I have a long-percolating post that I hope to finish soon (when everything else is finished!) on “Why String Theory Must Be Right.” Not because it actually must be right, of course; it’s an hypothesis that will ultimately have to be tested against data. But there are very good reasons to think that something like string theory is going to be part of the ultimate understanding of quantum gravity, and it would be nice if more people knew what those reasons were.
Of course, it would be even nicer if those reasons were explained (to interested non-physicists as well as other physicists who are not specialists) by string theorists themselves. Unfortunately, they’re not. Most string theorists (not all, obviously; there are laudable exceptions) seem to not deem it worth their time to make much of an effort to explain why this theory with no empirical support whatsoever is nevertheless so promising. (Which it is.) Meanwhile, people who think that string theory has hit a dead end and should admit defeat — who are a tiny minority of those who are well-informed about the subject — are getting their message out with devastating effectiveness.
The latest manifestation of this trend is this video dialogue on Bloggingheads.tv, featuring science writers John Horgan and George Johnson. (Via Not Even Wrong.) Horgan is explicitly anti-string theory, while Johnson is more willing to admit that it might be worthwhile, and he’s not really qualified to pass judgment. But you’ll hear things like “string theory is just not a serious enterprise,” and see it compared to pseudoscience, postmodernism, and theology. (Pick the boogeyman of your choice!)
One of their pieces of evidence for the decline of string theory is a recent public debate between Brian Greene and Lawrence Krauss about the status of string theory. They seemed to take the very existence of such a debate as evidence that string theory isn’t really science any more — as if serious scientific subjects were never to be debated in public. Peter Woit agrees that “things are not looking good for a physical theory when there start being public debates on the subject”; indeed, I’m just about ready to give up on evolution for just that reason.
In their rush to find evidence for the conclusion they want to reach, everyone seems to be ignoring the fact that having public debates is actually a good thing, whatever the state of health of a particular field might be. The existence of a public debate isn’t evidence that a field is in trouble; it’s evidence that there is an unresolved scientific question about which many people are interested, which is wonderful. Science writers, of all people, should understand this. It’s not our job as researchers to hide away from the rest of the world until we’re absolutely sure that we’ve figured it all out, and only then share what we’ve learned; science is a process, and it needn’t be an especially esoteric one. There’s nothing illegitimate or unsavory about allowing the hoi-polloi the occasional glimpse at how the sausage is made.
What is illegitimate is when the view thereby provided is highly distorted. I’ve long supported the rights of stringy skeptics to get their arguments out to a wide audience, even if I don’t agree with them myself. The correct response on the part of those of us who appreciate the promise of string theory is to come back with our (vastly superior, of course) counter-arguments. The free market of ideas, I’m sure you’ve heard it all before.
Come on, string theorists! Make some effort to explain to everyone why this set of lofty speculations is as promising as you know it to be. It won’t hurt too much, really.
Update: Just to clarify the background of the above-mentioned debate. The original idea did not come from Brian or Lawrence; it was organized (they’ve told me) by the Smithsonian to generate interest and excitement for the adventure of particle physics, especially in the DC area, and they agreed to participate to help achieve this laudable purpose. The fact, as mentioned on Bloggingheads, that the participants were joking and enjoying themselves is evidence that they are friends who respect each other and understand that they are ultimately on the same side; not evidence that string theory itself is a joke.
It would be a shame if leading scientists were discouraged from participating in such events out of fear that discussing controversies in public gave people the wrong impression about the health of their field.
@ anon
thanks for the answer. I don’t know exactly what E referred to, but my question was much more basic. what I mean is roughly: does the necessity for extra dimensions exist for the classical string? if not, isn’t it then caused by quantization? if so, couldn’t it be the reason is that we don’t understand quantization?
The need for extra dimensions is a direct result of quantization, in particular anomaly cancellation. My point is that we build string theory by quantizing a classical object. Shouldn’t we really start with something which is inherently quantum? I think that by quantizing a classical object, we are modelling whatever this true quantum starting point is, however classical degrees of freedom come along as extra baggage, e.q. extra dimensions. By compactifying the extra dimensions, we are restricting these extra classical degrees of freedom. So, what I’m saying is that the true theory will correspond to one of the vacuum states, while the other vacuum states are just mathematical gargabe. Thus, quantizing a classical string in 10 dimensions and compactifying the extra dimensions is nothing more than an approximate description which models the true theory. Essentially, this is what I believe Alon and others have in mind with compactifying on self-dual points.
Mark # 421,
In critical phenomena, which is more important than string theory because it is a physically successful application of CFT, we do have an infinite plane with boundary conditions at infinity. Any argument against Laurent polynomials in r is an argument against Laurent polynomials in z. Any argument against Fourier polynomials on the torus is an argument against Fourier polynomials on the circle. CFT seems to be doing fine despite these objections.
Anyway, the positive part of my message is that the mathematics of gauge symmetry in multi-dimensions now exists, and is ready to be applied to the physics of gauge symmetry in multi-dimensions. The most striking feature is that we must quantize the observer’s trajectory. This is philosophically very appealing, because every physical observer obeys the rules of quantum mechanics.
With an alternative available, there is no reason to believe in string theory, since nobody has managed to connect it to reality in the past 39 years.
Gina:I expected to be offered “QCD-ice cream”, to see “string bars” instead of the traditional “noodle bars,” or at least to see “open strings pomodoro” or “brane-lasagna” dishes in local Italian restaurants. In turn, the only thing remotely related to physics I saw in the whole one afternoon touristic trip to Santa Barbara was the sign on the highway: UCSB next exit.
Let’s not forget tomato soup?
It is always good to know how Lee is lining his point of view up? Against Symmetry?
Mark.
That was very useful – thanks! Some things which had been a bit muddled for me have suddenly become very clear. From your explanation I can deduce that lattice QED could only be useful for calculations at large momentum scales – but with unphysically small coupling (it would have to be no larger than e_c, but in the real world e(k) would no doubt be much larger than that for large momenta). By the way, is the exact beta function for lattice QED actually known for all values of the coupling below e_c? I have only heard of perturbative calculations at small coupling.
The situation for a lattice formulation of the SM will no doubt be similar in that only a quasi-continuum limit is possible there as well. (And my suggeston of a “landscape” of continuum limits in #397 is looking a bit silly at this point – I better take that back.) Still, I imagine that it would still be interesting to have a lattice formulation of the SM, to look for and investigate a phase with spontaneously broken electroweak gauge symmetry when the Higgs is stuck in. Also interesting is your suggestion in #382 to study strongly coupled chiral gauge theories, where the lattice is able to provide a full nonperturbative definition of the theory (i.e. a continuum limit is attainable).
amused,
The exact beta function for lattice QED is not known. (If it was, we wouldn’t need all those computers!) But the physical coupling e(m_e) = 0.302, where m_e is the electron mass, is actually very small; a good point of comparison is the pion-nucleon coupling, which is around 13. In general, the loop expansion parameter (which is roughly g^2/16pi^2) should be of order one in a strongly coupled theory; so I would expect e_c ~ 13. So there’s plenty of room for the physical QED coupling below e_c. Another way to say this is that the Landau pole (the scale M where e(M) formally becomes infinite) is predicted by the lowest-order beta function to be at M = exp(3pi/2alpha(m_e))m_e = 10^280 m_e. (Here alpha(m_e) = e^2(m_e)/4pi = 1/137.)
I do think it’s important to have a nonperturbative formulation of chiral gauge theories (or even non-chiral gauge theories with a controllable number of flavors). Lenny Susskind once remarked, decades ago, that not having such a formulation “will one day come back and bite us in the ass”. (Usual disclaimer on ancient quotes.)
Given such a formulation, and an arbitrarily large and fast computer, I suppose the first question I would try to answer is whether or not Seiberg duality holds for nonsupersymmetric theories.
Thomas,
You wrote, “With an alternative available, there is no reason to believe in string theory, since nobody has managed to connect it to reality in the past 39 years.”
However, your alternative, like string theory, and like all other proposed alternatives, has made no definite predictions for what will be seen at the LHC, or in any other experiment. Thus other criteria must be used to decide what is worth working on.
Mark,
It is true that QJT makes no definite testable prediction. If this is still true 20,000 man-years from now, I will be seriously worried. In lack of predictions, here are some alternative criteria:
Mathematical beauty. The algebraic structures underlying string theory are either one-dimensional (chiral algebras, Gelfand-Kirillov dimension = 1) or classical (no extension). QJT involves algebraic structures which are both four-dimensional and quantum in the above sense, as appropriate for a 4D quantum world.
Experiments. Although string theory makes no definite predictions, it makes several natural ones – supersymmetry, extra-dimensions, 496 gauge bosons, a large and negative cc, etc. Taken at face value, these predictions are wrong. Maybe God is giving us a hint here.
Logical consistency. A fundamental part of QJT is a quantized observer, which leads to quantized time. Time is what is measured by a clock, but clock time has a sharp value only in an eigenstate of the proper time operator. This is an obvious consequence of QM, yet it cannot be formulated in QFT. It is a natural consequence of QJT which explicitly involves the clock’s worldline.
I think that these are good reasons to think about QJT. Even if people don’t agree, they should know about them.
Good night.
Lee: Thanks for the thoughtful reply which I am honored to get from you. I never trusted that platonic pan-realism either. As for features themselves, I happen to think “as a philosopher” that the fine structure constant is about 1/137 is so “we” (intelligent life of some kind) can be here, more than any intrinsic “physical” reason. However, I understand that physicists will by definition want to explore naturalistic avenues. As for some other facts about the universe’s features, I think classical considerations play a larger role than is generally appreciated, which I can elaborate on if asked.
PS, a bit OT, but I give my condolances to the students and others killed in the horrific shootings at VA Tech.
Thomas,
> clock time has a sharp value only in an eigenstate of the proper time operator.
> This is an obvious consequence of QM
I am sure you are aware of the fact that there is no ‘time operator’ in QM.
Pauli pointed out that a (self-adjoint) time operator is incompatible with a Hamiltonian spectrum bounded below.
Thomas,
you wrote “Although string theory makes no definite predictions, it makes several natural ones – supersymmetry, extra dimensions, 496 gauge bosons, a large and negative cc, etc.”
I’m not sure what you mean by a “natural prediction”. Either a theory makes a prediction, or it doesn’t. It is true that some phases of string theory have full supersymmetry, extra-dimensions, and 496 gauge bosons, but these phases also have a cosmological constant that is exactly zero.
Other phases have different features. The problem, as emphasized by Peter, is that (as far as we know right now) there is no feature that is common to all the phases, and hence qualifies as a prediction of the string framework.
But, as I keep pointing out, there is currently no framework for particle physics that does any better.
Mark,
I think the lack of definite predictions is a worse problem for an old, well-established field than it is for a new idea. Speculative ideas take time to grow.
Wolfgang,
Reading a real clock is a physical experiment to which QM applies.
In QJT, all fields are expanded in a Taylor series around a 1D curve q(t), and everything is reexpressed in terms of the Taylor coefficients. This curve is parametrized by a c-number t. Energy is bounded from below in the sense that the vacuum is annihilated by negative frequency modes, where frequency is defined wrt t. However, one can write down a natural proper time operator tau(t), which is a quantum operator. The c-number t itself never runs backwards.
The reason why QJT differs from QFT is that q(t) is operator-valued. This is necessary for a well-defined action of diffeomorphisms.
Mark,
Thanks for your points. I wasn’t worried so much about whether the physical QED coupling was smaller than e_c, but there was a misunderstanding (once again) in my last comment which made it a bit incomprehensible. Rather than go into the details of that I’ll just mention that what I had forgotten at the time, but later remembered, is that the size of the lattice spacing `a’ needed to perform a reasonably accurate lattice calculation only needs to be smaller (by, say, an order of magnitude) than the inverse of the relevant energy or momentum scale for the stuff you are calculating. (I.e. 1/a needs to be larger than that scale.) Taking that into account, what I should have written in my last comment is that lattice QED can in principle give a good description of QED physics at all scales k that are at least an order of magnitude less than k_c, where k_c is the scale at which e(k_c) = e_c. (Taking the bare lattice coupling e_0 to be e_c (or a bit less than e_c – just to make sure we are properly in the Coulomb phase) then corresponds to lattice spacing a bit more than 1/k_c.)
Provided I got that right, the situation in a lattice formulation of the SM will no doubt be similar in this regard. So there will be some energy scale below which the physics can well described by the lattice model. Hopefully this will include the stuff to do with electroweak symm breaking.
Hopefully I got this more or less right this time, but if not I’ld appreciate being put straight. Thanks for your patience!
It is nice to see discussions about QED. Somehow I have the feeling that QED is somewhat neglected and yet there may still be fundamental and important issues concerning QED which may reflect on more advanced topics.
Let me repeat (and slightly rephrased) the thought from #392.
1. The idea:
What we need to find is a landscape of mathematical options regarding QED: Namely a vast number of mathematically different theories giving precisely the same predictions. (By mathematical theories I mean theories in the physics non rigorous standards. Among all these we will hopefully find some day, some theories consistent with rigorous mathematics)
And yes, we should embed QED in a theory involving non trivial representation of U(1), in a way that will not effect any empirical prediction.
2. Roots of the idea
The immediate root of this idea is Mark’s understanding (#330,#336) of Peter Woit’s rather vague ideas regarding non trivial representations of gauge groups. (Peter strongly objected (#335 #337) to the way Mark understood his ideas, and regard it as just a way for Mark to claim that Peter is not on top of things.)
Not very promising, I admit, but we have seen worse.
(But, of course, similar suggestions are floating around in blog discussions and perhaps even in more serious forums.)
3. Wasn’t it examined before and isn’t it precisely what physicists are doing?
Actually, I do not know (and be happy to learn) but I tend to think with little evidence that QED is somewhat neglected.
Let me mention something I learned from a paper by David Corfield, when I hanged out in the n Category cafe blog (while being on exile from Peter’s blog.) David described in a paper the “divorce” between mathematics and physics caused mainly by the non rigorous nature of QED. (Like any divorce there could have been other reasons.) An idea like the one above could have appealed more to mathematicians than to physicists, but it could have fall between the chairs because of the non rigorous mathematical nature of QED and the related “divorce” between mathematics and physics.
It is true that math and physics are dating again but it seems that the topic of conversation is much more advanced theories which now appeal more to both.
4. Isn’t Mark, Moshe and Herbert already explained that non trivial representations may not occur?
Maybe. I could not understand Herbert’s comment and even could not tell if he agrees with Moshe and Mark. I am not sure and I certainly cannot tell if Moshe and Mark’s appealing and kind explanations do not already rely on some extra math or physics assumptions.
Re: the QED divorce, I believe that Mathematics initiated the proceedings against Physics, and won the case on the grounds of Mental Cruelty.
Chris, It is always much much more complicated. After centuries together it is only natural that some period of seperation and individual soal-searching was called upon. No point to raise old difficulties now, after all math and physics are dating again, and there is some sense of happiness in the air. And certainly string theory got them close together and deserves a lot of credit. (And what other options do they really have?)
Hi Gina,
Where do you want me to start?
Chris, You did not understand me. Math and physics have no other options in terms of partners. As for the precise nature of the relation, there are many options and possibilities but let them find the right way. We should not interfere at this delicate time.
Gina,
I am not really in much of a position to “interfere at this delicate time” anyway. As Dr. Arnold Neumaier of Vienna University has accurately pointed out in one of the Usenet discussions, no-one cares what I think, especially as I have been out of academia for nearly 20 years.
HOWEVER, having said that, I grieves me to see the subject of fundamental physics at such a low ebb. Whole departments dedicated to a highly speculative idea and unwilling to even listen to alternatives. Fine if they were part of the Templeton Institute, but they are not. They are part of physics departments of once-great universities. I hope for a better future, but the only optimistic signs I see at the moment are that relative String theory outsiders, such as Peter Woit, seem to be able to bring pressure to bear. Note that this is EXTERNAL pressure. The fact that the criticism has had to come from outside cannot be a good sign.
Dear Chris, Your voice is heard on these weblog discussions, and your anti-renormalization stance is quite something; but I simply disagree with you. HEP and string theory had glorious achievements in the last two decades (and so are other areas), and Peter Woit, while coming across as a nice guy with good intentions, does not really have a case. (But the first part of Peter’s book which does not deal with string theory is very good!) Let’s agree to disagree!
Speaking of renormalization, which always seemed a bit fishy to me (a mathematical trick, but what *does* it in nature?): What is the “physical mechanism” of renormalization? What in nature makes it happen? I never heard any good answers, although I didn’t dig in far enough to maybe find out. Maybe string theory could help with that? Even then, I wonder how we can deal with the integration of field energy around an electron far exceeding its mass, even tho’ not infinite, as included radius goes below the classical electron radius (an electrons are “points” to far below that size….)
Gina,
I think you’re right – we will have to agree to disagree.
Neil,
Despite the fact that finiteness was one of the aims of the String Theory program, the best they aspire to nowadays is just reproducing effective field theory, a package which includes renormalization. So no, String Theory does not help. As regards classical models/analogies, I do not see that they are of much use, either. There is no obvious way to treat the infinities that appear when one has classical pointlike charges, whereas there are things one can do in the quantum world.
Speaking of renormalization, which always seemed a bit fishy to me (a mathematical trick, but what *does* it in nature?): What is the “physical mechanism” of renormalization? What in nature makes it happen? I never heard any good answers, although I didn’t dig in far enough to maybe find out.
Renormalization is understand these days in the context of effective field theory. Nothing in nature does it. Instead, it arises as we try to better approximate nature with a given theory. The infinities just reflect our lack of knowledge about the UV physics.
Niel B –
In fact there is a very physical interpretation to renormalization, which is presented in most modern textbooks (e.g. the second half of Weinberg ch. 12), but which is somewhat overshadowed by the historical (and efficient) cancellation-of-infinities presentation.
First, a historical note relevant to your question: Weisskopf showed in 1939 that the infinite classical self-energy of the electron is largely cancelled by the contribution of virtual antiparticle states, so that it exceeds the observed mass not at the classical electron radius, but at a scale beyond the Planck length. That said, the modern interpretation is that these energies are real, but ultimately cut off in a more complete theory. Thus, in some grand unified theories the difference of the tau and bottom masses is accounted for rather precisely by the difference of the self-energies up to the GUT scale. String theory is an example of a more complete theory in which all these diverges are cut off: a given string vacuum leads to calculable [modulo steadily improving technical capabilities] and finite values for the masses and other parameters.
But if there is ultimately a cutoff, what do we need renormalization for? In fact, it just parameterizes our ignorance of what the high energy theory is, so we can relate quantities measured at observed energies. In practice, however, it is simplest in calculation just to pretend that one is cancelling infinities, rather than making a long-winded statement about what one is really doing.
This may be what effective field theory is about, but I do not see that it is anything to be proud of. We do not have a theory of classical mechanics or classical electrodynamics that merely “parameterises our ignorance of what the high energy theory is”, we have principles from which are derived results which then turn out to have wide domains of applicability. The problem with QFT as currently practised is that the principles do not work. Rather than starting again, people choose to do meaningless infinite subtractions, calling their kludges “quantum field theory” when they are in reality much less than this.
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