Next week there will be a workshop in Munich with the title Why Trust a Theory? Reconsidering Scientific Methodology in Light of Modern Physics. It’s organized by Richard Dawid, to discuss his ideas about “non-empirical theory confirmation”, developed to defend string theory research against accusations that its failure to make any testable predictions about anything make it a failure as a research program.
I guess the idea of such a workshop is to bring together string theory proponents and critics to sort things out, but looking at the program and talk abstracts, this doesn’t look promising, with the central issues to be evaded, and speakers likely to just talk past each other.
While the workshop title refers to “Modern Physics” in general, the talks are mostly focused on one very narrow part of the subject: quantum gravity. String theory is supposed to be something much more than a quantum gravity theory, explaining the Standard Model and low energy physics. This has been a complete failure, and the plan at the workshop seems to be to deal with this elephant in the room by ignoring it, or worse, claiming it isn’t there.
From the talk abstracts, about the only person discussing particle physics will be Gordon Kane (Quevedo may mention it, although his main interest is cosmology). Kane will be claiming that string theory makes testable predictions about particle physics, ones about to be tested. The problem is that he has been making the same claims for thirty years, arguing back in the 90s in the pages of Physics Today and a book that string theory would be tested at LEP and the Tevatron (by finding superpartners). As his predictions have been conclusively falsified, he just refuses to acknowledge this and starts advertising new ones. Perhaps the most outrageous case of this is his latest book (discussed here), which is a reissue of the old one, with falsified predictions simply deleted and replaced, without any acknowledgement of what happened. I don’t think this behavior raises any philosophical issues about theory confirmation, just the sociological issue of why the physics community tolerates this, or why he’s the one person invited to this workshop to address the largest problem of the subject.
Another central problem here is the hype problem. If you give up on testability, and allow theory confirmation based on claims that “my theory is just better” by some ill-defined metric, you open up the obvious problem of how to deal with people’s natural human inclination to praise the wonderful characteristics of their intellectual children. At the workshop, Joe Polchinski’s talk is entitled “String Theory to the Rescue”. I see nothing in the program about any planned examination of the significant string theory hype problem, or even any acknowledgement that it exists.
I’m actually in a way more sympathetic than most people to the idea that “non-empirical” evaluation of a theory is an important and worthwhile topic. Fundamental physics theory is facing a huge problem due to the overwhelming success of the Standard Model and the increasing difficulty of exploring higher energy scales. If it is to continue to make progress there is a real need to do a better job of evaluating theoretical ideas without help from experiment. There is a group of scientists who have a lot of experience with this problem, and have a well-developed culture designed to deal with it. They’re called “mathematicians”. Despite the fact that this workshop is hosted by the Munich Center for Mathematical Philosophy, the organizers don’t seem to have thought it worthwhile to invite any mathematicians or mathematical physicists to participate, missing out on a perspective that would be quite valuable.
Update: It’s now “this week”, not “next week”. Some tweeting from the conference going on, you can try the hashtag #WhyTrustATheory. Massimo Pigliucci comments from the Q and A session about a problem with this kind of thing: some people “very very much like the sound of their own damn voice”. I hear that David Gross claimed to have 20 possible observations that would invalidate string theory, but didn’t say what they were.
Update: Massimo Pigliucci is blogging a detailed account of the conference, see here (he’s also a speaker, slides here).
Update: I don’t think I’d noticed before that Lee Smolin has a very much to the point review of the Dawid book here.
I would go in the opposite direction. What about really scrutinising the theories we already have, against the data we already have. The LHC is producing and has produced presumably petabytes of data. I presume Fermilab’s results and many others are also on file. Who among theorists is looking at this data, testing it against newer theories? Has all value really been squeezed out of these? Given the plethora of untested theories, my guess is that theorists really aren’t in the habit of looking, and/or experimenters aren’t in the habit of showing.
Could a lot of overly speculative theories be avoided if the speaker was required to say “I checked this against XYZ data sets and they didn’t immediately invalidate most of it”.
RandomPaddy,
As far as I can tell, phenomenological theorists and the experimentalists themselves are already trying the best they can to do what you suggest. Every HEP experimentalist I’ve talked to tells me its their fervent hope to discover something that disagrees with the Standard Model and that this is the main focus of their research.
The problem with speculative theories is not that no one is trying to confront them with experiment, but that they’re too ill-defined to do so, or carefully constructed to evade the possibility of such a confrontation.
Peter,
I don’t think it’s quite true to imply that Dawid has organised this conference on his own. I believe he’s also had inputs from George Ellis and Joe Silk, the authors of the short note in Nature last December which triggered the decision to hold this conference. That was a strongly-worded piece (aside from calling for a conference, they suggested that journal editors and publishers assign speculative work to research categories other than ‘physics’ and that ‘the domination of some physics departments and institutes by such activities should be rethought’).
I think it’s highly likely that the protagonists in this debate will tend to talk past each other, but Ellis and Silk will be joined by Carlo Rovelli, Massimo Pigliucci, Helge Kragh and Sabine Hossenfelder, all of whom have been critical of the string theory enterprise, the community’s tendency to hype and distort its promise and the threat it poses to the integrity of the scientific method and the public understanding of science.
I think there will be plenty of opportunity for argument, at least.
I don’t have high expectations, but I’m hoping that the conference will help to foster a better understanding of the role that the philosophy of science can play in all this. This should be all about seeking to define an acceptable approach to theory development and selection in high-energy physics and cosmology, against the background of a relatively slow evolution of experimental and observational science (satellites take decades to plan, build and put into orbit; colliders take decades to plan, build and put into operation). I’m sure that much could indeed be learned from mathematicians, as you suggest, but it may be that the first step is get some kind of agreement that there is a problem here, before working out how we might try to resolve it.
“There is a group of scientists who have a lot of experience with this problem, and have a well-developed culture designed to deal with it. They’re called “mathematicians”.”
Haha! Nice try. Back when I was in grad school, the mathematicians were still trying to prove that interacting quantum field theory exists. W. Arveson, Berkeley math prof 17 years ago: “Here is a good problem for 21st century mathematicians: show that this program for quantizing nonlinear PDEs like [phi^4 theory] can be carried out in four spacetime dimensions. In other words, show that Quantum Field Theory exists in rigorous mathematical terms.” (Have they succeeded yet? Does QED, by far the most accurately confirmed physical theory ever, exist?)
If we wait for the mathematicians to baptize physical theories as acceptable we’ll be waiting a very long time. It took them 25 years to figure out how to formalize something as simple as the Dirac delta function.
Anyway, aren’t there a bunch of mathematicians out there who absolutely adore string theory? As an ex-physicist, my difficulty with string theory was always that it seemed to be motivated mainly by the beauty of the math (and its offer of a way out of some of the more formal difficulties of field theory) – much closer stylistically to Einstein than to Feynman. (Think of Einstein’s quote about how he would have reacted if the eclipse observations hadn’t borne out his theory – “Then I would have felt sorry for the dear Lord. The theory is correct.” vs. the Feynman quote about not being able to fool nature.) I don’t mean that as a criticism of the field – it’s more about my own limitations – but looking to mathematicians to bail fundamental physics out of its current difficulties seems a bit perverse.
I will do my best to be the voice of reason 😉
Thanks Jim,
I do see that string theory critics will be represented, but they’re mostly ones concerned about other issues than the ones I mentioned (with Rovelli somewhat of an exception, although not an HEP theorist, and Sabine well aware of the hype problem). The Ellis/Silk challenge to Dawid was mainly on the multiverse front, and there I’m interested to see that it’s the multiverse proponents who don’t seem to be well represented.
Foster Boondoggle,
My point was not about mathematical physics and whether it’s the answer to any problems in physics, rather that mathematicians understand well the issues that arise when you try and make progress having only things like consistency as your guide.
Bee,
Good luck!
“If you give up on testability, and allow theory confirmation based on claims that “my theory is just better” by some ill-defined metric, you open up the obvious problem of how to deal with people’s natural human inclination to praise the wonderful characteristics of their intellectual children.”
It’s been a long time, and I’m not sure what’s happened since, but in the early 1970s the issue you mention was a problem in the field of Linguistics, specifically with the theories of generative syntax and generative semantics.
After 16 years as a professor I still bristle at the implication that the only “real” modern physics out there is high energy physics.
What am I missing about Dr. Kane? I can think of no equivalent in another scientific discipline. He’d maybe have to be a paleoanthropologist who not only helped convince the majority of the field that Sasquatch exists, but also convinced them that the only plausible explanation for not bagging a Sasquatch by now is that the beast has evolved, through a complex process of phyletic dwarfism, into a nanobacterium-sized extremophilic autotroph that lives in old lava tubes 5km below the Cascade Range. Until core samples reveal no such creature, in which case the estimate is revised to 5.5 km below the Cascades.
I’m not really trying to be insulting, I’m genuinely mystified by this character.
LMMI,
I don’t think he’s convincing anyone of this, with very few people in the field now taking his claims seriously. The real question is why he’s given a public forum to make them. I think that’s clearly because he’s making a case for string theory. There are different standards for claims about string theory than for claims about other ideas…
It’s a pretty darn weird thing to observe, whatever the standards.
I should add I’m using “Sasquatch” as an analogy for the kind of SUSY that “naturally” solves the hierarchy problem and gives us dark matter, etc., i.e. the kind of beast only cryptozoologists take seriously these days.
@Peter,
as a mathematician and having an experience of talks with other mathematicians about what directions of study are reasonable, the way according to common mathematicians would be: who is higher in hierarchy or generally in position of power.
PS Some mathematicians enjoy to pretend that their work has connections to empirical sciences, so that they can get more funding. It may explain why some mathematicians love the string theory…
@Jon Forrest,
decades ago I had seen a lot of ridiculing on linguistics. By now it seems that they solved a lot of issues by the big-data approach. If only particle physicists were able to do it alike.
Peter, I am also going to attend this meeting. If you have specific questions to specific speakers, email me.
shantanu
Thanks Shantanu, I look forward to hearing what you think of the event. By the way, I don’t have an e-mail address for you that works…
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Peter,
I’ll be attending the conference as well (and my e-mail address should work, if you feel like compiling a list of questions… 🙂 ).
Regarding Kane’s book, my feeling is that few of the actual experts in the field have actually bothered to read it, let alone both issues. So they are probably unaware of his “outrageous” behavior, or are reluctant to criticize him without investing some time to seriously read and compare what he said in the two issues of the book. For one, I am in that crowd, and I certainly have better things to do than read two almost-identical books on string theory hype.
Regarding mathematicians, I agree with you that they are underrepresented here, and it could be better. But on the other hand, my impression (based on working with and talking to mathematicians) is that they tend to shrug at any type of problem which cannot be formulated as a theorem. Or at least they are at a loss what to do with such a problem. Granted, I may have talked to wrong people or lousy mathematicians, but as far as I have seen, philosophers are much more adept to providing a clear formulation of a problem, especially when it is too vague to make rigorous sense.
Best, 🙂
Marko
I agree very much with the notion that we can learn from mathematicians on how to evaluate ideas and structures, which are not directly empirically verifiable, and also that mathematicians should be involved in the development of such structures. Collaborations of this kind do exist. One example is Chamseddine & Connes and there are others ‘out there’.
I didn’t find Dawid’s work particularly convincing. A question for the conference (or anyone interested): what’s the relationship between non-empirical theory confirmation (NETC) and Bayesian confirmation theory (BCT)?
It struck me somewhat that many of the NETC arguments could be interpreted as reasons for having a high prior belief in a particular theory in BCT, e.g. few or no viable alternative theories. The “scientific” aspect of BCT – updating a prior with experimental data – is of course absent in non-empirical confirmation.
Also, NECT seems to invoke induction – we’re told the fact that something qualitatively similar to a theory worked in the past helps to confirm that theory. How does this overcome Hume’s problem of induction (w/o BCT)?
vmarko,
I doubt experts paid attention to the books, but they’ve surely aware of his claims in papers and talks that he can use string theory to make predictions, as well as the fact that these predictions keep getting falsified, and he keeps making new ones.
I don’t think mathematicians will only discuss rigorous theorems. It is true that their reaction to an attempt to discuss with them a topic in current quantum gravity research would likely be “I’m not understanding, could you more precisely explain your assumptions and what the question is you are trying to address?” Wouldn’t hurt most physicists to try and engage in a discussion like this.
I hope to hear what you think of the conference, don’t have a lot of questions for the speakers myself. For better or worse, I think I have a pretty good idea how most of them would respond.
Peter,
Whenever I have tried to discuss quantum gravity with mathematicians, they always reacted in precisely the way you described.
But then if I try to engage them in a discussion, I end up realizing that they don’t have a good grasp on QFT, in particular the renormalization procedure. Once I even gave a three-lecture course on renormalization, tailored to mathematicians who do not want to invest a lot of time into learning QFT in all gory detail (a writeup of the resulting lecture notes is here). I don’t know if I did a good job or not, but I became painfully aware that even discussing QFT is way too remote from what mathematicians are used to, and we never reached the point where I could even formulate the problem of QG. And this experience was with the audience whose research is mostly related to TQFT, category theory and algebraic topology, which are arguably the areas of math closest to QG.
My point is that mathematicians live in a world of fully rigorous math (like TQFT), which is quite removed from what physicists deal with (QFT), already at the point of terminology, let alone any further common ground. They do tend to have good will and motivation to engage in QG, but when faced with a learning curve that involves a lot of things which are nowhere near as rigorous compared to the things they are used to, very few actually invest enough effort to swallow all that non-rigorous stuff in order to understand the basic concepts that QG deals with.
Note that I am not trying to criticize them, but only to point out that there is a huge divide in the background knowledge and a way of thinking of a mathematician versus a physicist. It’s just a very big hurdle to cross, in both directions. So engaging them in any discussion related to QG usually stops at the point of that divide, unfortunately.
Best, 🙂
Marko
vmarko,
What I was thinking of more was some of the discussion of new ideas of quantum gravity, where statements are being made like “ER=EPR”. Maybe my mind has been deformed from too long in math departments, but my reaction to a lot of current discussion about quantum gravity is that I can’t follow it not because there is some technical thing I don’t know, but because it’s very hard to figure out what the precise claim being made is. There’s some web of conjectures being invoked, but it’s often hard to understand what’s being assumed about what.
Peter,
Oh, now I understand what you mean, and I completely agree. Mathematicians are experts on stating explicitly all the assumptions of a certain claim or conjecture, and can provide nontrivial input into what is consistent with what, and how various conjectures do or do not fit together. That would certainly bring a lot more clarity into QG physics, and would certainly be a very good thing.
Best, 🙂
Marko
The histories I’ve read seem to indicate that mathematicians were helpful to Einstein because he was asking precisely the right kinds of questions. The equivalence principle he relied upon made the problem to be solved very clear. I look at current debates about, say, the firewall paradox, and there appears to be a distinct lack of clarity, namely because there is a lack of consensus that a “paradox” follows from what is understood about black hole physics. It could either the most important insight of the day, or an irrelevance built on faulty premises. It’s just an example, but the field of quantum gravity apparently has a disturbingly large number of arguments about basic premises, even among adherents of the same theoretical framework. Is it reasonable to expect mathematicians could help if QG physicists aren’t asking the right questions?
LMMI,
The point I’m trying to make (this is much like my comment to Foster Boondoggle) is that the culture of mathematicians might be helpful here, as opposed to the subject itself (which may or may not contain helpful knowledge). I think you’re right that a big problem is “distinct lack of clarity”, and mathematicians are trained to recognize that problem and treat it as one of central importance. Physics has a different culture, with doing an explicit calculation more at the center of things, and an inclination that it doesn’t matter much if the logic of the calculation is murky, since that’s something that can be cleaned up later if the result of the calculation is interesting and reproduces the real world. If your calculations can’t be checked against the real world, and all you have to go by is consistency, my argument is that you might have some things to learn from the way mathematicians operate.
Non-empirical physics really sounds like an oxymoron. Why bother? I was under the impression that the purpose of physical science was to explain the reality that we can see and examine. Perhaps if theoretical physics can come up with an system which specifically predicts the Standard Model and gravity and within which there is a proof that no other such theory can exist we could be happy without empirical evidence. This doesn’t seem likely. My concern is that the exuberance of theoretical imagination unchecked by any empirical examination over the last 35 years is exactly what has left us with the impasse of string theory/KKLT/landscape stuff where we now stand. Why should the application of more mathematical rigour and surety of internal consistency to any fervent ideas that may be forthcoming really take us any closer to understanding reality? This doesn’t seem to have happened yet.
vmarko:
In the early 90s I was involved in a similar effort with our maths department. A mathematician (a collaborator of Shelah – if I had known of the latter then I should have been warned!) in 10 lectures derived Weiner measure because we all knew the common lore of its equivalence to Feynman’s path integral. In return I in 5 lectures was able to derive (using this term flippantly) in the usual physics manner not only Feynman’s PI for the non relativistic case, but also the PI for the Dirac equation (the locally susy version with its grassman variables etc) to bout. All this revealed to me the chasm between physics and the ‘equivalent maths’. For the first time I was exposed to a mass of new (to me then and probably even to most field theorists today – unless they are genning up to become financial engineers!) ideas such as sigma algebras, measure theory, filtered probability spaces, martingales, large deviation theory … the list goes on, all needed just to define and compute Feynman’s PI (more accurately its imaginary time version as I think I remember reading that the naive Feynman’s real time version is known not to exist mathematically, even for non relativistic quantum mechanics – a sobering thought). If all this infrastructure is required just to properly formulate plain old non-relativistic QM, what hope do we have that mathematicians will help with QFT in the near term, let alone with ‘string theory’? A highlight (if that is the correct word!) of my lectures was to justify why all my paths were differentiable (so the action could be computed for each path) when previously the mathematician had shown with complete rigour that with probability unity all paths contributing were continuous but nowhere differentiable! At that point I mumbled something about the renormalisation group!
sm, for that reason one eventually needs a formalization of physics that captures the core mathematical structures of relevance “synthetically”, i.e. without breaking them up into a heap of constituents, but capturing the intended properties right away. There was a talk about such an system at IHES last week. A video recording is linked to here.
The January 2016 issue of Astronomy Magazine has a one-page article that is very pro-multiverse. You are mentioned in the article, entitled “Not science fiction” and subtitled “Three cheers for multiverses!”. The author, Jeff Hester, writes that if you have read his previous columns you know falsifiability is a big deal for him (I have not read all of his previous columns). In his current column he asks first if we can observe multiverses. He goes on to say that that is the wrong question. He says
“the right question is whether theories that rely on multiverses are more or less successful than theories that do not. Putting it differently, the statement ‘multiverse theories will make more interesting and correct predictions than theories without multiverses’ is itself a testable prediction.”
He mentions David Deutsch’s work on quantum information and that Deutsch himself says his work depends on Hugh Everitt’s “many-worlds interpretation” of quantum mechanics.
If I have violated any copyright issues by quoting the author then just delete my post, but if you can check out his article and offer any comment here please do. On to the other hand you may feel it’s just not worth the time responding to every popup supporting multiverses.
LMMI: Exactly. That is very much the point of Chern’s talk for an Einstein Centennial conference (1981) that I mentioned in a comment on another recent post of Peter’s. I got the impression that mathematicians are, for the most part, not particularly interested in groping their way to a clear formulation of a problem, when there are already plenty of clearly stated problems waiting to be investigated (and which show promise of being non-trivial and mathematically fruitful). Einstein was motivated to do this because he felt as a physicist that it was important and necessary. Most mathematicians would be content to say: “Good luck with that. Let me know how it turns out, and if so, whether you would like to consult me about anything.”
I think there is a lot of self-selection working against us here. If a mathematician had the cast of mind to take a serious interest in these problems at these difficult early stages then they probably wouldn’t be in a math department, or they would have already done some serious research bearing on it, despite being professionally identified as a mathematician. Such people are pretty rare, or at least their ideas on physics haven’t been seen as worthy of attention.
I’m a bit suspicious about the way the relation between physics and mathematics is described here. I spent a brief moment in a Theoretical Physics department and some parts of had a close relationship with the mathematicians at the university. This was certainly true for the Statistical Physics group. Some mathematicians even came to that group to get their PHD (an went back to the Mathematics department, got tenure etc.)
Isn’t the problem you are talking about here mainly typical for theoretical HEP, String Theory etc.? My pet theory is that renormalisation is the root cause of it. Mathematically dubious, but it worked – suggesting that a bit of sloppiness and mathematically ill-posed problems are, well, no problem. It worked! String Theory etc. doesn’t seem to “work” in that way, but the attitude is still there.
All,
Please, enough unfocused generic discussion of the uses of mathematics in physics. The issue I was trying to raise in this posting really is something different, the question of what mathematicians might contribute to the topic of this conference (how do you evaluate theories without contact with experiment?). This is about methodology, not the substance of either field. My impression is that most physicists understand so poorly how mathematicians conduct research that they can’t see the issue here (which would explain why no one seems to have invited any to participate).
Thanks Interested Layperson,
A bit of the article is at
http://www.astronomy.com/magazine/jeff-hester/2015/11/not-science-fiction
I haven’t seen the whole thing, but I don’t have a problem with the part quoted. That there are no interesting and correct predictions from the string landscape multiverse is the problem, and thus according to Hester, this sort of multiverse has already been falsified.
By the way, if people want a detailed defense of the string theory multiverse, together with a detailed documentation of priority claims that it was basically his idea, Andrei Linde has a preprint at
http://arxiv.org/abs/1512.01203
I’m somewhat curious why he or others with a similar point of view (Susskind, Vilenkin, Guth, etc. etc.) are not speaking at this conference next week.
Peter: “My impression is that most physicists understand so poorly how mathematicians conduct research that they can’t see the issue here”.
That is the point of my (perhaps simplistic) example – even questioning the differentiability (let alone continuity, which is true only for a narrow class of continuous time processes – as has been learnt the hard way by those have sought in vain to generalise Black Scholes to the real world!) of Feynman paths did not come naturally to physicists! The mathematicians were invaluable here.
I think it is obvious that the mathematicians’ specific deep understanding of relevant concepts to physics is what makes them special. If you just need a very good critical listener that does not let you get away with any ‘sleight of hand’ (no names mentioned!), and these are just as important in the general scheme of things, then a mathematician is not necessary – a physicist will do. Sydney Brenner in mock disgust commented that Francis Crick (a former physicist of course) ‘did not let him get away with anything’!
Peter,
The issue (isn’t it?) is how to evaluate physical theories without contact with experiment (at least provisionally). Do pure mathematicians ever have to worry about this? They evaluate their own theories without contact with experiment, but that’s because those theories don’t refer to the outer “observed” world, i.e., they aren’t empirical to start with. Their initial assumptions don’t even need to have a physical interpretation. The end game is proof that an assertion follows from certain assumptions. What happens when the empirical soundness—and not just the consistency—of the assumptions is a central issue, perhaps the central issue?
Applied mathematicians presumably operate differently, perhaps most of the time. Is that who you’re talking about?
Peter: ( sorry for my verbosity on this topic!). I looked at your link above to Linde’s recent (no doubt justified) ‘Lindecentric’ historical account of inflation/multiverse. Maybe my measure theory example above (differentiability of Feynman paths) where mathematicians helped enormously is not as simplistic as it seems.
Linde gives the usual (a la, Guth, Susskind, Page, … ) argument for the multiverse ‘measure problem showing by example how you can easily get yourself in a twist trying to define probabilities when your set ( ‘sample space’ ) is infinite. The problem with this oft used example is that its ‘measure’ (the Cesaro or counting density – note mathematicians don’t call it a measure) is not a measure. It does not satisfy all the criteria to be one – hence one easily (or naively, as in the case of philosphers of the past) produces a contradiction. What bothers me is that the reader is not warned,or at least I missed it. Is this to shield the poor reader from the horrors of measure theory or something else? Relevant mathematicians surely have something to say, if only because for 200 years they too have had all the confusion of an ill defined ‘theory’ without a foundation – probability theory. Amusingly, access to abundant empirical data did not help, if anything it hindered. Instead an rich array of logical problems associated with ‘thought experiments’ played an important role leading to Kolmorgorov’s final synthesis and satisfactory definition of probability theory – one that now looks so obvious that one wonders wny it took 200 years to find. Depending on ones personal conviction, one may hope (and in much less than 200 years, but as they say, ‘don’t hold your breath’) for a similar outcome with one or more of QFT, StringTheory, inflation theory … . Skim reading the abstracts of the Munich conference, I unfortunately don’t see any obvious reference to this interesting, and to my mind, obviously relevant history (relevant even at the technical level) of mathematics, perhaps reflecting your point about the absence of relevant mathematicians. Note also that is well known that philosophers did not always have a positive role in creating a solid probability theory.
Chris W.,
If your theory makes no contact with experiment, “empirical soundness” isn’t really a meaningful criterion, For example, the people doing quantum gravity these days like to announce that they are showing how to get rid of space (and maybe time too). If their replacement for space makes no testable connection to reality, the only way to evaluate it is by whether it is well-defined, internally consistent, consistent with some other specified assumptions based on how one hopes to connect the idea to reality. Methodologically, this is the kind of thing mathematicians are trained to do (this has nothing to do with applied mathematics). By the way, mathematicians also have a huge amount of expertise about different ways to think of generalizations of the classical notion of space (i.e. a differentiable manifold), but that’s another topic.
sm,
It does seem to me that mathematicians and philosophers of math would have something to contribute to a discussion of the supposed “measure problem” (my point of view though is that this isn’t the problem, the problem is more fundamental, that you don’t know the space your measure is supposed to be on). Again, I find it odd that there seems to be little discussion of the multiverse planned at this workshop. Perhaps this is because if proposed “non-empirical confirmation” is invoked as an ally by the multiverse maniacs, that would seriously discredit the whole idea in many people’s view.
Peter,
“I’m somewhat curious why he or others with a similar point of view (Susskind, Vilenkin, Guth, etc. etc.) are not speaking at this conference next week.”
I’m curious about that too. All speakers have been invited by the organizers, and there is no option for contributed talks. So the list of speakers reflects solely the choices of the organizers.
Best, 🙂
Marko
A curiosity tangent to the topic: here is the text of the “Samy Maroun center for Space, Time and the Quantum” whose Rovelli (one of the speaker of the Munich conference) is president (see http://www.centresamymaroun.com): “[…] Institutional agencies supporting theoretical physics research focus on the development of mathematical tools, but research cannot confine itself to these tools, neglecting direct physical intuition. Physical intuition based on experimental results and the qualitative content of the successful physical has always represented, historically, the essential source of our understanding of the physical world. The main objective of the Samy Maroun Center is to promote fundamental research on Time, Space and Quanta, grounded in the first place on the capacity of intuition to imagine and describe the world.”
I was quite surprised to read that mathematical physics is somehow over founded by institutional agencies !
Peter,
“my point of view though is that this isn’t the problem, the problem is more fundamental, that you don’t know the space your measure is supposed to be on”.
In the case of “probability theory” (as it was before Kolmogorov, or more accurately, before the early 1900s when the French mathematicians especially started to ‘get a grip’) the problem was even more fundamental than that – you didn’t even know you had to use a measure in the first place. Despite this, the “theory” had great calculational success (hence the reason to find a proper foundation), rather like some, but not all, of the “theories” we have now.
As I am sure you know, the history of the development of probability theory over 200 years is very rich and with the benefit of hindsight, counterintuitive, in places even comical, involving very colourful characters (to say the least!). The history our modern “theories” so far, to my mind, has great parallels with all this and we still have a lot to learn from Kolmogorov and ancestors (and maybe even his descendents – although at the moment it seems to be going other way as far as probability is concerned), possibly not only at the meta level.
Peter Woit: ‘my point of view though is that this isn’t the problem, the problem is more fundamental, that you don’t know the space your measure is supposed to be on’
This is supposed to be one of the good things about measure theory: you don’t need to know that. You just need to know a containing space, and that can be much bigger, then ask where the support of your measure is. Here is an example.
Suppose you are interested in (Lebesgue-) measurable functions from $[0,1]^2$ to $[0,1]$. You only care about these up to equivalence on sets of measure zero (meaning: you can do what you like to a function on a set of measure zero, and I will say you didn’t change it). Think of such a function as $f(x,y)$, and suppose you are interested in what functions show up as $f(x_0,y)$ for a given $f$ and any fixed $x_0$, called ‘points’ (I know this is a strange name! There is a reason for this construction, it is a combinatorial graph limit, but you don’t need to care). Now in principle such functions could be any function at all from $[0,1]$ to $[0,1]$, not necessarily even measurable, because $f$ is defined up to equivalence on a set of measure zero and the line $(x_0,y)$ has measure zero. So you only care about `typical points’, meaning that (in some sense which should be rigorous) you want to get rid of that kind of silly example.
To be more concrete, if you are given $f(x,y)$ is $0$ if $x\le y$ and $1$ otherwise, then the ‘typical points’ $f(x_0,y)$ are a one-parameter family, so you should get the structure of a line out of this.
Here is how you do it. You take any given $f$, and any measurable set $X$ in $[0,1]$. Now you generate a measure on $L_1[(0,1)]$ by setting the measure of $\{f(x_0,y):x_0\in X\}$ equal to the measure of $X$. Next, you declare the ‘typical points’ of $f$ to be the support of your measure.
The thing to note here is that $L_1([0,1])$ is a truly huge space, and you are looking for low-dimensional manifolds in it, but nevertheless the measure theory happily lets you do this. And because you had a measure to work with, you could do this construction rigorously.
Peter,
Sabine asked the question about the observations. He pointed out just one of them
saying if that there is evidence for a long range force, or a vectorial/tensorial force
or evidence for 5th force it would invalidate the string framework.
Shantanu,
I wonder what Gross is thinking of. I don’t see any reason you can’t have another long range force like the electromagnetic force, coupling to a charge. Presumably he means coupling to mass. Often one hears the exact opposite claim, that observation of a fifth force would be evidence for string theory, see for example here
http://www.math.columbia.edu/~woit/wordpress/?p=6561
In string theory you have potential long range forces due to moduli fields, in some sense the big problem of the theory is why you don’t see these (how do you stabilize moduli?). So, I’m guessing he meant non-scalar forces that violate the equivalence principle, coupling to mass, violating various principles of GR + QFT, not just string theory. It’s easy to come up with things that don’t fit fundamental principles of QM or QFT, and say those would falsify string theory. The real question though is whether you can falsify the characteristic properties of string theory that are different than QFT.
I would bet good money though that if experimentalists discover a fifth force, the headlines will be “string theorists claim evidence for string theory”, and if it’s not scalar, some “string vacuum” will be constructed to reproduce whatever is observed…
Shantanu: will the slides be put online?
I am not on the organizing committee. But I will check tomorrow, although I will pretty sure they will be at some point. Also they are videotaping the whole thing, so the videos will also be put online. However as a physicist, I didn’t really get much from the philosophy talks
and the main talks I paid attention to were by Gross, Rovelli and also Helge Kragh
who mentioned some very interesting things about Eddington’s fundamental theory, which I didn’t know.
Gross didn’t really explain why he thinks that a new long range force would invalidate ST, and I think that at that point the majority of people in the audience were very grateful for that. Some people just don’t distinguish between asking a question and giving a lecture, and don’t know how to give back the microphone…
In other news, the majority of the discussion centered around Dawid’s three-rule non-empirical theory confirmation criterion, and there was a big fuss about whether it’s a misnomer, because it’s more about theory assesement than confirmation (the latter being too loaded with different meanings).
Other talks were also interesting, but not controversial in any way. Overall it was nice today, we’ll see how tomorrow goes.
Best, 🙂
Marko
Douglas: I totally agree with you…in fact there is no paradigma shift, nor any crisis whatsoever in science, but, maybe, in some fields.
It’s fascinating, there really is some sort of deep misunderstanding of mathematics, among both physicists and philosophers. From Pigliucci’s blog – “Theorists may give up, or they may play with extrapolation, or toy models (i.e., thought experiments). They could also adopt strategies from other fields, like mathematics, where beauty is a criterion for success. [Uhm, that’s pretty dangerous territory…]” But beauty is neither a necessary nor a sufficient condition for success in math. The primary criterion for success is of course proof, unless you can prove something correct it will not succeed. If you can prove something, there are various reasons why it might be a success. One is certainly beauty, mathematicians love beautiful results. Another is usefulness, mathematicians love plenty of not beautiful things because they are very useful. Physicists of course don’t have proof really, even experiment isn’t quite “proof,” and this makes the use of the other secondary criteria a serious problem.
emile. The slides will be put online.
Today’s highlights was the fireworks between Gross/others and Kane, when Kane mentioned that M-theory predicted Higgs boson mass of 126 GeV. Probably Marko or
Sabine can/will add more either here or on Sabine’s blog.
Massimo Pigliucci’s post for today (“Why Trust a Theory? — part I“) described another tense exchange (brief) on a less substantive matter.
Ok, day two. 🙂 Arguably, the only thing more fun than a duel between a ST proponent and a LQG proponent is a duel between two disagreeing ST proponents… When Gordon Kane explicitly put on his slides “in 2011 M-theory predicted the Higgs mass at 126 GeV” (and he even gave the error bars of that prediction), David Gross had to intervene, and the fight was on! 😉 After some philosophers protested at the interruption and demanded that Kane continues on with the talk, Gross said (I’m paraphrasing from memory) “oh, we physicists have these discussions in the middle of a lecture all the time — you know, it’s called the ‘scientific method’…”
Eventually other talks went on, with some interesting but less controversial topics.
But the main party was in the afternoon, stolen by Slava Mukhanov. The incredibly funny yet lucid lecture spanned topics from inflation to dangers of falsifiability in the former USSR, including the equation which will probably become a classic:
inflation – theology = exp (-aH),
with a comment “even Lemaitre knew this”… You had to be there.
The party continued during the discussion session where Mukhanov played the role of “voice of reason”, telling everybody that if a theory cannot be tested it is not physics, and redefining falsifiability away isn’t going to change that. I’ll just paraphrase an exchange regarding eternal inflation and the multiverse:
Gross: Multiverse is an important problem where philosophers can help, and it’s a good topic to collaborate on.
Mukhanov: Maybe we should also invite theologists?
Really, you just had to be there… 🙂 I can only guess about tomorrow, when the multiverse will become the main topic.
Best, 🙂
Marko