Posts by Jarek

    But I will try once more in the the hopes that we still might get there. My position is not that the elementary charge is smeared over the probability distribution. It is that the supposition that the electron is a particle riding on a pilot wave is one among several competing explanations for what underlies the experimental results explained by quantum mechanics, and a minority one at that


    I am not asking about interpretations of our subjective theory (QM) ... often requiring human free will like in theology (humans are unimaginable small part of time and space of Universe),
    only while there are plenty of experiments showing that elementary charge is practically a point (e.g. scattering, Penning trap), is there a single experiment showing or suggesting that elementary charge is objectively smeared?
    After many threads you have finally given two such experiments ... but then didn't respond to my objections - why do you think they conclude objective smearing of elementary charge?

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    The main problem I see with Gryzinski's explanation has to do with the movement of the electrons around the nucleus, as we’ve already discussed. They’re like a planetary system, and a three-dimensional planetary system with many moving bodies will exhibit chaotic rather than ordered movement.


    So your objection is possibility of chaos - could you elaborate why do you think it would be a problem?
    I have two complementing views how quantum probability cloud emerges from trajectories:
    1) Trajectories should be thermodynamically pertubed e.g. by interaction with neighboring atoms - thermodynamics says that we should assume Boltzmann distribution among possible paths, what from euclidean path integrals (/Maximal Entropy Random Walk) we know that leads to probability clouds from QM,
    2) Everything is happening in a field, particle has to find resonance with: make it a standing wave to avoid synchrotron radiation - this standing wave is described by QM.
    Locally 2) is crucial - staying at resonance (field) prevents local chaos ... but still there are some thermodynamical perturbations and after a long time probability distribution for finding particle averages to predicted by QM due to 1) .

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    But you will have to choose either between pilot waves, which give predictions indistinguishable from other interpretations of quantum mechanics, and an approach that purportedly gives predictions that are better than quantum mechanics. You cannot have both.


    Why we cannot have both - as two complementary perspectives on the same system?
    For example imagine coupled pendula - you can describe evolution of their positions (classical), or go to normal modes - where you have exactly unitary evolution like in QM:
    https://en.wikipedia.org/wiki/…_mode#Coupled_oscillators
    Now take a lattice of pendula (crystal) and its normal nodes are called phonons, directly used in QM description ... but you can still ask for classical evolution of atom position in this lattice - alternative, complementing perspective.

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    I don't know of anyone who has suggested that tritium, in LENR or anywhere else, comes from fission.


    There are at least two ways to tritium from fission: through neutrons or direct: according to Wikipedia, in about 1:10000 fissions tritium is directly created: https://en.wikipedia.org/wiki/Tritium#Fission

    There are two experiments that I've given: (1) the electron interference experiments, and (2) the fact that electrons moving at different velocities interact with other objects at different orders of magnitude of extent. Both of these kinds of experiments give evidence of wave-like behavior, and not billiard-ball like behavior. I hope we can move beyond this request of yours, which has been duly answered several times now.


    (1) electron interference experiment shows that electrons have at least the wave nature, but how do you conclude that it shows objective smearing of elementary charge? or that electron doesn't have both natures simultaneously?: like in Couder's interference, the elementary charge travels one trajectory, while its couples 'pilot' wave travels all trajectories, affecting trajectory of the charge.


    (2) seems a general question of scattering, like the Ramsauer effect (increased cross-section for low energy), explained among others by Gryzinski (here using effective picture of atom as multipole + oscillating multipole): http://gryzinski.republika.pl/teor6ang.html


    Please elaborate, explain your point - how do you conclude that elementary charge is objective smeared here?
    Where do you see a problem with classical Gryzinski's calculations? - for scattering usually getting better agreement with experiment than quantum predictions.


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    These are interesting details which go back to the de Broglie-Bohm pilot wave theory. The pilot wave theory, I hope you'll agree, is speculative and not yet established by experiment.


    dBB is just substituting psi = sqrt(rho) * exp(iS/hbar) to Schrodinger, getting continuity equation for density (rho) and Hamilton-Jacobi for the action (S), with additional interaction with what is called the 'pilot wave'.
    https://en.wikipedia.org/wiki/…ion_for_a_single_particle
    What is 'speculative' about such substitution?
    What exactly has not yet been established by experiment here?


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    If we do not allow pilot waves, which are speculative, there are the experiments in which wave-like behavior seen in connection with electrons must be explained. One possibility is that electrons are waves that deliver energy in discrete packets.


    Sure, electrons have wave nature - we all agree on that.
    Our disagreement is that you claim that they are not simultaneously corpuscles - that against many experiments, their elementary charge is objectively smeared over e.g. micrometer size Rydberg molecule.


    Please finally give a single argument, experiment against the duality - against particles being simultaneously both corpuscles and coupled waves?


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    Tunnelling is relevant to fission and alpha decay. Also, Gryziński's picture is an equilibrium one, by your own admission, so there's a question about whether insight can be gleaned from it for the dynamic situations we've been considering.


    Sure Gryzinski considers dynamical equilibrium states (atoms) ... but often (mostly) as just a target for a particle (probe): in very non-equilibrium scattering scenarios - used to test the atomic model, because predictions are very dependent on the assumed model of target.
    Specifically:
    - as probability distribution of velocity of electron in the target (~1965 papers),
    - as effective electric multipole seen by approaching particle (since 1970 Ramsauer paper),
    - approaching low energy particle can modify trajectory of electron in the target (explanation of Helbig-Evenhart resonances)


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    Yes, the 19 keV is unreachable for thermal electrons. But we have beta decay electrons.


    Sure, but as I have written: the question is if such effect could have sufficient statistical importance to explain 10000x larger tritium release than from fission?


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    By this hypothesis, there should be a store of 3He waiting to be released. I wonder whether there's a way to test it.


    The He3/He4 ratio generally increases with depth, see e.g. http://www.mantleplumes.org/HeliumFundamentals.html

    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?

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    Both 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.


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    3He + 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?

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    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 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.

    Returning to Earth, there is a nice paper saying that tritium production from volcanoes can be >10000x larger than estimation for fission: http://lenr-canr.org/acrobat/JonesSEgeofusiona.pdf
    I have just used it in discussion here: http://physicsworld.com/cws/ar…n-on-rising-helium-prices


    This is a 2003 paper - does it still hold, especially the fission estimates?


    Also, natural helium concentration in rocks can reach 7% ( https://en.wikipedia.org/wiki/Helium ) - is alpha decay sufficient to explain such huge concentrations?

    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.


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    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.


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    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.


    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:

    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 ) :


    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).


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    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.


    Could you elaborate why there is a problem here with electron being simultaneously both wave and corpuscle?

    Sure QM is a good model, nobody doubts it.
    We can use e.g. Maximal Entropy Random Walk to derive its probability clouds as the safest assumption (maximizing entropy) - by using Boltzmann probability distribution among possible trajectories like in euclidean path integrals.
    https://dl.dropboxusercontent.com/u/12405967/MERWsem_AGH.pdf


    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?


    Like in Couder's orbit quantization: http://www.pnas.org/content/107/41/17515.full



    Particle (with wave-particle duality) has to find a resonance with the field - to get a standing wave to avoid synchrotron radiation.
    This standing wave is described by QM ... but additionally there is still also a trajectory of particle hidden behind it, leading to this standing wave created by particle's own wave nature.


    Why there cannot be a hidden electron trajectory behind the quantum description?

    Do you have any argument that electrons should be treated like tiny, localized billiard balls in the present context


    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),
    - none scattering experiment can imply nonzero radius of electron (?),
    - in Penning trap they have limited the radius of electron by 10^-22m : http://iopscience.iop.org/arti…88/0031-8949/1988/T22/016 ,
    - if we know atom and time releasing electron and the same for the one absorbing atom, we can determine trajectory of this electron,
    - because nothing fundamentally changes in vicinity of proton so that electron should loose trajectory to form e.g. orbital of Rydberg atom, we can perform e.g. e-p scattering and it is well described by classical considerations (see e.g. Gryzinski's paper with 1300 citations),
    - because in the "photos of orbital" experiments they could measure the final positions of electrons leaving the atom.


    Please give finally a single argument that this elementary charge is objectively smeared over a relatively huge volume, e.g. of micrometer size Rydberg molecule ( http://physicsworld.com/cws/ar…-are-the-size-of-bacteria ).
    That quantum probability cloud is not just an effective description, average over time.
    What is electric field (affecting surrounding particles) created by elementary charge smeared to micrometer size Rydberg molecule?

    Regarding 135Xe, sure it is a complex problem, but I don't see it related to tunneling(?) - otherwise, neighboring nuclei would be also affected.


    Regarding measuring electrons, in the above "photos of orbitals", they literally measure their positions before leaving the atom - with subatomic precision.
    They know electric field, time and position of capturing the electron - they could write their trajectory x(t) with good precision.


    But I am not talking about measuring these positions here, only that objectively electrons have positions/trajectories - hidden behind (averaging to) the quantum probability clouds. Elementary charge cannot be splitted - objectively smeared into a cloud.
    You can argue that if we cannot directly measure these positions, there is no point to consider them - analogously you can say that if we cannot probe the center of Sun, we cannot model it.


    No, we can model and test consequences of a model - not directly measure positions of electrons (probe solar core), but test their effective consequences - what Gryzinski does: e.g. with probability distributions for various scattering scenarios, diamagnetic coefficient, shifts in Stark effect, energy levels (energy of photons) and many others - sometimes getting even better agreement than QM (e.g. Stark).
    It is about getting below effective quantum description.


    Do you have any argument that electrons objectively don't have (lose) positions/trajectories in vicinity of proton (inside atom)?

    Whether nucleons are properly solitons or not, they do in fact behave like delocalized waves. Consider the case of a neutron passing by a 135Xe nucleus, when the impact parameter b is large:


    Indeed 135Xe has huge cross-section for neutron absorption: http://energyfromthorium.com/2010/06/20/neutron-poisons/


    However, if you are saying that it's due to tunneling, so why it also doesn't apply to other similar nuclei ???
    Tunneling is about crossing a barrier, while here it seems the nucleus just kind of swallowed.
    So 135 for xenon is a large mass ( https://en.wikipedia.org/wiki/Xenon ) - it has much more neutrons than it would like to have - it is believed that abundant neutrons can create kind of halo around the core of the nucleus ( https://en.wikipedia.org/wiki/Halo_nucleus ) - this seems a good candidate for looking for the explanation (better models of nuclei), while tunneling would also need neighboring nuclei to follow.


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    In addition, the Heisenberg uncertainty principle says that you’ll have a really hard time confining those electrons to a one-dimensional path between two protons.


    Heisenberg principle restricts measurement - that we cannot measure perfectly e.g. position and momentum.
    For example because measurement is a very destructive process, it's idealization is Stern-Gerlach experiment, where incoming atoms have random spins, which became aligned along strong magnetic field (otherwise there would be precession radiating energy) - choosing parallel or anti-parallel alignment.


    How do you imply from Heisenberg that electron objectively doesn't have a position in a given moment?
    Nice experiment where they measure positions of electrons leaving atoms - these density clouds are averages: http://journals.aps.org/prb/pdf/10.1103/PhysRevB.80.165404



    We can ask about trajectory of electron flying through empty vacuum - if we know when electron was produced and absorbed a kilometer further, we can write equation for x(t).
    ... but we cannot when there is a proton nearby - when we have to start seeing it as an orbital.


    So how far from proton electron has to be to stop having trajectory?
    What about Rydberg atoms/molecules which can be 1000x larger?
    http://physicsworld.com/cws/ar…-are-the-size-of-bacteria

    Indeed, that's exacly my point: the qualitative difference between solids and liquids is stability of molecular bonds - electron dynamics.


    From microscopic perspective, condensed matter means stable molecular bonds - electron dynamics, which could help fusion by remaining between nuclei.
    In contrast, in sun these electrons just randomly jump between nuclei.

    Eric,
    Sure, particles are kind of waves ... but very special waves - not only massive, but also maintaining shape, e.g. charge is not splittable. So technically they are solitons.
    Does soliton undergo tunneling?
    I have just found one paper and it has negative answer: https://arxiv.org/abs/hep-th/9704208
    And generally - what is wrong with electron trajectory between two nuclei - which could give a real explaination?


    And if we want energy source, not relying on just decay or fission, we need fusion - crossing the Coulomb barrier ...
    If one claims it is possible in 1000K, why it doesn't happen in entire volume of Sun? Or maybe someone has arguments that it happens?

    Eric, Gamow tunneling is in 3D, see e.g. slide 15 here: http://www.tunl.duke.edu/nnpss/lectures/17/UNC_2011.pdf
    I am currently reading "Nuclear physics of stars" book, but it will take some time.
    For this moment, my only objection is that, in contrast to Boltzmann distribution, tunneling is kind of a magical explanation - especially for nuclei, which are usually modeled with classical trajectories. This is a compact object which cannot just teleport through a potential barrier - we need a concrete mechanism for that.
    Indeed, in physicsforum there are cited papers that electron screening has minor effect - but they treat electron as probability cloud, which is great for dynamical equilibrium cases ... fusion is not.
    My point here is that asking for electron trajectory (averaging over a relatively long time to this probability cloud), there are trajectories remaining between the collapsing nuclei - screening the Coulomb barrier.
    That probability cloud is too blunt static tool for this subtle dynamical situation.


    Regarding my question, Gamow tunneling still weakens exponentially with low temperature - fusion still needs millions of Kelvins.
    If one believes in CF, tunneling is definitely not enough.
    Moreover, if proposing a CF mechanism, it should require a condition which is present in 1000K, but not present inside stars - otherwise their energy production, evolution should be drastically different (maybe it is - are there any arguments?)
    E.g. if one says 'hydrinos' or 'discrete breathers', he should also answer the question: why this explanation does not apply also to let say 100 000K region of the Sun?


    An example of such explanation (applying to 1000K but not 1MK) is requirement of stabilizing electron trajectory for molecular bond between two nuclei - in million kelvins fusion requires smaller assistance of electrons, but it's more difficult for fast electrons to find a stable trajectory between nuclei for the short moment of approaching to collision.


    Any other mechanisms which could grow in strength while lowering temperature?
    Or maybe you have seen some alternative models of stars - with included LENR?

    As energy production of most of stars seems well understood, they base on p+p, p+d fusion starting at a few million K by Gamow tunneling ... what are the responses of CF enthusiasts to the objection that fusion being still nonnegligible down to 1000K should dramatically change physics of stars?


    Is there any other way of defense than trying to rely on requirement of stable molecular bonds? - for which one possibility is electron bouncing between them on nearly a line, screening the Coulomg barrier.

    Padam, could you elaborate?
    Getting to 1pm distance is relatively simple, protons should get there all the time due to just thermal energy in 15MK core of the sun.
    However, getting to 1fm so that nuclear force can start acting requires 1000x more energy (without electron remaining between them) - how is it explained?


    Considering electrons, some could form low angular momentum orbit around one nucleus: ellipse deforming into nearly a segment in some direction. If another nucleus is approaching from this direction, this electron could stay between them, kind of bouncing between the two nuclei in a series of back-scatterings, screening the Coulomb barrier.


    How can it be explained without such electron assistance? - how proton could get 1000x larger energy than thermal to cross the Coulomb barrier?
    "Because tunneling" might be a good explanation for electron, but not for 2000x heavier proton - for which even mainstream consider trajectories and forces ...


    ps. It's ever worse - just having energy for getting to 1fm distance (~1.4MeV, 1000x more than thermal in solar core) would solve the problem only in 1D.
    In 3D you not only need this energy, but also have VELOCITY PERFECTLY POINTING THE SECOND NUCLEI - otherwise they will just bounce from the repulsion and fly away.

    Zephir, Eric - please just do the math.
    Solar core is believed to have density 150g/cm^3 ( https://en.wikipedia.org/wiki/Solar_core ).
    Assuming it's hydrogen only (N_A per gram), one can easily calculate radius of ball corresponding to every proton: I got I.38 * 10^-11m, what makes sense.
    As electron concentration is the same, one can imagine analogous ball around every electron.


    So free electrons would have there 10^-11m order of distance from the nearest proton.
    Assume we want p - p fusion. Thermal energy of 15MK gives 1.4keV what allows to get to 10^-12m distance.
    In this distance free electron is already 10x further than the target nucleus: Coulomb force is 100x smaller.


    But 10^-12m is just the beginning - we need 1000x more energy to get to range 10^-15m of nuclear force ... and interaction with free electrons become completely negligible during this trip - their screening doesn't matter here!
    The only way electron could really help here is having trajectory imprisoned between these two colliding nuclei.

    Under these extreme pressures the electrons will be pushed between protons again, i.e. their shielding effect would apply there more than inside the sparse plasmas.


    Still you have e.g. 1 electron per proton - concentration of electrons increases proportionally to concentration of nuclei.
    Maybe it could reduce average proton-electron distance let say from 100pm to 10pm ... while the most costly in fusion is going from e.g. 1pm to 1fm - where this screening from electron cloud becomes just negligible.


    Again, the only option for non-negligible electron assistance is that there is a single electron remaining between the two colliding nuclei.