Stimulated Emission in quantum mechanics

As I explained in the last post, about superradiance, we are gearing up to discuss Peter Hagelstein’s spin-boson model” theory of cold fusion. The theory relies very heavily on two effects that make it easier to transfer energy to an oscillation mode: Dicke superradiance and stimulated emission. This post goes over how stimulated emission works in quantum mechanics. It’s much simpler than the last post, don’t worry. As before, experts can skip this post.

Superradiance was first described by Dicke in 1954 in this paper (official link). If you are a laser / optical physics expert, then you already know all about it. For everyone else, this post is an introductory tutorial.

Motivation: What does superradiance have to do with cold fusion? Well, I’m gearing up to discuss Peter Hagelstein’s “spin-boson model” theory of cold fusion. This theory says that the 24MeV of energy from D+D→⁴He fusion goes more-or-less directly into exciting a billion or so phonons (all of them in a single phonon mode, i.e. all at the same frequency, wavelength, etc.). Normally, this process would be extremely unlikely. However, there are two famous effects that increase the probability of transferring energy to an oscillation mode: Dicke superradiance and stimulated emission. Accordingly, the spin-boson model relies very heavily on both of these principles.

Since it’s impossible to thoroughly understand the spin-boson model without understanding superradiance, and since I couldn’t find a suitable description online, I wrote out this post. Buckle your seatbelts, let’s do some physics!

Widom-Larsen 5: Would the neutrons actually be slow?

In Widom-Larsen theory, they say that the surface of a metal hydride has very energetic (“heavy”) electrons that can undergo electron capture $e^- + p^+ \rightarrow n + \nu_e$ (electron plus proton turns into neutron plus electron neutrino).

A central claim in the theory is that the electron capture process creates extremely slow neutrons. And I mean extremely slow! The neutron kinetic energy is supposed to be as low as $10^{-9}$ electron-volts, or even less! (Room-temperature thermal neutrons have millions of times higher kinetic energy. Even “ultracold neutrons” are fast by comparison.)

Widom-Larsen 4: The protons’ magical restoring force

As explained best in the 2008 paper, Widom-Larsen theory envisions a weird sort of surface plasma oscillation. Now, normal plasma oscillations (in solid-state physics) refer to a collective electron motion. But they’re talking about proton motion (the protons or deuterons embedded in the hydrated palladium). There is a vague suggestion that the electrons also move. But they certainly emphasize the proton motion by itself, and describe it in an explicit way here:

Widom-Larsen 3: Ponderomotive (quiver) energy

In Widom-Larsen theory, it is argued that there is a region at the surface of a metal-hydrogen (or -deuterium) system where electrons have an insanely high mass, as much as 10.5MeV/c², because of the electromagnetic environment they are in.

In the the previous post, I argued that you should understand that “insanely high mass” implies (or maybe is equivalent to) “insanely high energy”. In this post I will explain what exactly this energy is, according to Widom-Larsen theory. It’s simpler than you might think!

Widom-Larsen 2: The meaning of enhanced mass

As described in the last post, Widom-Larsen theory states that the electron-capture process $e^- + p^+ \rightarrow n + \nu_e$ (electron plus proton turns into neutron plus electron neutrino) can and does happen on the palladium hydride surface. (Discussed in Sections 1-3 of the paper.)

Now, if you compare the energy of the two sides in $e^- + p^+ \rightarrow n + \nu_e$, you’ll see that this would work if the electron mass is at least 1.3 MeV/c², rather than the usual 0.51 MeV/c². Well, that’s exactly what Larsen and Widom are arguing! They say that the environment at the surface of a metal hydride has properties which dramatically increases the electron mass.

Widom-Larsen part 1: Overview

The Widom-Larson theory of cold fusion started with this paper:

“Ultra Low Momentum Neutron Catalyzed Nuclear Reactions on Metallic Hydride Surfaces” by A. Widom, L. Larsen, 2005.

A follow-up paper with more mathematical details is here, while a follow-up with slightly more qualitative discussion is here.

This is apparently the most popular theoretical explanation of cold fusion. For example, it was the theoretical justification supporting NASA’s cold-fusion program. Apparently, lots of reasonable people are convinced by it.

In ordinary “hot” deuterium-deuterium fusion, you get:

• D+D → neutron + helium-3 (~50% of the time),
• D+D → hydrogen + tritium (~50% of the time),
• D+D → helium-4 + a gamma-ray (0.0001% of the time)

In palladium-deuteride cold fusion, you allegedly get more-or-less only helium-4, plus energy that winds up as heat. Very strange!

A reasonable guess is that the reaction is different because there is a third particle, besides the D+D, involved in the fusion reaction as a “spectator”:

• D + D + spectator → helium-4 + spectator

Goalposts: What are we trying to explain?

There are a variety of phenomena under the heading of “cold fusion”, but for now I’m primarily thinking about the oldest, most famous, and most-widely-tested aspect: Heat produced in palladium-deuteride systems, which is (allegedly) due to the D + D → He⁴ nuclear reaction.

If D + D → He⁴ is really what’s going on, it has a number of properties which are awfully hard to explain. The cold-fusion skeptic John Huizenga described these as the “miracles” of cold fusion, in the sense that they have no possible explanation. Anyway, everyone agrees that a plausible theory of cold fusion would at minimum need to answer the following two questions:

• Why doesn’t the Coulomb barrier prevent fusion from occurring in the first place? Since the two nuclei are positively charged, they repel very strongly until they get so close that they can fuse. It can happen at extremely high temperatures or pressures, as in a thermonuclear bomb, or a star, or a tokamak, or using a laser the size of a football stadium. It can also happen if you accelerate a beam of deuterons to a high speed, and shoot it into other deuterons, as in a Farnsworth Fusor (try it at home!). It can also happen in muon-catalyzed fusion, for well-understood reasons. But it is difficult to see how the Coulomb barrier could be overcome in a cold-fusion experiment.
• If D+D fusion is occurring, why does it only create helium-4, and why doesn’t it create comparable quantities of helium-3, tritium, neutrons, and gamma-rays? That’s what normally happens in conventional “hot” D-D fusion. In fact, if cold fusion produced neutrons at the same “branching ratio” as you expect from “hot” D-D fusion, it would be easily detected in the experiments … by the radiation-poisoning death of everyone in the room! Actually, neutrons and tritium are sometimes seen in tiny tiny amounts (if I understand correctly), but it’s such a low level that it could only be a “side-channel” at best, as opposed to the main event producing all that heat. So, obviously the reaction is proceeding in a different way than hot fusion. What is it, and why? (The constraints will be discussed more in the next post.)

Cold-fusion skeptics think that there is no theory that answers these questions. Proponents have offered a variety of theories that they claim DO answer these questions. Should we believe them? We shall find out! Stay tuned!

Is there experimental evidence of CF?

[UPDATE 5 YEARS LATER: After spending a lot more time studying this question, I wound up having stronger and more informed opinions on it; see the post The case against cold fusion experiments.]

I’ll kick off my new blog with an important question, a question that impacts whether this blog should exist in the first place: Is there experimental evidence of cold fusion? Here is my understanding, but this is all a bit new to me.

Cold fusion started with an experiment by Fleischmann and Pons. They did an electrochemistry experiment involving palladium and deuterium, and announced in 1989 that their apparatus produced excess heat (much more heat than could be accounted for by chemistry), and also signatures of nuclear reactions. Many labs immediately tried to reproduce these findings, and most failed, and it later emerged that those alleged signatures of nuclear reactions were misinterpreted. (Fleischmann and Pons are not nuclear physicists.)

Already here, the history becomes very contentious. For example, one of the groups that tried to reproduce the results was at MIT, and they said they couldn’t reproduce the heat signal. But in the cold fusion community, there’s a story that MIT actually did reproduce the heat signal, but reported to the contrary due to incompetence or fraud (allegedly to protect funding for the MIT plasma fusion program!). Conversely, the groups that claimed to successfully reproduce the results are accused by cold fusion skeptics of not actually doing so, again due to errors or fraud.

Anyway, by 1991 or so, mainstream science and society had decided that there’s no such thing as cold fusion, but a small group of proponents continued to believe in it and study it. And they still do to this day. According to proponents, the subsequent decades of work have brought dramatically better experimental evidence of cold fusion, refined procedures, more consistent lines of evidence, and so on. The mainstream view is that this is the cozy consensus of true believers in a pseudoscience, egging each other on.

It’s really hard to evaluate these decades of experiments, because pretty much all the mainstream subject-matter experts have long ago stopped criticizing specific experimental results and methods, and instead they just ignore the field entirely. I am very familiar with this dynamic, because sometimes I edit Wikipedia articles on all sorts of bizarre, obviously dumb fringe physics theories like this one, and it’s always really tricky because the only sources who ever mention these theories are their passionate advocates or inventors. So in some cases, literally everyone who is most qualified on paper to discuss Theory X (having published about it etc.) is a passionate believer in Theory X … but Theory X is still super duper wrong and dumb. So we can get the wrong answer by deferring to the subject matter experts. I’m not saying that cold fusion is necessarily following this dynamic, I’m just saying that this is a possibility to keep in mind.

So anyway, you read this old version of the Wikipedia article written by a proponent, and it sounds like there’s overwhelming experimental evidence for cold fusion. But if you digging, everything is murky. Did “Mitsubishi Heavy Industries [observe],…in a spectacular series of experiments that have proved 100% repeatable, host metal transmutations”? Well, “100% repeatable” may be a stretch when a different group could not reproduce the results despite spending millions of dollars and working closely with MHI. I’m not siding with NRL or MHI here—I haven’t tried to evaluate the back-and-forth—I’m just saying that it’s very hard to figure out what’s going on, it’s not immediately clear who to trust, and nothing can be taken at face value.

Are the theoretical and experimental questions really separate? The theoretical question is “is there a plausible physical mechanism for cold fusion?” The experimental question is “is there experimental evidence for cold fusion?” Many cold fusion proponents argue that these are independent questions. For example, here is an anonymous comment in a 2006 argument on the wikipedia cold-fusion discussion page:

you also say “the most important fact about cold fusion is that it cannot work” – no, the most important fact about [cold fusion] is the experimental observation that it does work; the fact that conventional theory cannot explain why it works is purely incidental.

In other words, cold fusion is an experimental observation, and experiments are the ultimate arbiter of truth in physics, and if theorists cannot explain an experiment, then they should get to work finding a better theory.

This sounds very nice. It sounds like The Scientific Method like we all learned in school and read about in Karl Popper. Who could object to The Scientific Method?

It sounds nice, but it’s wrong! It is rational to give experiments a complete veto over theory only if experimental results are always correct. That’s not the case! Sensors can be calibrated incorrectly. Procedures can be followed incorrectly. Results can be described and interpreted incorrectly. Experiments can be wrong for reasons that are extraordinarily subtle, reasons that are not understood for months, or years, or ever. This is not a nitpicking hypothetical, it is one of the most basic facts of life for everyone in experimental science and engineering.

Therefore it is not only extremely common in practice, but also entirely correct, to use theoretical physics to inform our guesses about which experimental results are trustworthy. In other words, we are doing a Bayesian analysis of what to believe, and both theoretical and experimental knowledge are legitimate inputs into this analysis.

(Example: Here is a link to a meta-analysis in support of parapsychology. Oh, you still don’t believe in parapsychology? Did you meticulously read that article and judge its methodological soundness on its own merits? Or did you rule it out based on prior expectations derived from theoretical physics?)

(Note: If the previous paragraph doesn’t work for you because you really do believe in parapsychology, you’re definitely reading the wrong blog.)

Finally, my answer to the question: Is there experimental evidence of cold fusion? Based on what I know so far (which isn’t very much!) my assessment is: There is enough experimental evidence of cold fusion to make it worthwhile to spend some time searching for a plausible theory of cold fusion … especially since this is the kind of thing I like doing for fun. But there is not SO much experimental evidence that I would believe in the existence of cold fusion without seeing such a theory! I would rather disbelieve even 100 independent cold-fusion experiments than throw out everything we know about quantum field theory and the Standard Model of Particle Physics, if that’s really the choice. (Whatever experimental evidence there might be for cold fusion, it’s absolutely dwarfed by the experimental evidence for our current best understanding of the laws of physics in general.)

So that’s my motivation for starting this blog. Is there a plausible theory of cold fusion? Let’s find out! The journey begins…