This is a quick progress report on my studies of the “spin-boson” theory of cold fusion advocated by Peter Hagelstein at MIT. I happen to work 2 blocks away from Dr. Hagelstein’s office, so he’s been nice enough to meet with me a couple times over the years to discuss some of the technical details. Despite those meetings, and much time spent reading his papers, and many posts about the theory, there are still plenty of aspects of it that I haven’t yet tried to understand in detail.

That said, there are currently a number of aspects of the spin-boson model where I’m that seem implausible or wrong to me. I don’t think any of these complaints is fleshed-out and detailed enough that I could, say, write up an airtight disproof of the whole theoretical program tomorrow. But together, they make me pretty confident that this is not a path to a viable explanation of cold fusion. Let me list them:

• I argued previously that cooperative effects don’t help the alleged reaction to start, i.e. that the math of the model implies that a microscopic grain of palladium with 10²⁰ D-D pairs is just as (un)likely to start the fusion reaction as a nanoscopic grain of palladium with 5 D-D pairs in it. But Dr. Hagelstein disagrees with this conclusion and said I will understand why if I read this 46-page paper. So I’m hoping to do that, and you can expect a post on that topic in the future. This is obviously important since it might affect the reaction rate by 20 orders of magnitude or so, i.e. the difference between a millisecond and the age of the universe.
• Probably related: I can’t see how any kind of nuclear-phonon interaction could be strong enough to enter the strong-coupling regime, at least until the process is well underway (which won’t happen if it can’t start in the first place).
• Propagation delays and decoherence: An interaction mediated by phonons will propagate at the speed of sound, which by the standards of nuclear physics (and even condensed matter physics) is just ridiculously slow. I find it very hard to imagine that coherent cooperative quantum effects could persist in the face of decoherence over such a very long time. And I see no reason to expect slow decoherence here; on the contrary, I think it should be very fast. We are talking about an interaction that replaces a D-D pair with a ⁴He inside a solid—it’s not a subtle change, it’s bound to be felt by nearby electrons, nuclei, every passing phonon, etc. I know for sure that decoherence kills superradiance and I suspect that it kills the whole lossy spin-boson model too. But to quantify that, I think I really need a working numerical computer simulation of the lossy spin-boson model. So I’m hoping to code something up and use it to reproduce Dr. Hagelstein’s results and then explore decoherence and propagation delays. You can expect a post when that’s done.
• The so-called “a·cP” phonon-nuclear interaction: I kinda understand this (see my posts a·cP and a·cP take 2) but it still continues to bug me. I thought I understood that the idea was: accelerating a nucleus can excite internal-state transitions (e.g. from the ground state to a nuclear isomer), because a fast-moving ground state looks a bit different from the stationary ground state (e.g. length contraction) and maybe you’re accelerating fast enough to avoid the adiabatic theorem. But now I’m not sure: It seems to me that general relativity should prevent mere acceleration from causing any real transitions, because (1) acceleration caused by a uniform body force is just like gravity, and (2) gravity is just like an accelerating reference frame, and (3) an accelerating reference frame obviously can’t cause any real transitions. (Though on the other hand, there’s this.) But I need to think about it more carefully. Dr. Hagelstein has this new 87-page paper on the topic of a·cP so I guess I should read that.

So, I have a lot of work to do! 😀