space. The fact being unable to discriminate between micro particles in a local space resulted in having to accept the existence of minimum time t₀ (>0) in the quantum mechanics. Based on t₀ and D obtained here, the theoretical validity of relation of matter wave was confirmed. Denying the density theorem in mathematics for time in physics indicates that the probabilistic interpretation is essentially indispensable for understanding the quantum mechanics. The logical necessity of quantum theory itself is thus understandable through introducing t₀ into the Newton mechanics. It is remarkable that the value of t₀ between 1.14×10^-17 s ≤ t₀ ≤1.76×10^-14 s obtained here is extremely larger than that of the well-known Planck time t_p=5.396×10^-44 s.

Quantum, Diffusion Particle, Matter Wave, Planck Time, Minimum Time

Okino, T. (2022) Remarkable Findings in Fundamental Theory of Quantum Mechanics—Matter Wave and Discrete Time in Physics. Journal of Modern Physics, 13, 256-266. doi: 10.4236/jmp.2022.132017.