# deBroglie's equation and heavy electrons

• Perhaps this topic will lead to a beneficial discussion.

Please look at this most fundamental quantum mechanical equation, considered "empirical" by Werner Heisenberg, but generally attributed to Louis deBroglie:

Lambda (that is wavelength, or RMS uncertaintly in position) = h/p, where p is classical Newtonian momentum, that is the product of mass and velocity. h is Planck's constant, known to be highly invariant, although sometimes given a few slightly different values depending on how it is derived.

Often somewhat misstated is the notion that one cannot specify an electron's position and its velocity simultaneously. More correctly it directly falls out of lambda = h/p, that is one cannot constrain MOMENTUM toward smaller values without simultaneously increasing lambda, that is the positional uncertainly of an electron. [The equation and the uncertainly relationship hold for larger and more massive objects, but the tiny mass of the electron make it particularly evident for that easily accessible particle.]

In all this is the assumption that an electron has a constant mass. And surely the Co-Data value for the electron is specified very precisely, even when it is locked positionally in a Penning trap. However, what happens to the deBroglie equation above if an electron is squeezed down to a quite fixed position AND it is constrained to a near zero velocity? If lambda, or positional uncertainty is to decrease because the electron is in fact being restrained, and if the velocity is nearing zero, it leaves only one variable to retain the relationship as described by the equation... that would be mass. Since the MEAN mass of the electron is precisely known, there may be only the possibility that the mass becomes time variant about that mean. Possibly related to this, an examination of "heavy electron" theory, will show that generally mass variation for electrons or "effective electrons" is vectorial, that is an increased effective mass in one direction is accompanied by decreases in at least one of the other spatial dimensions. I should note that the "deBroglie equation" has more complex variants that specify the variables with subscripts of x, y and z. Further there are relativistic versions. The general idea holds nevertheless.

One real world manifestation of the above discussion is the oft seen presence of oxides (and other electron deficient elements) in various situations involving unusual electron behavior. Such oxides are seen in high temperature superconductors, in low voltage work function electron emitters, such as oxides on electron gun filaments, AND very frequently in the literature of CF / LENR, for example calcium oxide and other oxides as critical components in the alloying of LENR devices. Why oxides? Is electron position and mass variation involved?

Does Planck length, mass and time, or quantum mechanics generally allow charge, position and mass components of an electron and/or proton to be dissociated sufficiently to tunnel one way [perhaps even around physics conventions] or another toward the empirically observed CF / LENR reactions? Can such interpretations be useful in selecting candidate materials and structures to facilitate high COP CF / LENR outputs? [Please also note that Planck mass is by far the largest dimensional quantum in our world, being in the microgram realm.]

It is not in my expertise to fully interpret any of this, but I do see something of interest in the "deBroglie equation", and I notice a distinct lack of mention of it in modern Physics discussions. The Nobel committee granted DeBroglie the Prize, but the Physics Community of the day apparently regarded him with some suspicion. Today this is essentially the same Physics Community undergoing a bit of a crisis with its currently criticized poor connection between grand theories and rather sparse and sometimes contradictory evidence.

Thanks for your attention! Perhaps we can evolve a useful theory as a group. It certainly seems important enough....

Edited 2 times, last by Longview ().

• At least a fair number of views. No comments?

I'll admit you can't just Google the subject and dive right in.

Topics related that might be searched:

"kinetic confinement"
"effective mass"
"deBroglie"
"inverse beta decay"
"mass deficit"
"heavy electrons"

• Google indexes the initial post of this thread. I can only be grateful for that--it's sort of like being published!

• Briefly, this post suggests a non-relativistic explanation for variation in effective mass of elementary particles such as electrons and protons. I hope it will benefit progress in understanding LENR.

It would be good to know if anyone felt it was useful....

Thanks!

• Longview has renamed this thread to reflect its possible significance. Professor Peter L. Hagelstein had written in the Journal of Condensed Matter Nuclear Science, Volume 12, 2013 an article titled "Electron Mass Enhancement and the Widom-Larsen Model" which deposed the notion of relativistic mass gain as an explanation of the source of heavy electrons. The lead article in this newly renamed LENR Forum thread may offer another route to an explanation of enhancement of electron or proton mass.

• Longview,
Good post.
To gain momentum or effective mass, the electron wave-function does not have to move at
a linear relativistic speed. I believe, both highly localized (e.g., inner shell electrons in high
atomic weight atoms), or electrons (moving at non-relativistic speeds) in intense, coherent,
ballistic currents can be called "heavy". Maybe a better choice of words would have been
"high momentum", since, I think, it is plausible that such electrons (and other particles) can
deliver momentum/energy in collisions beyond their rest mass by borrowing field energy
- maybe like an atom at the tip of an arrow borrows energy from the arrow body.

• Lou Pagnucco, I very much appreciate your comments on this issue and others. You are raising the level of the discussion, to be sure.

I too have thought that perhaps "heavy" is a misnomer. But I took this in the direction of allowing "weight" to substitute for "mass". That is under the argument that "effective mass" is surely something like "weight". The result cannot have been operative. Simple acceleration could make the weight of any mass thousands of times greater at far below velocities where relativity prevails. In retrospect I am sure that idea of mine was not correct. I am not certain my idea is far from what you suggest above. But, I'm open to consider the idea again.

Moving on a bit:

Certainly k-shell electron capture is a real phenomenon that can be the equivalent of inverse beta decay. But basically I read Hagelstein's JCMNS article as making it hard to argue for relativistic mass increase in the context of most if not all LENR / CF situations. In my initial post of this thread I offered my amateur assessment of what seems like another possibility based on the deBroglie relation.

Here for some of the flavor of his critique, in the form of a brief quote from Hagelstein's article cited:

"The biggest issue in the consideration of the part of the Widom–Larsen model from our perspective is the origin
of the mass enhancement in the Coulomb gauge when transverse fields are not present. Consequently, our focus

initially was on examining how such a mass enhancement could come about, since in the Coulomb gauge there are no
quantum fluctuations associated with the longitudinal field."
Further, I would note however that Prof. Hagelstein does not seem to acknowledge the by now well-known absence of radiation from electrons in what were once known as Bohr orbits. And in fact there is of course no such acceleration induced radiation that would be classically expected from orbiting charges. Instead QM has replaced the term "orbit" with orbital for this reason among others. So, while inner shell electrons might have enhanced momentum or increased effective mass, that does not seem to impress Dr. Hagelstein. Still I find most of that discussion of his compelling, even though his arguments, while very interesting and perhaps convincing, do not seem quite up to date with this aspect to Schroedinger et al.....

On another theme in his JCMNS article Dr. Hagelstein makes his blanket discountive assertion about the Coulomb gauge a couple of times, but I cannot help wonder if the assertion is true in the case of Surface Plasmon Resonance (SPR)in which very short range fields are orthogonal to the plane of reflection as I understand it. Curiously, he, Cravens and Letts did work that had some relation to SPR. That work would, in my mind anyway, implicitly manifest possible coulomb gauge effects. So in their article for example in the J. of Scientific Exploration 2009, the THz additive and subtractive laser excitations, which I believe corresponded in at least some cases to the "magic" angle of incidence necessary for SPR / evanescent waves. As I understand it these waves or transitory "fields" may be in the Coulomb gauge, and this confers some of the power of SPR as a tool. But, I should add, that I only know what I have read about SPR and evanescent waves.

So in short, I accept that relativistic effects cannot explain "heavy electrons" thanks mainly to Hagelstein, in spite of the reservations mentioned. This motivates my search for another source for the missing mass. A simple test of the nature of "effective mass" may once again be found in centrifugation. If mere "weight" is operative, then simple devices such as LED should have profound color shifts at high g-forces--- since the electron / hole recombination events would involve much more "massive" particles and hence yield much higher energy photons. Somehow I doubt that much other than a failure due to mechanical stress is likely to result from such a trial. But, at least that is easy to test....

• Longview,

In this messy, contentious issue, I would prefer to look at a simplified semi-classical version
- rather than a very abstruse QED/QFT analysis - hopefully, it does not mislead.

For example, it appears if an electron collides with a positively charged particle of
equal momentum in an intense current filament (which provides a huge "electromagnetic
vector potential",) both particles (but, especially the electron) borrow large momenta
,i.e., "effective mass," from this field. See, for example,

Feynman Lectures on Physics, vol.3 [21-3 "Two kinds of momentum," p.21-7]
http://bayanbox.ir/view/760537…III-Quantum-Mechanics.pdf
"What the electromagnetic vector potential describes"
http://exvacuo.free.fr/div/Sciences/Dossiers/EM/ScalarEM/J Konopinski - What the Electromagnetic Vector Potential Describes - ajp_46_499_78.pdf
"Thoughts on the magnetic vector potential"
http://abacus.bates.edu/~msemon/thoughts.pdf

This potential describes the coupling between the particles in currents.
It is essentially a momentum store.
I have calculated the momentum of such impacts in plasma current filaments attainable
in labs. Unless I miscalculated, electrons can attain momenta equivalent to free electrons
moving at speeds equivalent to MeV energies in fairly common electric discharges.

• Very interesting post Lou Pagnucco. Your scenario is worthy of experimentation, if it has not already been intensively investigated!

I do see that a substantial portion of CF / LENR reports involve "arcs" of one sort or another, but nowhere near a majority. I take those "arcs" to be possibly unrefined versions of the scenario that might result from colliding electron and nucleon (especially proton) currents. The approach seems simple enough. Measuring the expected ULM neutrons may require something akin to [Link to another discussion thread:] Ultracold neutron isolation and detection

I have not yet read your references / linkouts yet, although I tried the first one, with the Arabic and Farsi headers, only to then notice the ".ir". Curiously my message screen here became "blue" and the typeface changed. By logging out, then returning, I thankfully found normal function here at LENR Forum.

[I would advise against citing or following linkouts to sites with Iranian origin.... for practical and linguistic reasons and perhaps for security, at least for those in the USA--- with apologies to many wonderful folks of that ethnicity who have befriended me over the decades.]

Edited once, last by Longview ().

• From your calculations, Lou, what were your assumptions of current density? Beam diameter? Coulombic beam dispersion? and the potentially anti-Coulombic effect of the presence of the oppositely charged species in the beam? Also what length of path and potential difference brought you to MeV energies?

Thanks,
Longview

• Longview,

That website doesn't seem to work the same anymore.
I tried a couple of malware detectors, but it is not labeled as malicious.
Try the following URL instead (see p.21-4) - http://www.peaceone.net/basic/Feynman/V3 Ch21.pdf

I have posted some calculations in the past.
I would like to do them again with some new data, but cannot until next week.

• I get a "Not Found 404" error message. Clearly Asian ideograms or Kana.... no problem with that, but it does not work.

I will try to dig up my own Feynman lectures link. Thanks for the page numbers.

Edited once, last by Longview ().

• That link and an earlier one kindly given by Lou Pagnucco, as a source of a piece of information from Feynman's Lectures online, seem to have some problems, see my comments above. I suspect these sources may unfortunately be evading copyright obligations enforceable in the USA.

One still pays something substantial (about \$40 and way on up, at Alibris) for old hardcopies of Feynman's Lectures in the USA in the 2010 Edition.

• Longview,

Really strange things are happening at that website, too.
I have no idea why. Maybe some web-bot is interfering with these sites.
However, it seems if you get to that website (or some other) thru the Google search:
Feynman "two kinds of momentum"
- then the link to the pdf works.

The basic idea, though, is that a linear current flow generates a magnetic vector
potential depending on the current and its extent. At any point, this vector potential
is a vector pointing in the same direction as the current. It represents the coupling
between the charged particles.

The value of this vector potential is proportional to how much momentum
a charged particle in the current flow acquires in a collision -i.e., the more forcefully
it is impeded by an obstacle, the more momentum it draws from this momentum field
to push into the obstacle (say another charged particle), an continue on its path.

When two oppositely charged particles collide in an intense current, say a idealized
collision where both have equal and opposite momenta, then both will draw the
same momentum (but in opposite directions) from the vector potential. If the current
is intense, this momentum will be large, and light particles, like electrons, will acquire
a large gain in momentum, giving them very large effective masses in collisions.

It think this is sort of analogous to how the atom at the tip of an speeding arrow borrows
momentum from the arrow body when it hits a target, or how the lead car of long
train will impact an obstacle with much greater momentum than its own, by its
coupling to the rest of the train.

• Thanks for the explanation, Lou Pagnucco. It seems plausible. My main concern had been raised by Peter Hagelstein's critique in JCMNS. But, as I mentioned, the critique unfortunately shows a few "antique" notions (at least from a chemistry perspective) with respect to QM as it is practically applied.

The QSE, or quantum size effect-- [for a brief review, see work cited below], could be interpreted either as kinetic confinement in the sense you mentioned. It seems that my argument at the outset of this thread, that is essentially one of a qualitative shift as electron mobilities are both constrained in velocity and position.... But it seems also the deBroglie relation is relatively easily saved from "collapse near zero velocity" in other reasonable ways. The 3D version of deBroglie allows the other two dimensions (a plane) of momentum loss (with paradoxical and disallowed positional uncertainty DECREASE) by allowing, or pushing, enhanced positional and momentum uncertainty orthogonal to that plane.

So, with three dimensions of spatial freedom [and one of time?], the electron can be highly constrained in one or two dimensions and take its increased lambda [wavelength, or uncertainty of position] in one or both other dimensions. So an intuitive explanation of the role of oxides at interfaces, (or other immobilization, such as electrostatic Nernst pressure?) might be at hand. That is in thin layers such as in HT superconductors, the presence of the oxide layers pushes the orbital excursions greater in orthogonal to plane directions AND confers increased momentum (probably in the plane?). While this is in seeming conflict with a one dimensional deBroglie model [Lambda = h/mv], perhaps it is no problem in 3D space. In semiconductors the phenomenon of QSE is realized strongly only in the interfaces between very thin layers.

For anyone who might want a quick review of QSE [in words! --- although the book is loaded with higher maths] see page 4 of Bhattacharya and Ghatak 'Effective Electron Mass in Low-dimensional Semiconductors', Springer 2013.

And by the way, Lou, they interpret and even define Effective Electron Mass (EEM) consistent with your view, bottom of page 8: "The EEM is defined as the ratio of the electron momentum to the group velocity."

Longview

Edited 2 times, last by Longview ().

• Longview,
First a disclaimer. I can only speculate on this difficult subject. I make no assertions.

I think the "effective mass" term is used in two different ways - a source of confusion.

One way it is used is to average the "hidden momentum" in inductors over the conduction electrons.
E.G., this is done in "Extremely Low Frequency Plasmons in Metallic Microstructures"
- http://www.cmth.ph.ic.ac.uk/ph…hotonics/pdf/lfplslet.pdf
where (eq (13), p.6) it is shown that this leads to the conclusion that electrons in simple
nanowire arrays can attain the effective mass equivalent to a nitrogen atom's.
However, I believe, that this is only available as energy/momentum boost during head-on
collisions that occur extremely rarely, if ever, in such small currents.

Another way is to calculate the momentum gain during (what amounts to violent, abrupt)
collisions as described in the Feynman lecture ("Two Kinds of Momentum".) In this case, the
electron borrows all of the "hidden momentum" (i.e., from the magnetic vector potential)
allotted to it, allowing it to attain a real large effective mass. Srivastava-Widom-Larsen
calculate the momentum drawn by a colliding electron from its coupling to surrounding
conduction electrons using the Darwin Lagrangian, which makes coupling terms explicit.
See - "A primer for electroweak induced low-energy nuclear reactions"
http://www.ias.ac.in/pramana/v75/p617/fulltext.pdf
I believe both approaches the same results. I think that such collisions may occur in
intense arcs - for example, in the Wendt-Irion experiment (ref [28] in the S-W-L paper.)

If we pretend that the electron is a spin-less quantum particle, I think the wave function
could be pictured squeezed, localized and highly oscillatory, with a greatly increased
mass due to the kinetic energy gain represented by high frequency momentum spectrum
(due to localization, rather than linear relativistic speed.)
If we assume the electron is a fermion (with spin h/2) the oscillations are spinor quiver
or zitterbewegung. Hopefully, the simpler picture is good enough.

Certainly, Hagelstein may be correct, but I would need to know if/why a full QED analysis
differs from a simpler QM analysis.

• Lou Pagnucco,

Thanks again for your attention to this subject, I much appreciate your view(s). I won't attribute QED to Prof. Hagelstein in this situation, although a brief rereading still makes me think it is more like a classical-Maxwellian / QM hybrid, with some aspects borrowed as needed from each. And of course one of the great things about this gentleman is that he is able to make strong arguments and later come back and say, "No, I'm ready to bury that theory".

But of course I have no substantial familiarity with QED other than as a historical development, so I will defer for now.

I am not sure how intense currents must be to see substantial collisions of oppositely charged entities. It is often neglected, I think, that protons and neutrons are extremely small, so even though the proton has a high mass, its diameter should enable it to pass through insulators (such as oxides) with ease, as long as sufficient EMF is available to accelerate a measurable or usable current. So the important variable with respect to LENR in my mind would be the potential difference and not necessarily the current, although clearly some flow would be necessary for any steady state neutron production. But if the assay for production is secondary radioactivity or heat, then the "life" of the producing structure is likely to be short....

Much more to discuss.

• [Continuing, but with a plausible "reduction to practice" motif, which is given impetus by Lou Pagnucco's commentary here. Readers will note, that I am again suggesting, or even advocating, high EMF (voltage) WITH low current flow, keeping in mind Nernst pressure.]

Another implication is that nearly any electron-rich material can be on the negative side of a LENR cell and any proton-rich material on the positive side. The presence of a highly insulating, but proton-permeable "separator" may, or may not, be a necessity-- Whether a true proton conductor or a proton "handoff" type, such as Dupont "Nafion"--- implemented as a thin separator in an electrolytic cell, or some other form in a gas or plasma phase cell. Or perhaps more durably, a separator or coating of a newer ceramic frypan-type and/or diamond-like material. Such a cell, or reactive environment, would be constructed so as to impede or stop electron flow in at least one dimension and yet to encourage proton flow. Easy enough, I believe. And probably has been approximated many times in successful demonstrations of LENR / CF in what are largely electrostatically driven cells. And perhaps generalizable to gas with powder designs. [Recall Nernst, idea not dead yet.]

With the caveat that destruction or untoward alteration of any or all the cell components might rapidly result because of the high concentration of ULM neutrons. That is, a separator cannot retain its chemical and physical identity for long under such a concentration of heat, local beta flux and isotopic shifts. Of course there are work-arounds for those problems including using powders with continually renewed faces and so on.

I'm reminded of "catalyst drums" that essentially continuously, or stepwise, rotate new reactive surface in and out of the reaction matrix or flow to handoff products and perhaps undergo reactivation, cleaning and so on while oustide the reaction zone. There are other potential or actual "work arounds" many taking the form the arts and sciences of industrial chemistry, chemical engineering, process chemisry and catalytic chemistry,

[And as an aside, and based on possible structural similarities, anyone working developing or using ultracapacitors for short term very high energy storage-- useful auxiliary to batteries, see Google, Wikipedia etc.-- might be advised to judiciously observe ULM or ultracold neutron production within such devices (not easy!) and consequent short term beta fluxes (relatvely easy) and engineer to avoid their potentially destructive effects to the ultracapacitor itself, or possibly to nearby mammalian exposure to secondary beta emissions!]

Longview

Edited once, last by Longview ().

• Widom and Larsen have some patents on heavy electrons to cause LENR and they also predicted that heavy electrons in surface plasmons will block gamma rays. Has anyone demonstrated those phenomena in the lab?It seems like simple experiment test the effectiveness of surface plasmons in blocking a gamma source.
Is anyone interested in an experiment to test it?

• I'm interested,

Edited once, last by Longview ().