One of the great lessons of twentieth century science is that our most fundamental physical laws are built on symmetry principles. Poincaré space-time symmetry, gauge symmetries, and the symmetries of canonical quantization largely determine the structure of the Standard Model, and local Poincaré symmetry that of general relativity. For the details of what I mean by the first part of this, see this book. Recently though there has been a bit of an “Against Symmetry” publicity campaign, with two recent examples to be discussed here.

Quanta Magazine last month published K.C. Cole’s The Simple Idea Behind Einstein’s Greatest Discoveries, with summary

Lurking behind Einstein’s theory of gravity and our modern understanding of particle physics is the deceptively simple idea of symmetry. But physicists are beginning to question whether focusing on symmetry is still as productive as it once was.

It includes the following:

“There has been, in particle physics, this prejudice that symmetry is at the root of our description of nature,” said the physicist Justin Khoury of the University of Pennsylvania. “That idea has been extremely powerful. But who knows? Maybe we really have to give up on these beautiful and cherished principles that have worked so well. So it’s a very interesting time right now.”

After spending some time trying to figure out how to write something sensible here about Cole’s confused account of the role of symmetry in physics and encountering mystifying claims such as

the Higgs boson that was detected was far too light to fit into any known symmetrical scheme…

symmetry told physicists where to look for both the Higgs boson and gravitational waves

I finally hit the following

“naturalness” — the idea that the universe has to be exactly the way it is for a reason, the furniture arranged so impeccably that you couldn’t imagine it any other way.

At that point I remembered that Cole is the most incompetent science writer I’ve run across (for more about this, see here), and realized best to stop trying to make sense of this. Quanta really should do better (and usually does).

For a second example, the Kavli IPMU recently put out a press release claiming Researchers find quantum gravity has no symmetry. This was based on the paper Constraints on symmetry from holography, by Harlow and Ooguri. The usually reliable Ethan Siegel was taken in, writing a long piece about the significance of this work, Ask Ethan: What Does It Mean That Quantum Gravity Has No Symmetry?

To his credit, one of the authors (Daniel Harlow) wrote to Siegel to explain to him some things he had wrong:

I wanted to point out that there is one technical problem in your description… our theorem does not apply to any of the symmetries you mention here! …

It isn’t widely appreciated, but in the standard model of particle physics coupled to gravity there is actually only one global symmetry: the one described by the conservation of B-L (baryon number minus lepton number). So this is the only known symmetry we are actually saying must be violated!

What Harlow doesn’t mention is that this is a result about AdS gravity, and we live in dS, not AdS space, so it doesn’t apply to our world at all. Even if it did apply, and thus would have the single application of telling us B-L is violated, it says nothing about how B-L is violated or what the scale of B-L violation is, so would be pretty much meaningless.

By the way, I’m thoroughly confused by the Kavli IPMU press release, which claims:

Their result has several important consequences. In particular, it predicts that the protons are stable against decaying into other elementary particles, and that magnetic monopoles exist.

Why does Harlow-Ooguri imply (if it applied to the real world, which it doesn’t…) that protons are stable?

What is driving a lot of this “Against Symmetry” fashion is “it from qubit” hopes that gravity can be understood as some sort of emergent phenomenon, with its symmetries not fundamental. I’ve yet though to see anything like a real (i.e., consistent with what we know about the real world, not AdS space in some other dimension) theory that embodies these hopes. Maybe this will change, but for now, symmetry principles remain our most powerful tools for understanding fundamental physical reality, and “Against Symmetry” has yet to get off the ground.

**Update:** Quanta seems to be trying to make up for the KC Cole article by today publishing a good piece about space-time symmetries, Natalie Wolchover’s How (Relatively) Simple Symmetries Underlie Our Expanding Universe. It makes the argument that, just as the Poincaré group can be thought of as a “better” space-time symmetry group than the Galilean group, the deSitter group is “better” than Poincaré.

In terms of quantization, the question becomes that of understanding the irreducible unitary representations of these groups. I do think the story of the representations of Poincaré group (see for instance my book about QM and representation theory) is in some sense “simpler” than the Galilean group story (no central extensions needed). The deSitter group is a simple Lie group, and comparing its representation theory to that of Poincaré raises various interesting issues. A couple minutes of Googling turned up this nice Master’s thesis that has a lot of background.

FYI the Japanese IPMU article says the result *suggests* proton decay rather than claiming the proton is stable. I guess that makes more sense if B-L is violated ignoring the point about AdS (so the English article should be corrected).

Symmetries play an important role in theory-development because they are simplifying principles, they are patterns that you look for. Science is generally a search for patterns/laws, but in the foundations these appear in very strict, formal ways on the level of the equations, which makes them particularly powerful.

The trouble with using symmetry principles is that we don’t know that this type of simplification will continue to work, both because (a) it may be the wrong type of simplification and (b) the next deeper level may just not be simpler than the present one.

In other words, it’s nice that it works, but no reason to think it will continue to work.

If you want a more interesting take on the idea that symmetries are accidental, have a look at this paper:

https://www.sciencedirect.com/science/article/abs/pii/0370269380908424

It strikes me as the kind of idea whose time hasn’t yet come.

As to the Cole piece. I couldn’t even get myself to finish reading it. Unfortunately, it’s the kind of nonsense that sounds plausible to people who don’t understand the subject.

Thanks for clearing this up.

How much of superstring theory’s growth was fueled by pursuing symmetry no matter where it led?

Regarding global symmetries: Wasn’t there an old (as in from the 80s) argument by Banks et al that argues from a string world sheet perspective that a global target space symmetry would always produce a corresponding gauge field which would render the symmetry local?

From an effective field theory perspective it could also be that the ultimate UV theory is not symmetric at all and what we see at low energies is only the practically massless stuff that is protected by symmetries from becoming heavy (gauge symmetries for spin 1 particles, chiral symmetries for spin 1/2, just a good symmetry lacking for the Higgs, if you don’t have susy…). So our liking of symmetries is due to observational bias.

“in the standard model of particle physics coupled to gravity there is actually only one global symmetry: the one described by the conservation of B-L”

Sorry, am I missing something here? Can anyone tell me which process in the SM violates B and L individually (while conserving B-L)? And does coupling to gravity have anything to do with it?

Because in the ordinary flat-space SM I don’t see any Feynman diagram that could violate either B or L, and I also don’t see how coupling to gravity could possibly induce such a violation.

🙂

Marko

Sabine, I disagree with your opinion that the role of symmetries is in simplification. There is a difference between 1) I have this equation, I will study spherically symmetric solutions, because it is easier, and 2) I have this equation, I found out that it has these symmetries and I am going to study them because it helps me understand the solutions.

Is your suggestion that somehow gravity could be emergent in AdS space but not in other spaces? Doesn’t it seem difficult for a largely local effect to disappear based on changes to the global space? Now I’m merely a mathematician so I could be missing something but wouldn’t at least something gravity like have to be emergent even in non-AdS spaces? I mean the other differences about the models in which the holographic principle seems to hold might matter but I’m curious how a local property could emerge/fail to emerge (even approximately) depending on whether some global constraint on the space holds.

Sabine,

One problem here is that there are various types of “symmetry” arguments, and the term “symmetry” gets used with different meanings. What I have in mind (this is related to what commenter martin writes) is the symmetry properties of the fundamental equations of the theory. The Heisenberg commutation relations are precisely the statement that you have a representation of the Heisenberg Lie algebra, and largely determine the basic structure of quantum mechanics. Gauge symmetries and Poincare symmetry largely determine the structure of the Standard model.

It is quite possible of course that there is a better, deeper fundamental theory, in which gauge symmetries, the Heisenberg commutation relations, local Poincare symmetry are not fundamental, but approximate, emergent properties. I just don’t see such speculation as so far working out.

Anonyrat,

In some sense the fundamental problem with string theory is that no one has been able to find the non-perturbative version, to answer the question “what is M-theory?”. A lot of efforts in that direction have been to try to find fundamental symmetries that determine the theory, but this has so far not been successful. One can take this as an indication that searching for fundamental symmetries is misguided (and I think this is one thing driving the “Against Symmetry” agenda), but trying to find a non-symmetry based M-theory hasn’t worked either, so maybe what is misguided is the idea that M-theory is a fundamental theory of nature.

vmarko,

From what I remember, there is baryon number violation in the SM (at unobservably low rate) non-perturbatively due to instanton effects. Presumably B-L is not violated this way. This has nothing to do with quantum gravity.

Peter Gerdes,

The problem with emergent gravity is, emergent from what? You need an actual theory, not just a bunch of words and hopes that a theory exists. The actual theories with some sort of emergent gravity that I’m aware of are toy models, very different than the real world (AdS vs. dS, wrong dimension). A lot of the current work in this area is on low-dimensional toy models that exhibit emergent gravity. The hope is that this will lead to some understanding that can be applied to find a realistic model, but that still seems very far away.

This will be procedurally unhelpful, but anyway … when I was studying on my own relavistic field theory and the standard model, there was a book that explained “From what I remember, there is baryon number violation in the SM (at unobservably low rate) non-perturbatively due to instanton effects” but not as instanton effects. They had a discussion that I was able to follow. They explained it as essentially a nonperturbative passage through a (classical) barrier in the (classical nonrelativistic, thus allowing potentials) Lagrangian by (relativistic) quantum tunneling. They used what seemed to me to be essentially (classical) transition state theory with a quantum tunneling correction to calculate the (astoundingly low, compared even to the usual GUT estimates) rate. It required the participation of 3 particles each of lepton and quark, with at least 2 of each being different generations, like one electron neutrino, one muon antineutrino, and a charged lepton. Three leptons turned into three quarks or vice versa.

But I was never able to find this passage again in any book I could check out of the library at a later date. It was a dated but well known in its day (post QCD discovery day) textbook, in the “epilog” on nonperturbative effects. I’d love to find it.

Doug McDonald,

There’s an extensive later literature, but this goes way back to ‘t Hooft’s earliest work on instantons, see this 1976 PRL paper

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.37.8

Peter and everyone,

Ok, after some research, the relevant keywords are the “sphaleron” and the Adler-Bell-Jackiw anomaly, which seem to be responsible for B and L violation.

However, these effects have so far been unobserved (sphalerons ought to appear somewhere around 10 TeV), and they are nonperturbative. Given that the SM is an effective low-energy model, nonperturbative results are not to be trusted in general, unless supported by experiment (which is missing in this case). Therefore, I prefer to remain a skeptic regarding the B and L violation, until data starts to support it.

But it’s a nice read, I learned something new today. 🙂 Thanks for the info and the links!

And regarding the media frenzy around the paper by Harlow and Ooguri, it’s just business as usual — hype beyond any proportions. H&O of course also ignore that there is a difference between AdS and the real world (which is not even strictly dS, let alone AdS), which is also business as usual — string theorist’s ultimate hope that AdS/CFT could at some point become relevant for the real world physics.

Best, 🙂

Marko

Hi Peter,

If you want to read a popular article where the various caveats for our work are mentioned, see

https://phys.org/news/2019-05-constraints-symmetries-holography.html.

Best,

Daniel

Thanks Daniel!

It’s rather odd that the article referred to by Daniel Harlow starts out explaining that Harlow and Ooguri have presented new arguments supporting the conjecture that there are no global symmetries in quantum gravity, and then at a certain point starts dropping the qualifier “global”, as though it’s unnecessary (at least according to the piece’s author, Ingrid Fadelli):

…and later on:

Chris W.,

I think there are two serious problems with the way the Harlow-Ooguri result is being promoted:

1. The fact that, as Harlow notes, the only relevance to the symmetries that govern fundamental physics is to the highly obscure special case of global B-L symmetry is not made clear, replaced by nonsense about “QG means no symmetry”. Even Ethan Siegel was taken in by this.

2. Their argument does not apply to the real world at all. It takes place in a toy model (AdS/CFT), which is quite different than a viable model of real 4d world quantized gravity coupled to the SM. Claiming that this tells you anything about the real world seriously misrepresents what AdS/CFT is. Arguably it’s an interesting toy environment to use to think about quantized gravity, but it is not a solution to the problem of quantizing real 4d gravity.