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.
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