Wednesday, October 15, 2014

A good popular text on gravitons and its limitations

In recent 24 hours, I saw a couple of news reports and popular articles about particle physics that were at least fine. For example, Physics World wrote about an experiment looking for WISP dark matter (it's like WIMP but "massive" is replaced by "sub-eV", and axions are the most famous WISPs). The Wall Street Journal wrote something about the RHIC experiment – unfortunately, the text only attracted one comment. The lack of interest in such situations is mostly due to the missing "controversy" and thanks to the technical character of the information.

But I want to mention a text by a "daily explainer" Esther Inglis-Arkell at
What are Gravitons and Why Can't We See Them?
which is pretty good, especially if one realizes that the author doesn't seem to be trained in these issues. Before I tell you about some flaws of the article, I want to focus on what I consider good about it because that may be more important in this case.

First, the article is a product by an "explainer". Its goal is to "explain" some background. This activity is hugely missing in the "news stories" about physics, especially cutting-edge physics. Physics is like a pyramid with many floors built on top of each other and the newest discoveries almost never "rebuild" the basement. They reorganize and sometimes rebuild the top floor and maybe the floor beneath it.

Everyone who wants to understand a story about this reconstruction of the near-top floor simply has to know something about some of the floors beneath it. Unfortunately, most of the science journalists are pretending that the news stories may be directly relevant for someone who has no background, who doesn't know about simpler and more fundamental "cousins" of the latest events. It is not possible.

A related point is that this article tries to present a picture that is coherent. The storyline isn't too different from the structure of an article that an expert could construct. What is important is that it doesn't distract the readers with topics that are clearly distractions.

In particular, it tells you that the problem with the non-renormalizability of gravitons is solved by string theory, and why, without misleading "obligatory" comments about loop quantum gravity and similar "alternative" viewpoints on vaguely related matters. Most articles unfortunately try to squeeze as much randomly collected rubbish analogous to loop quantum gravity in the few paragraphs as possible so that the result is unavoidably incoherent. Almost all readers are trying to build an opinion that "combines" or "interpolates" in between all these ideas.

But if you try to "combine" valid string theory with "components" imported from some alternative "sciences", you may end up with an even more illogical pile of rubbish than if you just parrot the alternative "science" separately. Those things simply should be segregated. Even if there were some real doubts that string theory is the only framework that avoids the logical problems with the gravitons' self-interactions, and there aren't really any doubts, there should be articles that only talk about one paradigm or another – just like actual scientists aren't jumping from one framework to another every minute. And the articles shouldn't focus on the "spicy interactions" between the vastly different research directions because that's not what the good scientists are actually spending their time with, or what is needed to understand Nature.

Some people might argue that things like loop quantum gravity shouldn't be "obligatory" in similar articles because the people researching it professionally represent something like 10% of the researchers in quantum gravity, write 5% of the articles, and receive about 1% of the citations. So these are small numbers which is a reason to neglect those things. But I don't actually believe in such an approach or in such a justification of the omission. It is perfectly OK to investigate things that represent a minority of researchers, papers, and citations. What's more important is that someone thinking about physics must preserve some consistency and focus on the content – and constant distractions by sociologically flavored metaphysical debates are no good for genuine progress in physics.

OK, let me now say a few comments about the flaws of the IO9 article on gravitons.

It says that the gravitons are particles that self-interact, unlike photons and like gluons, and this leads to the non-renormalizability of classical GR, and string theory solves the problem by replacing the point-like gravitons by strings which makes the self-replication of gravitons manageable. The LHC has been and will be looking for gravitons in warped geometry scenarios in the form of missing transverse energy.

The writer offers some rather usual comments about the forces and virtual particles that mediate them. Somewhere around this paragraph I started to have some problems:
What we call "force" at the macro level seems to be conveyed by particles at the micro level. The graviton should be one of these particles. The trouble with gravitons - or, more precisely, the first of many troubles with gravitons - is that gravity isn't supposed to be a force at all. General relativity indicates that gravity is a warp in spacetime. General relativity does allow for gravitational waves, though. It's possible that these waves could come in certain precise wavelengths the way photons do, and that these can be gravitons.
The first thing that I don't like about these comments is that they suggest that there is a contradiction between "gravity is a force" and "gravity is a warp in spacetime". There is no contradiction and there has never been one. "A warp in spacetime" is a more detailed explanation how the force works, much like some biology of muscle contractions "explains" where the force of our hands comes from.

In this context, I can't resist to make a much more general remark about the laymen's logic. When you say that "a graviton is an XY" and "a graviton is a UV", they deduce that either there is a contradiction, or "UV" is the same thing as "XY". But this ain't the case. The sentences say that the "set of gravitons" is a subset of the "set of XYs" or the "set of UVs". All these sets may be different and "XY" may still be a different set than "UV" while the propositions about the subsets may still hold. "XY" and "UV" may overlap – and sometimes, one of them may be a subset of the other. Many laymen (and I don't really mean the author of the article who seems much deeper) just seem to be lacking this "basic layer of structured thinking". They seem to understand the only meaning of the phrase "A is B", namely "A is completely synonymous to a different word B". But no non-trivial science could ever be built if this were the only allowed type of "is". If it were so, science would be reduced to the translation of several pre-existing objects to different languages or dialects.

I also have problems with the last sentence of the paragraph that "gravitons could come with precise wavelengths" just like photons. In the Universe, both gravitons and photons are demonstrably allowed to have any real positive value of the wavelength (the Doppler shift arising from the change of the inertial system is the simplest way to change the wavelength of a photon or a graviton to any value you want) although particular photons and gravitons resulting from some process may have a specific wavelength (or a specific distribution of wavelengths). Moreover, she talks about gravitons although she should be logically talking about gravitational waves – which are coherent states of many gravitons in the same state, as she doesn't seem to explain at all.

In the section about gravitons and string theory, she writes that gravitons are technically "gauge bosons". It is a matter of terminology whether gravitons are gauge bosons. Conceptually, they sort of are but exactly if we add the word "technically", I think that most physicists would say that gravitons are technically not gauge bosons because the term "gauge bosons" is only used for spin-1 particles. She says lots of correct things about the spins herself, however.

Then she describes a "recursive process" of production of new photons and (using the normal experts' jargon) addition of loops to the Feynman diagrams. Things are sort of OK but at one point we learn
Although this burst of particles may get hectic, it doesn't produce an endless branching chain of photons.
It actually does. Loop diagrams with an unlimited number of loops (and virtual photons) contribute. The number of terms is infinite. The point is that one may sum this infinite collection of terms and get a finite result. And the finite result isn't really a "direct outcome" of the procedure. A priori, the (approximately) geometric series is actually divergent. However, the quotient (I guess that the right English word is the common ratio, and I will use the latter) that is greater than one (naively infinite) may be "redefined" to be a finite number smaller than one, and that's why the (approximately) geometric series converges after this process and yields a finite result.

This is the process of renormalization and the theory is renormalizable if we only need to "redefine" a finite number of "types" of divergent common ratios or objects.

(A special discussion would be needed for infrared divergences. When it comes to very low-energy photons, one literally produces an infinite number of very soft photons if two charged objects repel one another, for example. And this infinite number of photons is no illusion and is never "reduced" to any finite number. Calculations of quantities that are "truly measurable by real-world devices with their limitations" can still be done and yield finite results so the infinities encountered as infrared divergences are harmless if we are really careful about what is a measurable question and what is not.)

Concerning the renormalizability, she writes:
Because of this, photons and electron interactions are said to be renormalizable. They can get weird, but they can't become endless.
Again, they can and do become endless, but it's not a problem. It may be a good idea to mention Zeno's paradoxes such as Achilles and the turtle. Zeno believed that Achilles could never catch up with the turtle because the path to the hypothetical point where he catches up may be divided to infinitely many pieces. And Zeno was implicitly assuming that the sum of an infinite number of terms (durations) had to be divergent. That wasn't the case. Infinite series often converge.

When mathematicians started to become smarter than Zeno and his soulmates, they saw that Zeno's paradoxes weren't paradoxes at all and some of Zeno's assumptions (or hidden assumptions) were simply wrong. Similarly, when Isaac Newton and his enemy developed the calculus, they were already sure that Zeno's related paradox, "the arrow paradox", wasn't a paradox, either. Zeno used to argue that an arrow cannot move because the trajectory may be divided to infinitesimal pieces and the arrow is static in each infinitesimal subinterval. Therefore, he reasoned, the arrow must always be static. Well, of course, we know that if you divide the path to infinitely many infinitesimal pieces, you may get and you often do get a finite total distance.

In this sense, mathematicians were able to see that many previous paradoxes aren't really paradoxes. We may continue and present the renormalization as another solution to a previous would-be Zeno-like paradox. Not only it is OK if there are infinitely many terms in the expansion to Feynman diagrams. It is even OK if this expansion is naively divergent – as long as the number of the "types of divergences" that have to be redefined to a finite number is finite.

The author of the article similarly discusses the loops with many gravitons and concludes:
That huge amount of energy causes the newly-created graviton to create yet another graviton. This endless cycle of graviton production makes gravitons nonrenormalizable.
This is of course deeply misleading. As the article didn't mention (even though it claimed to discuss the gluons as well), the gluons self-interact in the same sense as gravitons do. But the gluons' self-interactions – which may also involve an arbitrary number of virtual gluons in multiloop diagrams – are renormalizable and therefore harmless because the series we have to resum is closer to a geometric series and it is enough to renormalize the naively divergent common ratio in order to tame the whole sum.

In the case of the gravitons, the common ratio is "more divergent" because the high-energy virtual gravitons have stronger interactions (gravity couples to energy and not just the constant charge) and the series is further from a geometric one because the common ratios are not so common – the ratios increase with the number of loops. That's why we face an infinite number of "types of divergences", an infinite spectrum of something that looks like a common ratio of a geometric series but it is not really common. To determine a finite result of this sum, we would need to insert an infinite amount of information to the theory – to redefine an infinite number of distinct divergent objects to finite values. And in the absence of a hierarchy that would make most of these divergences "inconsequential", this process renders the theory unpredictive because it's simply not possible to measure or otherwise determine the value of the "infinitely many different divergent integrals".

To summarize, the author has oversimplified the situation and said that the nonrenormalizability arises whenever the processes have contributions from arbitrarily complicated loop diagrams. But they always do and it is not a problem yet. The real problem of nonrenormalizability only arises if a sequence of "cures" that are analogous to Newton's cure of Zeno's arrow paradox is applied and fails, anyway.

She says that strings are extended which cures the problem and...
That bit of wiggle room keeps the creation of a graviton from being so energetic that it necessitates the creation of yet another graviton, and makes the theory renormalizable.
Well, again, string theory doesn't change anything about the fact that arbitrarily complicated multiloop diagrams contribute to the total amplitude. But strings cure the problems with nonrenormalizability. But is it quite right to say that "strings make the theory renormalizable"?

Not really. First of all, strings aren't "surgeons" that would cure a field theory. Instead, strings replace it with a different theory that isn't a quantum field theory in the conventional sense (if we're strict about its definition – and if we overlook conceptually difficult dualities that show that string theory and field theories are really inseparable and piecewise equivalent as classes of physical theories). So strings don't do anything with "the theory". Instead, they tell us to use a different theory, string theory!

Second, it isn't quite right to say that string theory (as a theory in the spacetime) is renormalizable. In fact, string theory as a theory in the spacetime is completely finite so divergences from short-distances processes never arise in the first place. So this "problem" or "disease" that arises in almost all quantum field theories doesn't arise in string theory at all – which also means that it doesn't have to be cured. (String theory changes nothing about the emergence of infrared divergences in many situations or vacua – they were real physics in quantum field theory and have to remain real physics in any valid theory going beyond field theory.) String theory still involves some calculations on the world sheet that has intermediate divergences that have to be treated and yes, the theory on the world sheet is a field theory and it is a renormalizable one. But because the dynamics of string theory in the spacetime isn't a field theory, it doesn't even make sense to ask whether it is renormalizable. The adjective "renormalizable" is only well-defined for field theories.

Finally, she talks about the possible detection of gravitons. She is aware that there are facilities such as LIGO that should look for gravitational waves but if you want to see a graviton, an individual particle, you need something as good as the LHC. I am adding something here because as I have mentioned, the article hasn't really clarified the relationship between gravitational waves and gravitons at all.

Her comments about the LHC are referring to the theories with large or warped extra dimensions that could make some effects involving gravitons observable. I think that it is "much less likely than 50%" that the LHC will observe something like that and I would surely mention this expectation in an article I would write. But there is really no rock-solid argument against these scenarios so the LHC may observe these things.

The only other complaint I have against this part of the text is that she used the word "hole" for the missing transverse energy – a potential experimental sign indicating that the gravitons were sent in the extra dimensions. I had to spend half a minute to figure out what the hole was supposed to mean – I was naturally thinking about "holes in the Dirac sea" analogous to positrons as "holes in the sea of electrons". There's some sense in which a "hole" is just fine as a word for the "missing transverse energy" but its usage is non-standard and confusing. Physicists imagine rather specific things if you say a "hole" or a "missing energy" – if you know what these phrases mean, you should appreciate how much harder it is for the laymen who are imagining "holes" in the billiard table or "missing energy" after a small breakfast, or something like that. It can't be surprising that they're often led to completely misunderstand some texts about physics even though the texts look "perfectly fine" to those who know the right meaning of the words in the context.

I've mentioned many flaws of the article but my final point is that those are unavoidable for an article that was more ambitious than the typical popular ones. And if one wanted to "grade" the article according to these flaws, he shouldn't forget about the context – and the context is that the author actually decided to write a much more technical, detailed, less superficial article than what you may see elsewhere. Writers should be encouraged to write similar things even if there are similar technical problems. They can get fixed as the community of writers and their readership get more knowledgeable about all the issues.

But if writers decide not to write anything except for superficial – and usually sociological and "spicy" – issues, there is nothing to improve and the readers won't really ever have any tools to converge to any semi-qualified let alone qualified opinions about the physics itself.


  1. Another article goes into the details about why no detector will ever detect a graviton:

  2. All the interpretations of the inequalities in the paper etc. are completely wrong. There is absolutely no universal principle in physics that would make it impossible to detect one graviton and the difficulty of the detection in the real world is nothing else than another consequence of the well-known weakness of gravity or highness of the Planck scale.

    So it is absolutely idiotic to even suggest that "a graviton could fail to be physical" or "gravity could be non-quantum" or similar stuff that paper is literally overflooding with. These claims are *exactly* equivalent to the comments that classical gravity is enough because it's hard to see quantum gravity phenomena at the colliders or other real-world current experiments.

    It's still possible and easy to show that any theory with a classical gravity and quantum rest is mathematically inconsistent.

  3. kashyap vasavadaOct 15, 2014, 6:11:00 PM

    Very interesting blog Lubos. I would like to understand the controversy on whether graviton is a gauge particle or not little bit more technically, if there are good references. My understanding is that GR is a gauge theory, more complicated
    than other interactions, but nevertheless a gauge theory. Only difference may be that because of curved space, the gauge transformations are more complicated. The simple picture (based on QFT) I have in mind is that particle
    world is divided into two groups, one ordinary “matter” particles and the other force carriers, gauge bosons. If graviton is not a gauge particle, this simple picture will be gone. It may be that ST has modified this simple picture. Of course, as you say, we cannot ask nature to be simple!!
    The other point is that, if someone is looking
    seriously at LHC for gravitons in missing energy, then there must be calculations backing them up that in spite of extreme weakness of gravity, gravitons may be produced at LHC energy. Are there believable calculations?

  4. In the case you don't know, she has a website:

    And it seems good. By the way, I think I should register to this site soon, my nick name is really common :)

  5. Nice post! Operation Bridge initiated.

  6. Haha, I am really stupid :D. It turnes out that I have already registered. Sorry for polluting you blog like this but I couldn't resist. I wrote as a guest for months because I was too lazy to register :D.

  7. Lubos (I think) has written a couple of articles on this.

    One good reference A. Zee's 'QFT in a Nutshell'. The final section of the book ('Gravity and beyond'), has a succinct description of these topics.

    Another reference is Weinberg's QFT series (especially the 3rd volume on supersymmetry and supergravity).

    Wald's book on GTR also has a nice classical discussion on linearized gravity.

    As all experts will surely agree, there is no controversy on this matter. The graviton is a spin-2 gauge particle. It is the linear approximation of Einstein-Hilbert action and the theory respects diffeomorphism invariance. Whether you can call it a particle or a 'tiny space-time ripple' doesn't really matter much as they pretty much represent the same thing in this case.

  8. One tiny correction: It is obtained by taking a weak field limit of GTR.

    The Einstein-Hilbert action will thus be quadratic in the graviton field and all the resulting equations of motion will thus be linear.

  9. kashyap vasavadaOct 16, 2014, 2:14:00 PM

    @TheDOC: Thanks for the comment.I understand the final book on quantum gravity is not written yet. Also your word "linearized" would worry me little bit about the conclusions,
    What do you think?

  10. Good to hear that some popular articles are not that bad and contain some real information ...:-)

  11. @kashyap: I understand where you're coming from. It seems like one is butchering Einstein's theory.

    But you must remember that a lot of the crucial evidence for GR was found in the weak field limit.

    It is not wrong to thing of Eddington's famous experiment as the scattering of photons and gravitons (in his QFT book, Zee approaches it this way and gets the correct answer).

    Newton's theory of gravitation can only be recovered (as far as I know) in this limit.

    I have also heard that string theorists have good technical reasons for sticking with the graviton.

    Hopefully, decisive results from upcoming experiments will be able to banish all of our (tiny) misgivings.