I know that everyone is waiting breathlessly for more opinionmongering about the String Wars. After Joe’s guest post, filled with physics and insight and all that stuff, it’s time for a punchy little polemic.
The folks at New Scientist noticed a comment of mine to the effect that, contrary to the impression one might get from the popular media, most string theorists were going about their research basically as they always have, solving equations and writing papers — curious about, but undeterred by, the surrounding furor. This surprised them, as their readers seemed to be of the opinion that string theory was “dead and buried” (actual quote). So they asked me to write a short op-ed piece, which appeared last week, and which they’ve allowed me to reprint here. Nothing deep about the substance of what physicists should be thinking about; just pointing out that string theory is still alive and kicking.
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A philandering string theorist is caught by his wife with another woman. “But darling,” he pleads, “I can explain everything!”
I didn’t invent the joke; it appeared in the satirical magazine The Onion. The amazing thing is that people got it! Apparently the person on the street is sufficiently caught up with current thinking in high-energy physics to know that string theory — the idea that the ultimate building blocks of nature are quantized loops of string, not pointlike elementary particles — is our leading candidate for a theory that would, indeed, “explain everything.”
But, despite capturing the popular imagination, string theory has fallen on hard times lately, at least in the public-relations arena. We read articles such as “Hanging on by a Thread” (USA Today), “Theorists snap over string pieces” (Nature) and “The Unraveling of String Theory” (Time). Much of the attention given to string skepticism can be traced to books by Lee Smolin and Peter Woit that appeared last year. But those aren’t the only sources; increasingly, professional physicists as well as fearless pundits outside the academy are ready to pronounce the failure of string theory’s ambitious project of uniting all of the forces of nature.
So is the jig up? Is string theory in its last throes? No, not at all. At least, not if we measure the health of the field by more strictly academic criteria. String theorists are still being hired by universities in substantial numbers; new graduate students are still flocking to string theory to do their Ph.D. work; and, most importantly, the theory continues to be our most promising idea for bridging the gap between quantum mechanics and gravity.
String theory is unique; never has so much effort been devoted to exploring an idea in physics without the benefit of any direct experimental tests. One important reason for this has been the absence of experimental surprises in all of high-energy physics; for thirty years, the Standard Model of particle physics has resisted all challenges. But even that would not have been enough to coax theorists into thinking about the famously difficult problem of quantum gravity if string theory hadn’t come along to present a surprisingly promising approach.
It was realized in the 1970’s that string theory was a theory of quantum gravity, whether we liked it or not — certain vibrating strings have the right properties to represent gravitons, carriers of the gravitational force. Already, this feature distinguished string theory from other approaches; whereas head-on assaults on quantum gravity tended to run into dead ends, here was a quantum theory that insisted on gravity!
In the 1980’s the triumph of the Standard Model became complete, and work by Michael Green and John Schwarz demonstrated that string theory was a consistent framework. Physicists who would never have though of devoting themselves to quantum gravity quickly dived into string theory. It was a heady time, when promises to compute the mass of the electron any day now were thrown back and forth. True, there were five different versions of string theory, and they all lived in ten dimensions. The trick would be to find the right way to compactify those extra dimensions down to the four we know and love, and the connection to observation would be established.
That didn’t happen, but the 1990’s were nevertheless a boom time. It was realized that those five versions of the theory were different manifestations of a single underlying structure, M-theory. Tools were developed, in certain special circumstances, to tackle a famous problem introduced by Stephen Hawking in the 1970’s — calculating the entropy of black holes. Amazingly, string theory gave precisely the right answer. More and more people became convinced that there must be something right about this theory, even if we didn’t understand it very well, and even if connection to experiments remained elusive.
Since 2000, progress has slowed. In the mid-90’s it seemed as if there was a revolution every month, and — perhaps unsurprisingly — that’s no longer the case. Instead of finding a unique way to go from ten dimensions down to four, current ideas suggest that we may be faced with 10500 or more possibilities, which is pretty non-unique. It might be — maybe — that only a tiny number of those possibilities are anywhere close to the world we observe, so that there are still concrete predictions to be made. We don’t know, and it may be wishful thinking.
The truth remains — the miracles that got people excited about string theory in the first place haven’t gone away. The biggest obstacle to progress is that we don’t understand string theory very well; it’s a collection of bits and pieces that show tantalizing promise, but don’t yet fit together into a coherent whole. But it is a theory of quantum gravity, it is compatible with everything we know about particle physics, and it continues to provide startling new ways to think about space and time.
Meanwhile, spinoffs from string theory continue to proliferate. Ideas about higher-dimensional branes have re-invigorated model-building in more conventional particle physics. The theory has provided numerous deep insights into pure mathematics. Cosmologists thinking about the early universe increasingly turn to ideas from string theory. And a promising new approach has connected string theory to the dynamics of the quark-gluon plasma observed at particle accelerators.
Ultimately, of course, string theory must make contact with data in order to remain relevant and interesting. But profound ideas don’t come with expiration dates; that contact might come next year, ten years from now, or a century from now. In the meantime, the relative importance of string theory within the high-energy physics community is bound to take a hit, as results from the Large Hadron Collider promise to bring us firmly beyond the Standard Model and present theorists with new experimental puzzles to solve. A resurgent interest in more phenomenological particle physics is already easy to discern in hiring patterns and graduate-student interests.
But string theory isn’t going to disappear. Gravity exists, and quantum mechanics exists, and the two are going to have to be reconciled. Ambitious theoretical physicists will continue to pursue string theory, at least until an even better idea comes along — and even then, the odds are good that something stringy will be part of the ultimate story.
If I fall to earth according to basic Newton, gravity pushes me as well as pulls me. The Graviton propegator must, in stringtheory at least, have two counter acting comprable modes of action, one positive and one negative?
Question: can I “push” two particle’s into a collision without the Graviton?
Paul: the best statement of why you need spin-2 gravitons to give an always-attractive force is in chapter I.5, ‘Coulomb and Newton: Repulsion and Attraction,’ in Professor Zee’s book Quantum Field Theory in a Nutshell (Princeton University Press, 2003), pages 30-6. Zee uses an approximation due to Sidney Coleman, where you have to work through the theory assuming that the photon has a real mass m, to make the theory work, but at the end you set m = 0. (If you assume from the beginning that m = 0, the simple calculations don’t work, so you then need to work with gauge invariance.)
Zee starts with a Langrangian for Maxwell’s equations, adds terms for the assumed mass of the photon, then writes down the Feynman path integral, which is {integral} DAe^{iS(A)} where S(A) is the action, S(A) = {integral} (d^4)xL, where L is the Lagrangian based on Maxwell’s equations for the spin-1 photon (plus, as mentioned, terms for the photon having mass, to keep it relatively simple and avoid including gauge invariance). Evaluating the effective action shows that the potential energy between two similar charge densities is always positive, hence it is proved that the spin-1 gauge boson-mediated electromagnetic force between similar charges is always repulsive. So it works.
A massless spin-1 boson has only two degrees of freedom for spinning, because in one dimension it is propagating at velocity c and is thus ‘frozen’ in that direction of propagation. Hence, a massless spin-1 boson has two polarizations (electric field and magnetic field). A massive spin-1 boson, however, can spin in three dimensions and so has three polarizations.
Moving to quantum gravity, a spin-2 graviton will have 22 + 1 = 5 polarizations. Writing down a 5 component tensor to represent the gravitational Lagrangian, the same treatment for a spin-2 graviton then yields the result that the potential energy between two lumps of positive energy density (mass is always positive) is always negative, hence masses always attract each other.
This is clearly a ‘not even wrong’ theory of gravity because it hasn’t been validated; it is one way gravity could work and the maths certainly works but there are other possibilities that might be easier to test.
Aaron Bergman wrote:
Hmm. That sounds like a “folk theorem”: a theorem without assumptions, proof or even a precise statement.
Whatever these results are, they need to have extra assumptions. There’s a perfectly consistent quantum field theory of a noninteracting massive spin-2 particle on good old flat Minkowski spacetime, and this particle ain’t no graviton.
Okay, you say: that’s a noninteracting spin-2 particle, one we’d never be able to detect! Maybe any interacting one has to be a graviton?
Well, you can write down lots of ways a spin-2 particle can interact with other fields. Most of these have nothing to do with gravity. A graviton has got to interact with every other field — and in a very specific way.
Of course, most of these ways give disgusting quantum field theories that probably don’t make sense: they’re nonrenormalizable.
But, so is gravity!
So, it would be interesting to look at the results you’re talking about, and see what they actually say.
Maybe the Einstein-Hilbert action is the “least nonrenormalizable” way for a spin-2 particle to interact with other particles… whatever that means?
John, there are two independent statements, both rely crucially on the masslessness of the spin 2 particle, there are no similar restrictions on theories of massive particles. One of the statements is the Weinberg-Witten theorem, the other is the statement that starting with linearized gravity around flat space, one can derive the complete non-linear Einstein-Hilbert action based on a few simple assumptions. I believe this was done first in Feynman’s lectures on gravitation, and it is also derived in Weinberg’s book.
In any event, those are not folk theorems- they have well defined assumptions and conclusions, and by now a whole slew of known exceptions.
alright. really dumb layman’s question. How can a particle be massless. This question has bothered me for about 40 years now. Just as strings got us away from pointlike particles, is it possible that there are no massless particles as well. If a particle has energy doesn’t it have mass? I know … the photon … can’t have mass because it travels at c.
does anyone else see the idea of a massless particle as a conceptual problem?
e.
I don’t have the book here, but I seem to remember that Weinberg actually gives some arguments why a spin 2 particle has to interact ala the equivalence principle in his QFT books.
Elliot, you should think of “mass” as representing “the amount of energy an object has when it is at rest.” Massless particles are simply unable to ever be at rest. They can have energy — and they do — but their rest energy is zero.
Chase (25)– neutrino oscillations were a fantastic discovery, but not all that surprising, when you get right down to it. They don’t give us as much help as we would like in going beyond the Standard Model.
B writes:
Oh? Why?
Not that I’ve ever gone through this in detail, but — the point is that the massless spin-2 field is described by a symmetric two-index tensor with a certain gauge symmetry. (The symmetry that, once you’ve interpreted the tensor as a metric perturbation, will just be infinitesimal diffeomorphisms.) So its source must be a symmetric divergenceless two-index tensor. Basically you don’t have that many of them lying around, although I don’t know the rigorous statement to that effect.
Hi John,
well, I don’t know much about string theory, but I was thinking along classical GR lines it needs to couple to a symmetric 2nd rank tensor (the anti-symmetric part wouldn’t couple), and that tensor should be gauge invariant? You are of course right that one could in principle have complicated higher order stuff.
Best, B.
ah, I see, Sean said it better… I am still confused though by the volume element. The spin-2 field in string theory, does it make an appearance in the volume element?
Regarding the relation to string theory, the statement is not that there is massless spin 2 particle and thus we conclude that string theory has gravity. Rather, the statement is that we find numerous properties of gravity coming out of various calculations, but we should not be overly impressed because we know they are all a consequence of having spin 2 massless particle.
In particular one can derive the Einstein-Hilbert action, including the volume element, by demanding Weyl invariance in general backgrounds.
For anyone interested, there is a pair of relevant papers by Weinberg:
1. Photons and Gravitons in S-Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass (Phys.Rev.135:B1049-B1056,1964).
2.Photons and gravitons in perturbation theory: Derivation of Maxwell’s and Einstein’s equations (Phys.Rev.138:B988-B1002,1965).
where the precise assumptions and the formulation of the results are spelled out in great detail. This is probably more relevant to the present discussion than the Weinberg-Witten theorem.
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Most of the other massless string modes are going to acquire a mass in a theory that goes beyond string perturbation theory – if the theory has any connection to reality. Presumably the spin-2 mode is protected from getting a mass in all those circumstances.
In reviewing your talk ‘Einstein’s Legacy’ referenced in comment #8, consider this play on words:
What is the weave of the fabric of the cosmos [ripples … spacetime in your slide #13]?
It just might be a helix.
Notice how easily one can visualize an ellipse [your slides 18-21] rotating through the virtual cylinder of the helix in figure 3 from:
SIGNAL PROCESSING & SIMULATION NEWSLETTER
Fourier Analysis Made Easy Part 2
Complex representation of Fourier series
From Gravitons to Gravity: Myths and Reality, by Padmanabhan (gr-qc/0409089):
For those interested, I welcome discussions on Padmanabhan’s specific points over at my blog.
Thanks,
Christine
How does one know the entropy of a black hole? You say “string theory gives precisely the right answer,” but since this isn’t observed (?) how do you know the right answer?
Thank you, Christine, for finding that paper. I remembered it well, but somehow I forgot the author’s name, though I should not have. I hope that people weighing in on this issue will read it carefully and not rely on vague folk-memories of the form “Feynman proved…” For my part I would really like to see someone demonstrate explicitly how AdS arises from the exchange of gravitons in Minkowski space. At least the topologies are the same…though seeing how that timelike conformal infinity arises from graviton exchange ought to be pretty interesting….of course, seeing how graviton exchange turns Minkowski space into deSitter would be even more entertaining……
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44 – Stephen Hawking computed the entropy of a black hole – it is proportional to the area of the event horizon – based on ideas about Hawking radiation, which is thermal radiation emitted from just outside the event horizon. It is not observed, but is based on relatively sound theory, that doesn’t include assumptions about quantum gravity (to my knowledge).
Personally, I think string theorists are bribing string-theory-naysayers under the table to keep producing invective; the nominal controversies keep people talking about string theory, even unto the popular press. If the discipline became “just” a bunch of string theorists plugging along slowly making progress toward the mathematics of a final theory that might take decades to achieve, they’d get as much media attention as a former child star who grows up to live a happy normal life in Peoria.
It is not entirely clear that computation of a thermodynamic quantity producing the correct result from a microscopic model means that the microscopic model must be correct. E.g., the blackbody radiation curve is quite independent of what the blackbody might be made of.
Secondly, the string theory blackholes are made up of rather exotic matter (referred to as stringy stuff henceforth). Either our ordinary baryonic matter and whatever the dark matter is transmutes into this exotic matter when a blackhole is formed in our universe, which raises the question – how?
Or it doesn’t, which means that there are blackholes made of stringy stuff and different blackholes made of regular stuff, with the same entropy, which goes to the point that two different microscopic models can yield the same thermodynamic result.
Maybe I’m confused, but it seems that string theory black hole models are simply models with computability, very nice to have, etc., but not necessarily real.
Just clarification on the history of the black hole entropy thing. First, I would have said that it was Jacob Bekenstein who introduced the entropy problem for black holes to the literature (I’ll dig out the reference if anyone really wants it). The anecdote I’ve heard is that Bekenstein based his conjecture that black holes carried an entropy associated with their surface area on his supervisor, John Wheeler’s, observation that if the universe is a closed system and you throw a hot cup of coffee into a black hole and that coffee disappears, haven’t you just violated the second law of thermodynamics? The question then arose how to reconcile the fact that a black hole which has an energy and, if Bekenstein was right, and entropy, could have no temperature, since the Gibb’s relation says that for an isentropic process dT = dE / S. This question was answered to most people’s satisfaction by Hawking’s discovery of thermal radiation emitted by a black hole. I must say, however, that I’ve always been somewhat puzzled that the energy and entropy manifest themselves in classical quantities of the black hole itself (mass and area) while we need to introduce quantum behaviour of other fields on the black hole background to get the temperature part. Finally, the question arose “In other thermodynamical settings, thermodynamic entropy is just a manifestation of indistinguishable microscopic states – what are the indistinguishable microscopic states of a black hole that lead to the entropy?” This is what Sean cryptically refers to as the problem that string theory has solved. A string theorist friend of mine once inadvertently referred to this result as “an observational result that string theory could have predicted, had we known it earlier”. It’s not an observational result in my books, but apparently the bar for what is varies :-). In any case, I’m a bit skeptical of the string theory state counting argument, but it certainly seems to be, if not the only game in town, at least the best grounded.
Hi Christine, thanks. Just to clarify, I didn’t say anything about re-iterating the linear approximation. Best, B.