On the velocity of waves in Quantum Mechanics

Huang Zhi-xun

Newton mechanics is great, Newton's contribution is indelible. But from Newton's classical mechanics, the definition of velocity (=) must mean that this physical parameter is a vector, so "negative velocity" only means the opposite direction of motion, no other meaning. It is difficult to understand negative velocity within the framework of classical mechanics. However, wave is a special form of material motion, wave mechanics has a unique method and meaning, and its concept and connotation are significantly different from classical mechanics. For example, wave velocity (whether phase velocity or group velocity) is a scalar quantity. "Negative wave velocity" does not mean that the direction of motion is reversed, but a special phenomenon that does not accord with causality from the surface view. In any case, research in recent decades has shown that negative wave velocity is not only theoretically possible, it has also been repeatedly shown to exist experimentally. Moreover, negative wave velocity is a special form of superluminal speed; The wave with negative velocity is the advanced wave. It corresponds to the leading solution of the basic equation of electromagnetic field and electromagnetic wave. The past practice (discarding the advanced solution) is wrong! As for causality, scientists have provided a new definition and interpretation. In short, both wave mechanics and quantum optics take a different approach from classical mechanics. This paper points out that it is unusual for the 2022 Nobel Prize in Physics to be awarded to Alain Aspect and two others, since Aspect's experiments on the Bell inequality were completed in 1982, Which still stands today as a crucial experiment that proved Einstein's EPR paper wrong and quantum mechanics (QM) correct. Aspect's award in 2022 showed that mainstream physical community had been forced to accept that quantum entanglement existed and that the "light-speed limit" theory of SR was a mistake. This paper discusses the proposition "negative characteristic motion of electromagnetic wave" put forward by the author in 2013, pointing out that it is an inherent physical phenomenon reflecting symmetry in nature. In this paper, the faster-than-light motion of waves found in the near-field of antennas is discussed. In addition, the realizability of "time travel" is also discussed.

Huang Zhi-xu

The velocity is a macroscopic concept. The question what is the meaning of velocity in Quantum Mechanics( QM) ,this problem itself is inno answersituation. In the semi-classical theory,for the reconstruction of the velocity definition,we have v→= ▽S / m[m is the particle's mass and ψ = Aexp( j S /h) ]. This method builds the relation of velocity and wave function,but it is not the necessary and useful concept of wave's speed. The velocity of light in vacuum is a common basic constant of physics,however QM also need this parameter obviously,i. e. the new wave mechanics is on need of this physical quantity.The process and result of people's practice show that,scientist has intended to bring forth in the measurement of c with very high accuracy does stand out,if he used the scalar equation c = fλ. Modern physics maintain that the wave velocities( phase velocityvp、group velocity vg) are scalars,not vectors.The wave has its special scientific features; the regular pattern is different from the Classical Mechanics( CM). It needs supports of the QM,but it is not identical with the serious QM. Now,it has not only a theory that can explain the wave problems perfectly,so it is support by the classical physics and quantum physics.The quantization process of EM fields explains the particle-wave duality mathematically. Post quantization,from the EM fields we obtained the photons. But scientist still is puzzled by a difficult question:what is photon. As the common knowledge,the matter waves of photon still a paradox in physics. In addition,the electronic probability waves corresponding the Schrdinger equation,but people says the photonic probability waves have not that wave equation. In other words,the physical meanings of matter wave's phase velocity are not clear,and why the phase velocity of de Broglie waves is faster-than-light,many explanations will be needed.Many instances similar to these examples make the particle-wave duality still the magic ghost in modern physics. Finally,the study on negative wave velocity( NWV) in recent years has a great deal of experience on wave sciences,and bring the new chance on theoretical thinking.

Yusuf Ziya Umul

Qiong-Gui Lin

In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet. In classical physics there is no precise counterpart to the center-of-probability velocity of quantum mechanics, in spite of the fact that there exist in the literature at least eight different velocities for the electromagnetic wave. We propose a center-of-energy velocity to describe the entire motion of general wave packets in classical physical systems. It is a measurable quantity, and is well defined for both continuous and discrete systems. For electromagnetic wave packets it is a generalization of the velocity of energy transport. General wave packets in several classical systems are studied and the center-of-energy velocity is calculated and expressed in terms of the dispersion relation and the Fourier coefficients. These systems include string subject to an external force, monatomic chain and diatomic chain in one dimension, and classical Heisenberg model in one dimension. In most cases the center-of-energy velocity reduces to the group velocity for quasi-monochromatic wave packets. Thus it also appears to be the generalization of the group velocity. Wave packets of the relativistic Dirac equation are discussed briefly.

Gennaro Auletta, Gino Tarozzi