The idea of the matter-wave dualism is very old. Actually De Broglie himself was strong supporter of non-zero mass of photon, what means that from his point of view, not only all the mass particles have a wave associated with them (De Broglie wave), but all the waves (photons) have something with mass associated with them (see, for example [1]). I am trying to infer some new ideas from the following hypothesis: any matter is simultaneously particle and wave. How to describe it mathematically is a difficult problem and probably such mathematical formalism does not exist yet. However, some interesting ideas may be inferred from the mere fact of such duality. The most obvious is the mass of photon - it should have a mass, despite it is clear that it is very, enormously small. However, this fact will instantly explain the quantization of the light absorption - the light is quantized because it is countable very much like any other particle.
The easiest phenomenon which would be possible to predict has already an analog in nuclear physics. This is Ramsauer Model for cross-sections of different events (like nuclear fission) [2]. According to this result, the smaller the energy of neutron, the better his chances to start fission, what is consistent with the quantum mechanics idea of De Broglie wave around the neutron. A similar contrary to usual sense behavior is observed in Ramsauer-Townsend effect - at certain low energy of electron the gas in the chamber becomes transparent (the De Broglie wavelength is around the mean free path for electrons). For future use the ultracold neutrons with De Broglie wavelength of 10 A are supposed to be generated in new sources [3]. So the idea of finding a phenomena, reciprocal to phenomena well known for light but being applied to matter wave considered as the main part of the wave-matter particle is appealing.
Some research groups are already observing for matter waves the phenomena, exactly like those previously described for light. For example, the rotation of particle beams in space without external fields was described in [4]. Authors correctly described the behavior as impossible from classical point of view for electrons (particles), easily observed for photons (wave) and now observed for electrons but created by the De Broglie part of electrons (wave part of the matter). This phenomena confirms the reciprocity idea: the phenomenon exists for pure waves (photons), thus it must exist for matter waves (in the case the wave part of the particle is essential, as for the case of ultra slow electrons [4])
The unusual example of the appearance of the wave properties of the particles (electron) would be
observation of the cathodoluminescence in some compounds for extremely low energies of electrons (1-3 eV). Usually the cathodoluminescence is easily observed and important phenomenon for energies of few kV. At this region the electron is working essentially as a particle only and simply creating excitation through hit of particle. But for usual light the luminescence is easily observed for energies of few eV - because they are waves. Even despite charge interactions, if the electron is working as a wave (reciprocity principle), the resonances may be predicted for very low energy electrons in the range 1-3 eV. The idea is that electron in this region has the essential wave admixture. Despite the De Broglie wavelength is still much smaller compare to light with this energy, it may be enough to be absorbed as a wave, not interact as a particle. In this situation the sharp in energy resonance is expected for the electron created luminescence due to the interaction of electron as wave, not as a particle.
References.
1. https://arxiv.org/pdf/hep-ph/0107122.pdf
2. https://en.wikipedia.org/wiki/Neutron_cross_section
3. https://physicsworld.com/a/neutrons-for-the-future/
4. https://iopscience.iop.org/article/10.1088/1367-2630/ab152d/pdf
Thursday, September 26, 2019
Thursday, September 5, 2019
Neutron enigma and Einstein's second coefficient: may the smaller lifetime of ultra-cold neutrons be explained by the induced decay (similar to fission process and lasers)?
Modern physics is quickly developing the unified theory of wave-particle mathematical formalism. While the exact equations, which would describe in one limit the particle (pure mass, Newton-Einstein mechanic) and in another limit the pure wave (Maxwell equation) are far from completion, the preliminary use of such concept may allow to explain some modern phenomena and predict new.
The idea is: any matter is neither particle nor wave but both. It means that it has two intrinsic parts: matter and wave, considered for some approximation as a sum. The closest modern approach would be consider De-Broglie wave as material and consider any particle as consisted of two parts: usual particle (inertial mass) and De-Broglie wave. In this case the photon must have a finite (despite enormously small) mass and any moving particle has the added energy associated with dragging De-Broglie wave. Photon is almost pure De-Broglie wave and stopped classical particle (neutron) is almost pure particle. However, even the highest energy gamma-quantum has some finite mass inside and even ultra-cold neutron has some energy associated with De-Broglie wave - the matter and wave are inseparable in principle.
In this case the idea of reciprocity of physical phenomena may appear: each phenomena for particles has the similar phenomena for waves and vice versa. Photon - almost pure wave - has Einstein's first and second coefficients associated with him. Any particle like neutron must have reciprocal coefficients associated with De-Broglie part of particle. First coefficient A is responsible for spontaneous decay of excited atom and the corresponding coefficient is simply spontaneous decay of neutron. Einstein's second coefficient is responsible for induced decay of excited atom (lasers) and the corresponding second coefficient for neutron would be the induced decay of excited nucleus (another neutron).
It is interesting that such idea is already applied to fission process, where the energy dependence of the cross-section of fission induced by neutron has in excellent agreement with squared De-Broglie wavelength (at least at lower energies and without consideration of resonances). From the wave-particle unification point of view the fission process is laser like process but for nuclei. It may be even possible that in fission the created neutrons have exactly the same De-Broglie wave as the initial neutron, but since in neutrons contrary to photons the De-Broglie part of matter is small, the neutrons as a whole are not looking exactly coherent as created photons in laser. The matter part of neutrons is obviously not synchronized and de-coherent. And the cross-section of both processes is governed by the similar equations:
Ramsauer model for fission: σ(E)~π(R+λ)2~ λ2 for small energies
Einstein's second coefficient:
For the case of neutron enigma it means that the effect of deviation of lifetime for neutrons would be even more pronounced in the case of ultra-ultra cold neutrons and it will also strongly depend upon the concentration of neutrons (very much like for efficient nuclear explosion the critical mass is necessary or critical density).
Hopefully the future experiments concerning the neutron enigma will involve more and more slow neutrons and this predicted effect will be observed.
Einstein's second coefficient was derived using perturbation theory by Dirak (P.A.M. Dirac, Proc.Roy.Soc., A114, 243, 1927 "The quantum theory of the Emission and Absorption of Radiation")
Most probably exactly the same formalism may lead to the derivation of the cross-section in the case of fission process and for neutron enigma, assuming the De-Broglie wave is considered instead of photons as in the article.
That does not mean that the De-Broglie wave may be treated separately as a similar to photons (see the beginning of the blog). The idea is that particle is a sum of De-Broglie wave and particle is a very rough approximation. The real mathematical description of such matter-wave object is absent now. However, even the simplistic treatment of the particle as a sum of matter and wave may help to establish the reciprocal phenomena for both particles and waves (like the idea of existence of Einstein's second coefficient for the particles).
Modern physics is quickly developing the unified theory of wave-particle mathematical formalism. While the exact equations, which would describe in one limit the particle (pure mass, Newton-Einstein mechanic) and in another limit the pure wave (Maxwell equation) are far from completion, the preliminary use of such concept may allow to explain some modern phenomena and predict new.
The idea is: any matter is neither particle nor wave but both. It means that it has two intrinsic parts: matter and wave, considered for some approximation as a sum. The closest modern approach would be consider De-Broglie wave as material and consider any particle as consisted of two parts: usual particle (inertial mass) and De-Broglie wave. In this case the photon must have a finite (despite enormously small) mass and any moving particle has the added energy associated with dragging De-Broglie wave. Photon is almost pure De-Broglie wave and stopped classical particle (neutron) is almost pure particle. However, even the highest energy gamma-quantum has some finite mass inside and even ultra-cold neutron has some energy associated with De-Broglie wave - the matter and wave are inseparable in principle.
In this case the idea of reciprocity of physical phenomena may appear: each phenomena for particles has the similar phenomena for waves and vice versa. Photon - almost pure wave - has Einstein's first and second coefficients associated with him. Any particle like neutron must have reciprocal coefficients associated with De-Broglie part of particle. First coefficient A is responsible for spontaneous decay of excited atom and the corresponding coefficient is simply spontaneous decay of neutron. Einstein's second coefficient is responsible for induced decay of excited atom (lasers) and the corresponding second coefficient for neutron would be the induced decay of excited nucleus (another neutron).
It is interesting that such idea is already applied to fission process, where the energy dependence of the cross-section of fission induced by neutron has in excellent agreement with squared De-Broglie wavelength (at least at lower energies and without consideration of resonances). From the wave-particle unification point of view the fission process is laser like process but for nuclei. It may be even possible that in fission the created neutrons have exactly the same De-Broglie wave as the initial neutron, but since in neutrons contrary to photons the De-Broglie part of matter is small, the neutrons as a whole are not looking exactly coherent as created photons in laser. The matter part of neutrons is obviously not synchronized and de-coherent. And the cross-section of both processes is governed by the similar equations:
Ramsauer model for fission: σ(E)~π(R+λ)2~ λ2 for small energies
Einstein's second coefficient:
σ21=A21*g(λ)*(λ2)/(8π*n2)
In both cases the cross-section is proportional to λ2For the case of neutron enigma it means that the effect of deviation of lifetime for neutrons would be even more pronounced in the case of ultra-ultra cold neutrons and it will also strongly depend upon the concentration of neutrons (very much like for efficient nuclear explosion the critical mass is necessary or critical density).
Hopefully the future experiments concerning the neutron enigma will involve more and more slow neutrons and this predicted effect will be observed.
Einstein's second coefficient was derived using perturbation theory by Dirak (P.A.M. Dirac, Proc.Roy.Soc., A114, 243, 1927 "The quantum theory of the Emission and Absorption of Radiation")
Most probably exactly the same formalism may lead to the derivation of the cross-section in the case of fission process and for neutron enigma, assuming the De-Broglie wave is considered instead of photons as in the article.
That does not mean that the De-Broglie wave may be treated separately as a similar to photons (see the beginning of the blog). The idea is that particle is a sum of De-Broglie wave and particle is a very rough approximation. The real mathematical description of such matter-wave object is absent now. However, even the simplistic treatment of the particle as a sum of matter and wave may help to establish the reciprocal phenomena for both particles and waves (like the idea of existence of Einstein's second coefficient for the particles).
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