Last week’s public lecture at the Institute for Advanced Study by Nati Seiberg is now available online. He was speaking with the title What’s Next? and promoting a story about where particle physics is and where it is going pretty much identical with that coming from his IAS colleagues. Despite the overwhelming failure of string theory unification and the dramatic evidence from the LHC ruling out popular ideas about SUSY, there was no admission of any discouragement about string theory or SUSY.
String theory was described as the best candidate for a fundamental theory, one that has been making “enormous and exciting progress with amazing new insights” and “all signs are that we will continue to make progress.” For more details Seiberg points to talks given by Witten such as this one. According to Seiberg, string theory has not problems and failures, but “challenges”. One challenge is that “we do not understand the principles” of string theory. Another is that “we need experimental confirmation”, which makes it sound like the problem is one of experiments not done yet, rather than the real problem, which is a “theory” that predicts nothing.
The hierarchy problem is emphasized as the central problem for particle theory, with almost exactly the same point of view as that of Nima Arkani-Hamed, which I’ve discussed here many times (see for example here and here). We’re told not to think of the LHC results as providing evidence against SUSY, but to interpret LHC results as choosing between two possibilities:
- SUSY exists at LHC scales and arguments about SUSY solving the hierarchy problem are vindicated. Things don’t look good for this so far, but hope is held out for the next run, with an admission that if it doesn’t turn up then, that’s it for SUSY as a solution to this problem.
- No SUSY at LHC scales just means it is at higher scales, and the multiverse is now brought in to deal with the hierarchy problem. In a recent Science Weekly podcast, Arkani-Hamed says he’s still willing to bet several years salary that SUSY exists, but now he thinks maybe it only shows up at higher energies than he’ll see in his lifetime. He’s willing to bet that SUSY will show up at the next LHC run, but just $50.
Since even enthusiasts who have devoted their career to the cause are now only willing to put up $50 in favor of SUSY at 13 TeV, it’s pretty clear that hardly anyone is now expecting to see this. We’re already in the era of trying to understand the implications of no SUSY at the LHC, with the multiverse the main argument now being deployed in favor of not giving up on cherished speculation about SUSY and strings, no matter what experiments say.
Seiberg does give a different historical analogy for the hierarchy problem, likening it to a fine-tuning problem that Newton was worried about, that of the stability of planetary orbits. Why does a small perturbation of such an orbit not lead to exponentially large changes, destabilizing the orbit? Seiberg lists three possible solutions to such fine-tuning problems:
- There really is no problem if you understood the theory well-enough.
- You need to invoke new physics as a stabilizing mechanism.
- The answer is “environmental”: the orbits are generically unstable, we just happen to live in an unusual place where they are stable.
The odd thing about his use of this historical analogy is that the lesson to be drawn is that of course the answer is the first alternative, but he quickly passes that one by as not worth talking about. I doubt the last alternative ever occured to Newton as anything other than a joke, and don’t know of any evidence that he tried to come up with models of things like new unseen planets to solve this supposed problem. Newton surely realized there was plenty that he didn’t understand about what Newtonian mechanics had to say about celestial mechanics. It’s just as clear that our best model of the Higgs, with its large number of undetermined parameters, is such that we just don’t fully understand where the Higgs potential and Yukawas come from.
The Seiberg talk seems to be one of a series (others listed here) of talks associated with the Milner Fundamental Physics Prize. IAS director Dijkgraaf introduced Seiberg as one of the four IAS winners of the $3 million Milner prize, with this leading his list of honors awarded to Seiberg. The talk was a public one of a sort that has for the IAS not just an educational role, but also a fund-raising one. Something is being sold here, the idea that SUSY and string theory are great successes, with the IAS faculty well-deserving the multi-million-dollar checks awarded to them for their work on these topics. Later this week they’ll be getting together in San Francisco to decide how to split up $3.6 million in new checks among five other string theorists (the announcement of the winner of the 2014 prize will be made Thursday). All of this I fear has something to do with why we’re not hearing from those at the IAS a truer picture of what no SUSY at the LHC means: the collapse of ideas that don’t work and evidence that we don’t yet have any viable conceptual framework for going beyond the Standard Model. This summer the IAS will host its usual PiTP program to train grad students and postdocs in what they need to know to face the future. The topic? String theory.
Peter, something OT but relevant to particle physics
I am the 50th anniversary of the texas symposium and Steve Weinberg (in his talk)
was discussing many papers by Shaposhnikov and others which proposed
a 126 Gev mass of Higgs boson based on asymptotic safety. (He also discussed
implications for models of inflation based on these asymptotic safety scenarios)
It is interesting to take the stability of planetary motion as example.
The only planetary motion that we knew about up until 10 years ago is solar system’s. The problem of the stability of the solar system remains, as far as I know, unsolved. Numerical integration shows that small perturbations of orbits and masses will indeed lead to exponentially large changes over *fractions* of the lifetime of the solar system and the current configuration has no à priori reason to be stable.
However, Earth did indeed stay reasonable habitable over the lifetime of the solar system.
So the answer could be any of the three ones proposed, or a mix of them: We are at a local minimum in phase space that we don’t understand yet (possible); there is some new physics at large scales we haven’t found yet (not at all impossible) or it’s environmental – we just happen to live in a solar system that happens not to have seen major excursions from a configuration in which Earth stays habitable over > 4 * 10⁹ years (quite possible if the weak anthropic principle is applied, but I don’t like it).
When I was a science student it was my dream and the dream of my colleagues to be at IAS. I find this very disheartening, the mix of big money and buying shelf space in the education Big Box store.
Much like economics has a ‘heterodox’ crowd for challenging the (by now embarrassingly false) mainstream, physics probably needs a similar break, and (like economics) it’s unlikely to come in an academia partially captured by interests that promote string theory.
That seems to make it a slightly politically dominated topic (far less so than economics mind) – so probably going to need to attract a large source of funding, for creating institutes that lobby against string theory as a field of study, and instead both promotes and directly funds large projects that study/develop alternatives.
It’s unfortunate how much scientific study seems to be corrupted by politics and good old cognitive bias, as pretty much any other area of human interaction.
When I was younger I was so lucky to have a few conversations with Dr. Dijkgraaf, back when he was teaching at the Amsterdam University, here in The Netherlands. I love how this professor seems to give a romantic twist to the the profession, not afraid of asking the big questions: Is there a certain system driving the world? Are we the only ones in the universe? Is the youth getting smarter? even asking if we are living in a matrix of created by a computer program. It’s typical for Dijkgraaf to grab the opportunity to give a second role to such a great event as the IAS, always thinking outside the box. A great and charismatic man, which the world can learn a lot of, and not just in hard science.
Like Yatima, I appreciate the analogy with Newton’s Laws and planetary motion. And I agree with Peter’s reaction – the first scenario is the best one and perhaps the most likely one.
Dear Peter, you once wrote a paper together with N. Seiberg:
How was your impression back then?
The previous story on Peter’s blog, ‘Peter Higgs: “Today I wouldn’t get an academic job. It’s as simple as that”’ is very related to this post.
What is happening in physics in recent decades is something I call the Paradigm Mountain. As the last 10 decades have rolled by, the speed of communication has increased by about three orders of magnitude. This of course will have consequences – mostly good.
The bad: even though many scientists have read and understood Khun’s thesis about scientific revolution, its still hard not to trivialize new theories as wrong because they don’t explain ‘result X’ or ‘effect Y’. With instant communication comes instant critique (often even instant ridicule).
In other words, the internet has made the ‘paradigm mountain’ of the Standard Model very hard to penetrate. To quote Peter Higgs “It’s difficult to imagine how I would ever have enough peace and quiet in the present sort of climate to do what I did in 1964.”
I wonder if, in the long run, this will damage the IAS “brand”.
This is in no way intended to be personally critical of Nati Seiberg (who I did work with happily way back when, but haven’t talked to in a long time).
As a general comment (not about Seiberg particularly) about the four IAS Milner prize winners and new director Dijkgraaf, are all quite good, hard-working physicists. They do though share a certain style that I’ve never found congenial (common among hep theorists, much less so among mathematicians), that of liking to work on the latest, hottest new idea appearing from within the dominant paradigm being followed by the most influential people in the field. I think this has gotten them into trouble as this paradigm has worked its way far down a blind alley. Unfortunately the Milner money has had the effect of painting this blind alley as some sort of success story, making the problem worse.
The first option you seem to ‘interpret’ from the talk, which is:
There really is no problem if you understood the theory well-enough.
was not what Seiberg said. He argued that Newton’s dilemma was shown to be unfounded as it was shown that the solar system is chaotic. But the analogous situation in the case of the standard model leads only to the conclusion that one’s logic is totally wrong. This, though a possibility, would be a vacuous and an uninteresting conclusion, therefore it won’t be pursued.
I did understand that Seiberg was justifying not discussing the first option (however you want to exactly interpret it) as “not interesting”, but this is where I fundamentally disagree with him. If you find that your argument leads to two possibilities, one ruled out by experiment, and the other saying you should give up on conventional science, it seems to me that this means you have learned there is something wrong with your argument. It’s not at all the case that the “hierarchy argument” is just a piece of logic, but rather it’s various possible sequences of assumptions. My take on the current situation is that the LHC has just told us that a certain popular speculative argument doesn’t work. Instead of standing up before the public and repeating this argument vigorously, making it sound much solider than it is, why not give a talk saying “here are the components of this argument that has been killed by the LHC, it’s exciting that we’ve learned one of them is wrong”. An example of where you go from there is the Weinberg talk Shantanu pointed out, which deals with one possible way around the hierarchy argument.
Dear Peter, thank you very much for your thoughtful comments.
Sorry, I couldn’t understand you. Are you saying that the hierarchy problem is not a problem? Just looking at the SM parameters show such a huge span of numbers, and isn’t it a valid question to ask why are the numbers distributed over the range they are? Secondly, if one can’t think of any ‘natural’ way (by which I mean some vague, qualitative principle at least, which may be made precise later) which makes sense of the span of the numbers, we’re left with the three possibilities which Prof. Seiberg spoke of. Now, unless you tell me some way (vague, qualitative would do, details may be worked out later) to understand your statement, which is:
“understand the theory (SM) well enough”
and we are sure we understand QFT well enough to say that such numbers can’t possibly arise unless delicate cancellations occur, we are forced to conclude that there is possibly no creative avenue analogous to the theory of classical chaos which may lead to ‘better understanding’ of the SM. The stability of these numbers is a very fragile issue as you know, because quantum corrections drag every (classical to begin with) number to the scale of the problem involved, and no one knows of a way to prevent it, apart from symmetry principles, which is why SUSY is such an attractive avenue. In the scenario that SUSY is not seen at LHC, what Prof. Seiberg says is that one would be forced to give up the notion that the SM as a gauge theory is special; it will herald another revolution analogous to the Copernican one. I fail to see why you call this giving up ‘conventional science’ any more that you’d say the same thing to people who were forced to give up the idea that the earth was the center of the universe. This time, it’s the SM and the rest of our models, which are defined by parameters that aren’t special, that’s all.
To conclude, a word about the asymptotic safety scenarios you point me to. They’re inherently perturbative in nature and any treatment of gravity based on such field-theoretic scenarios will eventually run into the fact that classical gravity has black hole states, which can’t be reproduced by any known local QFT, hence the dictum ‘gravity is not a QFT’.
The question of the SM parameters of course is perhaps the biggest question around, and we have no idea why they take the values they do, over the large range that they do. That’s not at all though what is commonly called the “hierarchy problem”, which usually refers to the quadratic sensitivity of the Higgs mass to the cut-off scale. The fact that SUSY theories (with SUSY-breaking scale at the weak scale) don’t have this feature has been one of the main arguments for SUSY, but it’s not at all an air-tight convincing argument.
One problem with what Seiberg does in his talk is that he doesn’t clarify what the “hierarchy” or “naturalness” or “fine-tuning” problem is, and that’s the interesting question now that the LHC has shown that the SUSY “solution” to it doesn’t work.
I describe the multiverse “solution” to the “hierarchy problem” as “giving up on science” because it’s completely untestable. It’s just an empty pseudo-scientific excuse for not understanding something. In fundamental physics, for anything we don’t understand, someone can always say “that’s something that’s different at different places in the multiverse, so what we see about it can’t be predicted”. Sure, this could be true, we could live in a Matrix, etc., etc. but such things are not science.
The argument that we should give up the idea that the SM is “special” because of LHC results is absurd: the LHC just dramatically confirmed a whole new sector of that theory, and the whole thing over a large new energy range. The LHC is telling us emphatically that the SM is “special”.
As for quantum gravity, we have zero evidence for it, zero evidence for what happens at the Planck scale, and only highly speculative and likely wrong ideas. Using this to argue for a multiverse or anything else isn’t a solid argument at all.
Of course the LHC has not only verified the SM, but probably is also hinting that there’s nothing beyond the SM. But very sound counter arguments show that there HAS to be physics beyond the SM. Just because the LHC confirms the SM doesn’t itself mean it’s special. It may be a **SPECIAL** feature of this particular phase or ‘vacuum’ of the relevant high energy completion of SM and gravity. You haven’t yet shown one serious flaw in the arguments, such as an invalid extrapolation or the failure of using EFT techniques or some such thing.
“As for quantum gravity, we have zero evidence for it,..”
I fail to understand this statement. Does it mean that you think quantum gravity doesn’t somehow make sense? What more ‘evidence’ can one need other than the fact that both quantum mechanics and gravity operate in one and the same universe, and thus when the two regimes meet, as they surely would at the Planck scale, one would need such a theory?
Next, no one is remotely suggesting the following:
“The argument that we should give up the idea that the SM is “special” because of LHC results is absurd:..”
Indeed that no one is immediately giving up on the idea of the SM being ‘special’; one would like to find the ‘special’ solution to the equations of the correct high energy theory once the task of unifying gravity and QM is completed. Sure, sounds awesome and it’s the dream of many physicists – Prof. Seiberg himself said he’d be reluctant to give up the idea that the solution that we currently observe isn’t somehow uniquely determined (in other words, ‘special’) – but unfortunately, if one doesn’t find a mechanism by which the apparent ‘specialty’ can somehow make sense, by which I mean that the parameters stay put where they are instead of getting dragged here and there by quantum corrections, what is one supposed to do? Keep sticking to the ‘prejudice’ of the SM being ‘special’ in the face of all evidence? Just like geocentric people who didn’t wanna give up the ‘special’ place of the earth in the universe?
“One problem with what Seiberg does in his talk is that he doesn’t clarify what the “hierarchy” or “naturalness” or “fine-tuning” problem is, and that’s the interesting question now that the LHC has shown that the SUSY “solution” to it doesn’t work.”
Prof. Seiberg very clearly elucidates (in my opinion in a beautiful way) what the ‘hierarchy’ or ‘naturalness’ or ‘fine-tuning’ problem is. It is the question of the stability of the numbers (the parameters) of the SM, and yes, the Higgs mass is one of them, particularly affected by the quadratic divergences you mention. Some parameters, like the fermion masses and mixing angles could have explanation in the physics at extremely high energy – he mentions the neutrino mass as an example – and some don’t. When they don’t – like the theta angle of QCD – one *HAS** to look for a mechanism which solves the problem at the energy scale in question. And, yes, SUSY was useful precisely for this reason and the expectation was that it would be seen at the LHC. It didn’t. So, back to the question: what keeps the numbers stable? SUSY hasn’t solved this set of issues, so what gives? The conclusion that SUSY doesn’t work has the important caveat – that it doesn’t work at the scales probed by the LHC.
Indeed the multiverse can’t be ‘tested’ in the sense that in case there are causally disconnected regions, no signal can ever reach us. But that such cases can occur have been around in the theory of inflation as well. What one does is then try and understand ‘our neck of the woods’ as Prof. Seiberg says. I still don’t see what issues you have with these (straightforward) argument.
We just don’t have any evidence one way or another about some completely different theory at high energies, with the SM only an effective theory (and thus “not special”). What we have learned in recent years is that those who argued that since the SM is just an effective theory, we should see new physics at the TeV scale were wrong.
Re quantum gravity, if you would read the rest of the sentence and not delete it, my meaning would be clear.
I’ve endlessly discussed the hierarchy problem here, don’t see much point in repeating myself. One basic point to keep in mind though is that there’s something highly speculative about any argument based on relating energy scales we have no access to or information about and the electroweak scale, as in “it’s a huge problem that small changes in physics at the Planck scale have enormous effect on physics at the electroweak scale”.
About predictivity and the multiverse, see
We surely do have evidence for a completely different theory at high energies, and most certainly at the Planck energy. Are you contesting the point the the very structure of QFT breaks down at (Planck) such energies? Even if the SM is (and surely it is not) the story all the way up the Planck scale, we surely need a **NEW** theory at the Planck scale. As for new physics (at the TeV scale), it was expected based on plenty of evidence, not empty speculation. The evidence, apart from numbers that can’t be explained at the level of the SM itself (numbers like neutrino masses etc) included numerous other observations. I am free to discuss what these ‘numerous other observations’ are in case you’re willing to indulge me.
The very fact that no new physics was seen is forcing a rethink of the whole paradigm, beginning with the ‘most flimsy’ so to speak – which may/may not include naturalness.
Of course I read your statement about quantum gravity fully, and understand it to mean that you think all ideas about it are not only highly speculative, but most likely wrong. This is wrong. What we DO NOT have is a complete theory of quantum gravity, but we do have a very good idea of what the high energy (trans-Planckian, if you wish) physics qualitatively looks like. Just to give you an idea, it’s certainly true that at very high energies, say energies exceeding the Planck scale, the states are dominated by large black holes. This is just one among very many concrete statements about physics at the Planck scale, which you seem to just ‘brush under the carpet’ as ‘speculative’ or ‘most likely worng’. Please feel free to indulge me in case you wanna know more.
“One basic point to keep in mind though is that there’s something highly speculative about any argument based on relating energy scales we have no access to or information about and the electroweak scale, as in “it’s a huge problem that small changes in physics at the Planck scale have enormous effect on physics at the electroweak scale”.”
Unless you tell me what you mean by ‘..there’s something highly speculative..’ I have to reply to the above paragraph with “..there is nothing speculative..”. This is because no one is ‘relating energy scales’ – at least in the arbitrary manner you seem to imply. It is a very sound procedure which is based on solid knowledge we know about the current energy scales, what the renormalization group has taught us, and so on. Again, feel free to indulge me in case you want to know, though I suspect that you already know what I’m on about.
In fact, I can also tell you about a very well known quantum theory of gravity, but the requirements of staying on topic prevent me from going into it. I have just read the FAQ you linked me to above, and what you write there is wrong. Let me explain. You say:
“The issue is not whether there’s more than the observable universe out there. That may very well be, and maybe someday we’ll even understand inflation well enough to have a good model of what that might be. The point though is that there is zero evidence that whatever else there is has different physical laws than ours, and that is what is needed to make the whole anthropic business work. In simple models of inflation, whatever else is out there will have the same laws as ours, so yes, you can get a multiverse, but a pretty boring one. You can use string theory or something else to come up with much more complicated models that give you pretty much any physics you want in different parts of the multiverse, but there’s no evidence for these, they are untestable and explain nothing.”
Sorry for copy-pasting the whole paragraph, I don’t want to be accused of ‘deleting’ sentences again. Whether or not the other universes have ‘different physical laws than ours’ is a question that involves detailed knowledge of the correct dynamics of the high energy theory, which includes knowledge of the fact that which numbers are of fundamental importance and which are not (i.e., which ‘laws’ are to be the same and which ‘laws’ can be/have to be/may be different), and such knowledge is beyond reach even in calculable models of quantum gravity, the ones of the kind which I mentioned at the beginning of my comment. Thus, it’s impossible to a priori say which ‘model’ of inflation wold be chosen, and consequently what the nature of the vacuum would be. Once this can be achieved, one may ask why is it that we happen to ‘live’ in this neck of the woods and not in others. Whether or not inflation may require the ‘laws’ in other bubbles to be same or not is irrelevant here, because full information about the high energy theory (to the point of having detailed knowledge of vacuum selection) would render any statement made on the basis of inflation (which surely you’d agree would probably naturally arise as a requirement of the detailed laws) redundant, and it’s yet to be seen which features survive to be considered ‘laws’ – i.e., which won’t change throughout the multiverse – this number may be zero such statements, and which may be just be reduced to mere environmental numbers – a la the radii of the orbits of the planets of the solar system, as Prof. Seiberg beautifully explained.
As for whether the anthropic argument ‘to work’ or ‘not to work’ once the main task of understanding the high energy dynamics of gravity is well understood, we may be in a position to argue which parts of the argument stand and which don’t, as I’ve already explained above.
“– i.e., which won’t change throughout the multiverse – this number may be zero such statements, and which may be just be reduced to mere environmental numbers – a la the radii of the orbits of the planets of the solar system, as Prof. Seiberg beautifully explained.”
Please excuse the sloppy editing of the above paragraph. I meant:
“– i.e., which won’t change throughout the multiverse – this number may be zero- and which may be just be reduced to mere environmental numbers – a la the radii of the orbits of the planets of the solar system, as Prof. Seiberg beautifully explained.”
Dear Umesh, these wonderful arguments that you are referring to and that supposedly tell us so much reliable information about how Planck scale physics and quantum gravity are supposed to behave certainly exist. Not only do they exist, they are quite well known to anyone who has spent enough time interacting with high energy physicists. And that most likely includes Peter as well.
However, now you must realize that it is possible for two reasonable people to be exposed to these same arguments, yet not be equally convinced by them. And that’s not because of lack of familiarity. So rehashing these arguments here is unlikely to help anyone. What make the difference are different standards of evidence. Once one adopts somewhat stricter standards of evidence than those that are common in the very mathematically adventurous high energy physics community, it becomes evident rather quickly that the state of the art of our knowledge about the non-perturbative and Planck scale behavior of QFTs (including gravity) is full of open problems. What all these well known wonderful arguments (and quite a few less well known ones) provide are conjectures (sometimes contradictory ones) about how these open problems could eventually be resolved.
So before making bold claims of certainty about how quantum gravity is supposed to behave in non-perturbative Planckian regimes, lets wait until a similar yet easier problem is solved and the Yang-Mills Clay Millennium prize is actually awarded to someone. Such a conservative position is not just hot air. If it were never adopted by anyone, we would still be quibbling about which model of aether is the right one, since an aether substrate is so absolutely mathematically necessary to explain the wave nature of electromagnetism.
Sorry Igor, but it’s not the ‘standard’ of evidence which is under question here. In case you, or anyone else for that matter can point out what ‘exactly’ reduces the ‘standard’ of the evidence presented above, it would be much better. It must be emphasized that the statements above (what you call rehashes) are not mere ‘high adventure’ maths, but arguments which are based on solid, well tested theories – general relativity for example. The Clay prize for the YM gap problem is one of proving in great detail the existence of the mass gap, which has nothing to whatsoever to do with the problems under discussion here. In case you really wanna know, we can discuss, but the blog owner would cry foul. I’m sure you’re’nt suggesting that until the Clay prize is awarded, one sit idle about other important conceptual questions. In case it gets solved and tells us something useful about QFT, great, but in the meanwhile we need to address other (more important) conceptual questions – and be sure they have nothing to with QFT – like the behavior or high energy gravity. Unless you can tell me – based on the best current theory of gravity – why are the arguments wrong – and these don’t include statements such as ‘we have to solve other easier problems’ etc etc – it is hard to essentially stop thinking about the quantum nature of gravity. Please feel free to point out (even vague would do) what you find invalid about the arguments which I presented above. You may choose any. There has to be some reason (mathematical reason) to believe that unless the YM mass gap is proved as required by the Clay committee, one mustn’t think about quantum gravity, and I’m sure there’s no such logical, physical or mathematical reason, except personal prejudice.
I’m sorry, but we seem to have fundamentally different views on how science works. My reading of the history of physics is that it is full of theorists who were convinced that something or other was “certainly true”, until someone did an experiment and showed it wasn’t, or some other theorist who better understood the matter showed that it wasn’t. Given this history, some humility and careful distinction between what one has experimental evidence for and what one doesn’t seem like a very good idea. People should study highly speculative topics like transplanckian physics and may learn something this way, but, personally I’m not about to take seriously their claims that they know what is “certainly true” about this.
Somewhat similarly, about the multiverse, when you have a solid theory with some evidence for it that determines what our possible laws of physics are, then I’m willing to discuss the question of what this means about what things are predictable and what are environmental. At the moment, from everything I’ve seen (and I’ve spent a lot of time looking), the people trying to sell this have nothing at all, just a bunch of conjectures about how to construct a theoretical framework designed to evade any confrontation with experiment. To me, this does not count as science.
Fair enough, then I think you wouldn’t believe any statement made about the nature of the interplay between quantum mechanics and gravity. But I would still like to know what you consider ‘highly speculative’ about the standard extrapolations made from known theories. Even for starters, the Planck scale is very well out of reach of any conceivable experiment to get ‘directly tested’. Going by your view, it’s a totally futile endeavor to even think about this. But unfortunately, it’s not about the scale, it’s about the concepts – both of which work too well – and it must be possible, with or without experiment, to formulate the correct unification. It’s not anybody’s fault that the scale (in our vacuum) at which the two effects come together is totally untestable. You still have to come up with a valid argument (by which I mean something like RG, some semi-quantitative argument) as to why this whole enterprise, by your judgement is totally doomed from the start. That experiments could be performed for every conceivable scale so far in history is because of the ready possibility. And it would be extremely foolish to completely ignore the issues posed by quantum gravity as futile just because there can be no experiment performed, even though that’s what is dictated by history.
I don’t believe thinking about how to quantize gravity is futile (I’ve spent some time doing so myself, and if I thought I had a good idea, would spend a lot more), I just believe those that do so have to keep in mind how large the uncertainties in such arguments are. In the question at hand (electro-weak scale physics and the hierarchy argument that the Planck scale has something to do with this) I’d argue that the uncertainties are large indeed.
Dear Umesh, of course, thinking about conceptual issues in quantum gravity is important. And I would actually be out of a job if it weren’t allowed. What I’m objecting to is claiming extreme certainty in what one comes up with along the way. Let me illustrate by closing a gap in my previous comments.
The reason I brought up the YM Millenium prize before has nothing to do with the specific question of the mass gap. My general understanding of the logic behind its formulation is that the mass gap is only a particular example of a non-perturbative property of a QFT. The main outcome of a solution is expected to be a proof that shows the existence of a non-perturbatively defined QFT and verifies that it has some particular property, like a mass gap. The mass gap could really be substituted with any other equally or more interesting property.
So, here’s a specific problem with all these wonderful arguments that you are very ready to ‘rehash’. In order to be really convincing, they need to include the following steps. Formulate a precise conclusion, construct a relevant non-perturbative QFT model (or your favorite QFT alternative), verify that the conclusion holds. Surprise! All of them are missing the step highlighted in bold. The main reason to pay attention to the YM Millenium prize is that, in case you are not following the literature on this subject, it acts as a helpful barometer for the completion of the construction step. So until then…
There is an alternative, though. Forget about all this mathematical stuff. Forget about all these wonderful arguments. Just take their conclusions as scientific hypotheses and test them! Then trust the ones that work. But in the case of quantum gravity I’m not holding my breath.
Wolfgang Pauli didn’t only say :”Nicht einmal falsch”! He also said:”Man muss nicht so viel reden “! I wish all concerned would heed the latter…
Very well, since we agree that thinking about quantum gravity is an important problem, we may proceed. Igor, the problem with the Clay prize problem is about ‘constructing’ in a mathematically rigorous manner a non-perturbatively complete QFT. But this has nothing to do with the physics per se. All asymptotically free theories are non-perturbatively consistent (as far as physics is concerned, and one can even show such consistency in controlled situations), because they behave more and more like free field theories in the UV. I don’t understand what a more rigorous construction of the said QFT can do for questions in other areas.
But, coming back to topic, we were discussing the hierarchies of the SM and allied problems. I haven’t still understood the nature of the ‘uncertainties’ you spoke about in your comments. What are they? How is the argument that the Higgs mass (which is related to the EW scale), which is quadratically divergent (in case you disagree with this statement, please explain) gets corrections from all particles all the way upto scales which lie much higher than it (namely, the Planck scale, or whatever scale you want to insert in b/w) possibly an argument that has **UNCERTAINTIES**? I ask again, what exactly is the nature of these uncertainties?
Are you claiming that the demand that parameters like the Higgs mass (which aren’t protected by symmetry) are unstable is somehow WRONG? This may be because you know something that others don’t; it would be nice to see what this argument is, which doesn’t need to invoke other high energy scales and somehow solves the problem at the EW scale itself. Please be sure that you can’t postpone this problem to higher energies and you HAVE to solve it at the relevant enrgy scale (in this case the TeV scale) itself. In case you can show a loophole or a flaw in this argument, you’re welcome, but I can’t see any. In the absence of such an argument, Wilson’s argument that scalar masses get corrections all the way upto higher energy scales stands, and nothing can be done about it. And given the fact that this ‘naturalness expectation’ is clearly false, i.e., the Higgs mass is really low compared to the Planck scale (this has been confirmed by the LHC) and looks quite stable, one is forced to conclude that the said parameter, namely the Higgs mass is UNNATURAL. Thus, there is no conceivable ‘computation’ one can do that doesn’t involve UNNATURAL cancellations that would give you the desired answer. In case you feel this is wrong, please feel free to point it out.
Please note that I have cherry picked the Higgs mass for the above argument just because it’s the easiest to demonstrate arguments/counter arguments about naturalness. In fact, I think that you want a NATURAL explanation for the Higgs mass (and consequently the EW scale) too, at least from your stance on the problem.
I’m afraid we’re just on different planets here. As far as I’m concerned, absolutely everything about physics at the Planck scale and how the SM we see at low energies is related to it is uncertain.
Since you invoke Wilson about the hierarchy argument, you might want to read what he had to say about it at
(he called it a “blunder”).
Precisely why is it blunder? I am yet to read the 17 page paper you’ve linked to, but even for a moment forgetting the Planck scale, what is wrong, according to you, about the fact that scalar masses are subject to quantum corrections? In case you opine that this claim is wrong, I would like know.
As I’ve written before, yes, in perturbation theory, scalar fields are quadratically sensitive to the cutoff. The question is what to make of that technical issue. Wilson, who was the one who first raised the issue, says the “naturalness” argument here is a blunder. You don’t need to read the whole 17 pages, just look for Section 5 on “Blunders”, and the second half of page 10 and first half of page 11. Then you can explain to my why Wilson is wrong and doesn’t know what he’s talking about.
OK, I looked up the relevant portion of the paper linked above. I quote Wilson here:
“The final blunder was a claim that scalar
elementary particles were unlikely to occur in
elementary particle physics at currently measurable
energies unless they were associated with some kind
of broken symmetry [reference #23].The claim was that,
otherwise, their masses were likely to be far higher
than could be detected. The claim was that it would
be unnatural for such particles to have masses small
enough to be detectable soon.”
I don’t see how this contradicts with what has been mentioned before; Wilson just says that the expectation that small scalar masses aren’t possible is the **BLUNDER**. He says that this expectation was based on ‘natural expectations’ (in other words, naturalness, because quantum corrections drag the mass up to the relevant scales), and it is indeed possible that small scalar masses may occur (and this has been confirmed by the LHC). What he goes on to say is that not every measurable number has to follow the NATURAL expectations, and goes on to provide the example of the nearest star to the sun as an example (a beautiful example, if I may be so bold). He explains how people during Copernicus’s time said that such huge distances were ‘unnatural’ and couldn’t occur; but today we indeed know that this is true. This in fact makes the case for ‘unnatural’ (or, environmental) characteristics of certain numbers even more robust, not weaker, as you claim.
In fact, what Prof. Seiberg says is precisely the above, though in a much more crisp and clear form; he said that the currently measured mass of the Higgs is uncomfortably low for technicolor schemes (to be natural) and uncomfortably high for SUSY schemes (to be natural). Thus, if there is nothing seen at the LHC that may provide some evidence for the above schemes, there might be no other choice left other than to say that unnatural numbers indeed occur in nature, and the Higgs mass is one of them. Please tell me where you disagree.
I think you’re misreading Wilson, who is not making an anthropic or “environmental” argument. He is making an argument against doing what you are doing: extrapolating one’s assumptions into regimes where you have no evidence and don’t understand things as well as you assume. Read the first part of page 11, where he explains that the problem was that people in the days of Copernicus had no way to measure the distances to stars, and no understanding of Newton’s first law of motion, and this is what led them to wrong reasoning. He then goes on to discuss quarks and the arguments against them, which were wrong, including an extremely relevant point for this discussion about non-perturbative qft having different behavior than expected.
Sorry, but I have read the parts you have suggested, and find nothing that contradicts the ‘environmental’ argument. Of course that Wilson hasn’t used the word ‘environmental’, but the example of the distance to the nearest star is surely environmental, do you disagree? He says, very clearly:
“There have been a number of cases where
numbers arose that were unexpectedly small or large.
An early example was the very large distance to the
nearest star as compared to the distance to the Sun,
as needed by Copernicus, because otherwise the
nearest stars would have exhibited measurable
parallax as the Earth moved around the Sun. Within
elementary particle physics, one has unexpectedly
large ratios of masses, such as the large ratio of the
muon mass to the electron mass. There is also the
very small value of the weak coupling constant. In
the time since my paper was written, another set of
unexpectedly small masses was discovered: the
neutrino masses. There is also the riddle of dark
energy in cosmology, with its implication of possibly
an extremely small value for the cosmological
constant in Einstein’s theory of general relativity.”
Clearly, in the above paragraph, isn’t it clear that he means numbers too large or too small indeed occur in nature, just like the distance of the nearest star to the sun? And isn’t he clearly likening this number to the (unexpected by today’s naturalness arguments) small scalar masses? What am I missing here?
He gives that example as a warning that one mustn’t ‘take numbers obtained from ‘naturalness’ arguments’ too seriously, as people in Copernicus’s time thought that distances which were far enough for the heliocentric model to be true couldn’t be ‘natural’. And how does non-perturbative QFT have anything relevant to the discussion about scalar masses?
He’s explaining that people were making assumptions about distance scales that were wrong, wrong because they had no experimental evidence, and their extrapolations based on their best current theories were wrong.
Non-perturbative QFT is relevant, because we don’t completely understand it, and our fundamental theory needs to be understood outside of perturbation theory. During the 1960s people were quite certain that a qft of quarks made no sense, based on extrapolating perturbative behavior. They found out they were wrong, when they better understood what can happen in qft. I think it’s quite likely we will sooner or later learn yet more unexpected things about qft, and such things might change radically what the “hierarchy problem” looks like.
“..sooner or later learn yet more unexpected things about qft, and such things might change radically what the “hierarchy problem” looks like.”
is so vague, and you don’t even point out what this might be makes it hard to take seriously. It looks more like a ‘hope’ or some sort of ‘non-perturbative QFT saves the day’ kind of emotion which really doesn’t tell one about what to and what not to expect. On the other hand, we know and have measured all the couplings of the SM, and it is clear the Higgs seen at the LHC is WEAKLY coupled, and it’s totally unclear to me as to how some claimed ‘non-perturbative QFT’ might come to the rescue of the quantum corrections that plague such scalar masses. In case you have some concrete ‘non-perturbative’ avenue that somehow might affect the Higgs sector, it’s futile to talk about help from ‘non-perturbative QFT’. All those lessons from history are sure nice to keep in mind, but you don’t seem to be indicating how to make progress.
The Higgs potential is very much a non-perturbative phenomenon (the mexican hat is not a paraboloid). All I’m saying is that the quantum dynamics of the Higgs field is not something we understand so well that we are sure we’re not missing something here (and I think this is also Wilson’s argument). This is an issue that people have certainly studied over the years, but it seems quite conceivable that something is missing. Quite likely actually that something is missing if you want to bring gravity into the picture. No, I don’t know what it is, if I did I’d be writing a paper and not wasting time arguing with you…
Indeed the Mexican hat is a paraboloid (can be approximated by) near the minimum, where the field rests, and one can perfectly use perturbation theory around this minimum. How is it that the quantum dynamics is ‘not understood’ in this simple enough regime? And all signs are that this perturbation theory works perfectly well. If there is something ‘not well understood’ as you claim, where is the proof of this? Any calculation or paper or something telling us this is so? Of course what you say is not Wilson’s argument. ‘Missing something here’ etc etc are simply words, whereas the perturbation theory performed assumming a weakly coupled Higgs gives perfectly satisfactory results. I don’t understand what you’re talking about.
This is going nowhere, and I really can’t understand why you find it so difficult to see the simple argument Wilson is making (which is the same one I am).
First of all, no, even near the minimum the Mexican hat is not a paraboloid, the potential is degenerate so things are more complicated than that. There are many subtleties in the quantization of a non-abelian gauge field coupled chirally to fermions and to a scalar with a vacuum state in a Higgs phase. Even before you add the scalar field into this, there are serious problems with defining the theory outside of perturbation theory (have you ever looked at lattice gauge theory with chiral fermion couplings?). Adding a scalar field with degenerate minima at non-trivial values and Yukawas (including a Yukawa coupling of almost exactly 1 to the top, 1 is not a number much less than 1…) add more tricky issues. Yes, there is a standard assumption that despite all this, the usual terms in the perturbation expansion capture everything. Maybe it’s right, but pretending to people that this is an open and shut case where we understand exactly what is going on and have full control of the approximations being made is just not true.
I don’t think these issues can be fully discussed in a blog post though, but I do think you need to answer the question of why you disagree with Wilson (who was someone who I’m sure understood these issues much better than either of us) about this.
Whether I disagree with Wilson or your interpretation of Wilson is something we can discuss over a whole new thread, but in my interpretation which I have given above, there is nothing that contradicts what I think about the hierarchy of scalar masses and what Wilson says in his paper you’ve pointed to. And be sure that many more people, which include people like Seiberg etc (who surely have understood these issues as well as Wilson did, and surely do understand the issues better than either of us) have exactly the same interpretation of the issue with the scalar masses which I have been discussing above. In case you want me to feel threatened by pointing me to some ‘QFT giant’ who knows much more (indeed he does), and are asking me to submit to some false understanding you want to promote, feel free to, but it doesn’t help matters, just like it wouldn’t help matters if I point to many of the aforementioned people (equally giants in their own right) and stake my claim to be right. At any rate, physics is not about who thought what, it’s about what works and indeed the perturbation theory works and gives correct answers. Your claim about the potential being degenerate doesn’t disprove anything; once we pick a minimum and shift the vev we can surely do perturbation theory assuming the potential being parabolic (near the minimum), there’s nothing conceptually wrong or invalid about it. All the talk about the subtleties of gauge fields coupled to chiral fermions, the degenerate minima scalar lead nowhere contradict the claim that small scalar masses are unnatural. I think you’re using all these words like ‘subtleties’, ‘lattice gauge theory with etc etc’ just to deviate from the main issue of is there or isn’t there a hierarchy. I am forced to ask you again: do you agree or disagree that small scalar masses are unnatural, and the SM Higgs faces this ‘hierarchy problem’?
If you don’t think there are any subtleties about the quantization of the electroweak part of the SM, that all there is to it is the story about how to construct Feynman diagrams that we teach beginning graduate students, fine. I don’t see any hope of waking you from your dogmatic slumber.
For about the 100th time: to have a serious, non-speculative hierarchy problem caused by two widely separated scales, you need two widely separated scales where you understand exactly the physics. Right now, we have one: the electroweak scale. Whatever is going on at some conjectural much higher scale we now know exactly as much about as the people in Copernicus’s day knew about the stars other than our sun. This is Wilson’s point, and mine. Your “hierarchy problem” is based on a speculative picture of what is going on at some scale we know nothing about.
Maybe I can say this in simple English, without using historical analogies or invoking any sacred names (for or against your point of view).
The “problem” with the Higgs is not a technical problem, but an esthetic one. It is a fine-tuning issue (at energy scales which are experimentally inaccessible). Some people would say, “alright, so we’ll tune very finely at some very-high-energy scale. No problem.”
Even if you don’t like this viewpoint (and I have to admit I’m uneasy with it), it isn’t self-evident that it has to be wrong. Experiment is king, not esthetics.
I never denied any of your subtleties, I just said indeed they’re there, but don’t have any effect on the issue at hand, the scalar masses.
“..to have a serious, non-speculative hierarchy problem caused by two widely separated scales, you need two widely separated scales where you understand exactly the physics. Right now, we have one: the electroweak scale. Whatever is going on at some conjectural much higher scale we now know exactly as much about as the people in Copernicus’s day knew about the stars other than our sun.”
I’m sorry but this statement is wrong. I don’t understand why should one understand the **EXACT** physics at the higher energy scale to even talk about it? There’s no assumption about the detailed dynamics at that scale at all, please note that the very existence of that scale is enough for quantum corrections to drag observables up to that scale. In fact it happens all the time with quantities that aren’t somehow protected by symmetry. If you claim that one needs exact knowledge of the dynamics of the higher scale, you have to show me a calculation or some such, whereas, on the other hand, there are plenty of examples in all sorts of QFTs where one may calculate continuously renormalizable quantities which get receive corrections. In fact, the fundamental lesson of RG is that the high energy effects decouple and cannot affect any of the low energy physics, but surely the quantum effects at a given low energy drag the unprotected quantities to any other relevant scale where new physics must appear. In this case it’s the Planck scale, but it could be any other high energy scale in b/w, like the GUT scale. How are you claiming, without at the same time contradicting RG, that one needs detailed knowledge of the high energy scale to say something about the nature of quantum corrections to observables computed at a given energy?
Perhaps I should amend my straw-man quotation to be, “alright, so Nature tunes very finely at some very-high-energy scale. No problem.”
Indeed, fine tuning is uneasy. Even if one somehow accepts some amount of fine tuning as OK, how can one say OK to fine tuning to one part in 10^32? Surely you’re not advocating that this is possible? Or are you saying that you believe that such things may happen, but for that one needs to know the detailed physics at the highest energy scales? If you’re saying that, then I’m willing to fundamentally disagree, because I feel that such impossible cancellations cannot occur. Indeed aesthetics have something to do with it, but it’s more than that. I think to ask cancellations of that order requires miracles, which cannot be expected from random integrals. But if you insist, I would be happy to disagree.
“Even if one somehow accepts some amount of fine tuning as OK, how can one say OK to fine tuning to one part in 10^32? Surely you’re not advocating that this is possible?”
Of course it’s possible. Just because you don’t like it (and I don’t like it much either) does not rule it out. Nature doesn’t care about our likes or dislikes.
Hi Peter O.,
That’s right, but I also think there’s another point, which is what Wilson was getting at, and which theorists typically ignore. Until you have a specific theory at your very-high-energy scale, you don’t know what exactly you mean by “tune the theory very finely”. Looking at the history of physics, theorist’s attempts to extrapolate to energy scales many orders of magnitude beyond what is experimentally accessible have often if not always turned out to be wrong.
You think you don’t need anything beyond what is in your textbook to understand what is going on at distance scales many orders of magnitude beyond what we can measure, I think those are great mysteries about which we will someday learn surprising things. Good luck with the multiverse….
“That’s right, but I also think there’s another point, which is what Wilson was getting at, and which theorists typically ignore. Until you have a specific theory at your very-high-energy scale, you don’t know what exactly you mean by “tune the theory very finely”.”
Hi Peter. You are right. We don’t really know what we are fine tuning, because we don’t know the theory at the high-energy scale. I guess I am just trying to say that without access to this scale, we shouldn’t take “solutions” to the fine-tuning “problem” seriously, without something compelling (like experiment). Maybe there is no solution (though I don’t advocate this).
I am not arguing against esthetic criteria in science. We need esthetics to lead us to try different models of Nature. I just think esthetics is not a substitute for real information.
Indeed one needs much more than what’s written in text books. But what you don’t tell me is why is it that it’s imperative to understand the full physics at the higher energies fully (indeed it would be fabulous to know it, but even without it we can make reliable statements about low energy, and this is why QFT works) even to make some qualitative statement about parameters at low energy. This is textbook stuff for sure, but a very valid and possibly the most important lesson about textbook QFT. Again, I fail to see why one needs detailed knowledge about the high energy theory just to make some statement about stuff at low energies.
” Again, I fail to see why one needs detailed knowledge about the high energy theory just to make some statement about stuff at low energies.”
Not any statement, Umesh. Your statement.