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The Solutions to Hard Problems about the Speed of Probability Wave
Now we have a try to solve those two hard problems about the speed of probability wave delivered in the first chapter with the new conception of “electric wave” and the “Chen’s Physical Model of elementary particle”.
1. The range of velocity of 0 < v < c is just the character of movement of spherical electromagnetic wave. (For details, please see my article of “Research on the Root of Special Relativity”.)
As a whole, spherical electromagnetic wave doesn’t demonstrate wave characteristic. It demonstrates particle characteristic only.
Wave is the wave characteristic of electric interaction, not the wave characteristic of the particle of matter state 1 such as electron itself. The “wave” and the “particle” are different independent things. It’s unnecessary for the speed of “electric wave” “u” to be in conformity with the moving speed of the particle “v”.
A vivid analogy: A boat moves on the water and activates water wave. The water wave and the boat are different independent things. It’s unnecessary for the speed of water wave to be in conformity with the moving speed of the boat.
2. The Chen’s physical model for a released photon is “a section of electromagnetic wave travelling in straight line”, “a section” is from the angle of “particle” while “electromagnetic wave” is from the angle of “wave”. Of course v = u = c. Perfect conformity. Notice, at this moment, “u” changes to be the speed of electromagnetic wave rather than the speed of the “electric wave”.
Addition:
In QM, for a free particle, ︱ Ψ ︱² = ︱ A ︱², A is a constant. It means the probability of presence of the particle is the same in the whole space. It’s not understandable. Even it’s not in conformity with fact. Now we have a try to employ the conception of “electric wave” explain it exactly.
Assume a free particle or say ideal neutral particle move relative to another free particle or say ideal neutral particle, no“electric wave” would be activated.
Ψ = 0, Ψ* = 0, ΨΨ* = ︱ Ψ ︱²= 0.
c∫0→+∞︱ Ψ ︱²d 𝛕 = 0
As illustrated ahead, the real physics meaning of “probability density” ︱ Ψ ︱² in QM should be to describe the electric force. The above equation can be interpreted as: for a free particle or say ideal neutral particle, the electric force it subjected should be zero, the same in the whole space.
The Chen’s physical model of elementary particle and the conception of “electric wave” can be in perfect consistent with Duc de Broglie’s original idea of “γ = E / h, while λ = h / P”.
The old flawed conception of probability wave should be given up.
QM should be the science to research the wave characteristics of electric interaction, or say, wave function should be to describe “electric wave”.
Liqiang Chen
陈力强
Pig Head Committee USA
Nov 26, 2025