Visiting the University of Maryland

Along with two senior postdocs (Andrey Katz of Harvard and Nathaniel Craig of Rutgers) I’ve been visiting the University of Maryland all week, taking advantage of end-of-academic-term slowdowns to spend a few days just thinking hard, with some very bright and creative colleagues, about the implications of what we have discovered (a Higgs particle of mass 125-126 GeV/c²) and have not discovered (any other new particles or unexpected high-energy phenomena) so far at the Large Hadron Collider [LHC].

The basic questions that face us most squarely are:

Is the naturalness puzzle

  1. resolved by a clever mechanism that adds new particles and forces to the ones we know?
  2. resolved by properly interpreting the history of the universe?
  3. nonexistent due to our somehow misreading the lessons of quantum field theory?
  4. altered dramatically by modifying the rules of quantum field theory and gravity altogether?

If (1) is true, it’s possible that a clever new “mechanism” is required.  (Old mechanisms that remove or ameliorate the naturalness puzzle include supersymmetry, little Higgs, warped extra dimensions, etc.; all of these are still possible, but if one of them is right, it’s mildly surprising we’ve seen no sign of it yet.)  Since the Maryland faculty I’m talking to (Raman Sundrum, Zakaria Chacko and Kaustubh Agashe) have all been involved in inventing clever new mechanisms in the past (with names like Randall-Sundrum [i.e. warped extra dimensions], Twin Higgs, Folded Supersymmetry, and various forms of Composite Higgs), it’s a good place to be thinking about this possibility.  There’s good reason to focus on mechanisms that, unlike most of the known ones, do not lead to new particles that are affected by the strong nuclear force. (The Twin Higgs idea that Chacko invented with Hock-Seng Goh and Roni Harnik is an example.)  The particles predicted by such scenarios could easily have escaped notice so far, and be hiding in LHC data.

Sundrum (some days anyway) thinks the most likely situation is that, just by chance, the universe has turned out to be a little bit unnatural — not a lot, but enough that the solution to the naturalness puzzle may lie at higher energies outside LHC reach.  That would be unfortunate for particle physicists who are impatient to know the answer… unless we’re lucky and a remnant from that higher-energy phenomenon accidentally has ended up at low-energy, low enough that the LHC can reach it.

But perhaps we just haven’t been creative enough yet to guess the right mechanism, or alter the ones we know of to fit the bill… and perhaps the clues are already in the LHC’s data, waiting for us to ask the right question.

I view option (2) as deeply problematic.  On the one hand, there’s a good argument that the universe might be immense, far larger than the part we can see, with different regions having very different laws of particle physics — and that the part we live in might appear very “unnatural” just because that very same unnatural appearance is required for stars, planets, and life to exist.  To be over-simplistic: if, in the parts of the universe that have no Higgs particle with mass below 700 GeV/c², the physical consequences prevent complex molecules from forming, then it’s not surprising we live in a place with a Higgs particle below that mass.   [It's not so different from saying that the earth is a very unusual place from some points of view -- rocks near stars make up a very small fraction of the universe --- but that doesn't mean it's surprising that we find ourselves in such an unusual location, because a planet is one of the few places that life could evolve.]

Such an argument is compelling for the cosmological constant problem.  But it’s really hard to come up with an argument that a Higgs particle with a very low mass (and corresponding low non-zero masses for the other known particles) is required for life to exist.  Specifically, the mechanism of “technicolor” (in which the Higgs field is generated as a composite object through a new, strong force) seems to allow for a habitable universe, but with no naturalness puzzle — so why don’t we find ourselves in a part of the universe where it’s technicolor, not a Standard Model-like Higgs, that shows up at the LHC?  Sundrum, formerly a technicolor expert, has thought about this point (with David E. Kaplan), and he agrees this is a significant problem with option (2).

By the way, option (2) is sometimes called the “anthropic principle”.  But it’s neither a principle nor “anthro-” (human-) related… it’s simply a bias (not in the negative sense of the word, but simply in the sense of something that affects your view of a situation) from the fact that, heck, life can only evolve in places where life can evolve.

(3) is really hard for me to believe.  The naturalness argument boils down to this:

  • Quantum fields fluctuate;
  • Fluctuations carry energy, called “zero-point energy”, which can be calculated and is very large;
  • The energy of the fluctuations of a field depends on the corresponding particle’s mass;
  • The particle’s mass, for the known particles, depends on the Higgs field;
  • Therefore the energy of empty space depends strongly on the Higgs field

Unless one of these five statements is wrong (good luck finding a mistake — every one of them involves completely basic issues in quantum theory and in the Higgs mechanism for giving masses) then there’s a naturalness puzzle.  The solution may be simple from a certain point of view, but it won’t come from just waving the problem away.

(4) I’d love for this to be the real answer, and maybe it is.  If our understanding of quantum field theory and Einstein’s gravity leads us to a naturalness problem whose solution should presumably reveal itself at the LHC, and yet nature refuses to show us a solution, then maybe it’s a naive use of field theory and gravity that’s at fault. But it may take a very big leap of faith, and insight, to see how to jump off this cliff and yet land on one’s feet.  Sundrum is well-known as one of the most creative and fearless individuals in our field, especially when it comes to this kind of thing. I’ve been discussing some radical notions with him, but mostly I’ve been enjoying hearing his many past insights and ideas… and about the equations that go with them.   Anyone can speculate, but it’s the equations (and the predictions, testable at least in principle if not in practice, that you can derive from them) that transform pure speculations into something that deserves the name “theoretical physics”.

144 responses to “Visiting the University of Maryland

  1. Oh my dear Lord :) You have *not* read my papers! You know… the ones regarding theory of everything and stuff ;) There is equations, laws, derivations etc… You make me cry :)

  2. 5- Or there may exist a Super pattern creating information Field that dictates only a life allowing unjverse to exist .
    It impossible to prove this wrong.

    • Focusing on things that can be proven wrong makes sense then, correct? What is the point of considering things that can’t be proven wrong? We can say no more than you just said.

      For example: Maybe the universe was created by a giant accordion that blew the universe into existence and then spontaneously disappeared. It is impossible to prove this wrong. So there’s no point in having a scientific discussion about it.

  3. “I’ve been discussing some radical notions with him, but mostly I’ve been enjoying hearing his many past insights and ideas… and about the equations that go with them.”

    Now I’m jealous :)

    Anyway, the problem I have with (2) is that we have no strong evidence that the ‘multiverse’ exists. The probability of existing (really the expectation value of the number of objects like ours) in any anthropic-like scenario is directly proportional to the number of objects (planets, universes, etc) that exist in total. Thanks to Kepler we have very strong evidence that the universe is chock full of planets, so there is no ‘naturalness’ problem for life happening to exist on this plant. However, I don’t feel we have enough evidence to say this is true for universes. Do you agree?

    • You should distinguish a fundamental problem with an idea (i.e. it fails to explain what it claims to explain) from a practical problem with an idea (i.e. we have no easy way of testing it.)

      Your problem with the idea is practical… and you should remember that we have no strong evidence that the multiverse *doesn’t* exist, so whether it exists or not is simply an open question at this point.

      My problem is that even if we *had* that evidence, it wouldn’t resolve the problem anyway. [That is in contrast to the cosmological constant problem, for which the multiverse (i.e. highly complex and diverse universe with many patches that have different laws of particle physics) is one possible solution.] In short my problem is an in-principle problem, which is much more serious; your practical problem might be resolved someday if someone thinks of a clever measurement technique (and don’t underestimate human ingenuity), but a problem of principle may never be resolvable.

      • Hmm, maybe I’m not completely understanding your argument.

        As a quick thought experiment then: assume you had an alternate universe portal (I know such things cannot exist). and could travel to these other patches of the universe and directly observe the physics there. If you saw:

        1) That there are a large (infinite?) number of alternate universes.
        2) That the local constants in these universes were distributed by some power law (or other nice distribution).

        Given this evidence, I would have a hard time not believing the anthropic reasoning for the Higg’s mass, even if technicolor was simpler theory. Of course we do not have this evidence, but if we did I’m not sure how you would argue against it.

        • Yes I think you are missing the argument; it has to do with how technicolor works. Technicolor scales are *EXPONENTIALLY* small where the Higgs mass in the Standard Model is POWER-LAW small; thus if you distribute the strengths of forces etc. according to power laws, the probability that the technicolor scale is so far below the Planck scale is 0.03 or so, while the probability that the Higgs mass is so small is 10^{-32} = 0.000000000000000000000000000000001. This difference is the whole point.

          • I think I see where you’re coming from. If you hold that all of the patches just have different physical constants, then you can use anthropics (like with the cosmological constant case). But if you assume that different patches have different physical laws, and not just different constants. Then there are sets of physical laws that are much more natural then ours (Technicolor); and, in all likelihood we should live in one of those.

            Considering that we don’t have any evidence to rule out different patches having different laws, the anthropic argument doesn’t work at all for the Higgs mass, since it still seems like the universe we live in is improbable, even if you just look at the set of all possible life containing universes.

            Thanks for the clarification Matt.

          • That’s right. If you assume the Standard Model is present in every patch of the universe, with its Higgs, and you only vary the parameters of the Standard Model, you might come to your conclusion. But in fact, if you think of any complicated field theory of which the Standard Model is only a part, then you would expect that you would find different patches with very different sets of particles, forces etc. at low energy. And of course we have no reason to think there aren’t additional particles and forces around — there is dark matter, which suggests there might be more, and there are neutrino masses, which also seem to require them.

            Not only field theory but also string theory, the only quantum gravity theory we have some control over so far, would seem to predict the latter situation, not the former. Different string vacua have wildly different particle physics at low energies (which is part of why string theory is almost useless as a predictive framework, at least so far.)

  4. About option (2), do you think technicolor would come back if people give up on SUSY altogether? Or the two issues are unrelated and technicolor is gone for ever.

    • Technicolor predicts no observable Higgs unless you stand on your head; and when you do that, the resulting Higgs is usually heavier than the one we’ve discovered; and when you avoid that, the Higgs you get usually has properties that deviate significantly from the Higgs of the Standard Model; and even if you could avoid that, there are other particles we should have seen by now. Technicolor was a great idea, but it happens to have been wrong — which is no fault of the inventors, who deserve some fame for their great idea. Nature happens to have chosen something else. Technicolor is dead; long live technicolor.

      • SUSY Is Also Dead !! RIP !! SUSY

        • No, natural supersymmetry is not dead. That’s simply false. I spent six months checking this myself: . So don’t tell me you’ve done as careful a job as I have, unless you’ve got a paper that contradicts ours and has a heck of a good argument as to why we’re wrong.

          I honestly just don’t understand how people can so regularly confuse facts and opinions. Your statement is either a mistake (you think it is a fact but you are wrong) or it is an opinion (which is not appropriate to state as though it is a fact.)

          It is a fact that technicolor is almost impossible to imagine saving: by its very nature, it predicts no lightweight Standard Model-like Higgs particle should exist, and that is a false prediction.

          It is not a fact that supersymmetry is ruled out by the data. There is nothing observed in LHC data that is inconsistent with supersymmetry. Supersymmetry predicts superpartner particles, but it allows for gluinos as heavy as 1.5-2 TeV without a serious problem: see for example . I am not defending supersymmetry as an idea, I’m just stating the facts on the ground. It is quite reasonable in supersymmetric models to have a lightweight Standard Model-like Higgs particle, and that until you reach the gluino, squarks, and other heavy colored particles, the Standard Model will agree with the data. At this time we cannot conclude that supersymmetry is dead.

          The only thing that is dead is what was called the “Constrained Minimal Supersymmetric Model” (which I always viewed as an unrealistic convenience anyway) and probably the Minimal Supersymmetric Standard Model, in which you put in the smallest number of particles consistent with supersymmetry. You almost certainly need something extra.

          Those are the facts.

          Other non-dead ideas:Composite or Little Higgs, Warped Extra Dimensions, Twin Higgs, Folded Supersymmetry, Two Higgs Doublet Models, etc.

          • Paul Lillington

            Perhaps I was a bit hasty to declare SUSY Dead. Sorry if i caused offence. Yes there is a paper in the works, and it does not support SUSY. If it turns out that SUSY is indeed disproved or at least no sign of it is found at the LHC at higher energies, then it strengthens my theory. My paper is still in its early stages with a lot of work and research to be done, before i am prepared to publish it. So far the theory is consistent with the standard model( and Higgs field), but it includes gravity and dark matter. There is still a lot of maths to be done, which I will need help with, but a lot of the latest discoveries support the theory. It falls into the Option 4 area
            Thanks for the Raman Sundrum references. I will read them with great interest, and comment if I can. If you have any more references in the option 4 area I would appreciate them

  5. Yes, I see you move from the question of what super-symmetry offers and see that it brings you here to the most current questions about the naturalness of things.

    I then wonder that if such simplicity is to exist, does it not reveal something much more complex about nature that we had not seen before? This is an expectant feature of any discovery? So really while it is very simple in its deduction, it is a very informative as an adjustment.

    Cosmologically, it has to make sense?

  6. (A problem of principle may never be resolvable ) Matt. strassler .
    Then why did you make fun of the possibility I menthioned above ?
    It is a problem of principle , and ALL of scientific effort w.r.t. Naturalness might be in vain ……being funny will not prove your point .
    Respect your readers please .

  7. In addition , do you really think that all that speculations of extended/multi/meta /extra /super verses are better than thinking about a meta-principle which dictates that only life friendly universes exist ,?
    Where are all those biased talks about parsimony and okkkkam,s razor ?
    Or it is used only when it fits our prejudice and arrogance ?

    • The issue is: can we measure something? I am not very interested in any of these arguments unless someone can measure something to test the idea. One of the important points made by Dimopoulos and Arkani-Hamed, early in the discussion of these ideas, is that in some cases the notion that the properties of the universe are finely tuned *can* be tested. Tell me how to test your ideas, and I’ll become interested.

  8. What is the difference between the a/m principle and the UCP or PP or the one which dictates Geometry of space according to M/E distribution ?
    Or we pick only what does not refute our world view ? Well , the UCP ,PP ,M/E /Geometry P , even every single Equation in QM refutes your world view Period

  9. By the way , this is the view of a great physicist , Henry Margenau ,,,,,
    Read his book The Miracle Of Existence for example .

  10. As a non-specialist. what “naturalness” says to me is that the net energy of an expanding universe into a multiverse is zero.

    It also feels “natural” that the mechanism of quantum entanglement is mediated via compactified dimensions, so the light speed barrier is not challenged. My question is then would the mechanism cause detectable property variations between entangled and unentangled particles?

    Finally, a question I have seen asked is whether that means all the “original” particles would be entangled by being present at the original expansion. My gut says “no” – on a principle of least information (and determinism), I would expect the phase change of compactification to go hand in hand with expansion in a way that critically balances the two.

  11. IMHO unnaturalness manifesting in the form of unstable or dynamic equilibrium is a necessity otherwise the universe would be dead still which would violate the uncertainty principle. Unnaturalness provides selfconsistency within the laws of nature and is therefore “natural”.

    • Give me an experiment to test this idea. Otherwise it’s just speculation. Physicists learn early that what “feels right” or fits with our “opinion” is of no value. We don’t do physics the way Aristotle did — he relied on his opinion, and he misled the western world for 2000 years.

      • The example of naturalness you give of a vase ontop of a table and the other broken on the floor illustrates two possible states of the vase.The vase on the edge of a table is in a mixed state -neither broken nor stable. Mixed states are what nature prefers. You can see that in ‘sum over histories’, resonance states in molecules.Perhaps our universe is mixed state of all possible universes

        • No, you are confusing two issues. The vase on the edge of a table is in a pure state.

          • The vase on the edge is in a state of unstable equilibrium compared to the one at the center of the table-a state between falling and being stable thus making it a mixed state.

          • No. And this is besides the point anyway — because, as I emphasized, the universe is not in a state of unstable equilibrium, but rather stably at a transition point — which is precisely why my analogy is imperfect.

      • Agreed that Aristotle misled on physics, big time. The irony is that Aristotle insisted that (what Lamarck came to name) biology was an experimental science, and he sent students to observe and report.
        Buridan, around 1320, proved Aristotle wrong about inertia. Buridan discovered/invented inertia (he called it “impetus”) and enounced perfectly what came to be known, four centuries later, as Newton’s first law. Then Buridan proposed his heliocentric theory that Copernic learned at Cracow, nearly 200 years later.

  12. One aspect that is cited as ‘unaturalness’ is the extreme weakness of gravity as compared to other forces. Vic Stenger has pointed out that this is a consequence of considering the gravitational attraction of essentially massless particles (with a little correction from Higgs). If instead you consider the gravitational force between to unit charged Planck masses the gravitational force is greater by a factor of 137.

    • If you want to learn physics from Mr. Stenger that’s up to you, but he’s so thoroughly misunderstood the problem that it just made me giggle.

    • kashyap vasavada

      I strongly agree with Matt’s statement. DO NOT TRY TO LEARN PHYSICS FROM VIC STENGER. I had a recent close encounter with him on his blog! He is a retired experimental high energy physicist (he calls himself distinguished!) and has written some 10 or so popular level books which gullible people have bought. His article on Higgs boson was totally confused and misleading. I tried to steer some readers of his blog to Matt’s blog. Actually I was not really trying to understand physics from him. His arrogant views on science and religion led me to his blog! His views on religion are also obnoxious. But I should not discuss them on this nice physics blog!

  13. Option 4 Is the only answer. We have all the tools to test new theories, we just need to think outside the box ( Standard model ). The clues may come from finding a theory or explanation for dark matter. And why it has not turned up in the LHC. or other experiments. Perhaps the observation of very high energy neutrinos coming from beyond our solar system may be a clue. It just needs some very initiative thinking. Now is the time, Let go to it

  14. Here is a probable source of a problem in (3): the rest mass of known sub atomic particles. Inwhich reference frame is the rest mass measured? Is using an accelerating spacetime as the “background” rest frame logical in defining rest mass?

    • All subatomic particles may have the same “rest mass” but existing in different reference frames which makes their masses different

      • Not entirely correct, because of the inconsistency with what I use on this website. Be careful about the use of the term “mass”. On this website, “mass” = “rest mass”, which is common usage in particle physics. The mass you are referring to is “relativistic mass”, but particle physicists never use this. To say it again: particle physicists do not view mass as something that increases with velocity. Einstein himself held both views during his lifetime. See

        • I spent many hours trying to work out how a partial could increase its mass with velocity. I had many ideas but none worked, until i figured out that the relativistic mass was caused by the partials movement through the Higgs field. This made much more sense. Rest mass and relativistic mass are caused by different mechanisms , but both are linked to the Higgs field.

          • I think the notion of “movement through the Higgs field” is problematic. The Higgs condensate is relativistically invariant, that means it “looks” the same to all observers, independent of their relative velocities. In other words, when you move, you do not feel the Higgs condensate “moving past”. If it were otherwise, the condensate would single out a particular non-moving reference frame, which we know does not exist. Moving “through the Higgs field” is just moving through the vacuum.

            Unfortunately in popular expositions physicists often use the picture of the Higgs field offering resistance to moving particles. This is a completely unphysical picture that contradicts all the important lessons that people have learned in the last 100+ years.

      • The rest mass of an object is Lorentz invariant, i.e. it does not depend on the frame of reference you use to evaluate it. That’s why we can regard a particle’s rest mass as a property of the particle rather than a property of the particle’s state of motion (as for example energy or momentum).

        The expansion of the universe – if that’s what you are referring to – is completely negligible in the length and time scales in which particle physics is done (unless you go back in time and get really close to the big bang), so I don’t think there is any connection.

        • Thanks Steiner and Matt

          Here is what I was alluding to. The rest mass of a quark curves spacetime more than the rest mass of an electron. Therefore the quark exists in a different reference frame than the electron.

          • “The rest mass of a quark curves spacetime more than the rest mass of an electron.”


            “Therefore the quark exists in a different reference frame than the electron.”


          • Are you suggesting that the quark is in the same accelerated referance frame as the electron even though the spacetime curvature in their respective proximities is different?

          • The curvature created by a particle like a quark or electron is incredibly tiny, and does not affect the particle itself. In some sense this could fail to be true once the particle is sufficiently heavy — heavy enough to form a black hole, or nearly that heavy. But quarks and electrons are vastly too lightweight for there to be any effect.

    • There is no problem with this at all.

  15. Matt could you tell us any of the radical notions that you discussed with Sundrum?

    • Maybe at some point. At least I can try to tell you about the ones that are already in the literature. But you have to understand (a) they didn’t work [or you'd have heard about them already] and (b) they’re very subtle [or people would have thought of them much longer ago.] So this is not the easiest task for me to take on.

  16. Hi Matt. I too would like to read his papers. Can you give us links to them. or perhaps put some extracts on your site for comment.

    • Here are a few

      A Symmetry for the cosmological constant
      David E. Kaplan, Raman Sundrum (Johns Hopkins U.).
      e-Print: hep-th/0505265 | PDF

      Gravity’s scalar cousin
      Raman Sundrum (Johns Hopkins U.). Dec 2003. 25 pp.
      e-Print: hep-th/0312212 | PDF

      Fat euclidean gravity with small cosmological constant
      Raman Sundrum (Johns Hopkins U.). Oct 2003. 31 pp.
      e-Print: hep-th/0310251 | PDF

      An Alternative to compactification
      Lisa Randall (Princeton U. & MIT, LNS), Raman Sundrum (Boston U.). Jun 1999. 10 pp.
      e-Print: hep-th/9906064 | PDF

      A Large mass hierarchy from a small extra dimension
      Lisa Randall (Princeton U. & MIT, LNS), Raman Sundrum (Boston U.). May 1999. 9 pp.
      e-Print: hep-ph/9905221 | PDF

      A Small cosmological constant from a large extra dimension
      Nima Arkani-Hamed (UC, Berkeley & LBL, Berkeley), Savas Dimopoulos, Nemanja Kaloper, Raman Sundrum (Stanford U., Phys. Dept.). Jan 2000. 10 pp.
      e-Print: hep-th/0001197 | PDF

  17. Has anyone looked at naturalness from an evolutionary perspective? Perhaps we observe a large patch with our particular laws and constants — not because the rules in our patch are probable, but because our particular combination of field values would consume or absorb a system of fields with different values in a free-for-all. That would make the physics in our causal patch “natural” in the sense of “natural selection.” This is all vacuous speculation, but it has the feel of something which might be mathematically tractable. It might even be testable eventually, if we ever figure out what dark matter is. (The leftovers and waste products of a set of conflicting patches really ought to have the signature of stuff with no non-gravitational interactions).

    • There have been ideas of “cosmological natural selection”, for example by Lee Smolin, based on the idea that universes can have “children” via black holes. These are certainly highly speculative ideas. There seem to be some predictions connected to these ideas, but I don’t know how well they are doing. I just recalled hearing about it and had a quick look into Wikipedia, so I cannot comment meaningfully on it.

      • I am of the opinion that the likes of Lee Smolin believe they now have the scientific ‘license’ to delve into pure speculation based on their popularity as if they were some gurus. This undermines the scientific method and may put young aspiring physicists to think metaphysically and not scientifically.

      • Thanks for the interesting reference. I was actually thinking along the lines of more traditional condensed matter physics: e.g., incompatible systems of long-range order in a solution or at a phase change. “Progeny” universes aren’t useful in explaining the naturalness problem via selection unless one can show why the progeny would have properties similar to the “parent.” Even if we could find some cosmological DNA code, the notion also has no obvious feedback mechanism to explain fine tuning. It would select for “fecundity” (Smolin’s word, I think) rather than selecting for the kind of universe in our patch.

  18. Hey guys. I have not been here for a while. I wanted to share this movie trailer with you. Controversial, yes. But I think it is time to step back and rethink where we are headed.

  19. “Sundrum is well-known as one of the most creative and fearless individuals in our field, especially when it comes to this kind of thing. I’ve been discussing some radical notions with him, but mostly I’ve been enjoying hearing his many past insights and ideas… and about the equations that go with the”
    I cannot find words good enough to stress the importance of Matt’s altruistic outlook in this quote. I wish a large portion of physicists where quick to recognize an important idea like the venture capitalist in Silicone Valley. Sadly most physicist are after promoting their own ideas and egos without considering the possible contributions of others. This also applies to the many amature ‘physicist’ who will not pay attention to advise from the professionals. Most are still chasing the lone genius pipe dream. Physics could experience rapid developments if physicist could collaborate more and be quick to spot potentially revolutionary ideas.

    • Two scholars cannot agree. All the Professinals were not inventors, particularly in basic science. I think the deep context of the subject is important here. To identify a correct subject need enormous genius than the identified. It is not altruistic.

    • I would say this more strongly. ONLY amateurs “promote their own ideas and egos without considering the possible contributions of others.” In fact, this is the quickest way for me to spot a crackpot; a person who talks only about his or her own ideas, without appreciating what others have done in the distant and recent past, is inevitably a crackpot. I have NEVER met a professional who did not, fairly regularly, publicly admire and promote other people’s good ideas. Not even Bob Laughlin. And certainly not Lenny Susskind or Ed Witten or Lisa Randall or Juan Maldacena or Nima Arkani-Hamed or any of the other leaders in my field. [Einstein, for instance, greatly admired Lorentz and Planck and Boltzmann at the time of his early famous work... and that's why he was able to use their insights to such great effect.] The most important ingredient to a great discovery is inevitably someone else’s ideas… and people who ignore the work of others are never the ones who make the big discoveries.

  20. Once again I am disappointed by the mention of possible basic modifications in QFT and/or gravitational theory without the mention of the space roar. The space roar IS mainstream physics. Name one reputable astronomer or astrophysicist who publicly states that the space roar is empirically wrong.
    The space roar is empirically valid and it’s a big deal.

    • Is there an unaccounted excess Extragalactic Cosmic Radio Background?, Ravi Subrahmanyan and Ramanath Cowsik,

      “We conclude that there is no compelling evidence for an unexplained `excess’ uniform background: careful and realistic modeling of the Galactic emission, which include a spherical halo, a flattened spheroidal disc, and a set of highly anisotropic features attributable to sources, laments, SNR’s, etc., can account for all of the anisotropic Galactic emission leaving an isotropic component consistent with known extragalactic source counts.”

  21. The Invariance of vacuum (before in 1890s was luminiferous ether) was understood by FitzGerald’s conjecture that, bodies in motion are being contracted. Lorentz independently presented the same idea in a more detailed manner, which was subsequently called FitzGerald–Lorentz contraction hypothesis.
    They extended the FitzGerald–Lorentz contraction hypothesis and found out that the time coordinate has to be modified – made the assumption that the speed of light is constant in moving frames. Larmor is credited to have been the first to understand the crucial time dilation property inherent in his equations ?

    • To my knowledge it was Einstein who understood that the FitzGerald-Lorentz contraction hypothesis was to be interpreted not as a contraction of objects but as a contraction of space itself (and with a corresponding expansion of time) as viewed by a observer relative to which the objects are moving.

  22. Matt: I think there’s a fifth option, which goes something like this:

    5. Cleanly resolved by new understanding obtained from “within the standard model” work that takes input from relativity, classical electromagnetism, and TQFT.

    If I can illustrate a little: the Coulomb force is said to be immense. If you started with a gedanken row of electrons and a row of metal ions, the two rows move together with a huge “electric” force. If you then move the electrons along the row whilst keeping the metal ions stationary, you have the current-in-the-wire. A much smaller “magnetic” force causes two such wires to move together (or apart). This force is a “trace” force, wherein larger forces are not quite in balance. When you then stop the electrons, an even smaller trace force causes the wire to move together. We call it gravity. Note this from Minkowski’s space and time:

    “Then in the description of the field produced by the electron we see that the separation of the field into electric and magnetic force is a relative one with regard to the underlying time axis; the most perspicuous way of describing the two forces together is on a certain analogy with the wrench in mechanics, though the analogy is not complete”.

    The electron doesn’t have an electric field and a magnetic field. It has an electromagnetic field. It’s ONE field and TWO forces. When it comes to charged particles, electric force is associated with linear motion, and magnetic is associated with rotational motion. Think cyclones. Now take a look at Einstein talking about electromagnetic and gravitational fields in 1929:

    “It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds…”

    Einstein refers to a field as a state of space. What he’s basically saying is the electron has ONE field. It doesn’t have an electromagnetic field AND a gravitational field. Which means virtual photons and (virtual) gravitons must in some respect be two aspects of a greater whole. Ditto for gluons. A lion is not a tiger, but is a cat.

      • LOL! I don’t know what sort of response I was expecting, but it wasn’t that.

        Matt, with respect, people like Minkowski and Einstein didn’t talk nonsense. Again, I would urge you to pay attention to the simple little things. By the by, I would also urge you to always be civil.

        • I am not impressed with people who preface what they say with “meaning no disrespect” who in fact mean plenty of disrespect. You have insulted my intelligence, wisdom and knowledge repeatedly, and done so with a smile.

          • I haven’t insulted your intelligence etc. Where’s the insult in pointing out what Minkowski and Einstein said? There isn’t any. The insults are in your replies. Now, if you want to have a serious thoughtful blog that continues to be respected, please cease the insults and address the physics. Starting with this:

            How many fields has an electron got?

            If your response is “Apologies I must decline, that would take me off topic and I’m pushed for time”, no problem. If you don’t respond at all it won’t be a big problem. But please don’t be insulting instead. Because that’s insulting our intelligence.

          • You’ve already shown you won’t listen to my answer.

          • Field is not an important, the Invariance of vacuum is important. The deformation of, energy of the vacuum. We mean “electron” as a field quanta in thermodynamical sense – the manipulative part of the fields ?

            Maxwell, at first, did not adopt the modern concept of a field as fundamental entity that could independently exist. Instead, he supposed that the electromagnetic field expressed the deformation of some underlying medium—the luminiferous aether—much like the tension in a rubber membrane. If that were the case, the observed velocity of the electromagnetic waves should depend upon the velocity of the observer with respect to the aether.

            Later the luminiferous aether was replaced by speed of light as constant (special relativity) ?

          • Noted veeramohan. IMHO it gets interesting when you read the original material, but it is Matt’s blog, so let’s talk about it some other time.

          • Thanking you Mr.duffieldjohn,
            open speculation is an important part of theoretical research and even if it is all wrong it may help others to crystallise their own opposing views more clearly.

            A super-Planck-scale collision is a collision between two fundamental particles where the total energy (rest energy (Er) plus the kinetic energy) exceeds Ep. At the Planck scale, quantum-gravity effects are expected to start playing a role in the interaction. However, at energies greater than Ep (and no-one knows exactly how much greater), classical gravity dominates the interaction.
            This is the “crucial ingredient in the argument that super-Planck-scale collisions form black holes. If black holes were formed, it would strongly indicate that there are extra dimensions , which would be a very profound discovery,” says Frans Pretorius Princeton University in US.

            A new boson around 125 GeV without specific spin has been observed by both ATLAS and CMS at the LHC. Since its decay into a diphoton excludes the spin-1 case by the Landau-Yang theorem,it leaves 0 or 2 as the possible lowest spin for the new boson. Instead of the well-established spin-0 Higgs-like boson, we take this new boson to be a spin-2 massive Graviton-like particle denoted as G, which exists copiously in extra-dimension theories , and concentrate on its phenomenology. In particular, we calculate the three-body decays of G→Vff¯′ with V and f(′) the gauge boson and fermions in the standard model (SM) and compare our results with those of the SM Higgs boson. The couplings between G and Vs are also estimated by fitting the data. A new observable that can distinguish G from the Higgs is proposed. — Note on 125 GeV Spin-2 particle/ Chao-Qiang Geng, Da Huang, Yong Tang, Yue-Liang Wu.

  23. I’m a bit confused about the statements presented regarding option (3). I would have thought that the argument is that the radiative corrections to the Higgs’ mass vary quadratically with the energy scale and, thus, display high sensitivity to short-distance effects. So to mitigate this a mechanism is expected to suppress the quadratic dependence (supersymmetry, realized, would eliminate it, broken would mitigate it). Am I missing something here?
    I think that the radiative corrections aren’t, simply, zero-point energy fluctuations, so I’m surprised this is stressed-am I missing something here?

    • The radiative corrections you refer to are nothing other than the dependence of zero point energy on the Higgs field. This is a precise and rigorous statement.

      Technical Digression:

      1) Feynman diagrams that consist of loops but with no external legs are contributions to the cosmological constant — the radiative corrections from zero point energy to the energy of the vacuum.

      2) The same diagrams with two Higgs lines attached, which are the radiative corrections to the Higgs field’s mass, are nothing other than the second derivative of the diagrams in (1) with respect to the Higgs field.

      You can also say this non-diagrammatically by working with the full Quantum Field Theory path integral. It’s a precise statement, with no approximations.

      Let me add: the physics behind this statement is simple enough. The full potential energy density of the universe is V(H^2) [i.e. it depends on the Higgs field --- and possibly on other fields, but that's not essential here] and in a Taylor series expansion the first term is the cosmological constant ]given by (1) above] and the second and third terms are the H^2 [given by (2) above] and H^4 terms that determine the final value of the Higgs field.

      • kashyap vasavada

        Matt: I would like to know, if they find SUSY particles at LHC (2015) runs, would it still help with the cancellations in Higgs mass calculation, or these particles have to have much lower mass to be useful for precise cancellation?

        • The most important particle in the Higgs mass cancellations in supersymmetric theories is the top squark. The limit on the top squark’s mass right now is 100 GeV, the same as it was before the LHC started running. That’s because (as I mentioned in my recent post) although our searches comprehensively cover gluinos no matter how they decay, they don’t comprehensively cover top squarks. Some variants of top squarks are ruled out up to 700 GeV, but there are big gaps in the search strategies extending down to 100 GeV. (I do expect some of these gaps to be filled in the next year with further studies of existing [2011-2012] data.)

      • Aren’t there (at least) two issues here, namely: corrections that shift the value of the minimum of the potential energy, i.e. affect the cosmological constant and corrections that shift the *position* of the minimum, i.e. affect the value of the expectation value of the Higgs? The first is the “cosmological constant problem” and the second the “hierarchy problem”, right? After all the value of a function and the values of its derivatives are quantities independent from one another. So I must be misunderstanding what you’re saying, because I was referring to the corrections that shift the position of the minimum and you seemed to be addressing the corrections that shift the minimum itself, when you talk of zero-point energy fluctuations-is it obvious that the two types of corrections are related?

  24. I agree, of course-it just didn’t appear that obvious to me, on first reading, that this way of phrasing the hierarchy problem highlights the issue of the mitigation of the quadratic divergences to the Higgs mass. Did I miss something you’ve written about previously?

  25. Indeed, I reread your previous posting: and see what you mean. Thanks!

  26. Strange Representation

    Hi Matt,

    Re your item(3) about vacuum fluctuations of quantum fields…

    It’s disappointing to see the never-ending misunderstandings about how the vacuum of free QFT is not the same as that of the interacting theory, — and hence that the Hilbert space of the interacting theory is inequivalent (disjoint) from that of the free theory. Cf. Haag’s thm. Unphysical virtual particles in a physical vacuum are still unphysical. An infinite number of particles in an unphysical (free) vacuum is also unphysical. So where is the naturalness problem? Maybe it’s just a virtual problem? :-)


    • You can rewrite the whole apparatus of QFT without talking at all about virtual particles (by gauge fixing and using certain different formalisms for ‘dressing’ particles) and you will arrive at the same conundrum. Alternatively, you regulate the whole problem by putting it on the lattice and all those complications go away (yet the cc problem remains).

      Further attempts at trying to ‘degravitate’ the virtual contributions to the physical cosmological constant typically run into major conceptual problems. For instance, why do those same types of diagrams that contribute to the mass of particles (like eg the Lamb shift) gravitate (and are measured to do so by precision tests of the equivalence principle), but not the ones contributing to the cosmological constant.

      • Columbia: I don’t know about the diagrams, but maybe I can say something conceptual. A gravitational field is a region where spatial energy density is not constant, whilst the cosmological constant is “the energy density of the vacuum of space”. Turn the “bowling-ball” rubber sheet upside-down to depict energy density. Add more energy in the middle, and the central peak gets higher so you’ve got more gravity. But add more energy to the ground all around and it gets higher until eventually there is no peak and no gravity at all.

  27. The gravity has been excluded from increase in entropy in observable universe – means, “the massless particles” put a barrier (water in iceberg analogy) between the deformation (cause) and deformed (effect) of, energy of the vacuum.

    This means, the higgs field has been toggled (like tip of an iceberg) between dark universe (gravity?) and manipulative (invariant or tip) universe. Thus keeping the masses of W and Z particles consistent with experiments ?
    The non zero small value of Higgs particle(s) is more associated with energy (deformed) than the momentum (cause) ?

  28. The expansion of space is due meltdown of ice under the water barrier (massless particles?).

    /Sundrum (some days anyway) thinks the most likely situation is that, just by chance, the universe has turned out to be a little bit unnatural — not a lot, but enough that the solution to the naturalness puzzle may lie at higher energies outside LHC reach./

    If we “un-cover” the barrier (massless particles) by higher energies, then the increase of entropy will be up to “no electromagnetic radiation” – means disappearance of mass-energy ?

  29. Prof. Strassler: You write: “I am not defending supersymmetry as an idea …” Would you please give us a short list of physics textbooks and papers that we (your blog readers) would need to understand in order to independently evaluate supersymmetry (i.e. evaluate SUSY at the level of a first-year graduate student in physics)?

    • I was not able to evaluate supersymmetry in the context you’d like until I was a second year graduate student in particle physics. You typically need a healthy dose of Quantum Field Theory before you can really begin; you need to fully understand quantum fields, fermions, operator relations, renormalization. I have given lectures on the subject, but always assuming the students had one year of quantum field theory under their belt.

      But you can learn something about supersymmetric quantum mechanics if you had a quantum mechanics class. And from there you can infer *some* of what is relevant in supersymmetric quantum field theory. You could try
      but the notation may prove very challenging if you’re not familiar with it.

  30. Prof. Strassler: Thank you for your reply to my SUSY education question. According to Motl, “By far the most important argument in favor of supersymmetry is the fact that it seems to be implied by string theory …”
    Do you agree with the preceding opinion stated by Motl?

    • Of course not. It’s wrong in two senses: (a) we have no idea whether string theory is right, so we can’t use string theory to argue in favor of supersymmetry, and (b) even if string theory is right, there’s no reason to be sure supersymmetry would be *observable* in our lifetimes or in the next few centuries.

      Motl is a religious man; he has faith in string theory and needs no experiment to confirm it for him.

  31. Matt,
    I’ve lost all respect for you.
    I grant you know your buzzwords, and I grant you are proficient in the present esoteric theories of an incredibly narrow field of expertise. You are however, an idiot when it comes to the history of western civilization or an appreciation of the contributions of those whose shoulders you actually stand on. Aristotle ‘misled’ no one for two thousand years you ignorant cretin, he had his irrational conceits obviously (as you certainly do), and made mistakes (as do you, and all humans). Aristotle’s immense contribution to formalized logic, rational debate, almost all the known sciences of his time, ethics, philosophy, art, poetry, and a very wide range of human concerns and endeavors, by far outstrips anything you have yet done in your tiny little niche of one theoretical science, or most likely will ever do.
    How much of your precious expertise will be even remotely valid or remembered in even ten years? A hundred years? How about two thousand years? Get some perspective, ditch your blinding hubris, and please learn some actual history from a source that isn’t trying to be politically correct or contemptuous of western civilization.
    **I’m full well aware this will be deleted, that’s fine, I didn’t write it for your hero worshipping followers to see, or your peers, I wrote it for you to see and maybe think about just a teeny bit. I’m doubtful I’ll ever post another entry on your blog, which will suit you just fine, but please know: You are not very informed about the past and its contributions to your present, and apparently lack the ability or curiosity to correct for this vast hole in your understanding.

    • You can draw up a list of Aristotles achievements all you want, its entirely irrelevant to the point at hand. Nobody implied that Aristotle didnt make great contributions, nor did they claim their own discoveries were superior.
      The point is that even the ideas of Aristotle, one of the greatest minds in history misled us because of the lack of empirical evidence. Which is a statement of fact. (You can choose to refer to it as ‘irrational conceits’ and ‘mistakes’ rather than misled. It really makes no difference.)

      There are many great people in history and we all stand on their shoulders, but much more has been discovered in the meantime. We have a scientific method now and, unless it is improved upon in such a way that mitigates these requirements, it needs testable evidence not blind faith and opinion. Even when it concerns the work of Aristotle let alone the people commenting here.

      Im aware that some of Professor Strasslers comments come off sharp to say the least but your interpretation is venomous and ironically illogical.
      In future you ought not to assume the person you are talking too is quite so ignorant. Youll find you have much more respect for a great many people when you do.

    • Torbjörn Larsson, OM

      I on the other hand lost all respect for Aristotle a long time ago. The reason he was successful and not the atomists goes deeper, but people’s deification of him, ironically for religious reasons, was a large part.

      Aristotle is an excellent response to the question “what good is religion/theology/philosophy?” None.

    • Aristotle was a complete idiot about inertia: he overlooked air resistance, big time (as Buridan pointed out). Aristotle was dumb about slavery, too. In a way, Aristotle self-contradicted in physics, because he did not apply the experimental method he had promoted for studying life forms.

      Morality: It’s not because one is extremely smart about something that one cannot grotesquely self-contradicts oneself about something else contiguous in the topology of thinking. Thank you, Aristotle!

  32. Pingback: Nonsense of the un-nature Nature | The Great Vindications

  33. Torbjörn Larsson, OM

    “Specifically, the mechanism of “technicolor” (in which the Higgs field is generated as a composite object through a new, strong force) seems to allow for a habitable universe, but with no naturalness puzzle — so why don’t we find ourselves in a part of the universe where it’s technicolor, not a Standard Model-like Higgs, that shows up at the LHC? Sundrum, formerly a technicolor expert, has thought about this point (with David E. Kaplan), and he agrees this is a significant problem with option (2).”

    I don’t get this. How is other physics relevant, if the answer to the naturalness puzzle is selection bias? You can only select over physics once.

    • Torbjörn Larsson, OM

      Oops, I should have read the thread. You assume, rightly, a selection over physics akin to the string landscape (in your reply to Ben Mahala). Thanks!

      Then either that doesn’t happen and/or selection has a constraint (making it less likely than a generic scan over possible physics). That may or may not be a problem (and I assume Sundrum et al concludes that it is).

  34. Some one replaced my post intended after CFT post to where it is now , this I take as a dishonest deception……..Shame.

    • That someone would be you… When replying to a post you do not use the reply box at the bottom, you click the ‘Reply’ button next to that post. If you do not anyone who does successfully reply to the post will come ahead of you.

      Its not a dishonest deception, you just dont know what you are doing. Quite a fitting metaphor really.

    • ou people is wierd. when I saw 139 comments I thought to myself.. wow lots of.good.interaction in the comments… instead I find you and a collection of cranks spamming the thread.

      as a layman, I read a few hep and theory blogs to keep up with developments… and even I can tell the cranks when they type out thier screeds. you sound like creationists in an evo devo blog.

  35. @Bob,
    Oh well, that’s what you get for putting blind ideology in front of your ignorance. You don’t know how to use the word metaphor either, as ‘a dishonest deception’ in not a metaphor, so stop trying to be smug until you know what it means. You might also invest in a philosophy course, followed closely by a course in basic logic which covers Aristotelian logical arguments and common logical fallacies.

    As for your Aristotle assertion, The physicist Carlo Rovelli would more than beg to differ:

    Please, before you open your mouth again, do a little bit of research. Also look up the word ‘misled’, and put it in the context of anyone in the past. If Aristotle ‘misled’, so did every other scientist and physicist who ever lived and had opinions about anything. Newton was into alchemy as a hobby. Einstein made simple math mistakes and blundered about at times , and Feynman openly admitted his renormalization was ‘hocus pocus’, (i.e. a trick). Hawking openly screwed around with poking additional matter into non linear equations and division by zero to get away with his ridiculous black hole nonsense. Michael Mann took great liberties with his tree ring proxies to promote his environmental agenda. Look around you carefully, pay attention, and get back to me some time about how empirical science really is. You might also want to look up the definition of the word ‘hubris’, it might spare you future embarrassment.

    For someone who enjoys buzzwords, You lack basic understanding of your own terms and how they are applied. If you deify someone, that is your doing, and not the fault of the person you are doing it to, especially if they are dead. Basic logic buddy, you need a refresher course. Badly.
    * As for your ‘what is it good for?’ crack, Math is a subset of logic, and logic is a subset of philosophy. Theology and Religion are two entirely different subjects with some overlap which actually does overlap with math as metaphysics. In essence, your math and physics are only as valid as the underlying philosophy in which it is grounded. If you don’t know ‘how’ it is grounded logically and then philosophically, you make stupid reasoning errors, like confusing math with reality. Logically, Math is only a description (it may or may not be correct) of reality, it is not a cause or priori (a la mathematical Platonism which is purely a metaphysical position). Just like any language, math can be used to describe something in an entirely self consistent way, which may or may not be true.
    * For these reasons, it becomes abundantly clear why informed people in the sciences need to have an understanding of philosophical thought, as their own disciplines rely upon the logical and philosophical inferences and hierarchies that underlie their respective fields. All the mathematical complexity and piled on jargon in the world does not change this, or absolve you from needing to understand it.

    • AMEN…….
      To CFT ,,, despite other,s arrogance.

    • I didnt say a ‘dishonest deception’ was a metaphor…
      Whether it is through your insistence on thinking badly of other people, or a result of my poor communication skills, youve misunderstood, misrepresented, or ignored practically everything I said.
      Either way, there is little point in discussing this any further.

    • your comments display a certain Victorian Hysteria. “mislead” can also mean to lead in a wrong direction, without any inference of lying.

      Aristotle did lead the western world.into a serious error regarding physics, and it persisted for thousands of years. anyone who looked could have seen that his assertions were false.

  36. Hi Matt
    Are you absolutely sure that the Higgs field does not have a stationary reference to Time Space
    First: The first part of my argument looks at gyro’s. When you spin a Gyro it locks onto some point in time space as its reference. If you are in a spaceship with no widows you can still tell if you are rotating or diverging from a straight line by using your gyro as a reference. As all of time space is filled with the Higgs field, it is a logical step to say that the local reference is the Higgs field. And it must be stationary with respect to Time Space for this to be a correct assumption.
    Second: We know from Einstein’s work that the presence of gravity can warp time space. We also know from the Gravity Probe B satellite experiment, that as our planet rotates it drags time space with it to a small extent, ( also predicted by Einstein ). It is not a big step to assume that the atoms and particles that the earth are made from, do have a drag effect on time space. If we expand this by replacing time space with the Higgs field, then the particles in the earth are spinning through the Higgs field. The drag effect is a result of this interaction of the earth and the Higgs field. It is only a short jump from this to look at the Higgs field as a type of liquid through which all particles and electromagnet waves are passing. Any particle’s moving through the Higgs Field, will also experience the Lorentz contraction, so it is not easy to detect movement through the field, or indeed that the field is stationary with respect to Time space.
    Last: It has been stated, by you, that the Higgs Boson is a disturbance in the Higgs field. This gives it a rest mass. It is a logical extension of this to postulate that all particle’s will cause a disturbance in the Higgs field, thus giving them rest mass. The extension of this is when a particle is moving relative to the Higgs field, it will cause a larger disturbance in the field, giving it relativistic mass as well. It is not a frictional drag , which would use energy , but a disturbance in the field.
    I know that this looks a lot like the old either. Can you comment.

    • If I understood this, the relativistic mass varies depending on the observer not on any motion compared to the Higgs field. The rest mass of elementary particles is constant to all reference frames and that is what the Higgs field helps to define.
      If the Higgs field was a sort of fixed grid then two separate experimenters who are unaware of each other could always calculate the same mass for a particle while that mass varies depending on how the particle was moving in relation to that Higgs grid, but thats not true.
      You can only ensure it is the same mass if you bring yourself to rest with reference to the particle, otherwise all the different observers moving in different frames will read a different apparent mass/energy (The relativistic mass.) no matter how much they know about the Higgs field.

      I hope someone will correct me if I have gotten this wrong.

      • @ Paul Lillington and Bob. Yes I agree completely with Bob. The word relativistic mass is confusing, old fashioned usage. If you look at any modern physics book or particle data book , they always talk about rest mass, i.e mass measured in the rest frame of the particle, where v=0. Matt has emphasized this repeatedly. So you need only rest mass m and energy= m*c^2 / sqrt (1-v^2/c^2). You do not need any concept of relativistic mass. Relativistic mass is only mentioned in some popular books and newspapers!! Photons and neutrinos( if their mass is zero), are special cases, where m=0 and v=c, E is finite. Higgs field is very subtle. It is every where in a condensate form. So there is no relative motion with respect to Higgs field.

    • If the Higgs field had a preferred reference frame, we would easily know it by now, experimentally. In fact we would have known in long before we discovered the Higgs field, because rest-masses of particles would depend on the frame of reference. This is easy to measure, and the limits on this type of dependence are extraordinarily strong. There are several other ways to check this too; but it’s late.

  37. Prof. Strassler,

    Can you please elaborate on this article claiming that the hierarchy problem does not exist because the light Higgs is self-protected at the electroweak scale?:



    • I believe it is the same mistake I’ve seen made a couple of times before.

      • OK, but you have not one but many highly respected professionals stressing that the hierarchy problem can be discarded without the need for fine-tuning. The author of this paper is from Humboldt University in Berlin and he cites, among others, theorists from the KEK theory center and the Saga University in Japan. Similar views were previously harbored by Bardeeen and Lykken from Fermilab.
        Are you implying that all these people are on the wrong track?

        • Yes. That’s exactly what I’m implying. Lykken and I have had extensive discussions and he conceded that there is no known theory that does what he requires it to do.

          You should note that although a few people have made this claim recently, there are far more people NOT writing papers making this claim. And they include people as highly respected as the ones you mention.

          People got very confused about this in the 1970s, and now they’re simply rehashing the mistakes of the past.

          The problem has *nothing* to do with infinities — or with standard perturbative renormalization. It’s much deeper than that.

          Furthermore, all of these people are ignoring the fact that the force known as hypercharge has a “landau pole” — it becomes infinitely strong at a very high scale. There are theorems that nothing can be done about this without new particles/forces being added. You don’t see this in the perturbative methods people are using, but it introduces a high energy scale into the problem, and screws up all these arguments that Bardeen makes.

          • Ervin Goldfain

            “There are theorems that nothing can be done about this without new particles/forces being added.”
            So, if no new physics exists above the electroweak scale up to a deep UV scale, are we to conclude that the hierarchy problem is ill-defined? What if the concept of Landau pole is an artifact of perturbative renormalization and we’re missing something fundamental about the Renormalization Group and the high-energy cutoff, for example non-perturbative aspects?

          • The concept of “Landau Pole” is NOT an artifact of perturbation theory or of renormalization. That’s what the theorem I mentioned proves. You cannot have an abelian gauge theory (as hypercharge is) without a Landau pole in four dimensions. The proof is non-perturbative. The only way out that I’m aware of would be to have a scale-invariant theory that is not conformally invariant in four dimensions… but no such theory is known.

            The hierarchy problem IS somewhat ill-defined. That’s why not everyone agrees about it. It’s conceptual, not technical. The statement is that the Standard Model, among similar models in its class, is extremely unusual. Well, to make this argument you have to decide what “similar models” are. That’s not well-defined. However, no one has ever come up with an example of “similar models” where this statement is false. Jegerlehner is arguing that the statement is false even with the usual definition of similar models; this is wrong. Lykken is arguing that the Standard Model is very unusual for a very particular reason; this requires a magical theory that no one has invented yet. Bardeen was originally arguing that the Standard Model (without gravity) is in a class of theories that has no hierarchy problem; but because of the Landau pole, this is false, and with gravity included it is also (presumably) false, though the latter statement is one you could question if you were brave. As an aside, I would point out that in general these contrarians are saying different things; it isn’t as though they all agree and there’s a growing consensus. Quite the contrary!

            Anyway, it would be great if one of the contrarians was correct. But so far the arguments that I’ve seen people make have been completely unconvincing… and the arguments in favor of the problem are far more convincing. [Namely: in any model in which I can calculate, I have a hierarchy problem if I have a light spin-zero particle; we do not see light spin-zero particles in any other particle physics context except where there are symmetries involved, and the naturalness argument always works; we do not see light spin-zero particles in condensed matter contexts, except when a material is tuned, by the experimenters, to be near a phase transition.]

  38. There is no rest mass without invariance. There is no invariance without inertia. There is no inertia without momentum. Momentum is not an invariance – because, mass decay into energy in radioactivity.
    Speed of light as constant keep photon massless. Massless photon prevent proton decay.
    Higgs field and rest mass are same like water and ice. The mechanism inside proton keep the ice from melting (decay) ?

  39. Prof. Strassler, you say:

    “The only way out that I’m aware of would be to have a scale-invariant theory that is not conformally invariant in four dimensions… but no such theory is known.”

    Here are three references that point to the contrary:




    • Look, if you think every paper that appears on the arXiv is correct, you’re being a bit naive. I don’t believe everything I read, and for good reason. It’s important to have a filter, and taste, and not simply consume everything that’s out there as though it’s of equal quality.

      Of the three you mention, only Yu Nakayama’s is one I would trust. And what does he say? “As of January 2013, our consensus is that there is no known example of scale invariant but non-conformal field theories in d = 4 under the assumptions of (1) unitarity, (2) Poincar´e invariance (causality), (3) discrete spectrum in scaling dimension, (4) existence of scale current and (5) unbroken scale invariance.” [boldface added by me.] In other words, Dr. Nakayama agrees with me.

      • By the way, these folks came close to proving that such theories cannot exist [i.e. that any scale-invariant theory in three spatial dimensions and one time dimension is conformally invariant] . There are still a couple of loopholes in the proof to close.

      • But he also goes on saying that “…We also try to make this lecture note a good reference for examples of scale invariance without
        conformal invariance. We have tried to collect as many interesting examples as possible.” And in the body of his paper, he states: “As we will see, scale invariant but non-conformal field theories are intimately connected with the possibility of such a cyclic or chaotic behavior in the renormalization group flow”

        • You’re reading selectively, and not sufficiently carefully. What he says is that if such theories exist in three spatial dimensions, they have these odd features. He does not prove they exist in three spatial dimensions; he merely shows what odd behavior they would have to have if they exist. As he says clearly in the abstract (and as I told you earlier) they are not known to exist, and in fact there are papers more recent than Nakayama [specifically the one in my most recent comment], by some of the best people in the field, that claim to have nearly proven they are impossible.

          Why don’t you trust me? I work upstairs from a group of smart young people who have been talking about this stuff over lunch pretty often. In fact I had a conversation with two of them (Clay Cordova and Dan Jafferis) today about a very closely related subject. Don’t you think I would know if someone had shown that there existed a theory in three spatial dimensions that had scale invariance but not conformal invariance? It would be huge news in our field.

          • And, by the way, even if someone showed that such a thing existed, that would not necessarily save the Standard Model.

          • Ervin Goldfain

            Let me make it clear that it is not a matter of trust. The reason for my reservation is that all these proofs are crucially based on premises that may or may not hold as we deepen our understanding of high energy QFT and BSM physics. A good dose of skepticism should always be welcome in this context.

            Please note that this is my last comment on the topic.



          • I’m perfectly happy with the idea that we should be testing all our premises. That’s what I’m doing with my own time. But we should test our premises without making mistakes.

  40. Charge = mass = energy
    If we increase charge, mass increases = no invariance.
    For invariance, guage fields (quantized) should be massless. The connection between imaginary field and real field need speed of light as constant – otherwise, it is conformal invariant ?

    • Charge does not equal mass. Neutrons and protons have almost equal mass; neutrons have no charge, protons do have charge.

      • You have a great deal of patients professor… phyc patients! no of.course I mean patience. your students are very lucky…

        do they often tell you.”You are however, an idiot when it comes to the history of western civilization “?? and do you mark them down for it?

  41. Thankyou Professor,
    there is no distinguish between proton and neutron. Difference is, we can manipulate the charge(+ve) in this nucleon cloud as proton.
    And most of that mass comes from the chaos intrinsic to a proton or neutron — from the motion-energy of a nucleon’s quarks, gluons and anti-quarks, and from the interaction-energy of the strong nuclear forces that hold a nucleon intact. —

  42. Pingback: Teaching at a “Winter School” | Of Particular Significance

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