There’s a new book out this week from Princeton University Press, Paul Langacker’s Can the Laws of Physics Be Unified? (surely this is a mistake, but there’s also an ISBN number for a 2020 volume with the same name by Tony Zee). It’s part of a Princeton Frontiers in Physics series, in which all the books have titles that are questions. The other volumes all ask “How…” or “What…” questions, but the question of this volume is of a different nature, and unfortunately the book unintentionally gives the answer you would expect from Hinchliffe’s rule or Betteridge’s law.

This is not really a popular book, rather is accurately described by the author as “colloquium-level”. Lots of equations, but not much detail explaining exactly what they mean, for that some background is needed. The first two-thirds of the book is a very good summary of the Standard Model. For more details, Langacker has a textbook, The Standard Model and Beyond, which will have a second edition coming out later this year.

The last third of the book consists of two chapters addressing the question of the title, beginning with “What Don’t We Know?”. Here the questions are pretty much the usual suspects:

- Why the SM spectrum, with its masses and mixing angles?
- The hierarchy problem.
- The strong CP problem.
- Quantum gravity.
- Problems rooted in the cosmological model: Baryogenesis, dark matter, dark energy and the CC,

In addition, there are problems listed that are only problems if you philosophically think that a good unified model should be more generic than the SM, leading you to ask: why no FCNC? why no EDM?, why no proton decay?

The last chapter “How will we find out?” lists the usual suspects for ideas about BSM physics: SUSY, compositeness, extra dimensions, hidden sectors, GUTS, string theory. We are told that this is a list of “many promising ideas”. While in general I wouldn’t argue with most of the claims of the book, here I think the author is spouting utter nonsense. The ideas he describes are ancient, many going back 40 years. In many cases they weren’t promising to begin with, introducing a large and complex set of new degrees of freedom without explaining much at all about the SM. Decades of hard work by theorists and experimentalists have not been kind to these ideas. No compelling theoretical models have emerged, and experimental results have been strongly negative, with the LHC putting a large number of nails into the coffins of these ideas. They’re not “promising”, they’re dead.

Langacker does repeatedly point out the problems such ideas have run into, but instead of leaving it at “we don’t know”, he unfortunately keeps bringing up as answer “the multiverse did it”. On page 151 we’re told the most plausible explanation for the CC is “the multiverse did it”, on page 160-163 we’re given “multiverse did it” anthropic explanations for interaction strengths, fermion masses, the Higgs VEV, and the CC. Pages 167-173 are a long argument for “the multiverse did it”. The problem that this isn’t science because it is untestable is dismissed with the argument that it “may well be correct”, and maybe somebody someday will figure out a test. On page 203 we’re told that string theory provides the landscape of vacua necessary to show that “the multiverse did it”.

The treatment of string theory has all of the usual problems: we’re assured that string theory is “conceptually simple”, despite no one knowing what the theory really is. The only problem is that of the “technical details” of constructing realistic vacua. I won’t go on about this, I once wrote a whole book…

In the end, while Langacker expresses the hope that “sometime in the next 10, 50, or 100 years” we will see a successful fully unified theory, there’s nothing in the book that provides any reason for such a hope. There is a lot that argues against such a hope, in particular a lot of argument in favor of giving up and signing up for a multiverse pseudo-scientific endpoint for the field. I suspect the author himself doesn’t realize how much the argument of the book is stacked against his expressed hope and in favor of a negative answer to the title’s question.

**Update**: If you just can’t get enough multiverse mania, you can watch Joseph Silk’s talk Should We Trust a Theory? (more talk materials here). I’m not quite sure, but I think we agree that the multiverse is not currently science (he writes “The multiverse might or might not exist, but no physicist should waste his or her time chasing the unchaseable”), but not about about string theory. I have no idea what is behind his claim that “String theory has been very successful”, and, since he’s not a string theorist, I suspect that neither does he.

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I hesitate to say this on a physics blog, but maybe the answer actually is “no.”

Jeff M,

Well, the answer is certainly “no” if the way you approach the question is by refusing to give up on ideas that have failed, and devote your research program to the construction of pseudo-scientific justifications for why your failed idea really is right, just inherently untestable.

Personally I don’t see any reason why one day we shouldn’t some day better understand the relation of space-time symmetries and internal symmetries, and thus “unify” gravitational and other forces. Maybe this is possible, maybe not, one can’t know in advance. But if you decide you have an argument for impossibility, that’s the end of it, and that’s the existential danger for the field of “the multiverse did it”.

There’s the saying in math, “theorems are proved by those who believe in them”, same goes for physics: progress towards unification will come from someone who thinks it is possible, not from someone who has become convinced by “the multiverse did it” argument. Having such people write books that convince others to give up hope is even more damaging…

The points you list are very different in the kind of problem they pose. It might well be there isn’t any explanation for the mixing matrices or masses of particles. Quantum gravity is, however, a problem of an entirely different kind – it’s needed for consistency. And even if it wasn’t for quantum gravity, the SM would still have a Landau pole and what physical sense does this make?

Unfortunately most of the work on unification has focused on problems that I don’t think are problems at all. Eg, yes, maybe U(1)xSU(2)xSU(3) isn’t pretty, not to mention chirality, but if that’s the way nature works then that’s that.

The multiverse is merely a conflated way to say that they’re trying to answer questions that aren’t scientific to begin with, it’s beyond me how this has become acceptable.

But what if it is true? I mean, there is no question that the multiverse argument is lame, but Nature has no obligation to be interesting. Or testable, for that matter.

I thought a good “understand[ing of] the relation of space-time symmetries and internal symmetries” is the reason physicists cared so much about supersymmetry — this is the only nontrivial symmetry allowed by the Coleman-Mandula theorem. Is there another possibility?

Bee,

please tell me one point of experimental evidence that gravity needs to be quantized. I know of none whatsoever. And the Landau pole is a perturbative concept. Nobody yet knows how the nonperturbative RG running of QED looks.

I think our host is quite right to put all these in the same basket.

Peter,

I agree completely, I think I wasn’t clear. Multiverse is just silly. One cannot of course eliminate it as a possibility, but that’s the point, one can’t do anything scientific with it. You’re right if any progress is made, it will be by someone who believes it can be done, not with the multiverse. I just don’t know that I think there is progress to be made (though of course I’m a mathematician, so what do I know about force unification?) I must say though I’m kind of with Chris on this, who says gravity has to be quantized? Probably just the math, but GR is truly beautiful. The SM, not so much.

I’m surprised with the number of questions in the comments above, it’s not so usual for Peter’s blog. With Peter’s permission, maybe I can help a little:

Mateus Araújo,

Of course nature has no obligation to be interesting, or testable. Or even self-consistent, if you ask me. But our mathematical models of nature do have that obligation. There are in general many different mathematical models which can describe nature equally successfully (infinitely many models, finite amount of experimental data). Among all of those models, we are looking for those that are self-consistent, testable and interesting. Otherwise they are useless to us. So it’s a self-imposed restriction, for a good reason.

clayton,

Yes, SUSY is not the only way to circumvent the Coleman-Mandula theorem, there are others, though apparently not so popular. For example, the approach based on 2-categories (and higher), see for example 1003.4485.

chris and Jeff M,

Quantizing gravity is a requirement of self-consistency, since quantum mechanics does not tolerate being combined with anything classical. This has nothing to do with experiment, but with the axiomatic structure of the resulting theory. Namely, if one attempts to combine QM with classical GR (or classical electrodynamics, or anything else classical), one is lead to a clear-cut mathematical contradiction (violation of the superposition principle). So we either give up QM as we know it, or we give up GR as we know it. Something has to give, and of course research is being done in both directions.

HTH, 🙂

Marko

Mateus Araujo,

The problem is that you need some kind of serious argument, just saying “my complicated, ugly model doesn’t predict anything, so maybe the multiverse did it, let’s give up” isn’t one.

clayton,

Standard supersymmetric models don’t unify internal and space-time symmetries. They extend the Poincare group by new spin-1/2 generators that commute with internal symmetries. This is why SUSY tells you nothing about the SM.

Bee/Chris/Jeff M.,

My take on the quantum gravity problem is that GR and the SM are based on very closely related mathematical structures: a matter particle is coupled to gravity by a connection and to the SM forces by connections. Our problem is that we don’t understand the relation between these two kinds of connections. You can just say “there is none”, maybe that’s right. If you want to claim “let’s quantize the SM connection, not the GR connection”, besides consistency issues to worry about, you really should have some argument why you are treating these in a completely different fashion, other than the fact that applying a standard quantization recipe to the GR connection leads to problems.

vmarko,

How could Nature avoid being self-consistent? I find that literally inconceivable. As for the rest of your argument, I think you have a point. It unfortunately draws a line between what Nature is and what we can say about Nature, but I guess there is no way around it.

One should, however, not be too strict about testability, otherwise one is led to ridiculous positions such as saying that we don’t know whether Galileo’s remains are still inside Jupiter.

chris and Jeff M,

You can’t just say the gravity is classical and you don’t need to quantize it. You need to actually formulate how a “non-quantum gravity” acts on atoms. The most straightforward way is to do fails miserably.

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.47.979

Thanks for the replies to my question, vmarko and Peter! But, to respond to Peter, I thought that Coleman-Mandula provided a proof that there is no nontrivial product of spacetime and internal symmetries. They went on to make the (incorrect) claim there were no additional symmetries beyond the product of Poincare with internal symmetries; but this (incorrect) latter statement was, I thought, logically independent of the rest of the proof. Is this an accurate characterization? By the way, I am also confused with how the BMS “infinite dimensional” symmetry works in this respect, so my confusion is quite broad 🙂

clayton,

Yes, Coleman-Mandula is a real problem, it means that there has to be a more subtle relation between internal and space-time symmetry groups than just naively finding a larger group they both fit into and making that act in a conventional way. The BMS story is a really interesting one, I haven’t thought about the relation to Coleman-Mandula, but there (BMS) the group is acting non-trivially on the vacuum, which may be one reason Coleman-Mandula isn’t applicable.

If you look at the history of “no-go” theorems, I think you’ll find that typically sooner or later someone realizes that there is a way around one of their assumptions, so one should be very careful about drawing a conclusion from the “theorem” without paying very close attention to exactly what its assumptions are.

It seems that the correct title of the book should have been “Did Our and My Ideas so far Allow the Laws of Physics to be Unified?” Here the answer is of course “no”.

A honest summary would have clarified that the ideas in the last chapter all failed, and that a unifying ideas must differ from them.

A second honest summary would have added: Yes, the laws can be unified, because we can talk about *all of nature*. Therefore we can also talk *with precision* about all of nature. And therefore we must be able to unifiy all known laws.

It is obvious that unification is possible. But how to achieve it is not.

Whoever says the opposite is spreading disinformation.

thanks for the clear answer, Peter!

Bee, Mateus – I think the fact that the ‘multiverse’ argument is dressed up as a statement about reality makes one think that ‘a multiverse’ is a real thing, a single object which represents reality.

Given a system of (mathematical) axioms, one can deduce some statements; some statements have a truth value which is forced from the axioms (and these are not the same!). Other statements (if your axiom system is interesting) do not; they are independent. Some of these other statements have interrelations; if you fix one to true another is then forced to be also true, et cetera.

A model of a system of axioms is then an assignment of truth values to statements which is consistent (or at least is inconsistent only if the axioms themselves are inconsistent).

For example, one can take a standard set theory (ZFC say) and ask whether there exists a set of cardinality between the naturals and the reals. For ZFC this turns out to be one of those independent statements (the Continuum Hypothesis, CH, is the negative assertion); it doesn’t have a defined truth value.

One can construct models of ZFC in which CH is true, others in which it’s false, in either case asking ‘why is it true/false’ doesn’t have a reasonable answer (unless you weren’t looking at CH when you made your construction, anyway). It’s that way because you set it that way.

Of course, one can consider the class of all models, or ‘multiverse’. Then you answer ‘why is CH true/false’ with ‘because we are in that bit of the multiverse’; same logic dressed up differently.

Now, if you take an axiom system which you think describes reality, it will have (for the same reason) many different models. These are not logically related, they cannot ‘interact’ because there is nothing to ‘interact’ with. This is the (Platonic mathematical) multiverse which is (sometimes) being used in place of an explanation in physics.

Another possibility is that our current view of `the universe’ is one among a collection of interacting structures; in other words, that our current idea of ‘the universe’ sees only a slice through some more intricate structure of reality. That rather hypothetical ‘more intricate structure’ also gets called a multiverse, whereas if one posits it, what one actually asserts is a more complicated universe of which we currently (as far as we know) witness only a slice. It should be clear that two different slices through a single mathematical structure (which is a single model of an axiom system) potentially do interact and in any case are not the same thing as two different models of an axiom system. But since the same word is used for both, the two rather different concepts have been conflated.

And finally, what our host is objecting to, in these terms, is prematurely classifying statements as independent of the axiom system when we do not know this (especially since we presumably do not know the full axiom system). Incidentally, it’s worth noting that an independence statement is never itself independent (one cannot logically criticise our host for asking for certainty on this point). A statement S is independent of an axiom system A if there are models of A in which S is true and others in which it is false; letting T be ‘S is independent of A’, if T can be true then these models exist and hence T is definitely true (though it need not have a proof in A, or indeed in any given bounded axiom system if A is reasonably complicated, so our host might not ever know why the multiverse did it).

Peter,

The serious questions here are questions of what science is, what reliable scientific knowledge is, and how to pursue it. I don’t think the kind of framework of axiom systems and models that you discuss captures the issues at all (and it has nothing at all to do with the topic of this posting).

Peter,

do you believe that the laws of nature can be unified – and why?

What is your experience: how many of the researchers in the field believe in a positive, and how many in a negative answer?

Johannes,

Yes, in the sense that I think there is a better theory out there that we don’t yet know about, which would for instance tell us something deep about the relation of space-time and internal symmetries. Part of my reason for believing this is that there are all sorts of intriguing connections between the mathematical structures involved. This does not look like the kind of situation where one understands things well enough to know why you’re not going get some deep relation, it looks a lot more like a situation where something important is going on that one doesn’t understand. To get some idea of the general thing I’m talking about, see my essay

http://www.math.columbia.edu/~woit/mathphys.pdf

but there are also much more specific ideas that I’m hoping to get to writing about after I finish work on my book (any day now…).

I’d assume people who work on trying to find a deeper understanding of the Standard Model do so because they believe there is something there. Undoubtedly there are lots who, faced with ideas they devoted a lot of time to not working, have given up. Some go and work on other problems, a few unfortunately write books aimed at getting other people to give up too…

I am not a mathemetician or a physicist or even very intelligent but I have 3 points to make

1) It seems obvious Peter is so right on his points, especially in how much effort has been wasted in failed directions and there are directions in math that haven’t been fleshed out fully yet. It is absurd to “give in” so early with this multiverse nonsense when there are things we don’t even know about number theory for instance

2) I enjoyed looking at Peter’s PDF. It seems he is setting himself up to be the “I told you so” laureate when in 20 years a new Einstein comes along and inevitably shows us that the universe is just math and couldnt be any other way.:) Penrose seems to do this explicitly in his book Road To Reality

3) Peter talks about number theory in his PDF but doesn’t specifically mention the Reimann zeta function. I’m wondering if you have/have had any general thoughts on it? Again, I’m not a mathemetician, but I am fascinated by the fact that there might actually be something unrandom in prime numbers. It seems to me if there is anything fundamenal about the nature of reality it might be found in that

James Cooper,

Thanks, you’re quite right that I hope that someone smarter then me shows my prejudices about this topic to be right. Of course it’s a lot easier to have the right prejudice than to successfully justify it.

I don’t have any serious ideas about the Riemann hypothesis. If we ever know why it is true, that will surely tell us something deep about number theory which very well may elucidate its connection to quantum theory (and maybe a new deep idea about quantum theory will explain why the Riemann hypothesis is true). Actually yesterday in my Fourier analysis class I went through the proof of the functional equation for the zeta function, based on using Poisson summation to first prove the functional equation for the theta function. This morning it struck me that I have no idea if there’s a version of the Riemann hypothesis formulated directly as a statement about the theta function, would love to hear from anyone who can point to that.

Peter,

I cannot for the life of me remember if there’s a version of the RH for the theta function, it was too long ago when I was in grad school thinking I wanted to be an analytic number theorist. I do remember there are versions of the RH for the Dirichlet L functions, the generalized RH says that the zeros for any L function have real part 1/2. L functions are just zeta but with a multiplicative character as the numerator.

Jeff M,

A few minutes of Googling have turned up a version of this question on mathoverflow

http://mathoverflow.net/questions/14083/modular-forms-and-the-riemann-hypothesis

I don’t see much of a satisfactory answer there though…

Paper on arXiv, 1608.03679, on RH, to be published in PRL.

jd and others interested in proofs of the RH,

Please, very low on the desirability list of things to do over my spring break is moderate a discussion of people’s ideas about how to prove the RH. If you have a pointer for where someone discusses what the RH says about the theta function, I would like to see that.

Peter,

If you’re really curious, the person to ask is Peter Sarnak, at Princeton/IAS. I assume several people at Columbia know him well. Met him at UCLA when I met you, he was a few years out of grad school then and the hot new analyst, student of Paul Cohen at Stanford. Right after that he was around the GC a lot while I was working on my thesis. FYI, as far as proofs for the RH go, i wouldn’t hold my breath….