Just wanted to say a few quick things about Haag’s theorem, now that Marian (Gilton), David (Freeborn), and I have finished our first paper on it (hopefully! it was conditionally accepted prior to this most recent revision).
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I’ve heard quite a few folks react to our interest in Haag’s theorem as an instance of a no-go theorem, especially in our capacity as philosophers, with something like “who cares, we know it’s not really ‘about’ the fundamental ontology–why don’t you look at no-go theorems more like Bell’s theorem”?
And honestly, fair enough! I think it’s probably right to say that Haag’s theorem isn’t “fundamental” in anything like the ontological sense–our usual renormalization techniques do an end-run around the problem, and we even have some plausible physical explanations for what’s going on (evinced in reactions like “:eye_roll: just put the system in a box–problem solved”).
But at least for me, this is precisely why Haag’s theorem is an interesting case! One, that it seems so trivial today should–if we’re being good-faith historians–tell us that something interesting has changed between when the theorem was proven and now; these were (presumably) smart people, so it’s worth trying to figure out why they worked toward it and found it so interesting. Did they, for instance, really think–as many people imply when they brush it off–that it was a deep and insurmountable barrier for QFT? Or, rather, did they find it interesting for more specific, and perhaps unfamiliar to us, reasons? (Hint: it wasn’t the former.) What were these reasons, and why don’t we think this way today?
Second, I think this sort of no-go theorem is ecologically much more typical. Sure, Bell’s theorem seems to still be stuck in our craw even 50 years later, but this doesn’t seem to be normal. More to the point, I doubt that many mathematicians, physicists, etc. expect no-go theorems to retain their foundational status in the Bell-type way. Which should–I think–suggest to philosophical onlookers that maybe there’s something more to no-go theorems than their ontological consequences. Maybe their utility is better cashed out in some other way? And maybe it’s worth engaging with our colleagues in physics and mathematics to figure out when and why they generate them today?
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At the same time, I’m still surprised that Haag’s theorem seems to be experiencing a resurgence of interest of late (e.g., this twitter post accruing more than 34k views in a day). Of course, Marian, David, and I have our reasons for thinking the theorem is worth thinking about. But despite having spent the past few years thinking about it, I’m still not sure I can give a (unified) explanation for why interest has spiked now. My current guess is that it’s somehow downstream from the bump in quantum gravity research the past few decades and increasing anxiety about the hierarchy problem, but I also get the sense that interest is coming from several different directions at once. :shrug: Maybe I’ll scrape some social media data at some point to see if there are any identifiable patterns.
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I can’t help myself–I got too good a chuckle out of this one not to share it:
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Finally, I also want to give a shout out to the two reviewers of our paper (mentioned above). The reviewers were (very!) thorough, charitable, and insightful, and the final paper is much better for their reviewing. Plenty of negative vibes out there about reviewers, so I want to go out of my way to note how deeply grateful I am for their hard work. Thank you, whoever you are!
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