Electron-assisted fusion
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You mean Rabi model, or no?
The quantum Rabi model: solution and dynamics
Qiongtao Xie, Honghua Zhong, Murray T. Batchelor, Chaohong Lee
(Submitted on 2 Sep 2016 (v1), last revised 26 Sep 2016 (this version, v2))
This article presents a review of recent developments on various aspects of the quantum Rabi model. Particular emphasis is given on the exact analytic solution obtained in terms of confluent Heun functions. The analytic solutions for various generalisations of the quantum Rabi model are also discussed. Results are also reviewed on the level statistics and the dynamics of the quantum Rabi model. The article concludes with an introductory overview of several experimental realisations of the quantum Rabi model. An outlook towards future developments is also given. -
Here are some:
- electron is elementary charge, what means it has electric field proportional to 1/r. Additionally, it is a magnetic dipole (tiny magnet), what also means singular configuration of magnetic field (idealized - it can be regularized), ...
Indeed, an electron behaves like a particle in some contexts. It also behaves like a large wave at lower energies, as evidenced by electron diffraction experiments and by the fact that the de Broglie wavelength (a function of energy) is what determines whether an electron probe “sees” an atom as a whole, one of the individual nucleons, or a quark within a nucleon. At lower energies, the electron interacts with larger things, and at higher energies, it interacts with smaller things. A diffraction grating is very large indeed. There is no classical analog to this kind of behavior that I am aware of. These things cannot be understood in terms of billiard balls alone.QuotePlease give finally a single argument that this elementary charge is objectively smeared over a relatively huge volume ...
Please give finally a single argument that the elementary charge is not objectively smeared over a relatively huge volume. In its wave-like behavior, it sure seems to be. What about the elementary charge would preclude this? -
As my old physics teacher said. ' Is an electron a wave or a particle? Maybe, but the key fact is...it's always an electron.'
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What I am asking is if it is a fundamental model - if you can prove that there cannot be a hidden electron trajectory behind it?
It's possible there's a hidden trajectory. I am actually quite sympathetic to the de Broglie-Bohm theory, to the extent that I understand it. But if you go for "100 percent particle" as a description of the electron together with perturbations of some related field, you must explain the phenomenon I was describing relating to the de Broglie wavelength and the size of target that the electron interacts with, mentioned above. And even then you will not necessarily get your electrons to remain confined between two protons in the core of the sun, for (1) this is not to my knowledge the kind of behavior we see in plasmas and (2) in the solar core there are many particles interacting with one another and disturbing the trajectories of one another.But we're not there yet. You still need to show that the electron is best described as a point particle and has a hidden trajectory.
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You still need to show that the electron is best described as a point particle and has a hidden trajectory.
Now, there is a tall order! How about the probability of materialization is maximally distributed in between the two protons? If I recall correctly that is consistent with the Copenhagen interpretation.
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Now, there is a tall order! How about the probability of materialization is maximally distributed in between the two protons? If I recall correctly that is consistent with the Copenhagen interpretation.
It's a tall order indeed. It's one that Jarek has signed up for with his classical interpretation of the electron and its trajectory. I like the probability distribution approach better, even though I am not sympathetic to the Copenhagen interpretation. But there's still the other confounding factors, such as all of the other things going on in the solar core, where you have other sources of charge (positive and negative) that will deflect our electron, as well as photons zipping around and scattering. -
You still need to show that the electron is best described as a point particle and has a hidden trajectory.
I gave you lots of arguments, like behavior in low and high energy scatterings, in Penning trap (low energy "classical atom") ... but you still didn't give a single one that this elementary charge is objectively smeared over e.g. a micrometer size Rydberg molecule.
That a feature of our (imperfect) model is indeed a fundamental feature of nature, like saying that thermodynamics works and it uses smooth rho(x) function so atoms are literally smeared into uniform density of vacuum. No, smoothing/averaging into densities is just what we often do in our effective models.Regarding de Broglie's wavelength, it is the base of pilot wave view ( https://en.wikipedia.org/wiki/Pilot_wave ) which has classical (Couder's) analogues ( https://en.wikipedia.org/wiki/Hydrodynamic_quantum_analogs ) :
External Content www.youtube.comContent embedded from external sources will not be displayed without your consent.Through the activation of external content, you agree that personal data may be transferred to third party platforms. We have provided more information on this in our privacy policy.So it just says that the wave-particle duality does not mean magically switching between these two natures, but being both simultaneously: being a corpuscle with a coupled "pilot" wave.
The corpuscular part performs some complex trajectory - it is not just a classical trajectory as it is additionally affected by the pilot wave e.g. for interference or orbit quantization.
The coupled wave leads to wave-like behaviors, for example interference (corpuscle goes a single trajectory, its 'pilot' wave goes all trajectories - affecting path of the corpuscle), or orbit quantization (the coupled wave has to synchronize with the field to get standing wave to avoid synchrotron radiation).Effectively, atom in equilibrium can be well described by QM wavefunction: as the standing wave or average over trajectories.
But there is still a hidden trajectory behind it, and there are many arguments that very low angular momentum trajectories are dominating (e.g. electron capture).However, this QM picture requires stabilization to dynamical equilibrium, so it has a problem with dynamical situations like scatterings.
Here is a nice figure for approaching the (known!) experimental values with quantum approximations (year in a bracket) for kind of a simplest situation: cross-section for hydrogen ionization with low energy (<600eV) electrons from Gryzinski's book:Another non-equilibrium situation is fusion ... sure we should remember that electrons still have wave natures there, but considering trajectories of their corpuscular nature drastically changes the situation: these trajectories can theoretically remain between the two collapsing nuclei - screening the Coulomb barrier, making possible fusion below GK (including our Sun - "because tunneling" is insufficient explanation for the corpuscular part).
QuoteBut there's still the other confounding factors, such as all of the other things going on in the solar core, where you have other sources of charge (positive and negative) that will deflect our electron, as well as photons zipping around and scattering.
Could you elaborate why there is a problem here with electron being simultaneously both wave and corpuscle? -
The major physical process that is going on in LENR is marked when atoms, electrons and photons pack themselves together into a cavity, where they eventually become entangled. The cavity keeps these items close enough together for a long enough period for the electrons to become entangled with many photons.
The cavity is of a size where the uncertainty principle adds to the confusion of cavity processes as atoms, electrons and photons interrelate.
This right sized cavity acts like a quantum mixer to blend matter and energy together in ways that usually don't occur.
According to the Rabi model, when an atom interacts with light in a cavity, and they reach a state of equilibrium, the atom becomes "dressed" with photons. Because this takes place at the quantum scale, the system is, in fact, a superposition of different states—the excited and unexcited atom—with different numbers of photons.
As the density of electrons and photons continues to increase, more and more photons become entangled with the electrons. A single electron can have tens of photons connected to it through entanglement.
The electron is termed to be deeply dressed with photons. The electron/photon system exists in a superposition of states where the electron becomes a boson by assuming the character of the photon and the spin of the electron is indeterminate through a large range of possibilities. The photons add together their spins to the electron/photon mix and the electron’s spin can be as low as .1 to as high as 10,000 and beyond.
The superposition of these states is like a spinning roulette wheel with many possible outcomes. The little red ball of outcomes circles the wheel of potential until it eventually drops into one of the many possible slots of outcomes when potential becomes fact and where causation asserts itself onto reality.
This is what super-radiance is all about. When possible outcomes build and build, when electrons, photons and atoms can pack together in unconstrained density, when the press of possible outcomes becomes large enough, when the quantum wheel stops on the most massive result and the super spin condition is actualized, when the power of the magnetic spin field is powerful enough to be felt by the far field, then the electron/photon condensate will affect its environment in a state of decoherence when potential becomes reality.
What goes on inside that cavity, the mix of potential and reality, the real and unreal, the roiling cauldron of possibilities is not yet understood by science and this confusion of potential and actuality is what those who would understand LENR must eventually face.
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The presence of large amounts of hydrogen inside the core of the sun is counterintuitive. The core of the sun should hold heavy elements like iron and nickel as has been assumed for the other planets. Iron will not produce a fusion reaction. Has someone…
Revised ? I think, the sun is as much observed as our earth, by specialists.
Not only this https://en.wikipedia.org/wiki/Solar_core
tells You, that solid iron can not exist under the circumstances, which the solar core and pressure offer.
It is too hot for solid iron, for sure, and the pressure will even produce more heat and add it to the existing 15 million degrees in some way.
The reason, why iron cannot be created is the immense amount of hydrogen, which is still available in the sun to allow the standard fusion, by the way, the simplest fusion, we now until now.
But, in fact, this fusion process is much more complicated, than we might think.
Appearently there are also fission procedures taking place, both resulting in an energy(heat) excess.
So the sun is in some kind of controlled fusion balance, in its core, as long as there is enough hydrogen, only this will be substance to fusion, because the
necessary energy for that is realtively low, compared to the following elements in the periodic table. As already posted in here, iron cores inside stars are the indicator for the last eon of a star's live, no matter how it will die in the end.
If the star explodes in a supernova, those iron could already have been created inside the outer areas of the star, therefore the supernova would simply spit out a lot of iron into the galaxy. This can be measured, it is called metalicity. It is an indicator, for the age of a galaxy, for example.So I doubt, that anyone should revise the ongoing physics behind the sun-cosmology. Our experience, which we collected by obvserving the sun, helped us to unserstand, how to observe other stars, and appearently the observed results met the theoretical calculations.
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IMHO....The temperature at the core no doubt allows heavy nuclei (in the supercritical fluid), at least up to iron and other nuclei not susceptible to fission. So Axil has that right. There is even the possibility of a moderately sized neutron core-- but that cannot be too large, in order to maintain known gravitational parameters--- and also to avoid a central black hole.
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I gave you lots of arguments, like behavior in low and high energy scatterings, in Penning trap (low energy "classical atom") ... but you still didn't give a single one that this elementary charge is objectively smeared over e.g. a micrometer size Rydberg molecule.
My position is not that the elementary charge is smeared over the electron probability distribution. My position is one of agnosticism, which is to a large extent the mainstream position. You are the one seeking a fundamental theory of what is going on at a deeper level. You, then, assume the burden of showing that competing alternatives, such as the possibility that the elementary charge is smeared over the probability distribution, are at odds with the experimental data. What I take away from the experimental data you refer to is that the electron sometimes behaves like a particle, which was never in doubt.QuoteRegarding de Broglie's wavelength, it is the base of pilot wave view ( en.wikipedia.org/wiki/Pilot_wave ) which has classical (Couder's) analogues ( en.wikipedia.org/wiki/Hydrodynamic_quantum_analogs ) :
I find the de Broglie–Bohm theory interesting and thought-provoking. But on this topic, I would be interested in knowing how a particle with a pilot wave can explain the fact that the electron at slow speeds interacts with large targets and at higher speeds interacts with smaller targets. That does not sound like something a billiard ball would do.Quote(including our Sun - "because tunneling" is insufficient explanation for the corpuscular part).
You have yet to make a good case that tunneling is insufficient. When we last discussed this I made the point that there were going to be calculations invoking tunneling that quantitatively explain the fusion rate in the solar core which would contradict the simple calculation you attempted to use to demonstrate that tunneling is inadequate. You were going to take a look at these calculations. Arguing that tunneling is insufficient outside of the context of those calculations is to argue against a straw man position.QuoteCould you elaborate why there is a problem here with electron being simultaneously both wave and corpuscle?
I was not arguing that an electron does not exhibit both wave-like and particle-like behavior. My point was that even if one allows that electrons in the plasma at the solar core behave like a point charges, you will still have difficulties showing that they can produce screening through confinement along a one-dimensional path between two protons. This is because the solar core is a very dynamic, many-body system, and there will be plenty of other charged particles and photons to deflect the electron out of its putative confinement. -
My position is not that the elementary charge is smeared over the electron probability distribution. My position is one of agnosticism, which is to a large extent the mainstream position. You are the one seeking a fundamental theory of what is going on at a deeper level. You, then, assume the burden of showing that competing alternatives, such as the possibility that the elementary charge is smeared over the probability distribution, are at odds with the experimental data. What I take away from the experimental data you refer to is that the electron sometimes behaves like a particle, which was never in doubt.
As I have written, there are plenty of experiments directly testing that electron is practically a point - e.g. scattering, Penning trap ... is there a single one showing that this elementary charge is objectively smeared?
And I emphasize that electron not only behave like, but just objectively is simultaneously (wave-particle duality):
- a corpuscle (indivisible elementary charge) traveling through some complex trajectory (including interaction with the pilot wave), and
- a coupled wave, generated e.g. by some intrinsic periodic process (like in breathers), or maybe just precession of spin - behavior of this wave is directly described by QM.How do you understand the wave-particle duality? Is particle switching between these two natures? Under what conditions?
Or maybe it is just simultaneously both - what means that there is still a hidden trajectory hidden behind quantum waves, probability clouds.Quote
I find the de Broglie–Bohm theory interesting and thought-provoking. But on this topic, I would be interested in knowing how a particle with a pilot wave can explain the fact that the electron at slow speeds interacts with large targets and at higher speeds interacts with smaller targets. That does not sound like something a billiard ball would do.
You are now talking about scattering scenarios - Gryzinski was the master at, scattering has turned him away from quantum description as unsatisfactory for such dynamical situations - just see his papers: https://scholar.google.pl/scholar?hl=en&q=gryzinski
I don't resemble he was using pilot wave in his scattering calculations (beside orbit quantization), still getting good agreement with experiment - even for small energy its influence is nearly negligible. Wave nature is crucial e.g. for interference, or to find equilibrium to form an atom: resonance of the wave nature (orbit quantization).
- for high energy scattering see his 1965 papers, this lecture: http://gryzinski.republika.pl/teor3ang.html
- low energy scattering is more complex, e.g. incoming proton is modifying trajectory of electron of target hydrogen in Helbig-Evenhart resonances.
Generally Gryzinski uses effective picture of oscillating electric multipoles for atoms for low energy scattering, e.g. the Ramsauer effect - reduction of cross section for low energy scattering. See http://gryzinski.republika.pl/teor6ang.html
fig.4 there: "Cross section of Argon for small angle scattering of low energy electrons: points represent experimental data, solid lines are the
results of theoretical calculations at various assumptions on the character of the asymptotic form of the electrical potential of the
atom; n is the power with which electric field decreases with the distance from the atom. The observed decrease of the cross section
at very small electron velocities is a characteristic feature of the oscillatory interaction between the scattered particle and the scattering center.":\
Regarding tunneling, the corpuscular part of the particle (shape-preserving construct of the field: a soliton) needs a concrete trajectory, forces - maybe the pilot wave could give it some extra kick counted as tunneling in solar core ... I don't know, but if one believes in CF, tunneling is definitely not sufficient.
QuoteI was not arguing that an electron does not exhibit both wave-like and particle-like behavior. My point was that even if one allows that electrons in the plasma at the solar core behave like a point charges, you will still have difficulties showing that they can produce screening through confinement along a one-dimensional path between two protons. This is because the solar core is a very dynamic, many-body system, and there will be plenty of other charged particles and photons to deflect the electron out of its putative confinement.
If we would like to explain CF, there is needed a mechanism requiring low temperatures - not to drastically change energy balance of the sun.
And stabilization of molecular bond (also possible with electron traveling on nearly a line joining two nuclei) seems such factor present while hypothetical CF, but not the solar core.
However, there are electrons flying everywhere in solar core, they are attracted by protons - it seems there is a non-negligible chance that it will accidentally find a trajectory between the two collapsing nuclei.
Just this probability is lower than for stabilized molecular bonds, however, less electron assistance is needed as the temperature is much larger.
Sure, there are needed solid calculations here - I would like to reach some day, but it's hard, not a one-man task ...ps. picture from Gryzinski's book interpreting crystal as having tetrahedral electron trajectories:
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Also, natural helium concentration in rocks can reach 7% ( en.wikipedia.org/wiki/Helium ) - is alpha decay sufficient to explain such huge concentrations?
Assuming the helium does not escape, this question could devolve to whether minerals can originally have levels of alpha decaying isotopes at a level of 7% or more? I imagine the answer is "yes".
Another factor may be that some minerals may have a high capacity to sequester helium as it "passes through".
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As I have written, there are plenty of experiments directly testing that electron is practically a point - e.g. scattering, Penning trap ... is there a single one showing that this elementary charge is objectively smeared?
And I emphasize that electron not only behave like, but just objectively is simultaneously (wave-particle duality):
- a corpuscle (indivisible elementary charge) traveling through some complex trajectory (including interaction with the pilot wave), and
- a coupled wave, generated e.g. by some intrinsic periodic process (like in breathers), or maybe just precession of spin - behavior of this wave is directly described by QM.How do you understand the wave-particle duality? Is particle switching between these two natures? Under what conditions?
Or maybe it is just simultaneously both - what means that there is still a hidden trajectory hidden behind quantum waves, probability clouds.
I think we're talking past one another to a certain extent. You've made the point that sometimes an electron behaves like a particle, a point that I've accepted from the start of our conversation. I made the further point that it behaves like a wave, one that you appear to accept. You have gone beyond this minimal picture and said that not only does the electron act like a particle sometimes, but also (1) it is a point particle, (2) its elementary charge cannot be smeared over the probability distribution. Both of these statements go beyond what I understand to be the experimental evidence into speculation about things that have not yet been determined for sure. This is natural enough, for you are seeking out a fundamental theory, one that looks behind the veil of quantum mechanics to try to understand things as they really are. I have responded by asking whether we know that the elementary charge cannot be smeared over the probability distribution. You have then responded by asking me to prove that it can. That discussion will get nowhere because we're talking about stuff that goes beyond the experimental evidence, and my position is not that the elementary charge is smeared over the probability distribution. How about we leave that discussion there, and revisit it once one of us has more details to add to that picture.I understand wave-particle duality in vague, qualitative terms. There are experiments that present one picture of things and other experiments present another picture of things, roughly analogous to what we experience in our macroscopic lives as "waves" and "particles". I am not particularly wedded to electrons being particles. It seems clear that they have wave-like behavior in certain contexts. That is about as much as I know. I am open to electrons being point particles riding on pilot waves. I am also open to the elementary charge being smeared over the probability distribution.
You are now talking about scattering scenarios - Gryzinski was the master at, scattering has turned him away from quantum description as unsatisfactory for such dynamical situations - just see his papers: scholar.google.pl/scholar?hl=en&q=gryzinski
Both CF and fusion in the solar core have one very important thing in common: they are dynamic situations.Regarding tunneling, the corpuscular part of the particle (shape-preserving construct of the field: a soliton) needs a concrete trajectory, forces - maybe the pilot wave could give it some extra kick counted as tunneling in solar core ... I don't know, but if one believes in CF, tunneling is definitely not sufficient.
I'll just mention it again at the risk of tiring people that CF doesn't require us to adopt fusion as a hypothesis. So fusion as a result of tunneling is not necessarily relevant to understanding CF. If one believes that there is fusion going on, I suppose that will be a different matter. -
Regarding: "its elementary charge cannot be smeared over the probability distribution"
You'r wrong...
See that yellow colored field there, that is a charge distribution.
from this summary
physics.aps.org/articles/v9/43
"To explain their results, the researchers conducted first-principles calculations and found that a water molecule can occupy six symmetrical orientations in a beryl channel, in agreement with the known crystal structure. A single orientation has the oxygen atom roughly in the center of the channel, with the two hydrogen pointing to the same side (like a “<” symbol) toward one of the channel’s six hexagonal faces. Other orientations point to other faces, but are separated from each other by energy barriers of around 50 meV. However, these barriers don't stop the hydrogen from tunneling among the six orientations and thereby splitting the ground-state energy into multiple levels. The energy differences among these levels were consistent with the seven peaks observed in the neutron scattering data, the researchers found."
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Returning to Earth, there is a nice paper saying that tritium production from volcanoes can be >10000x larger than estimation for fission:
Although my working assumption is that induced fission plays part of LENR, I also assume that there is induced beta decay and electron capture. Regarding tritium, I have wondered whether the mechanism I suspect can explain induced fissioning (superabundance of electron charge) will also lead to the occasional endothermic reaction along these lines:- 3He + e- → t + v - 19 keV
Also, natural helium concentration in rocks can reach 7% ( en.wikipedia.org/wiki/Helium ) - is alpha decay sufficient to explain such huge concentrations?
This is a very interesting question. It would be very interesting to see a calculation. Note that the ratio of 4He/3He is 100 times larger on the earth than in the interstellar medium. The current understanding is that 80 percent of the earth's internal heat comes from radioactive decay. -
I think we're talking past one another to a certain extent. You've made the point that sometimes an electron behaves like a particle, a point that I've accepted from the start of our conversation. I made the further point that it behaves like a wave, one that you appear to accept. You have gone beyond this minimal picture and said that not only does the electron act like a particle sometimes, but also (1) it is a point particle, (2) its elementary charge cannot be smeared over the probability distribution. Both of these statements go beyond what I understand to be the experimental evidence into speculation about things that have not yet been determined for sure. This is natural enough, for you are seeking out a fundamental theory, one that looks behind the veil of quantum mechanics to try to understand things as they really are. I have responded by asking whether we know that the elementary charge cannot be smeared over the probability distribution. You have then responded by asking me to prove that it can. That discussion will get nowhere because we're talking about stuff that goes beyond the experimental evidence, and my position is not that the elementary charge is smeared over the probability distribution. How about we leave that discussion there, and revisit it once one of us has more details to add to that picture.
I am not saying that particles sometimes behave like corpuscles, but that they are always both corpuscles (e.g. elementary charge) and coupled waves.
There are plenty of experiments showing that elementary charge is practically a point, but you still didn't give a single experiment showing that elementary charge can be objectively smeared (?)
What is smeared is its coupled wave, but it doesn't mean that there is no hidden trajectory of the elementary charge behind.
There is this "quantum superstition" that elementary charge is also smeared, to project our effective model into the nature using argument "because QM works" ... like inferring from "because thermodynamics works" and it uses smooth density function, so atoms are uniformly smeared over the vacuum ...It seems all dedicated experiments show that elementary charge is nearly a point, we also need its coupled "pilot" wave, described by QM.
You write like there is some freedom in interpreting the nature here, like saying that evolutionism and creationism are just alternative theories and so should be taught alongside in schools ... please point any evidence, especially experimental, showing that there is indeed an alternative explanation to that particles are simultaneously waves and corpuscles? What alternative?QuoteBoth CF and fusion in the solar core have one very important thing in common: they are dynamic situations.
Indeed, QM is great at working with (dynamical) equilibrium situations, where resonance of the coupled wave is crucial e.g. to form an atom.
But if we want model non-equilibrium situations, like scattering or fusion, the influence of this wave nature (force from the pilot wave) becomes less important - in such situations the most crucial is the corpuscular nature of particles, we should focus on.Quote3He + β → t + v - 19 keV
19keV seems completely unreachable for thermal electrons inside Earth, but high energy electrons indeed might come from some beta decay.
The question is if its rate could realistically help explaining the high release of tritium from volcanoes?QuoteAssuming the helium does not escape, this question could devolve to whether minerals can originally have levels of alpha decaying isotopes at a level of 7% or more? i imagine the answer is yes. Another factor may be that some minerals may have a high capacity to sequester helium as it "passes thorugh".
Indeed filtering might be the answer - as helium (He4?) is the only element diffusing even through thick glass (better than hydrogen!, maybe because of helium being needle-like as Gryzinski claims: http://gryzinski.republika.pl/teor5ang.html ) ... so helium might be the only one percolating through some rocks.
Also, I think Gryzinski has written that it does not apply to He3 (interaction with spin of nucleus perturbs electron trajectories) - it might affect the He3/He4 concentration - I will think about it. -
occasional endothermic reaction along these lines:
3He + e- → t + v - 19 keV
As written, that would be exothermic.....
