Particle-wave dualism: clearly

"If you think you understand quantum theory ... then you don't understand quantum theory." - Feynman R., lectures "The nature of physical laws" (1964), ch. 6.

This and similar statements about the incomprehensibility of the laws of quantum mechanics have always irritated me. Corpuscular-wave dualism , the properties of quantum particles to behave like waves and like particles - is it really impossible to understand them clearly, to see not as the behavior of mathematical solutions, but with your own eyes? In this review, I will present results challenging this mysticism.

Derivation of the de Broglie ratio

Louis de Broglie knew the ratio$$$E = h\nu$ (Planck's formula) and$$$E_0=m_0c^2$ (equivalence of mass and energyin the special theory of relativity) where$$$m_0$ - rest mass, i.e. mass in its own frame of reference.

According to the theory of relativity, there is no absolute time, and each point in space has its own - the fourth coordinate t. Own time, as Louis de Broglie reasoned, is like a personal watch. Both the person and the electron have them. What does it mean?

He suggested that each particle has an internal periodic process (tick-tock with frequency), which serves as a measure of its own time [1]. This innermost process with a frequency in its own frame of reference allows us to link two energy formulas

$$

$$E_0=m_0c^2=h\nu_0$$

A stationary observer perceives an oscillatory process $$$\nu_0$ particles flying with a speed$$$v$ at point$$$x$ like

$$

$$\psi=\exp(2\pi i\nu t)$$

The transition to the particle reference frame gives in the exponent

$$

$$\underset{\nu}{\underbrace{\nu_0\sqrt{1-\frac{v^2}{c^2}}}}\cdot\underset{t}{\underbrace{\frac{-t_0+\frac{v}{c^2}x}{\sqrt{1-\frac{v^2}{c^2}}}}}=\frac{v}{c^2}x-\nu_0t_0$$

– , $$$\exp(2\pi i\nu_0t_0)$

$$

$$\psi=\exp(2\pi i(\frac{v}{c^2}x-\nu_0t_0))$$

,

$$

$$\psi(x,t)=\exp(2\pi i(\frac{m_0c^2}{h}\frac{v}{c^2}\cdot x-\frac{E}{h}t_0))=\exp(2\pi i(\frac{m_0v}{h}x-\frac{E_0}{h}t_0))=\exp(\frac{i}{\hbar}(p\cdot x-E\cdot t))$$

, $$$v$

$$

$$\lambda=\frac{h}{p}$$

$$$p=mv$ – , $$$h$ – .

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It should be noted that similar ideas were discussed in Russian science much earlier, for example, in the book of the Tomsk scientist B.N. Rodimov "Self-oscillatory quantum mechanics" [3]. He also designed a particle-wave. Unfortunately, his ideas were not picked up.

Literature

1. L. de Broglie "Waves and Quantums" 93 178-180 (1967)
2. Robert Brady and Ross Anderson. Why bouncing droplets are a pretty good model of quantum mechanics. 2014.
3. B.N. Rodimov “Self-oscillatory quantum mechanics”, Tomsk 1967.