Let’s just be clear: It’s not impossible to do world-beating invention and technological development despite having a terrible understanding of how the technology works microscopically. Just look at the pharmaceutical industry.
OK now that that’s out of the way: There’s a company from Berkeley, California called Brillouin Energy. Its CTO and founder, Robert Godes, has posted a theory of cold fusion he calls the Controlled Electron Capture Reaction Model. And I think it’s just terrible. I believe with high confidence that, if there exists a microscopic theory of cold fusion at all, this paper does not offer any insight into it.
That said, I did my best to decipher this paper but apologies if I mischaracterize it. It is pretty confusing in places. I’m just going to go through the theoretical part in order, section by section.
Neutrons (Sec. 2.1)
Like Widom-Larsen theory, Godes proposes that neutrons are created as a first step, both via (proton + electron + 0.782MeV = neutron) and via (deuteron + electron + 3MeV = “di-neutron”). He says that a di-neutron is not bound, but it’s “very nearly” bound!
The obvious question is: Where does that 0.782MeV or 3MeV come from? The correct answer in my opinion is: In the type of system we’re talking about, an electron would never get that much energy, and neutron production would never happen. There may be plenty of MeV’s of energy splashing around in a large volume, but that energy won’t all spontaneously localize into the kinetic energy of a single electron. To do so would be a dramatic reduction of entropy in violation of the laws of thermodynamics. (I don’t mean literally that neutron production is universally ruled out by the second law of thermodynamics. There is, after all, a low-entropy power source present in the system. But I haven’t seen any remotely plausible description of how it could happen microscopically without violating the 2nd law.)
OK, Godes acknowledges that “This large energy barrier seems insurmountable”. But then quotes Peter Hagelstein as having proven that “it is entirely possible to localize [several MeV]”. If you open the paper by Hagelstein, Godes is quoting a sentence in which Hagelstein is saying pretty much exactly the opposite thing!
(Hagelstein was investigating something different, found that it could only happen if several MeV could be localized, and finds this so implausible that he considers it a proof that this scenario will not occur!)
Beta decays of Hydrogen-4 (Secs. 2.2-2.3)
Since I don’t believe hydrogen-4 could possibly be created (if it even exists), I don’t see any reason to discuss this topic. A little tip — Section 2.3 is a paper excerpt, it’s not written by Godes. I was confused by that at first.
Phonons, Brillouin zone, Molecular Hamiltonian, Lennard-Jones (Secs. 2.4-2.7)
These sections cover some basic physics topics as background. They are mostly copied from wikipedia (with attribution, not plagiarized, for the most part). That’s a good thing! The stuff copied from Wikipedia is by-and-large correct and readable!
Amusingly, despite dedicating a section to explaining what Brillouin zones are, Godes never uses them or refers to them anywhere else in the paper!
The Lennard-Jones section is worse than the others: The meaning, origin, and role of the Lennard-Jones potential is described very poorly and confusedly. But I won’t get into it here. I don’t think it’s too important for the overall picture.
Quantum compression, skin effect (Secs. 2.8-2.9)
“Quantum compression pulses” (Q-pulses) are a fancy name for very short bursts of current through a thin palladium wire, causing very high current density. The current density is even higher than you might think due to the skin effect.
There is a suggestion that this current flow alone can provide the MeV’s required for electron capture (“This momentum transfer between conducting electrons and core, drive the values of the evaluated Hamiltonian to the magnitude required for capture events”). The statement is not justified in detail, and I don’t believe it. (Update: In a comment on this post, I wrote out my back-of-the-envelope calculation of the electron speed associated with this current pulse. I found that it was negligible: 0.2m/s.)
Heisenberg Uncertainty Principle (Sec. 2.10)
This is more basic physics background. The description is poor, but I won’t bother nitpicking.
Heisenberg Confinement Energy (Sec. 2.11)
The basic idea is that if you put a particle in a smaller and smaller box, its position becomes more and more certain, which means (by the Heisenberg Uncertainty Principle) its momentum becomes more and more uncertain, and the expectation value of kinetic energy increases. Godes calls it “Heisenberg confinement energy”, but it’s ultimately a form of kinetic energy, so I’ll call it that.
So far, this is true. Indeed, if you take a quantum mechanics course, you might go over the Particle in a Box on your first homework, and you’ll find that kinetic energy increases as the box shrinks.
If I understand correctly, Godes believes that the confinement of a proton in a box is the source for the huge 0.782MeV of kinetic energy that we would need to form a neutron by electron capture. (Or the 3MeV to turn a deuteron into a “di-neutron” etc.)
One problem is, if that’s the case, it had better be a really really really really small box. Indeed, if a proton is to get a kinetic energy of 0.782MeV by being in a box, I calculate that the box should be something like m wide, i.e. thousands of times smaller than the typical spacing between an atom and its neighbors in a solid. I don’t see how that could ever happen.
A more basic problem is, the confinement-related kinetic energy still has to come from somewhere. As you move in the walls of the box, the particle pushes back with increasing pressure as you squeeze it. So instead of asking “How does a proton get 0.782MeV of kinetic energy?”, this theory makes us ask a slightly different question: “How do we get 0.782MeV of energy needed to create a tiny box around a proton?” The answer to the new question is the same as the answer to the old question: We don’t.
I think it’s worth mentioning a telling error in this section. Godes emphasizes how tritium (T) is physically bigger than deuterium (D), which in turn is physically bigger than hydrogen (H). Therefore the same size box will “squeeze” tritium the most and hydrogen the least. This is intuitively appealing but totally wrong. In fact, the nuclear radius of all three is so small that it might as well be zero, it makes no difference here. He actually got it backwards: The more massive a particle is, the smaller a box you can squeeze it into, for a given increase in its kinetic energy. This is a direct consequence of the Heisenberg uncertainty principle.
To bolster his (incorrect) theory that nuclear radius is important, he brings up the fact that H absorbs into palladium more easily than D. I’m willing to believe that H absorbs more than D, but I say: No way is that related to nuclear radius. It’s just that H has less mass. So it moves faster for the same kinetic energy, it is better at quantum tunneling, etc.
To close out the section, I quote Godes: “The slightly larger size causes deformation of the lattice electron wave functions and the “Heisenberg Confinement Energy” is a 1/x type function that increases exponentially once the inflection point is reached.” LOL, find all the errors in that sentence!
Section 2.12 is by-and-large a recap of things we’ve already discussed, so that brings us to…
…Then everyone dies of radiation poisoning, the end (Sec. 2.13)
Studious readers of this blog will recall that one of the great challenges of explaining cold fusion is that if it were a normal nuclear reaction creating this amount of power, everyone in the room would die of radiation poisoning within minutes. This paper does not offer any useful directions towards solving this mystery.
He proposes that the energy is released in the beta decay of hydrogen-4 into helium-4. That would mean, specifically, that each nuclear reaction creates an electron with kinetic energy ~27MeV, i.e. traveling 99.98% the speed of light.
So why isn’t the apparatus producing deadly radiation? Godes says: “One possible explanation is that the mean free path of electrons in a conductor (familiar to electrical engineers) causes the absorption of β− radiation through direct nucleon interaction and the formation of additional phonons.” I don’t think most electrical engineers are familiar with the behavior of electrons traveling 99.98% the speed of light! …I might surmise that Godes is not familiar with it either. 😛
Maybe Brillouin Energy is doing great experimental work and technological development. I wouldn’t know, I haven’t looked into it, and I certainly wish them luck. But if there is a plausible microscopic theory of cold fusion, it sure isn’t The Controlled Electron Capture Reaction Model. 😛