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The talk was to non-technical philosophers, so had to steer clear of the kind of technical content in my Vienna talk.
Someone raised a natural question that I hadn’t considered. Friedman makes much of the idea that new mathematical languages make possible the expression of physical principles which via coordinating principles allow for the formulation and testing of empirical regularities. As things proceed, there is a shift in status (slides 13/14 of the latest talk), e.g., what was an empirical regularity may become a coordinating principle. The question was do we see the same thing happening with my ’third exemplar’.
In that Vienna talk, I just had ’quantum gauge field theory’ as coordinating principles. But can I cast this in promotion/demotion terms from an earlier stage?
Regarding your question above:
I may have to read more closely, but isn’t the unification of the empirical regularity of anomaly cancellation conditions into a single postulated source for these a good such example?
Re “curious lack of interest” on slide 17:
I suppose the hesitancy among honest but lay philosophical thinkers in entering territory of contemporary HEP speculation is that they at least sense its ill-defined and hence esoteric nature, even if they can’t themselves pinpoint which segments are well-founded and which are not. In contrast, they are happy to refer to, say, GR even if possibly not fully grasping it, for feeling certainty that it can be grasped without relying on insider agreement. The other side of this medal is that the superficial philosophical thinkers happily ignore such restraints and hence are filling the public domain with grandiose-sounding but shallow nonsense.
That’s one reason why it’s imprtant to try to find solid mathematical foundations for the cutting edge folklore in HEP.
Thanks!
I may have to read more closely, but isn’t the unification of the empirical regularity of anomaly cancellation conditions into a single postulated source for these a good such example?
So it wouldn’t just be the uniting of a range of empirical phenomena under a single empirical law. There has to be a promotion to something almost definitional. E.g. for Newton’s , if something’s appearing not to fit, you must have the , , or wrong. It’s like claiming that the standard metre rule (while it played that role) is not a metre long.
So it’s about baking something which appeared empirical into your principles. We’ve spoken about this in the context of maths, e.g., baking in the equivalence that mathematicians discovered they wanted inside the HoTT setting.
But now maybe we can do something with anomalies, because what did you once tell me about them?
Is there any way to say when ’all’ cancellations have been dealt with, to know when some theory is anomaly-free?
This has a tautological answer:
Recall that physicist’s “anomaly” is mathematician’s “obstruction” read in reverse:
The mathematician first lays out design plans of what exactly they are about to construct, and then looks ahead to see if anything obstructs the path ahead to that goal.
The physicist instead storms ahead without further ado. When they hurt their nose running into that boulder lying in the way, they mumble something about “this is not what happened last time to me, this does’t seem normal – indeed, since we are used to lucking out, we have to say that the situation we find ourselves in is outright anomalous!”
In either case, an obstruction/anomaly just means that a certain would-be construction does not actually exist.
So:
If you really know what it is you are constructing, then you know you have lifted all obstructions, hence cancelled all anomalies, when you have actually constructed the darn thing.
If however, as here with M-theory, you do not know in advance what you are constructing, it’s a different story.
What is happening here is that the full theory itself is unknown but various limiting cases of it are prescribed and understood (close analogy: the would-be theory of the “field with one element”). So then at least those limiting cases should actually exist hence be consistent, hence be anomaly free.
But without knowing what thing the full theory actually is, there is, tautologically! no way to know if all its anomalies have been cancelled.
But the idea with working towards M-theory is the opposite: If a natural mathematical structure implies an indefinite but already long list of expected consistency checks/anomaly cancellations, then chances are that this mathematical structure is the elusive theory, and then, since that exists it is anomaly free.
Can we cast this as a promotion from empirical findings of anomaly cancellation to it being baked into the constitutive framework?
Regarding #2
I suppose the hesitancy among honest but lay philosophical thinkers…
That’s interesting. But stretching right back through quantum physics, what to say if you’re Friedman? He himself mentions that philosophical attempts to understand were not ’timely’. He gestures to the kind of transformation that might be needed, such as quantum logic.
But what if it were a case of physics and mathematics needed to work themselves out and they just hadn’t done this until recently? Maybe as Witten does we place the emphasis on geometry,
I would consider trying to elucidate this proper generalization of geometry as the central problem of physics, certainly the central problem of string theory.
So that there’s been plenty of scope for ’metascience’ over the past 90 years, but it’s only when now we have a suitable logic-geometry in place, and then physics, that the philosopher proper comes in.
Funnily enough, the person who asked about the promotion/demotion issue also made this point of where was I in this? If the new revolution is not complete, one is engaged in meta-science.
Hegel makes for another question, if the Science of Logic is really on track. Collingwood, who observes that a physicist like Eddington begrudgingly admits the Hegel was right
The discovery by a very distinguished scientist that there are grains of sense in Hegel’s Naturphilosophie, and that he feels himself obliged to apologize for having made the discovery, is a sign of the times. How far was the habitual and monotonous execration of Hegel by nineteenth century scientists due to the fact that he violently disliked the science of his own day, and demanded the substitution for it of a physics, which it turns out, was to be in effect the physics that we have now?
also observed that there was little point in philosophers anticipating what scientists would have to find out for themselves. Odd, because Hegel himself is famous for the idea that philosophy comes in after the event
“The owl of Minerva spreads its wings only with the falling of the dusk.”
Lots of aspects here, where to start!? :-)
By the way, it may be easier for people to think about the big open questions of solid state physics than those of high energy physics, e.g. about strange metals and high -superconductivity rather than M-theory. As we speak some solid state physicists are going all in on suggesting that these are AdS/CMT dual to each other. The recent Zaanen 2021 is a fascinating read in this respect, as it transmits the excitement.
Indeed, everything comes together here: Experimental solid state physics, cutting edge technology (quantum computers), deep quantum physics (entanglement to the extreme, already in ground states), gauge theory, and dual to all that: GR, black hole physics and BH microstates in the large limit, and then string- and M-theory for realistic small .
It’s fascinating to read the accounts about this from solid state physicists like Zaanen who did not start out as being interested in gravity or even strings, but who realized this is where the answers to the big open questions in CMT may be found.
Much to think about here for the alert philosopher…
Fascinating stuff, but still I think Friedman would be particularly interested in the formation of the new geometry of higher gauge theory. Your observation
it is fascinating to see that the higher category/higher homotopy theory is not just descriptive, but there are indications that it is in fact constitutive for string theory
contains a term he loves – ’constitutive’.
Oh, yes. that’s what I eventually formulated (slide 5 here) as saying that homotopy theory is the mathematical embodiement of what is the gauge principle in physics, namely the paradigm that it is wrong to ask if any two things are equal, instead one must ask for gauge transformations between these, and higher gauge transformations between those. (I.e. the physics analog of the story of identity types as higher groupoids, but physicists arguably got there first with their ghosts-of-ghost fields…)
But above I meant to say that if somebody loves constituitive statements like this but can’t seriously see themselves thinking, let alone speaking, about string theory or anything related to modern HEP, then essentially the same statement can be made with “string theory” replaced by that sector of solid state physics which, apparently, is currently being rebranded as “quantum supreme matter”: The previously missing theory of high temperature superconductors and their “strange metal” phases.
I see. Well a couple of questions after my talk alluded to the lack of empirical evidence for string theory. It’s certainly filtered into philosophers’ consciousness.
Did you see poor Zaanen’s Wikipedia page? 13 references and 6 are to criticisms of his use of string theory! Editing required.
But that raises an interesting point – what is the relationship between Zaanen et al.’s use of string-theoretic ideas and string theory itself?
There’s John Baez’s line from one of those 6 references:
the application of mathematical techniques from string theory to the problem of heavy ion collisions is completely separate from the issue of whether string theory is a correct theory of fundamental particle physics. The stuff you’re talking about is just a clever new way of doing calculations in Standard Model physics. Even if it works, it doesn’t mean the universe is made of strings.
But I take it from your suggestion in #7 and #9 that you don’t take them to be merely clever new calculation techniques. But then what’s a good comparison of their relationship? At the tightest end there’s something like:
Kirchoff’s laws for circuits are no less real electromagnetism for being concerned with a limited situation. It’s what happens when you apply Maxwell’s equations to circuits. The cohomological aspect of the former derives from the latter. Evidence for the former counts as evidence for the latter.
I guess physics allows for more subtle relations, like belonging to the same universality class.
I see in that thread Polchinski is quoted
String-theory skeptics could take the point of view that it is just a mathematical spinoff. However, one of the repeated lessons of physics is unity — nature uses a small number of principles in diverse ways. And so the quantum gravity that is manifesting itself in dual form at Brookhaven is likely to be the same one that operates everywhere else in the universe.
Re #10 That referencing and these quotes are all straight out of Monty Python’s “What did the Roman’s ever do for us?” with just some words replaced.
But it’s okay, I am not talking about teaching the masses some sense, I am talking insider knowledge to you. This is not known on Wikipedia or in TWF, and it need not be.
What confuses people is (most won’t know that this is what confuses them) the predominance of the early story of the heterotic string, where realistic gauge fields exist in the bulk and no D-branes are present. In all other corners of the M-theory amoeba, (type IIA, IIB, I, M, , F) realistic HEP physics arises in exactly the same general way in which quantum supreme matter arises in AdS/CMT, namely localized on coincident branes which sit at the center of AdS black brane throat geometries inside an RS-like bulk. Here the bulk strings are identified with the QCD-string “flux tubes”, completing – in a remarkable story going full circle – the historical origin of the idea of strings. Polyakov understood this qualitatively already in 1998 (“The wall of the cave”), and is has been brought out in quantitative detail through the modern WSS-model, and its variants, in AdS/QCD.
But I wish I had proper insider knowledge. As it is, I manage to glimpse only some outlines. One of these days I really have to go back to basics and systematically learn some physics, with all this fine detailed exposition on the nLab to hand.
Sure, that’s why I was trying to point it out. I was just venting my frustration with the anti-intellectualism of that Wikipedia article and its sources.
Zaanen addresses the need to be prepared to learn something new, e.g on p. 7:
When one first encounters this the way it works may appear as absurd: fanciful black holes under the reign of general relativity act as quantum computers to describe the observable properties of the quantum supreme stuff. … the correspondence reveals such meta-principles governing the properties of quantum supreme matters being entirely different from nearly anything found in the textbooks …. In a very exciting recent development evidences are accumulating in the condensed matter laboratories that these general principles are operational in rusty copper and related systems.
On the other hand, it’s not all that much of a secret anymore, with two textbooks already 5 years old now. Zaanen’s recent review tries very much to convey the cutting edge insight to a lay audience. Also the thesis Amoretti 17 is a good introduction, though I admit I forget how this may read to somebody who may not have seen a Brillouin zone before.(?)
Actually, it shouldn’t be that much of a mental leap: It is already familiar that the existence of hadrons – which we can see, e.g. via the tracks they leave in bubble chambers – is explained by hypothetical constitutents termed “quarks” that nobody has ever seen or even indirectly detected. One shouldn’t forget this: Just because everybody got used to saying “quark”, they have never been seen.
All that is being added here to this story of the unseen quarks is that the unseen flux tubes connecting them actually extend into an unseen bulk spacetime.
The claim is that this little addition to the quarks picture completes its explanatory power to the non-perturbative regime.
Removed an article by a different Michael Friedman, now at Michael Friedman (historian).
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