Wednesday, January 03, 2018

Sometimes I believe in string theory. Then I wake up.

They talk about me.
Grumpy Rainbow Unicorn.
[Image Source.]

And I can’t blame them. Because nothing else is happening on this planet. There’s just me and my attempt to convince physicists that beauty isn’t truth.

Yes, I know it’s not much of an insight that pretty ideas aren’t always correct. That’s why I objected when my editor suggested I title my book “Why Beauty isn’t Truth.” Because, duh, it’s been said before and if I wanted to be stale I could have written about how we’re all made of stardust, aah-choir, chimes, fade and cut.

Nature has no obligation to be pretty, that much is sure. But the truth seems hard to swallow. “Certainly she doesn’t mean that,” they say. Or “She doesn’t know what she’s doing.” Then they explain things to me. Because surely I didn’t mean to say that much of what goes on in the foundations of physics these days is a waste of time, did I? And even if, could I please not do this publicly, because some people have to earn a living from it.

They are “good friends,” you see? Good friends who want me to believe what they believe. Because believing has bettered their lives.

And certainly I can be fixed! It’s just that I haven’t yet seen the elegance of string theory and supersymmetry. Don’t I know that elegance is a sign of all successful theories? It must be that I haven’t understood how beauty has been such a great guide for physicists in the past. Think of Einstein and Dirac and, erm, there must have been others, right? Or maybe it’s that I haven’t yet grasped that pretty, natural theories are so much better. Except possibly for the cosmological constant, which isn’t pretty. And the Higgs-mass. And, oh yeah, the axion. Almost forgot about that, sorry.

But it’s not that I don’t think unified symmetry is a beautiful idea. It’s a shame, really, that we have these three different symmetries in particle physics. It would be so much nicer if we could merge them to one large symmetry. Too bad that the first theories of unification led to the prediction of proton decay and were ruled out. But there are a lot other beautiful unification ideas left to work on. Not all is lost!

And it’s not that I don’t think supersymmetry is elegant. It combines two different types of particles and how cool is that? It has candidates for dark matter. It alleviates the problem with the cosmological constant. And it aids gauge coupling unification. Or at least it did until LHC data interfered with our plans to prettify the laws of nature. Dang.

And it’s not that I don’t see why string theory is appealing. I once set out to become a string theorist. I do not kid you. I ate my way through textbooks and it was all totally amazing, how much you get out from the rather simple idea that particles shouldn’t be points but strings. Look how much consistency dictates you to construct the theory. And note how neatly it fits with all that we already know.

But then I got distracted by a disturbing question: Do we actually have evidence that elegance is a good guide to the laws of nature?

The brief answer is no, we have no evidence. The long answer is in my book and, yes, I will mention the-damned-book until everyone is sick of it. The summary is: Beautiful ideas sometimes work, sometimes they don’t. It’s just that many physicists prefer to recall the beautiful ideas which did work.

And not only is there no historical evidence that beauty and elegance are good guides to find correct theories, there isn’t even a theory for why that should be so. There’s no reason to think that our sense of beauty has any relevance for discovering new fundamental laws of nature.

Sure, if you ask those who believe in string theory and supersymmetry and in grand unification, they will say that of course they know there is no reason to believe a beautiful theory is more likely to be correct. They still work on them anyway. Because what better could they do with their lives? Or with their grants, respectively. And if you work on it, you better believe in it.

I consent, not all math is equally beautiful and not all math is equally elegant. I yet have to find anyone, for example, who thinks Loop Quantum Gravity is more beautiful than string theory. And isn’t it interesting that we share this sense of what is and isn’t beautiful? Shouldn’t it mean something that so many theoretical physicists agree beautiful math is better? Shouldn’t it mean something that so many people believe in the existence of an omniscient god?

But science isn’t about belief, it’s about facts, so here are the facts: This trust in beauty as a guide, it’s not working. There’s no evidence for grand unification. There’s no evidence for supersymmetry, no evidence for axions, no evidence for moduli, for WIMPs, or for dozens of other particles that were invented to prettify theories which work just fine without them. After decades of search, there’s no evidence for any of these.

It’s not working. I know it hurts. But now please wake up.

Let me assure you I usually mean what I say and know what I do. Could I be wrong? Of course. Maybe tomorrow we’ll discover supersymmetry. Not all is lost.


  1. Hopefully I'll get more detail on this question once the book comes out, but for now:

    Is it really the case that beauty / elegance provide *no* evidence for a theory? I've been assuming they provide some evidence, since regardless of what you're Bayesian prior is there are (at least asymptotically) more theories that are complex than there are theories that are simple, so asymptotically you have to assign less probability to more complex theories on average.

    But by some evidence I only mean some evidence, and once you find other evidence that some evidence may need to be discarded. This new evidence can either be experimental or theoretical.

    Does this "beauty provides some but not enough evidence" match your view, or are you making the stronger case that it provides zero evidence?

    1. The beauty can just be a limitation of human mind because we cannot analyse arbitrarily complex theories so we do things like linearization to make the equations easily solvable or pick theories wchich are close enough for our recent experimental knowledge. For example people once believed planets orbit in circles because circles are somehow beautiful only to later discover these are actually elipses.

  2. ---- Quote -----
    There’s no evidence for grand unification. There’s no evidence for supersymmetry, no evidence for axions, no evidence for moduli, for WIMPs, or for dozens of other particles that were invented to prettify theories which work just fine without them. After decades of search, there’s no evidence for any of these.
    It seems to me that Dr. Hossenfelder also has an antipathy for magnetic monopoles :-)
    My post got blocked.

  3. A typo, I think:

    ""...correct theories, there isn’t even a theory for why that should be so.""


  4. IMHO very well said! I think it is about time for sure someone to tell String Theory fans "Emperor is naked!" :-)

  5. A great argument for common sense, Dr. Bee. Hope is never lost for SUSY and strings when all you have to do is keep moving the goalposts back. Those goalposts are now pretty close to the unreachable Planck energy scale, but so what? Also, I love to hear a native German speaker use the word "prettify" correctly. It's commonly used in America to justify all manner of political, military and religious atrocities.

  6. In the beauty debate are there Lee Smolin echoes in seeking evolutionary reasons for lack of realised beauty as in the origins of flatfish asymmetry being uncertain while no transitional forms linking flatfishes with their symmetrical precedents have been found.

  7. Happy new year Sabine to you and your family.

    If nature is a can of worms physicists won't even look... so I vouch for simplicity rather than beauty.

    In my opinion, the true problem is the misuse of experimental data - not the lack of it. What do you do when you parameterize a theory? e.g. alpha, do you really believe in virtual photons? I do, but only as a method of calculus.


  8. All very beautifully put, but it does seem that if you have a theory that is good for very many reasons but it is not beautiful to the mathematical eye, you'd better be ready for a long haul.

  9. The old saying “beauty is in the eye of the beholder” should not be ignored.

  10. Geoffrey,

    Simplicity is a good criterion. But (as I explain in my book), simplicity is only a relative criterion. Among different theories that achieve the same, you pick the simplest. It's not an absolute criterion, for there are many theories simpler than the ones we know. It thus doesn't help you to find new theories. Best,


  11. You are not alone in believing that beauty is a poor guide to the truth of theories. You are in a minority, but certainly not alone, and you are a particularly important member of that minority because you express your views so clearly and energetically. Please do not give up. I have preordered the book and I shall read it carefully.

    Mike Thomas

  12. You labeled it properly. It was a rant, no doubt.

    I actually (mostly) agree with you, but then again, I'm an experimentalist.

    I disagree with, at least in a vague and weak sense, with your statement that there is no evidence for grand unification. Strictly speaking, of course you're right. But...more broadly...there is considerable historical precedence for newer theories to subsume and combine older theories. You know the list as well as I do.

    Accordingly...and this is just induction and not doesn't beggar the imagination that this pattern will repeat. This is a statement of how humanity has better and better appreciated the connections in the inner workings of the universe. It >>ISN'T<< a statement about physics...just the messy mechanism whereby we learn about our world.

    I'd bet that future theories will show connections not yet appreciated between phenomena that we currently describe using independent theories. And I don't think that this is a very aggressive bet.

  13. Don,

    I actually agree with what you say. I am aware of all the good reasons for unification. I still hope it'll work out. I just can't see a rational reason for this hope. That there's no way to prove induction works has been known since centuries. Best,


  14. As beautiful as epicycles!

    Is there any evidence that the elegance or clunkiness of epicycles played any role in their fading into history?

  15. Arun,

    My reading of history is that astronomers held on to epicycles because they thought circular motion to be more beautiful than elliptical. They won, eventually, because they were simpler. Beauty standards then adapted.

  16. Sabine

    Wouldn't a Quantum Gravity Theory be a GUT ?

  17. Hi Sabine, Happy New year! I've ordered your book, and there is no problem with the hype. I'm not sure when the book comes out, but as part of the hype I wanted to suggest you look into doing a pod cast with Sam Harris. He's done a few other physics types, (Max Tegmark and Lawrence Krauss to name two.) Maybe you could have a joint discussion with Sam and Max. That would be fun, and bring your ideas (and book) to a wider audience.

  18. Beauty may be an unreliable heuristic, but the challenge for the doubter is to come up with something better - I mean something that works.

  19. It often seems to me that people have it backwards. You do not find truth in beauty, but beauty in truth. If there is a working (true) theory, someone will formulate a beautiful version of it.

    I'll blame philosophers for this misconception.

  20. IMHO, thinking that "String Theory can never be disproved" maybe wrong.

    If, because of the experimental results, now strings need to be much smaller than any elementary particle, then there are only two physical possibilities:

    1) Each elementary particle is made of an extremely tiny string in the center and an extremely large energy/force field(s) around it.

    2) Each elementary particle is made of an extremely large number of tiny strings.

    The question is, can either possibility be true (mathematically fully consistent with QM/Relativity)?

    My guess is the answer would be found to be no, if any physicist really checked.
    (And if turns out to be really so, then it would mean ST can never provide a physical explanation for elementary particles!)

  21. "My reading of history is that astronomers held on to epicycles because they thought circular motion to be more beautiful than elliptical. They won, eventually, because they were simpler. Beauty standards then adapted."

    More or less. Goes back to Aristotle, basically, the so-called super-observer (interested in the real world more than in Plato's Ideals) who, despite having been married more than once, that women and men have different numbers of teeth. (Perhaps an unjustified jump from the specific to the general.)

    Of course, a large part of the problem was the Catholic church, which upheld the old worldview after Thomas Aquinas merged Aristotle and the Bible. It's hard to get better ideas accepted when your speaking platform is the burning stake.

    Tycho's observations and Kepler's work led to Newton's laws, which provided a much better understanding of the orbital motion of planets. Also, epicycles make testable predictions which have now been falsified, such as the distances of the planets from the Earth as a function of time.

    The general idea---building up an arbitrary periodic motion from cyclical motions at different speeds---is still around, of course; it is called Fourier synthesis.

  22. I remember
    from a reading long ago, that epicycles were still used long after
    Kepler or Newton. For manual calculation they are much easier/faster
    than gravitation based math.
    Think of epicycles as a approximation series apt for circular systems.
    Even the computers on board of the Apollo ships still used epicycles,
    was a story then.
    What about the tables used today to aim telescopes at planets?
    Maybe those tables were calculated long ago based on epicycles?
    I think Epicycles are much more beautiful than Gravity law :=)

  23. AFAIK, String Theory is based on the idea "everything is made of strings" and it uses QM and Relativity as boundary conditions. IMHO, a real TOE would not use them as boundary conditions but would provide derivations for both of them from a more basic/fundamental theory (itself).

  24. I can’t resist adding this quote, from St. Augustine (?): “ Beauty is indeed a good gift of God; but that the good may not think it a great good, God dispenses it even to the wicked.”

  25. Fantastic post. It's not much different from Kepler being sure that the beauty of Platonic Solids would give him a theory of planetary orbits... Only when he abandoned his preconceived notions of beauty that finally he was able to figure out his famous 3 laws.

  26. Excellent and funny piece. GRU is you indeed :) But let me ask you this: how do you (or others) define beauty?

  27. Even if all valid theories are beautiful, beauty can’t be used as an effective guide. We know that if A implies B, that doesn’t mean B implies A. The number of beautiful mathematical structures is very large, the subset being valid theories is likely a small subset. Therefore it’s not likely to be a good guide.

  28. While beauty is in the eye of the beholder, I think you also have to ask yourself when you decide a theory was beautiful. In my opinion, a theory becomes more "beautiful" when a number of previously unrelated observations suddenly become related, when a number of "What on earth is the reason for that?" suddenly becomes explicable. A new theory that merely has a lot of convoluted mathematics and no relation to observables can be quite ugly, even if the maths are elegant in some eyes.

  29. I've probably got the following questions wrong, but to my amateur mind isn't a particle breaking down from su3 to su2 something that needs understanding? Surely there's a relationship that string theory is trying to describe? Whether it's right or wrong, there's a geometric shift in the translations which suggest there's a connection between the two states?

  30. Sabine, you provide several examples of "beautiful" theories that failed. These seem insufficient to support your thesis. How about some examples of "ugly" theories that prevailed? If none, how do we know that any can exist? (I am neutral on this topic, but interested.)

  31. Re. epicycles you say "Beauty standards then adapted." Right. Today, a circle looks no more beautiful than an ellipse. If something works well for a generation, then it starts to look beautiful. Planck originally thought his quantum was ugly, didn't he? A good history-of-science project would be to examine how aesthetics changed as new ideas became accepted. It would probably support your point. "If you have only a hammer, every problem looks like a nail." And, no doubt, "if you have only a hammer, that hammer looks beautiful."

    There's one obvious reason why physics theories should be beautiful. If an intellect (somewhat in tune with ours) designed the laws of nature, that would explain why they should be 'beautiful': intuitive, simple, logical. It's hard to think of any other reason. Since few physicists believe there was a designer, that also constitutes an argument in your favor.

    I predict your response (if there is one) will be: "Both those points are in my book"

  32. pete,

    Quantum gravity doesn't necessarily need a grand unification. It has to unify the interactions in the sense that it must include quantum field theory, but there's no reason the other interactions must be joined to one. (Or that all of them must be joined to one, that being a theory of everything.)

  33. CIP,

    No, you got this wrong. Why would it be my task to come up with something else these people can spend their time on? Having said this, of course personally I think the sensible thing to do is look for experimental evidence for quantum gravity, which is why I work on that. (Or try to, if I can find the money.) Best,


  34. FB36,

    I didn't say here and not elsewhere that string theory is not testable because that's wrong, at least in principle.

    Having said that, string theory is for all we know consistent with quantum mechanics and general relativity, at least if you allow general relativity to be modified by adding some more fields. I don't know what makes you think it's inconsistent.

    More generally, you have the problem backwards. Internal consistency isn't sufficient to find out which theory is a correct description of nature because it always depends on the assumptions. In the end you can only go and see if it describes observations. Best,


  35. Tam,

    No one ever defines beauty. In my book, I didn't define it either, but I offered a summary for how I think people use the word in practice. For this, I distinguish between three different components of beauty: simplicity, naturalness, and elegance. The first two I think you probably know (if not, I'm happy to explain more). The last, elegance, is the most subjective one. Roughly speaking, I have found people associate with it an element of surprise or unexpected connections. Also, rigidity is often mentioned in this context. Best,


  36. jon,

    I don't know what 'particle breaking down' you are referring to, sorry. Of course if there's a grand unified symmetry it must be broken in case that's what you meant.

  37. Andy,

    I have examples of this in the book. There have been various instances when beauty standards shifted and what was once considered ugly became accepted and later acknowledged as beautiful. The mechanistic world view, for example, was once thought to be something to strive for. Maxwell was really unhappy that he couldn't come up with some electrodynamical theory working by gears and so on. Now we're used to just dealing with fields. Quantum mechanics was considered ugly by many. Some of course still think it's ugly, but who cares as long as it works? Dirac and others of his days thought quantum electrodynamics is ugly because it required renormalization to get rid of the infinities. I don't think you would find anyone today who thinks QED is ugly. And as someone mentioned earlier, that the universe isn't static was also thought to be ugly. In the end, none of this mattered. But of course the only reason it didn't matter was that they had data. Best,


  38. George,

    No, I don't discuss arguments from design in the book, because I don't think any one in the community would try to pull such an argument.

  39. I think it would be beautiful if gravity was consistent with Coulomb's law, or if gravitational theories further refined it.

    Beauty is always in the eye of the beholder, and this beholder is just an electrical engineer, not a physicist.

  40. a comment on "Liralen": "I think it would be beautiful if gravity was consistent with Coulomb's law, or if gravitational theories further refined it."

    The old gravitational potential 1/r appears, because in the trajectory of the classical test particle on the static spacetime the time component dominates the space component.
    For the electrostatic potential 1/r to appear from QED also the two particles have to be static.
    But contrary to GR now in QED the space component of the photon propagator dominates the time component - way off mass shell, having no energy but only momentum.
    This is a blunt violation of the relativistic energy-momentum relation, but the QM exchange particle only exists in the unitary evolution of QM.
    This is already a hint how GR and QM work together and a hint for a hypothesis: virtual particles do not contribute to the curvature of spacetime.

  41. If the theory consists of valid arguments - ones in which the conclusion does follow from the premises - then it is maximally beautiful, simple, elegant etc. If there are invalid arguments, or if some conclusions are just guessed, not deduced from clearly defined initial assumptions (axioms), then the theory is not even wrong.

  42. Wonderful...I feel like in the midst of a scholastic debate. Next question: How many angels can dance on the tip of a pin?

    P.S. don't think I'm trying to be negative.

  43. I feel there has been a quantum shift (pun intended) between evidence and mathematics, Sabine. Once upon a time, evidence ruled -- mathematical physics strived to explain the array of available evidence, and occasionally got ahead of the game to make some predictions. Now it seems that not only is mathematics an immutable achievement that cannot be questioned, but that it's hard to debate a point, or make a suggestion, unless you "speak" in the latest mathematical runes, and that your notions are representable using mathematics.

    We seem to be "creating" the universe as we would like it. I have said elsewhere -- possibly here -- that there is much read into our mathematics that is not an innate part of its form. In effect, we have lost the ability to separate mathematics and our perceptions of reality. Does equation blah-blah really say that "this" happens, or does it simply describe a relationship between certain mathematical quantities that may or may-not have observable counterparts?

  44. If i can make few observations as a non-expert:
    1) Maybe the Grand Unification and Quantum gravity frameworks cannot be successfully put together yet because we are still missing some key ingredient in the recipe. All the imagination, skill and work will not be enough if something fundamental is absent. Trying to guess that missing part (without experimental clues) and then to work out how it all fits together might require too many imaginative steps at once - very easy to get in the wrong direction. Maybe it would be worth not to spend as much time on it, like it currently makes little sense to argue how fundamental laws came into existence (as we have no ways to observe law-forming processes in the nascent universe or verify out speculations about multiverses.)
    2) Aesthetic feelings probably have their Darwinian purpose, and in the case of beautiful theories, I would guess it is a built-in reward mechanism for effective problem-solving. And in the same way like jokes can be entertaining in several different ways (as long as they tickle our taste for curious absurdity), and to different audiences, the new, more encompassing law that describes physics beyond the SM, once found and confirmed, will be also a thing of beauty to younger people, just not beautiful in the currently fashionable direction.

  45. Isn't string theory the best candidate (at the moment) for a TOE/GUT due it being the only candidate where gravity is built in to its foundations whereas everything has gravity added/bolted on?

  46. String theory is mathematically remarkable, but let me remind everyone that the interest in string theory is not just about aesthetics and pretty ideas.

    Any theory of reality has to include fermions, gauge forces, gravity and the quantum. String theory contains all those things (and it doesn't *have* to contain grand unification and supersymmetry).

    From a perspective of consistency and completeness, it is uniquely attractive as a theory of quantum gravity (with the asymptotic safety program in second place, in my opinion).

    Also, in theory an individual string vacuum is infinitely predictive - all the phenomenological constants are completely determined - although in practice, the calculational state of the art is that string phenomenologists aim just for order-of-magnitude or qualitative retrodictions e.g. of particle mass matrices.

  47. Hi Sabine, I agree that simplicity can be a component of beauty, but obviously complexity can also be beautiful (look at peacock feathers, for example, or fractal art). Naturalness is a term that I feel adds very little to the definition b/c it's entirely subjective and generally a copout for "I think this is right" rather than anything remotely objective/intersubjectively confirmable. Elegance is also very tricky b/c it generally reduces to simplicity and fit for function. But I look forward to reading your book and hopefully interviewing you about it. Here's an article (with a follow up Part II at the same website) on my thoughts about a "science of beauty" if you're curious:

  48. Rovelli i think would consider LQG more beautiful than strings

  49. Sabine One question i'd like you to elaborate on, is that i had asked someone from PF to ask you if universities and top physics departments that have string on their faculty should have LQG faculty for which you said no.

    Do you think top physics departments only have string theorists then in their department?

  50. Wait! Physics au naturel? No, I’m too old to imagine that. Should the next M-Theory conference being held at Garden of Eden Resort, Bocas del Toro, Panama? BTW I can feel my own protons decaying; but that might be some medical condition.

    As a spectator, physics seems to have become too much like PURE mathematics, which is detached from the universe. That’s fine for someone else; at this point I don’t understand or care. (e.g. zeros of the complex zeta function)

    Experiment! (not in the way Cole Porter sang about) “We'll be saying a big hello to all intelligent lifeforms everywhere and to everyone else out there, the secret is to bang the rocks together, guys.” -Hitchhiker’s Guide to the Galaxy

    I’ll order your book as soon as it is available. Keep plugging away.

  51. This comment section gets a lot of comments which I don't approve because they violate our comment rules. As a reminder: Please do not submit links unless to published papers, do not repeat questions that were previously answered, and please do not submit off-topic comments such as, for example, what you think I should be working on. Thanks,


  52. Sabine, I speak as someone who thinks that string theory is likely to be a big part of the answer in fundamental physics. One thing I can tell you is that I don't come to that conclusion because I think string theory is beautiful. In fact I don't even think it is beautiful, and it certainly isn't simple. Yes it has its moments of elegance, such as supersymmetry and its dualities, but taken as a whole it is an ugly mess. Perhaps in the future we will find a more elegant and complete formulation but for now beauty is certainly not the convincing factor for me, and I suspect that many string theorists would say the same.

    The reason that string theory looks promising is that when you start from quantum field theory and try to explore all the ways you could generalise it to include gravity and bigger gauge theories you find that everything is inconsistent except this one path. Well we know that nature has a way to generalise quantum field theory that includes gravity and gauge theory, so if it is not string theory, what is it? Other ideas such as Loop Quantum Gravity come from a different direction and arrive at something even less cpomplete that could equally well be part of the same picture, but without being able to match up with QFT in the way strings can. I find these observations much more compelling than any argument based on beauty. Mathematical beauty can be a good guide to the right theory and so can simplicity, but they are not nearly as good as the requirement for consistency.

    You worry that there is no evidence for supersymmetry, but there is no evidence for anything else that might replace it either. You are the expert on quantum gravity phenomenology, so tell us how much empirical data there is that can provide any help to theorists. As far as I know it is just a few negative results. Even the evidence beyond standard models at lower energy is limited to a few mysteries and negative results such as inflation, dark matter, dark energy, proton stability, CP violation and neutrino mass. There is nothing that can give a direct handle on which direction to take. So lack of evidence is not a problem specific to string theory or supersymmetry. It is a problem for any potential theory that attempts to go beyond the standard models.

    I know that a small number of string theorists sometimes hype up the significance of beauty when writing popular books or talking to journalists, and this is a valid thing to criticise, but I doubt that it is the main motivation they have for investigating the possibilities that string theory may offer. It is far from complete. There are still big gaps to fill, but from my point of view your criticisms seem to be just lashing out in the wrong direction.

  53. Sabine, thanks for admission despite the provocation!
    A long way to beauty:
    Even though having made fun of scholasticism in my previous post, I yet think that the medieval scholastic debate was the ‘dance school’ or ‘spearhead’ of modern languages without which we would have much less to say today. The scholastic method was in the argumentative refutation (by reductio ad absurdum) of whatever endangered to diminish the almightiness of God, which for the purpose of this discussion can be equated to the idea of unity, namely, the unity of language and knowledge. So, the dogmatism of scholasticism, at least before empiricism gained significant influence, was the earnest and honest attempt at the refutation of novel claims by demonstrating their linguistic inconsistency, i.e. by censorship in the best sense of the word. The reductio, however, isn’t truly logical, for it discards on the grounds of absurd consequences. Hence it is suited to judge non-logical (non-reductive) unities or wholes.

    Enlightenment, in as much it was ‘empirical’, created science as a positive undertaking, which made the logical proof move center stage. The consequence was that scholars began to create and promote their own ideas, rather than trying as hard as possible to trash those of others in defense of some canon. Today’s science industry and its fatal incentives are the direct consequence of scholars having changed camp. Popper was the last defender of quasi-scholastic idea of scholarship. His theory of falsification – and this is important – was a purely theoretical/linguistic (armchair) task and if so prior to any experimentation. He insisted that sentences can only be falsified by sentences and that there is nothing like pure observation or empirical proof. Hence ‘falsifiability’, for Popper, required of valid theories no more than conforming to the syntactic and semantic rules of language such that they can be communicated and discussed in a context (no mention of mathematics or measurements there). Theories having passed this gate were then to be judged as to what Popper called their Folgerungsmenge, which has nothing to do with making predictions, let alone numerical predictions. Folgerungsmenge, if mighty enough, is what switches on the light in a hitherto dim and murky room. The ‘beauty’ of a mighty theory lies in its disposition to action.

  54. PhilG,

    "I find these observations much more compelling than any argument based on beauty."

    Explain this without using an argument from beauty. We all know that mathematical consistency is merely a necessary, not a sufficient requirement for a theory. We all know that the "no-alternative argument," which you are raising, is contaminated by sociology.

    As to quantum gravity phenomenology, I wrote about this eg here.

    The excuse that you name, that it's just something physicists write in popular science books is extremely implausible because all evidence speaks for them paying attention to it, and that includes people just plainly telling me.

    Btw, these are all arguments that I have heard many times and that are discussed in my book.

    About me "lashing out in the wrong direction". I name all the benefits of both supersymmetry and string theory and also why these speak for the theory. What you call "lashing out" amounts to not forgetting to also mention the shortcomings.



  55. "much of what goes on in the foundations of physics these days is a waste of time,"

    This revelation is not new, and should astound no one who has ever been to a physics conference, especially one on the foundations of physics. Feynman said much the same, and that was during an era in which more progress was being made. Keep up the good fight.

  56. I already explained my arguments in favour of string theory without appealing to beauty.

    It's simply a question of looking for something consistent in the weak field limit that includes quantised gauge theory and gravity. I am sure you must be aware of what a tight constraint that turns out to be. It is not "merely a necessity." It is a powerful guiding principle. There are many alternative approaches to quantum gravity and unified theories but none of them go far enough to provide a framework for this limit of the theory. Of course we don't know with mathematical certainty that this is conclusive evidence that string theory is the only way forward, but nobody has shown a good way to avoid it, so I consider that good evidence. The fact that this route requires gauge symmetry and supersymmetry and leads to a unique result in higher dimensions through dualities may be considered beautiful to some, and it does provide a small increase to the likelihood of correctness, but consistency is what really counts here. There has been plenty of sociology in the debates on these issues but the underlying arguments in favor of string theory are not sociological at all.

    Please don't refer me to your book for answers. I have given up on popular physics books because they always either cover at great length stuff I know already, or are negative about what else can be done (usually both). I don't feel negative about anything in physics except the future experimental side of HEP so I am quickly bored by such things. I am sure your book will have lots of success with those who think the same way as you do.

    The main shortcoming of string theory is that it does not make any connection to experiment, but we understand why that is and why it could be true for any theory of quantum gravity for the foreseeable future, barring a big dose of good luck. Epistemological arguments can't rule out a physical theory. That was not part of what I meant when I wrote about you "lashing out." I am talking about how you assume here that people believe in string theory because of beauty. I disagree that beauty is the main reason to think it has a good chance of being right, so you are attacking the wrong thing while playing down the role of consistency which has a more important role than beauty.

  57. Many years ago, as a graduate student, I read some parts of the two-volume 'Superstring theory', by Green, Schwarz, and Witten. I never became a convert; I never found string theory beautiful.

    Perhaps a bit off-topic: To my amazament, Einstein's equations in vacuum, i.e., the vanishing of the Ricci tensor, was in Vol. I 'derived' by the requirement that the quantum theory of the curved spacetime string world sheet action be Weyl/scale-invariant, as far as I understand it. Is that still done today, or is gravity derived otherwise? For to me such a 'derivation' does not really qualify as a proper derivation, but more as a sort of consistency requirement, analogously to, say, the U(1) hypercharges of fundamental fermions in the standard model being so that the total chiral anomaly cancels out.

  58. This discussion is necessary to just the extent that physics has become less the study of physical reality and much more the study of mathematical models. Beauty is not a proper scientific concept because it is only definable subjectively.

    Beauty is only a valid aesthetic judgement in non-scientific areas such as the arts, philosophy, and mathematics; it has no meaningful scientific standing.

  59. Sabine

    do you think top physics departments like harvard princeton yale stanford should create a non-string QG research group?

    if not, why not? if so,

    what non-string QG research do you think top physics departments should sponsor research groups, faculty and grad students, if not LQG?

    or do you think only string theory should be funded at top physics departments?

  60. Hi Sabine

    Agree 100%, although I believe the correct answer is likely to be simpler. Maybe it's just a small part of the big picture that's missing, and that's why the SM works so beautifully well but happens to be incomplete. And, as always, the truth is surely in the details, not in hand-waving arguments like beauty or simplicity. But that's just my guess.


  61. SH>> I don't discuss arguments from design in the book, because I don't think any one in the community would try to pull such an argument.

    Just so I'm not left hanging, please let me point out: I think they do. Dirac, Penrose, Motl and others do indeed 'pull such an argument'. But I see you're not interested in the topic, so, thanks for your time.

  62. PhilG,

    I say it's merely necessary not sufficient in a technical sense because no one has proved that string theory is the only way to do it, and no one ever will because no proof is better than its assumptions. Lacking both proof and evidence, why do people like you believe in it anyway? Sociology is the only explanation that I can come up with.

    You'd be well advised reading my book, but of course the reason I wrote it is that I know there is nothing in the world that could possibly convince you that social biases might affect your interests. Best,


  63. "The main shortcoming of string theory is that it does not make any connection to experiment,...". Whatever theoretical framework proves to be the correct path forward, there was once a seeming opportunity for those of us who are mechanically inclined tinkerers to uncover experimental evidence for new physics, as I intimated in a comment using my disqus account, at Sabine's Nautilus article: "What Quantum Gravity Needs Is More Experiments", which she linked above. Unfortunately I found nothing out of the ordinary, despite a fairly extensive effort. However, I was stymied by YBCO superconductors that always were irregular in shape frustrating my plans. For those of us who enjoy tinkering with things to have an impact in the field of experimental physics, as amateur astronomers have had on professional astronomy, we will need to move up several grades in sophistication, and thus cost. Perhaps nothing will be found, but as the saying goes - "Never venture, never gain".

  64. Sabine, my argument does not require a proof that string theory is the only way to do it. If we had that there would presumably be no room for disagreement at all. Nevertheless, the evidence provided by the need for consistency is good. I don't claim that string theory must be correct because of it. I am just saying that the arguments in its favour are much more than an appeal to mathematical beauty as you claim.

    I don't think it is helping your case to fall back on social bias as an argument just because you can't see the merit in what I am saying. I could just as easily accuse you of social bias because I can't see why you don't get it, but I wont. I am sticking to scientific arguments.

  65. PhilG,

    IMHO, the argument of being the only game in town, thanks to its ontological potential, is as much a hand-waving argument as beauty or simplicity. String theory has probably been the most remarkable effort to overcome the shortcomings of the SM so far. And it has led to impressive mathematical achievements. But maybe it's not the correct physical answer after all. And then? You know, the ways of the Lord are infinite, and the ways in which physical theories can be approached are almost as many. Have we been left almost without further experimental guidance? Well, perhaps our best option is to return to the starting point and throw imagination. We've got a quantum field theory that matches experiment up to many decimal places but happens to be incomplete. Maybe the whole picture is too small and we have to move on to a larger framework (as string theorists did some years ago) or maybe it's just that some subtle part of the puzzle is missing. Subtle, but surely not unimportant.


  66. I think your claim that people should stop considering beauty a guiding principle in science is a straw man.
    Many people do string theory because of it's elegance in certain regimes.
    But as soon as you want to do pheno it becomes messy and i doubt many believe it to be a true theory of nature because of any beauty in semi-realistic string vacua.
    It is - and this is worth saying at least as often as you want to mention your book - the only game in town when it comes to consistent theories of quantum gravity.
    LQG is not a candidate. There is no reason to believe that it has anything to do with general relativity.
    Asymptotic safety might be true but it is no better than wishful thinking.
    The statement is basically that maybe our problems go away at high energies.
    All calculations have been done in truncated coupling spaces and no one knows
    why that should generalize.
    As for CDT, which you previously mentioned as a candidate, it has also not even been shown to reproduce general relativity as a continuum limit.
    The sine qua non of a quantum theory of gravity is that it is in fact a theory of gravity.

  67. Dr. H.,

    I sympathize overwhelmingly when you appeal to the intersubjectivity of the sense of beauty, but at the end of the day, beauty, like "elegance", or even "simplicity", is anthropic and will always defy objective definition. This, if anything, is why it is not a meaningful or useful criterion.

  68. PhilG,

    The whole point of this blogpost was to say that I do see the merit of these arguments. But you're just pushing around the bump under the carpet by saying things like "evidence provided by the need for consistency is good". Where is the evidence that it is "good"? What makes it "good"? Back to head counting and no-alternatives? Or are you trying to pull David's "meta-inductive argument"? (Which has as little logical support as any inductive argument.) Really I get the impression you haven't thought about this at all. You believe in string theory for what you think are good reasons, but don't ever bother to analyze why these reasons are supposedly good. Best,


  69. Cobi,

    I find it interesting you believe that asymptotically safe gravity and loop quantum gravity are inconsistent. Why don't you write a paper about your amazing insights? I am sure the community will be interested.

  70. Sabine,

    i did not say that LQG is not consistent. I said there is no reason to believe that it is a theory of gravity. In this regard, the burden of proof is on the side of the LQG community.
    Urs Schreiber has pointed out many times why Barretts theorem does not apply anymore when you depart from the space of all smooth connections and instead consider the space of general functions from loops into the holonomy group.

    Neither did i say that ASG is inconsistent. The assumption that there is a finite dimensional UV critical hypersurface makes sense.
    It is just not clear how to assess such a statement.
    If you know any ASG paper where the authors provide a clear argument why extrapolating from the truncated coupling space to full GR is a reasonable thing to do, i would love to read that.
    Apart from that, the claim that gravity can be described by a local quantum field theory at all scales has been criticized for example here:

  71. Sabine, your counterarguments are always that I am biased and have not looked at things carefully. You are not addressing the points I made at all. I agree with Susskind who said this in a 2013 interview for The Econimist,

    "Basically, from the time of Einstein’s [theory of] general relativity there was no good idea about how quantum mechanics and gravity fit together. They were always at each other’s throat, apparently inconsistent. String theory’s biggest and most important impact is to show that gravity and quantum mechanics can and do fit together. That, more than anything else, has maintained interest in it.

    He says nothing about beauty, it is about finding consistency between GR and QM. He is not talking about some complete mathematical proof. This is just about how string theory passes consistency tests in the perturbative limit. He says that is why people are still interested in it. Are you going to accuse Susskind of not having thought about it too?

    I don't claim that other approaches such as LQG are inconsistent. I claim that they have not yet provided a theory for the limit of weak quantum gravity where string theory comes from. If they were complete theories of quantum gravity they would have to do that. If LQG did, it would come up against the same problems that string theory solved and the most likely conclusions would be either be that LQG is inconsistent or it has to be modified to become a non-perturbative version of string theory. If it provided a different unexpected solution that would be great, but we are still waiting for it.

  72. Phil G: " I am just saying that the arguments in its favour are much more than an appeal to mathematical beauty as you claim."

    As a somewhat disinterested (in the topic) observer, I do not agree that Dr. Hossenfelder claimed that. I think she claimed that there are arguments but beauty should not be one of them, and it is. (Here I keep trying and failing to summarize her exact position in a few sentences which I have concluded is too dangerous to attempt, but re-reading her post will, I think, support me.)

  73. The sum of all positive natural numbers (1,2,3,4...) is multiply demonstrated to be -1/12, consistent with string theory, etc. The residual countable infinity was renormalized.

    What is the sum of 0,1,2,3,4...? Perhaps nothing can change physics' trajectory. "8^>)

  74. PhilG,

    I am not countering your arguments because you don't have any. There's no logical reason to believe that string theory is a correct theory of quantum gravity and you haven't named any. You just say "mathematical consistency," "meta-induction," and "no-alternative" like a broken record, though I told you several times that none of these amounts to evidence for anything.

    If you don't want to call the kind argument you raise an argument from beauty and you don't want to call it sociology, fine. Then give it some other name. Fact is, as I hope we both agree, that there is zero evidence that string theory describes quantum gravitational effects in our universe and yet people like you who call themselves scientists continue to believe in it.



  75. JimV,

    The problem is that too many theoretical physicists in the foundations no longer recognize when they make what is really an argument from beauty. As this comment section illustrates. They really, really, do believe that they are so much smarter than that. Same with no-alternatives as with naturalness as with grand unification and so on and so forth.

  76. PS: Did you just claim that asymptotically safe gravity doesn't reproduce the weak-field limit?

  77. Cobi,

    Your point being that there isn't evidence either of these approaches correctly describes nature? I'll certainly agree on that. Has it yet been proved that string theory is UV finite? Has someone yet found the standard model in the landscape?

  78. Sabine,

    you keep misrepresenting my statements.
    I did not criticize that there is no evidence that LQG or ASG describe nature.
    I criticized that there is no evidence that they are quantum theories of gravity.
    I don't even demand a proof, just convincing evidence.
    There is plenty of evidence that string perturbation theories are finite at any given order.
    Of course, the perturbative expansions do not converge which is expected from the
    theory of resurgence.
    There is another large set of evidence that indicates that they are the asymptotic expansions of a single consistent underlying theory.
    Most importantly, it is easy to show that string perturbation theories are theories of gravity in the sense that they reproduce GR in some limit.

  79. Cobi,

    I am merely trying to find out what you are saying. You seem to still be complaining that LQG and ASG are somehow worse than string theory. You seem to be saying there is no "evidence" that they are "quantum theories of gravity" where "evidence" has nothing to do with, well, evidence (that being about observation) and "quantum theories of gravity" are theories that do not describe nature (because you explicitly said describing nature is not what you are referring to). So what are we even talking about here? Why would I care? And of course if you talk to someone who works on either of these approaches they'll tell you it's something with quantum and something with gravity, so it's something with quantum gravity.

    That you don't expect the perturbative expansion to converge doesn't prove the theory is UV finite it merely means that the non-convergence doesn't prove it's not finite. Best,


  80. Sabine,
    This has been a very interesting and informative discussion. Thank you for being courageous enough to stimulate it. The impression I get from the comments of Cobi, PhilG and other string theory practitioners is that, as you state, their use of phrases such as “mathematical consistency," "meta-induction," and "no-alternative" to describe string theory are what you are referring to as “beauty”. These string theory supporters also emphatically suggest that string theory, at least formally, provides a natural extension to combining “quantum” and “gravity”. For an outsider like me, could you comment on this? What is it about string theory that is so appealing? Is that appeal, by itself, any sort of argument for its value as a physical theory.

  81. David,

    Mathematical consistency isn't a beauty requirement. A theory that isn't consistent (within its regime of applicability) is just wrong and in need of being fixed. This requirement isn't optional.

    Mathematical consistency is also not enough to get a theory of nature. Even if you could prove that a certain solution (say, string theory) is the only solution for a certain problem, then that proof would depend on the assumptions and you cannot prove the assumptions themselves to be true - they can merely be useful for a theory to describe nature. Example: Pretty much every one in the business assumes that the procedure of quantization itself does not depend on resolution (or energy respectively). If you think quantization is emergent, that assumption is just not valid, hence falls every single approach to quantum gravity in existence (this is also why I think they'll all turn out to be wrong).

    Having said that, there isn't any proof for either approach to quantum gravity (string theory, lqg, asg, cdt, etc) that it's the only one with certain requirements. At least I never heard of any such proof. Though certainly if only you make sufficiently many assumptions it'll be easy to prove anything.

    Now, since mathematical consistency isn't enough to tell you which theory is the right theory of quantum gravity (right in the sense of describing our universe), you need further requirements. If you are doing science, these requirements are empirical adequacy, ie comparison to observation. There isn't any such observation, so then theorists draw on other criteria. All these other criteria are belief-based. I lump them together as arguments from beauty, but you could equally well call them spiritual beliefs or philosophical attitudes or what have you. Doesn't matter, point is they're not scientific. They have no logical basis.

    Then you can ask why do they believe in them anyway? To which my best answer is sociology: They have told each other for decades that these are good arguments and they still say that. It's hard to overcome such positive reinforcement. (Also funny to note how they all say the same thing, using almost identical phrases.)

    Meta-induction is the argument that a theory is more likely to be correct because it uses the framework of already known and established theories. But the only thing that you really know is that it must reproduce available data to within measurement precision. Yes, it's the obvious thing to try first. But that doesn't mean it's correct.

    No-alternatives is as dumb an argument as it gets because a) it's wrong, there are alternatives, it's just that string theorists don't like to hear about these and b) that few people so far have worked on alternatives might say more about humans than about the fundamental laws of nature.

    The interesting thing is now that many theoretical physicists come to mistakenly think that such arguments of belief or intuition are indeed solid scientific arguments.

    See, if they'd just go and admit these are arguments from beauty or just insist they want to believe, then at least it would be out in the open. Instead they claim their beliefs can be justified on rational grounds (without ever being able to provide such justification).

    Maybe the most depressing thing is how easy it is to pull out the carpet under such "arguments." David Hume already went on about the impossibility of justifying induction and that was more than 200 years ago. It seems that we haven't learned much since.

  82. The relationship between mathematics and the physical world is a subject of deep philosophical speculation, so I'm not going there. However, instead of talking about "beauty", how do folks feel about "redundancy"?

    I think we can all agree that theories with too many degrees of freedom are less attractive than those with just enough to explain evidence, and with little or no arbitrariness. I'm sure that with enough degrees of freedom, we can make our mathematics come up with whatever numbers and relationships that we need. Maybe this is how we subjectively measure the notion of "beauty".

  83. "No-alternatives is as dumb an argument as it gets because a) it's wrong, there are alternatives, it's just that string theorists don't like to hear about these and b) that few people so far have worked on alternatives might say more about humans than about the fundamental laws of nature.
    Maybe the most depressing thing is how easy it is to pull out the carpet under such "arguments." David Hume already went on about the impossibility of justifying induction and that was more than 200 years ago. It seems that we haven't learned much since."

    Your reference to Hume sheds some light on your position.
    Is your claim that there is no distinction between the logical underdetermination and the ampliative underdetermination in the sense of Dawids definition?
    In other words, would you say Russell's Teapot is as good a theory of quantum gravity as LQG and ASG?
    How should the existence of a teapot behind the moon explain gravity you may ask, but that is exactly the point i try to make about LQG and ASG.
    If you rigorously demand that the only valid type of evidence is empirical, than how do you distinguish them?
    And even if you can make a measurement and find a theory that fits, how can you believe that the theory that matched observation today will be the same theory that matches observation tomorrow?

  84. Cobi,

    "In other words, would you say Russell's Teapot is as good a theory of quantum gravity as LQG and ASG?

    How should the existence of a teapot behind the moon explain gravity you may ask, but that is exactly the point i try to make about LQG and ASG."

    Russell's Teapot isn't a theory according to the present quality standard in physics which is that theories are mathematical in their formulation. The use of mathematics is evidence-based.

    "If you rigorously demand that the only valid type of evidence is empirical, than how do you distinguish them?"

    I do not demand, and have never demanded, that empirical evidence is the only criterion that is allowed in theoretical physics - of course not, that would be entirely nonsensical. So please stop assigning opinions to me that I do not hold. I am not against meta-inductive arguments, I am not against arguments from beauty, I just want them to be clearly stated as hypotheses so that we know what we are talking about. That's all. You believe in string theory because you have the hypothesis that so many smart people can't possibly be wrong, then just go and say it, clear and loud, upfront in your next talk.

    You ask me how do I tell whether one theory that has no empirical evidence speaking for it is any better than some other. But that's the question that you should be answering. You somehow seem to be assuming that we have to make a choice between what's presently available. But that's a big mistake. The question you have to ask here is whether that's something scientists should be doing, period.

    "And even if you can make a measurement and find a theory that fits, how can you believe that the theory that matched observation today will be the same theory that matches observation tomorrow?"

    I know it's a belief, not knowledge, and I've never claimed otherwise. It's a belief that underlies all of scientific inquiry. But it's not the same belief that you are referring to (which you don't want to admit is merely a belief) which is not an extrapolation from yesterday to today but from accessible energies to higher energies. Best,


  85. Sabine,

    Now you say

    "I do not demand, and have never demanded, that empirical evidence is the only criterion that is allowed in theoretical physics - of course not, that would be entirely nonsensical.",

    yet you previously replied

    'You seem to be saying there is no "evidence" that they are "quantum theories of gravity" where "evidence" has nothing to do with, well, evidence (that being about observation)'

    to an argument which was clearly about the theoretical and not empirical viability of LQG and ASG.

    'You somehow seem to be assuming that we have to make a choice between what's presently available. But that's a big mistake.'

    The complaint that you seem to make in your book, according to the abstract, is about the allocation of resources in science.
    That is a choice one has to make.
    I never said that i believe that String Theory is true as a theory of nature.
    I argued that there is a good reason why more people work in it than for example on LQG or ASG or on making up completely new approaches.

    'But it's not the same belief that you are referring to (which you don't want to admit is merely a belief) which is not an extrapolation from yesterday to today but from accessible energies to higher energies.'

    To get this out of the way once and for all: I do not believe string theory is realized in nature.
    For scientific reasons it is plausible to me that it is.
    But as you rightfully point out, there is no need to prematurely start believing.
    Yet the degree of plausibility justifiably affects the allocation of resources.

  86. Cobi,

    You seem to mistakenly think I am for some reason "against" string theory. Or against quantum gravity (theory) in general. Of course this is not the case. (The book, btw, isn't about string theory. String theory is mentioned merely as an example for the reliance on mathematical consistency.)

    The complaint I am raising in my book is the widespread use of deceitful arguments. This is bad both for funding (of the foundations of physics as a whole, not string theory in particular) as well as for the practice of research.

    I hope that my comments above - which you seem to have trouble making sense of - will fall into place once you take into account that I merely wish you would be clear about stating your assumptions. If you assume meta-induction, then say so. It's an assumption - call it a hypothesis, an axiom, or a belief - not something that's derived from evidence. If you assume that a lack of alternatives found so-far is relevant for the promise of a theory, then say so. Only that way can we argue about such arguments, about whether or not they are justified.

    "For scientific reasons it is plausible to me that [string theory] is [realized in nature]."

    Well, then let's see again if we have made any progress here. You claim "scientific reasons," but none of the reasons you have named so far are scientific. They are postulates, beliefs, arguments from beauty, and so on. Do we agree on that now?


  87. Sabine and Cobi,

    a new theory is always belief and intuition triggered. But after over 30 years the belief should long have been replaced by facts and a more consistent way to describe nature.
    For me and probably for the rest of us following this blog it would be very helpful (interpreting e.g. David´s comment), since both of you represent different views, to regard a concise experiment:

    Put a glass of water on the table. (cold water, to cool down ;-)
    Here we have the quantum (light, glass, water) and gravity (the water stays in the glass).
    Nature obviously found a consistent way (physically/mathematically) to let QM and GR work together.

    Maybe you could comment on the following questions to make your points of view clearer.
    1.) Do you really think gravity (GR) needs to be quantized?
    2.) If you quantize gravity (circumventing somehow the renormalization problem) how could you prevent the energy of the vacuum fluctuations blow up the curvature of spacetime? (cosmological constant problem)
    [String Theory wants to use SUSY, but SUSY is not observed, or at least broken at energies where it does not help anymore]
    3.) Are there really no alternatives? What about the proposal by Roger Penrose? And would not be a granularity (simply a maximum resolution) at the Planck level much more promising than trying to quantize gravity?
    [This goes in the direction of Penrose, but instead of his non-unitary Schrödinger-Newton equation, the conflict between QM and GR could be used to define a new process. In a way a boundary process like in LQG, but without quantizing gravity.
    This immediately would solve the cosmological constant problem, because QM particles in superposition cannot couple to a non-quantized gravity (no gravitons), not being able to be in a superposition.
    This tension between QM and GR would also trigger ongoing measurements independent of observers, solving the measurement problem. And it is unitary in between measurements. Only when the particles are put on-mass shell (and not superposed anymore) a backreaction (no pun intended ;-) on the curvature can happen.]

  88. David, you said
    "The impression I get from the comments of Cobi, PhilG and other string theory practitioners is that, as you state, their use of phrases such as “mathematical consistency," "meta-induction," and "no-alternative" to describe string theory are what you are referring to as “beauty”."

    I can clarify this. mathematical consistency and uniqueness are not the same thing as mathematical beauty. Beauty is a subjective concept whereas consistency and uniqueness are well defined ideas. A mathematical demonstration of consistency or uniqueness may have mathematical beauty, or it could be horribly ugly.

    When you see mathematical beauty in some physics theory it could be a good sign, but not a very strong one. When you find consistency and uniqueness you have something much better. If you could prove definitively that string theory was a consistent and unique solution to the problems of quantum gravity, there would be no room left for dispute, but of course that kind of proof is not possible in physics. There are always assumptions and often the proofs have big gaps. Only experiment and observation can close those gaps.

    What string theorists have found is that if you analyse the limit of quantum gravity in a weak gravitational field where it should behave like gravitons, then you get very strong mathematical indications that string theory gives consistent solutions and that they are all derived from a unqiue M-theory in 11 dimensions. Neither the physical assumptions nor the mathematical demonstrations are anything like watertight, but string theorists consider them good enough to believe that string theory is worth further research. This belief is strengthened by other considerations including mathematical beauty, but beauty alone would not be at all convincing.

    There could also be some sociology at work, but there have always been people ready to explore other directions. They may complain about lack of funding, but in truth that affects everyone. It would be good to see more money for everything, but the reality is that the best people often go off to do more lucrative things anyway. These sociological factors are slowing progress, but that's all.

    Loop Quantum Gravity and other approaches to quantum gravity avoid the uniqueness argument by not providing a solution to the graviton limit. People interpret this in different ways. Some people will say that the graviton limit is not part of real physics so the assumptions of string theory are wrong. Others will say that LQG could provide a different solution to the graviton limit exploiting some loop hole in the string theory claim to uniqueness. Others simply say that LQG is wrong. My hope is that LQG can be modified to give a graviton limit but it would then become equivalent to string theory.

    The question of testability of string theory is an important but different issue. The fact is that there are no empirical observations relevant to quantum gravity apart from some weak negative results, so this is a problem that any theory of quantum gravity would face. Therefore it cannot be regarded as an argument to rule out string theory. Testing quantum gravity will be a big challenge for the future, but meanwhile there is still a lot of work to do in understanding the foundations of string theory and what relation if any it has to other quantum gravity approaches.

    Some people have argued that even without experiment, the mathematical arguments for consistency and uniqueness could become strong enough to be accepted as conclusive by "meta-induction." I don't think that will happen. It would not be a very satisfactory outcome from an epistemological point of view. However, nature is not bound by the rules of the scientific method to provide us with a technologically viable means of testing any theory of quantum gravity. That is a problem for quantum gravity phenomenologists.

  89. PhilG,

    I basically agree with what you wrote, except that you seem to imply that asymptotically safe gravity doesn't have the correct weak-field limit, or maybe I misunderstood that?

  90. Reimond,

    The mathematical inconsistency between quantum field theory and non-quantized gravity has to be resolved. This resolution might or might not imply quantizing gravity, but somehow the two theories have to be made consistent.

    Regarding your question about the cosmological constant, please read this. In contrast to quantum gravity, it's an aesthetic problem, not an actual problem.

    Of course there are alternatives. It's just that string theorists don't like these for one reason or the other. Take loop quantum gravity, as an example. The "meta-induction" that people in LQG use puts a strong emphasis on background independence. For string theorists, this doesn't count so much. They are much more concerned about the links to quantum field theory. String theorists also like the idea of getting a grand unification along with quantum gravity, while those in asymptotically safe gravity (to name another example) don't care all that much about unification. Those who work on causal dynamical triangulation take as starting point the path-integral, which again you could think about as "meta-induction," and so on. You can complain that the UV fixed point of asymptotically safe gravity hasn't been proven to be unitary, or you could complain that string theory hasn't be proved to be UV-finite, and you can always complain that LQG has an issue with Lorentz-invariance.

    The bottom line is, in the end it comes down to what you think are the important criteria to hold on to. Even if you could pull a proof of uniqueness proof, the conclusion would still depend on your starting assumptions. And of course string theorists think string theory is the right thing to do. Everybody thinks what they do is the right thing to do - that's hardly surprising. But unless one of them manages to come up with a scientific way of assessing these beliefs, I don't buy any of that. Of course I have my own beliefs, but as I was trying to express in this blogpost, I am skeptical these are of any relevance to find a theory that describes nature.

    "But after over 30 years the belief should long have been replaced by facts and a more consistent way to describe nature."

    Well, that would be nice, but maybe it just takes that long. However, it is almost certainly true that progress in the field is being slowed down by sociological factors and also by sloppy argumentation. There is no telling how large an effect this is. But I think it's a good idea to try to remove these brakes and see if it helps. Best,


  91. Sabine, as you said in the previous blog:
    "... Afshordi and Nelson pointed out that the cosmological constant, if it arises from the vacuum energy of matter fields, should be subject to quantum fluctuations." ...
    "And since matter curves space-time, the matter fluctuations lead to space-time fluctuations - which can screw with our cosmological models." ...

    Precisely of this I made the case for NOT quantizing gravity, but also NOT treating the energy-momentum tensor in a semi-classical fashion.

    The new assumption is to regard nature as a process of unitary evolutions followed by triggered measurements.
    Matter in unitary evolution cannot curve non-quantized spacetime, only matter on-mass shell, not in superposition has a backreaction.

    As I said:
    "This immediately would solve the cosmological constant problem, because QM particles in superposition cannot couple to a non-quantized gravity, not being able to be in a superposition."
    "Only when the particles are put on-mass shell … a backreaction … on the curvature can happen"

    This makes the cosmological constant just a free parameter of GR again and it has nothing to do with QM.

  92. Reimond,

    Sorry for the misunderstanding. I was thinking you were referring to the 'usual' cc problem. If you just want to throw out the semi-classical limit you are creating more problems than you solve, for now you have to demonstrate that you get back general relativity at least approximately. Besides, we know that virtual particles do gravitate since they make contributions to particle masses, so you can't just wave away the problem.

    In any case, this is quite off-topic and a discussion which doesn't belong here.

  93. Sabine, I am not saying anything specific about ASG because I have not studied it enough. Would it be more accurate to say that it does not have a perturbative weak-field limit? A weak field limit which is non-perturbative seems counterintuitive, but weak fields are perhaps not quite the same as weak coupling. If that is what happens then it explains how it can avoid the analysis that points towards string theory.

  94. PhilG,

    For all I know ASG starts with the usual weak-field limit, ie the perturbative quantization. The point is just that it's wrong to conclude from this approximation being perturbatively non-renormalizable that the theory is fundamentally sick. Instead, so the argument, it may still be non-perturbatively renormalizable, end up at a non-Gaussian fixed point, and hence be "asymptotically safe." To put this differently: Asymptotically Safe Gravity starts with general relativity at low energies qua assumption. The approach does have its problems, but that isn't one of them. (For all I know no one has calculated the UV behavior of the graviton propagator, at least not yet.) Best,


  95. Not quite sure why you have not posted this but, to meet the Capitalist Imperialist Pigs challenge "Beauty may be an unreliable heuristic, but the challenge for the doubter is to come up with something better - I mean something that works."

    Eli suggests parsimony, explaining the most things with the tersest description.

  96. Eli,

    I don't know what you think I haven't posted.

    I also don't know why you or CIP or anyone else thinks it's my task to come up with something to replace criteria from beauty. I am pointing out using them is bad scientific practice, and that's that. If people who use them cannot come up with anything better, maybe they shouldn't be scientists. I don't know why I should give them something else to do.

    I already commented above on arguments from simplicity (or call it 'parsimony'). These are fine as long as you realize they relative, not absolute. A theory can be 'the most parsimonious to explain something,' but 'the most parsimonious (period)' is just another criterion from beauty. (And also nonsense, because no theory would be the simplest theory ever.)

    As I expressed elsewhere, I think we'd be better off if people focused on problems that are indeed problems - ie problems from mathematical consistency or actual conflicts with data - this would prevent more waste of time. Best,



  97. The most "beautiful" things in physics are concise and consilient, for example, Newton and Maxwell's laws, Nother's thm, relativity, etc. and Eli can make an argument that a good theory should be so because otherwise you get engineering.

  98. As others have posted 'beauty' and 'elegance' are subjective perceptions of the human mind, evolved in a relatively narrow context of the sensible universe. Where 'beauty'/'elegance' and objective (as far as can be determined) truth coincide, it's likely that this happens the more that the described quantity/quality lies to the ability of human senses to ordinarily perceive such.

    Before exploring (and poking at) the links between beauty/elegance and truth, it might serve to ask "why do humans perceive the various manifestations of beauty and elegance in the first place?" In answering that question it would also serve to ask how that perception happens the further from sensorial detectability. Once those answers are established one may have material with which to discuss the link between truth and beauty/elegance in a physics context.

  99. In mathematics beauty is a great guide - as long as you can back up your beautiful ideas with theorems! I think the problem comes when people want to combine the fun of pretending to do beautiful math with the fun of pretending to talk about the physical universe without doing the hard work of either proving theorems or predicting results of experiments.

  100. The beauty of beautiful theories is that they make many things (calculations) simpler.
    Since we are lazy and limited by nature we prefer to study simpler theories.
    That's OK,
    at least as long the simpler theories explain the same natural phenomena
    as the complicated alternative.

    occam's razor

  101. Various people insist that beauty is the wrong guideline, but simplicity is. Personally, I like simplicity much more than beauty. Most physicists mean "simplicity" when they say "beauty". The great theories of physics are beautiful, but above all they are simple.

  102. I often find it helpful to reformulate discussions about beauty-as-truth in terms of the (perhaps somewhat dated) distinction between the 'context of discovery' and the 'context of justification'.

    Most commentators here seem have no quarrel with scientists making use of powerful heuristics - like simplicity, (self-perceived) beauty, mathematical consistency, meta-induction - in their search for promising directions or methods that will enable them to extend current knowledge. Anything goes if it triggers your creativity. Hey, it may actually turn out to work, or it may eat up your whole grant without delivering on its promises, that's in the nature of research.

    The disagreements start when such heuristics start to creep into the act of justifying any theory arrived at in the discovery phase. An empirical science like physics usually relies heavily on experimental or observational support in the assessment of the acceptability and/or usability of a new theory. But what to do if this support is unavailable and not likely to be in reach within our lifetime? It is sure tempting to opportunistically abandon your empiricist credo and lapse into a rationalistic mode of justification. Who needs the billions spent on experiments like the LHC when you can sit comfortably in your armchair and declare that your theory is necessarily correct due to such-and-such a mathematical or logical argument. This is an unfortunate regression to pre-empiricist times, those of Descartes, perhaps, or the (unjustly vilified) scholastics.

    Beauty makes for good heuristics but bad epistemology.

  103. I feel that I have to comment on some deeply un-historical remarks on epicycles made earlier in this thread.

    In the late middle ages there were (essentially) two competing cosmological systems: the system of homocentric spheres introduced by Eudoxus and championed by Aristotle (both 4th c. BC), and the system based on deferents, epicycles and eccentrics introduced by Apollonius and Hipparchos (3rd-2nd c. BC) and improved on by Ptolemy (2nd c. AD).

    It appears the two systems were popular with very different groups. Professional astronomers, both hellenic, muslim medieval and latin medieval, preferred the deferent/epicycle system, since it gave by far the more exact results. It was, however, directly at odds with Aristotelian natural philosophy, so more philosophically (we would today say physically) inclined thinkers preferred the ontologically conformant homocentric spheres, never mind their empirical irrelevance. The general opinion, then, was that the deferent/epicycle system was a mathematical contrivance that gave the right results for the wrong reasons. But that was OK if you were only in the astronomy business to cast horoscopes for your princely benefactor or for calculating the dates of ramadan or easter.

    It should be emphasized that the Copernican system lives entirely in the deferent/epiclycle tradition. Copernicus made two important changes to the Ptolemaic model: switching place between Earth and Sun, and throwing out the mechanism of equants introduced by Ptolemy, at the expense of adding a few epicycles. The new reformed epicycle system very quickly caught on as an improvement over that of Ptolemy as an astronomical calculational tool. It took much longer for the heliocentricity of the new system to become accepted as a physical reality, since it was in contradiction with the best comprehensive system of physics of the day, the Aristotelian. It was only 144 years after Copernicus, with the publication of Newton's Principia, that we got a new system of physics that provided both a physical explanation of planetary motion and vastly superior mathematical tools. It was this double act that finally dethroned Aristotelian natural philosophy and killed the epicycles of Ptolemy and Copernicus, not any change in the perception of "beauty" in cosmological models.

    And why were the epicycles circular? The argument for the physically-minded philosophers: In most ancient cosmologies, like that of Aristotle, everything got better the further away from Earth and the closer to god you came. In the super-lunar celestial region everything was timeless perfection, so obviously the only natural motions were circular, as a direct reflection of the perfection of god. For the mathematically-minded astronomers: Circles are easy to calculate with. And with a clever combination of epicycles you can simulate many other kinds of motion, like linear or spiral. If it works (which it did, for almost 2000 years) don't break it. Or ask silly questions about beauty.

  104. Great rant! For the sake of us laypersons could you list the names of these imposter and fictional or hypothetical particles. Just wondering where the cut-off is. Presumably we have if not proof of the existence of, at least good evidence for . . . atoms? electrons? Higgs bosons? We take this all on faith and it is annoying to know that our faith is being abused.

  105. astrodreamer,

    I have a list in my book. All particles in the standard model (including the Higgs) are well-confirmed.

  106. FYI. Epicycles where used in Roman and Greek science to describe motions of planets and stars because they could be used to build geared mechanisms that functioned like calculators/computers to calculate their positions.


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