My current LK99 questions

So this morning I thought to myself, “Okay, now I will actually try to study the LK99 question, instead of betting based on nontechnical priors and market sentiment reckoning.” (My initial entry into the affray, having been driven by people online presenting as confidently YES when the prediction markets were not confidently YES.) And then I thought to myself, “This LK99 issue seems complicated enough that it’d be worth doing an actual Bayesian calculation on it”—a rare thought; I don’t think I’ve done an actual explicit numerical Bayesian update in at least a year.

In the process of trying to set up an explicit calculation, I realized I felt very unsure about some critically important quantities, to the point where it no longer seemed worth trying to do the calculation with numbers. This is the System Working As Intended.

On July 30th, Danielle Fong said of this temperature-current-voltage graph,

‘Normally as current increases, voltage drop across a material increases. in a *superconductor*, voltage stays nearly constant, 0. that appears to be what’s happening here—up to a critical current. with higher currents available at lower temperatures deeply in the “fraud or superconduct” territory, imo. like you don’t get this by accident—you either faked it, or really found something.’

The graph Fong is talking about only appears in the initial paper put forth by Young-Wan Kwon, allegedly without authorization. A different graph, though similar, appears in Fig. 6 on p. 12 of the 6-author LK-endorsed paper rushed out in response.

Is it currently widely held by expert opinion, that this diagram has no obvious or likely explanation except “superconductivity” or “fraud”? If the authors discovered something weird that wasn’t a superconductor, or if they just hopefully measured over and over until they started getting some sort of measurement error, is there any known, any obvious way they could have gotten the same graph?

One person alleges an online rumor that poorly connected electrical leads can produce the same graph. Is that a conventional view?

Alternatively: If this material is a superconductor, have we seen what we expected to see? Is the diminishing current capacity with increased temperature usual? How does this alleged direct measurement of superconductivity square up with the current-story-as-I-understood-it that the material is only being very poorly synthesized, probably only in granules or gaps, and hence only detectable by looking for magnetic resistance /​ pinning?

This is my number-one question. Call it question 1-NO, because it’s the question of “How does the NO story explain this graph, and how prior-improbable or prior-likely was that story?”, with respect to my number one question.

Though I’d also like to know the 1-YES details: whether this looks like a high-prior-probability superconductivity graph; or a graph that requires a new kind of superconductivity, but one that’s theoretically straightforward given a central story; or if it looks like unspecified weird superconductivity, with there being no known theory that predicts a graph looking roughly like this.

What’s up with all the partial levitation videos? Possibilities I’m currently tracking:

2-NO-A: There’s something called “diamagnetism” which exists in other materials. The videos by LK and attempted replicators show the putative superconductor being repelled from the magnet, but not being locked in space relative to the magnet. Superconductors are supposed to exhibit Meissner pinning, and the failure of the material to be pinned to the magnet indicates that this isn’t a superconductor. (Sabine Hossenfelder seems to talk this way here. “I lost hope when I saw this video; this doesn’t look like the Meissner effect to me.”)

2-YES-Z: This is actually some totally expected thing called a “toroidal Meissner effect”, which is exactly what we should expect to see given the one-dimensional nature of the superconducting arrangement of quantum wells, and supposedly looks just like some previous video for carbon nanotubes. This was said by a Russian catgirl.

2-YES-Y: There is so much diamagnetism on display here that you wouldn’t see it without some superconductivity.

2-NO-B: There’s an unusual/​unprecedented amount of diamagnetism here, but in a way that fits pretty well with “they found some magnetically weird material after screening for magnetic weirdness” better than “superconductivity”.

How much of a surprise was Sinead’s flat-band calculation? On the NO story, how likely or unlikely was the logical observation, “a result like this is calculated, for an actually-non-superconducting material, that was prescreened by the filters we already know about”?

Possibilities that are obvious and/​or that I’ve seen claimed online:

3-NO-A: LK were deliberately seeking out materials like this, and the materials they screened were selected to all be the sort that would have a calculated flat band; therefore, arguendo, the result is not too surprising on NO.

3-NO-B: Most materials in the potential-superconductor class would have a calculation like this; it’s not a hard result to get by making weird unrealistic assumptions.

3-NO-C: LK found a weird material that isn’t a superconductor, and a weird material like this is much more likely to have a result like Sinead’s calculation be true about that material or some plausibly mistaken neighboring postulated structure.

3-NO-D: We understand so little about the origins of superconductivity that a calculation like this is not even probabilistic evidence about whether something is actually a superconductor. You could probably find a calculation like that for anything magnetically or electrically weird at all.

3-YES-Z: This is a fact we didn’t know from LK’s paper and LK didn’t do any prior selection against it; Sinead’s result is a previously unsuspected-given-NO calculation, that would be very unlikely as a calculation result unless the LK-postulated material was actually a superconductor. (This is how Andercot initially presented Sinead’s result, and there was a large prediction market jump immediately after; based on the subsequent crash, it looks like this was not the conventional reception after some review.)

3-YES-Y: LK already knew this fact, already did some calculation reflecting it, and this is how they found the material in the first place.

3-YES-X: LK didn’t know the Sinead-calculation, but the already-known weirdnesses of the material, and a very high false positive rate of calculations like these, mean the calculation wasn’t all that informative about YES and we don’t say “game won”.

Q4: Do any other results from the 6-person or journal-submitted LK papers stand out as having the property, “This is either superconductivity or fraud?” Like the stuff with thermal capacity or whatevs? Are there any claims—not replicated observations, just claims—that somebody wants to point to and say: “This seems quite improbable to get as an honest mistake, or as the result of other weirdness from this sort of material, absent superconductivity”?

Q5: When the early results hit, many online skeptics were scoffing about improbable or inconsistent results or points which supposedly showed the authors didn’t know physics. Are any standout nits like that still being picked with the 6-person or journal-submitted LK papers?

And finally, while it’s probably not that important, I would like to ask “What are we pretty sure we know and how do we think we know it?” with respect to the dramatic social story.

Supposedly, Lee and Kim have been researching LK-99 since 1999 as the last wish of their dying professor, albeit with a lot of breaks because they couldn’t get any funding and had to go on living their lives.

Q6: Is there any external verification, if we don’t trust LK’s word alone, that they’ve actually been working on this project for that long, and were on the tail of materials in this category from the start?

You may notice that I’m not trying to point to anything as a “prior”, as many layfolk incorrectly imagine to be the essence of Bayesianism. I don’t particularly think that pointing to any particular starting point and calling it a prior would be helpful in figuring things out, at this point.

What Bayesianism really has to say is more of a coherence constraint on how your beliefs should look; a reminder to ask questions like: “What’s the best explanation for Fig. 6 given NO, and how a-priori-probable would that explanation have sounded before we saw the graph?”

Bayesianism, or rather probability-theoretic coherence, inspires me to say that what I’d hope to see laid out by experts or collaborating Internet citizens, is a list of...

(1) Every observation, claim, fact, diagram from a paper, etcetera, which is supposed to be confusing or surprising given some possible states of the world, or bear in any way as evidence upon our probable beliefs;

(2) An account of the best ways to explain each such point, from both a YES or NO standpoint, as somebody who honestly believed YES or NO would give their own best account of it. enough detail that you could notice if any parts of the best combined YES story or NO story stood out as a priori improbable, themselves surprising, or incoherent between points.

Possibly if we had that whole list, it would still seem worth the trouble of trying to yank out numbers, and attempt an explicit calculation of how probable the best YES story and the best NO story seemed. Or possibly it would seem like, as so many people on the Internet claim—and the more forthright ones have bet—that it’s time to call it, in one direction or another.