This would apply for a sustained gap, where no re-contact between conductors would happen to re-draw the arc. And in reality, we can see these series arcs happen with very very narrow (smaller than a millimeter) gap. In addition to the air gap breakdown voltage, there is a voltage drop characteristic, much like seen in semiconductors, whenever you have transitions between different metals and the arc. I have only found a small amount of science on these aspects of arcs. But they do play some role in gas-discharge lighting.
Arc damage is cumulative and it tends to be self perpetuating. Arcs damage points and damaged points arc more. Once you have a high resistance contact it will just get hotter, making the resistance higher, rinse, repeat.
A spark is an arc unless you are really splitting hairs. I agree with the author who says it is hard to maintain an arc at normal household voltages and currents but I have a buzz box welder that can maintain an arc at some pretty low voltages.
Yup ... anyone who has welded knows you can do an awful lot with 1500 watts .... even at a modest 12v setting. That's car battery voltages.
FWIW, I've drawn some pretty good arch simply by jump-starting cars. Available energy? Well, enough to detonate one such cars' battery. Yet ... could the arc have been maintained for any length of time? I have not tried it.
"Peer review" is what we're doing here. We are checking the assumptions, assertions, and logic of Mr. Engle. That means finding his sources.
Mr. Engle also makes statements in his paper that infer the composition of the electrodes matters. For a broken wire, that's a pair of copper electrodes. He asserts that there is a difference between and arc and a spark. He asserts there is a not enough energy to light cotton. He asserts that there is a difference between a 'series' arc and a 'parallel' arc.
Yet, the biggest assertion is that the laws of physics precludes arc creation. He refers us to Pashchen's Law. Well .... does the law really say that?
I would say that this matter must be resolved before the AFCI debate can proceed.