Are Physical Laws Inevitable?

The last couple days have seen various discussions online generated by a piece at Quanta Magazine with the dubious headline Why the Laws of Physics Are Inevitable and an even worse sub-headline claiming “physicists working on the ‘bootstrap’ have rederived the four known forces” (this is utter nonsense). For some of this discussion, see Sabine Hossenfelder, John Baez and Will Kinney.

One reason this is getting a lot of attention is that the overall quality of reporting on math and physics at the relatively new Quanta Magazine has been very high, a welcome relief from the often highly dubious reporting at many mainstream science media outlets. The lessons of what happens when the information sources society relies on are polluted with ideologically driven nonsense are all around us, so seeing this happen at a place like Quanta is disturbing. If you want to understand where this current piece of nonsense comes from, there is an ideology-driven source you need to be aware of.

A major line of defense of their subject by string theorists has essentially been the claim that, while it may lack any experimental support, string theory is “the only consistent way to combine quantum theory and general relativity”. I’ve often explained what the problem with this is, won’t go on about it again here. Nima Arkani-Hamed is at this point likely the most influential theorist around, for some good reasons. The roots of the problem with the Quanta article lie in taking too seriously the kind of arguments he tends to make in the many talks he gives. He’s trying to make as strong as possible a case for the research program he is pursuing, so unfortunately gives all-too-convincingly a very tendentious take on the scientific issues involved. For more about this, see a posting here about the problems with the recent Quanta article that motivated the latest one.

Debates over generalities about whether the “laws of physics are inevitable” are sterile and I don’t want to engage in them here, but I thought it would be a good idea to explain what the serious ideas are that Arkani-Hamed and others are trying to refer to when they make dubious statements like “there’s just no freedom in the laws of physics”. Here’s an attempt at outlining this story:

Quantum mechanics and special relativity:

A mathematically precise implication of putting together fundamental ideas about quantum mechanics and special relativity is that the state space of the theory should carry a unitary linear representation (this is the QM part) of the Poincare group (this is the special relativity part). You also generally assume that the time translation part of the Poincare group action satisfies a “positive energy” condition. To the extent you can identify “elementary particles”, these should correspond to irreducible representations. The irreducible unitary representations of the Poincare group were first understood and classified by Wigner in the late 1930s. My QM textbook has a discussion in chapter 42. If you impose the condition of positive energy and for simplicity consider the case of non-zero mass, you find that the irreducible representations are classified by the mass and spin (which is 0,1/2,1,3/2, etc.). Non-interacting theories are completely determined by the representation theory and exist for all values of the mass and spin.

Extensions of Poincare and the No-go theorem of Coleman-Mandula

To get further constraints on a fundamental theory, one obvious idea is to extend the Poincare group to something larger. States then should transform according to unitary representations of this larger group, carrying extra structure. Restricting to the Poincare subgroup, one hopes to get additional constraints on which Poincare representations can occur (they’ll be those that are restrictions of the representations of the larger group). The problem with this is the Coleman-Mandula theorem (1967) which implies that for interacting theories the larger group can only be a product of Poincare times an internal symmetry group. Representations will just be products of the Poincare group representations and representations of the internal group, with space-time symmetries and internal symmetries having nothing to do with each other. This is why the Quanta headline about “rederiving the four known forces” is nonsense: the three non-gravitational forces are determined by internal symmetries, have nothing to do with what the Quanta article is describing, work on space-time symmetries.

One way to avoid the Coleman-Mandula theorem is to work with not Lie algebras but Lie superalgebras. Here you do get a non-trivial extension of the Poincare group and a prediction that Poincare representations should occur in specific supermultiplets. The problem is that there is no evidence for such supermultiplets.

Another possible extension of the Poincare group is the conformal group. Here the problem is that the new symmetry implications are too strong, they rule out the massive Poincare group representations that we know exist. One can work with the conformal group if one sticks to massless particles, and this is what the methods advertised in the Quanta article do.

The idea that our fundamental space-time symmetry group is the conformal group is mathematically an extremely attractive one, with the twistor picture of space-time playing a natural role in this context. I strongly suspect that any future truly unified theory will somehow exploit this. Unfortunately, as far as I know, no one has yet come up with a way of exploiting this symmetry consistent with what we know about elementary particles. Likely a really good new deep idea is missing.

Quantum field theory

To get stronger constraints than the ones coming from Poincare symmetry, one needs to decide how one is going to introduce interactions. One way to go is quantum field theory, with a principle of locality of interactions. This gets encoded in a condition of (anti)commutativity of the fields at space-like separations, which then implies various analyticity properties of correlation functions and scattering amplitudes. The analyticity properties can then be used to prove things like the CPT theorem and the spin-statistics theorem, which provide some new constraints.

Given a method of constructing a Poincare invariant quantum field theory, typically done by choosing a set of classical fields and a Lagrangian, one can try and realize the various possible Poincare group representations as interacting theories. What one finds is that, for spins greater than two one runs into various seemingly intractable problems with the construction. One also finds exceptionally beautiful theories in the spin 1/2 and spin 1 cases that exhibit an infinite dimensional group of gauge symmetries. An example of these is the Standard Model. Unfortunately, we know of no principle or symmetry that would provide a constraint that picks out the Standard Model. If we did, we might be tempted to announce that the principle or symmetry is “inevitable” and thus the “laws of physics are inevitable”. We’re not there yet…

Amplitudes and the S-matrix philosophy
In the S-matrix philosophy one takes the analyticity properties as fundamental, working with amplitudes, not local quantum fields. The 1960s version of this program (also often called the “bootstrap” program) was based on the hope that certain physically plausible analyticity assumptions would so tightly constrain the theory of strong interactions that it was essentially uniquely determined. This didn’t work out. In his recent introductory lecture for his course at Harvard, Arkani-Hamed explains why. The research program he and others are currently pursuing is in some sense a modernized version of the failed 60s program. The hope is that new structures in amplitudes can be found that will replace the structures one gets from local quantum fields.

Amplitudes based arguments about, for instance, why you don’t see fundamental higher-spin states, and why spin 1/2 particles have forces of the kind given by gauge theory have a long history, see for instance work on massless particles by Weinberg in the mid-sixties and Weinberg-Witten in 1980.

As far as I can tell, the work referred to in the Quanta article gives new amplitudes-based arguments of this kind for massless particles, exploiting conformal symmetry. It’s not clear to me exactly what’s new here as opposed to earlier such arguments, or how strong an argument about real world physics one can make using these new ideas. One thing that is clear though is that the Quanta quote that what has been discovered implies that “There’s just no freedom in the laws of physics” is as much nonsense as the “we rederived the four known forces” business.

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This and That

First, a few physics items:

  • Mark Alpert has a new novel out, Saint Joan of New York, a thriller subtitled “A Novel About God and String Theory”, which is an accurate description. It’s published by Springer, so you may be able to get access to it like I did through an institutional license here.

    The plot revolves around Joan, a talented high school student here in New York, who has been learning more advanced material through a mentor at City College, and in particular has learned about string theory and Calabi-Yaus. This Joan plays the role of a modern-day analog of Joan of Arc, using divine help to do battle not with the English, but with more modern dark forces. This divine help includes a revelation about Calabi-Yaus and the theory of everything. It’s a thriller, so I’ll avoid telling more about the plot so as not to spoil it.

    I quite enjoyed reading the book even though I’m not much of a fan of thrillers, although a lot of enjoyment was due to the fact that much of the action takes place here in New York on the Upper West Side, and that the main plot revolves around the question of string theory and existence of a TOE. Edward Witten plays a role in the story.

    If you like this one, you might also want to read some of Alpert’s other novels, a couple of which also involve themes of a TOE.

  • Most theorists have abandoned the search for a TOE, or the idea of explaining anything about the Standard Model, in favor of concentrating on hopes to find some sort of emergent theory of quantum gravity. For the latest on this, talks from the recent misleadingly titled Quantum Gravity in the Lab conference at Google might at some point be available. John Preskill’s slides are here. He indicates that the general idea is that quantum gravity will emerge from “Massive Entanglement, Quantum Chaos and Complexity.” This week the IAS will host a similar event, a workshop on Qubits and Spacetime. Wednesday evening many of the participants will be put on a bus to Manhattan, where they’ll continue with the 2019 meeting of the Simons Foundation-funded “It From Qubit” collaboration.
  • Also here in New York this week, Roger Penrose will be at Pioneer Works Friday night for a public program involving a conversation with Janna Levin. I have no idea whether his presence in New York at the same time as “It From Qubit” is a coincidence or not. If not, maybe the “It from Qubit” people will get back on the bus and head out to Red Hook Friday night.
  • Instead of being at the IAS, Nima Arkani-Hamed has been spending the past semester at Harvard, with activities that include teaching a course, Physics 283B: Spacetime and Quantum Mechanics, Total Positivity and Motives. Videos of his lectures are online here (first one here). It would be great if someone could put together a written set of lecture notes from these videos.
  • Finally, for some multiverse-related book reviews that have the unusual feature of showing some skepticism, see John Horgan here, Matt Leifer here, also Chris Fuchs here. Fuchs explains the problem with multiple worlds as a solution to the measurement problem:

    Its main shortcoming is simply this: The interpretation is completely contentless. I am not exaggerating or trying to be rhetorical. It is not that the interpretation is too hard to believe or too nonintuitive or too outlandish for physicists to handle the truth (remember the movie A Few Good Men?). It is just that the interpretation actually does not say anything whatsoever about reality. I say this despite all the fluff of the science-writing press and a few otherwise reputable physicists, like Sean Carroll, who seem to believe this vision of the world religiously.

Some mathematics items:

Update: In case you haven’t been getting enough hype about the multiverse recently, Scientific American has Long Live the Multiverse! for you, from Tom Siegfried. Siegfried assures us that “multiverse advocates have been right historically”. He also assures SciAm readers that multiverse theories are testable, in a way similar to the way Einstein demonstrated the existence of atoms in 1905 using Brownian motion:

For that matter, it’s not necessarily true that other universes are in principle not observable. If another bubble collided with ours, telltale marks might appear in the cosmic background radiation left over from the big bang. Even without such direct evidence, their presence might be inferred by indirect means, just as Einstein demonstrated the existence of atoms in 1905 by analyzing the random motion of particles suspended in liquid.

He doesn’t mention that his analog of the Brownian motion experiment has been done: people have looked for the predicted indirect effects of other bubble universes on ours, and found nothing. To the extent that the multiverse is testable, it has been tested and found to not be there.

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News From HEPAP

For presentations a couple days ago at the latest HEPAP meeting, see here. One piece of news, from this presentation, is that there likely will be a delay in the scheduled startup of the HL-LHC, with the next LHC run (Run 3) extended for an additional year (through 2024), and the next shutdown (LS3) extended by a half year. The HL-LHC would then start physics in 2028.

Most of the HEPAP discussions have to do with funding. The pattern of recent years has been one of huge decreases in funding proposed by the Trump administration. These are completely ignored by both the Democrats and Republicans in Congress, which passes large increases in funding (then signed into law by Trump). For FY2020 this continues: at DOE the HEP budget for FY2019 was \$980 million, for FY2020 the White House budget request was a massive cut to \$768 million. This was taken no more seriously by anyone than the last few of these, with the FY2020 House Mark \$1,045 million, the Senate Mark \$1,065 million. The FY2020 budget remains to be finally finished and passed, in the meantime the federal government has been operating under a sequence of continuing resolutions.

Specifically on theory funding, JoAnne Hewett has a presentation on The State of Theory. It has no numbers in it, but the DOE numbers given here show an increase from \$60 million in FY2017 to \$90 million in FY2019 for Theoretical, Computational and Interdisciplinary Physics. But within this category, pure theoretical HEP is pretty flat, with big increases for Computational HEP and a huge new investment in Quantum Information Science (\$27.5 million in FY2019). There does seem to have been some sort of decision to de-prioritize conventional theoretical HEP in favor of newer trendy areas.

Hewett describes the general consensus on current problems with theory funding as

  • Universal concern on ever decreasing levels of funding for university groups: concern that university programs are dying.

    -Private institutions attempt to offset cuts with non-federal funding sources.
    -Cuts to program further accumulated in 2019. Many postdocs learned in May 2019 that their contracts would not be renewed for the fall. It was then too late to apply for new positions.

  • Lab theory programs are also losing researchers.
  • Even distribution of cuts across U.S. theory program has indirect proportional effect to small programs.
  • Large fluctuations cycle-to-cycle is making groups less cohesive and more inclined to opt for “safer” research projects.
  • There is the perception that the recent emphasis on QIS comes at a cost to more traditional HEP theory research.
  • Summer salary has been capped or reduced to 1 month in many cases. Removal of summer salary across the board is demoralizing.

and ends with

The situation is becoming increasingly unstable.
University-based theory is suffering its most serious crisis in decades.
Its future is in jeopardy.

It would be interesting to see some numbers on the size of new private research funding going to HEP theory (for instance funding from the Simons Foundation or the private funding of the CMSA at Harvard). I don’t know of such numbers but I’m curious whether what is happening is that the total funding level has seen reasonable growth, but increases in funding are going to a small number of elite institutions, with the rest of the field in decline.

On the question of caps or reductions in summer salary, I doubt that any significant number of researchers is reacting to only getting 1 month of summer salary by signing up for another job (e.g. teaching summer school) and not doing research during the other two months of the summer. There has been another huge influx of money to the field that in some sense replaces grant-funded salary supplements: the multi-million dollar Breakthrough Prizes. A sizable number of HEP theorists have now partaken in all or part of one of the \$3 million prizes. If you add in this money, on average HEP theorists may have been seeing significant increases in income, however with almost all of it going to a small number of people (at the same elite institutions that are doing well). What we’re seeing may just be the same trend as in the rest of the US economy: a move to a star system with ever larger increases in inequality.

Another problem for the field of HEP theory may be that funding is stagnating because the DOE and NSF are skeptical about its intellectual health. Hewett notes that “Formal theory resides solely in university environment and has undergone significant funding cuts.” Trying to make the positive case for this part of the field, she lists three areas of advances, but oddly, the first two are identical. The two areas of advances in formal theory she describes are:

Advances in strongly coupled quantum field theory (gravity/field theory duality, bootstrap program, amplitudes) has implications for particle physics, cosmology and beyond.

Geometric advances in particle physics constructions from String/F-theory has implications for the “swampland program”.

For the second of these, it’s quite possible that most physicists don’t see this as an advance at all.

Update: Physics World has more about the delay here. It is supposed to be announced on Tuesday. The cause evidently is a budget gap caused by some planned contributions from non-member countries now not happening. The story doesn’t explain which non-member countries are involved or why their planned contributions are now not expected.

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Terrifying Odyssey Through a Cursed World

The great German artist Anselm Kiefer now has a show up in London at the White Cube Bermondsey gallery, with a review in the Guardian entitled Terrifying Odyssey Through a Cursed World. The review describes some of the works as follows:

Another room is given over to panoramic blasts of brown and black that map sweeping vistas of desolate fields. A road twines through a morass of mud and collaged sticks. Lines of fence poles vanish in the distance. These scenes are drawn in black on a vertiginous scale. Kiefer uses perspective, the Renaissance technique of showing the real world shrinking towards a single vanishing point, to define his landscapes – but the perspective view is a transparency on top of a muddy tumult of colour and texture, with real, 3D stuff stuck over that in turn. From the right distance, the picture of a landscape can be read clearly, like a painting by Van Gogh. Go closer and the picture dissolves in a mess of bulges and muck.

What’s the inspiration for these works (besides the Holocaust)?

These landscapes are entitled Superstrings, a reference to string theory, an influential idea in contemporary physics that seeks to unify quantum mechanics with Einstein’s relativity.

and the show is entitled Superstrings, Runes, The Norns, Gordian Knot. The gallery website explains:

White Cube is pleased to present an exhibition of new work by Anselm Kiefer. The exhibition brings together many of the interests that have characterised Kiefer’s work for decades, including mythology, astronomy and history. Located across the entire Bermondsey space, it features a large-scale installation and paintings that draw on the scientific concept known as string theory.

The Guardian review continues:

The main gallery at White Cube Bermondsey is already pretty bleak in its featureless emptiness. Kiefer makes it work for him by heightening the chill, turning the White Cube into a morgue for Europe. Snow-covered landscapes with none of the cheer of Bruegel stretch away to infinity. They are marked with sticks as black as gravestones and nets that catch at nothing. Kiefer’s science reading clearly hasn’t cheered him up. The curvy grids of space-time become horrible wire traps in a devastated nowhere. We might be on the no-man’s land of the Ukraine border. Anyway, this place has got death in its hard black furrows.

Another review, at City A.M. tells us more about Kiefer’s motivations:

This is where we come to string theory – the monolith of Kiefer’s new show. Though he admits that he doesn’t quite understand what string theory is, Kiefer professes complete fascination with the idea that there is a scientific equivalent to the allegorical Gordian Knot – an idea that he picked up after thirty years of subscribing to Spektrum, a German monthly science magazine…

String theory cannot be verified empirically. Rather, it is an attempt to provide an all-encompassing description of the universe. And that, says Kiefer, is just why it is beautiful. “I suppose it’s like painting,” he says. “You cannot prove if a painting is good or bad. That is the point of it – it is descriptive… and there’s something sublime in that.”

From the images available, the work does look quite amazing. Kiefer quite possibly has gotten to the very heart of superstring theory, seeing in it a dark, desolate and blasted mythology which “cannot be verified empirically.”

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The Man Who Solved the Market

There’s an excellent new book out about Jim Simons and Renaissance Technologies, The Man Who Solved the Market, by Gregory Zuckerman. I recommend it enthusiastically to anyone interested in the story of how a geometer ended up being worth \$23 billion. Lots of other mathematicians and physicists have also been involved in this over the years.

I first heard about Simons and his investment operation when I was a postdoc at Stony Brook in the mid-eighties, and have heard bits and pieces of this story from various sources over the years, sometimes clearly distorted in the retelling. It’s very satisfying to finally get a reliable explanation of what Simons and those working with him have been up to all this time. For those with more interest than me in the details of quant strategies, the book provides far and away the most information available about how Simons and RenTech have been making so much money so successfully. The author managed to get some degree of cooperation from Simons, and was thus able to get a lot of those involved with him to talk. As a result, while this isn’t an “authorized” biography, it’s written from a point of view rather sympathetic to Simons.

One question that keeps coming up in the book is that of motivation. Why did Simons abandon a highly successful career doing research mathematics in order to focus on making as much money as possible? Part of the answer is that, from the beginning, Simons always had one foot out of the research math world, playing poker and trading commodities even when he was a graduate student working with Chern at Berkeley. Later, while employed at the IDA in Princeton, he spent time working not just on government projects but on the mathematical analysis of stock market trading strategies. While I’ve often heard the story of how he was fired from IDA after publicly criticizing the Vietnam War, less well known is that a big problem was that he was quoted in Newsweek saying he planned to work on his own projects, not government ones, until the war was over.

Unfortunately, the book has very little to say about a question I’m fascinated by: what does Simons intend to do with the \$23 billion (and counting, the RenTech Medallion Fund that he has a large piece of continues to be an incredible money-making machine)? There’s very little in the book about his philanthropic activities, the most visible of which are at the Simons Foundation, which now has assets of nearly \$3 billion with amounts of the order of \$300 million/year coming in as income and going out as research funding. I think that on the whole Simons had made excellent choices with the math and physics that he has decided to fund, from the Simons Center for Geometry and Physics at Stony Brook to a wide array of programs funded by his foundation.

A question that keeps reappearing throughout the book is that of the social significance of RenTech. It’s a rather pure test case for the moral question about quant investing: would the world be better off without it? In the case of the main money-maker, their Medallion fund, it’s hard to argue that the short-term investment strategies they use provide important market liquidity. The fund is closed to outside investors, and makes money purely personally for those involved with RenTech, not for institutions like pension funds. So, the social impact of RenTech will come down to that of what Simons and a small number of other mathematicians, physicists and computer scientists decide to do with the trading profits (calculated by Zuckerman at over \$100 billion so far).

Simons himself has engaged in some impressive philanthropy, but one perhaps should weigh that against the effects of the money spent by Robert Mercer, the co-CEO he left the company to (Zuckerman discusses Mercer in detail). Mercer and his daughter have a lot of responsibility for some of the most destructive recent attacks on US democracy (e.g. Breitbart and the Cambridge Analytica 2016 election story). In the historical evaluation of whether the world would have been better off with or without RenTech, the fact that RenTech money may have been a determining factor in bringing Trump and those around him to power is going to weigh heavily on one side.

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Various Links

Now back from a trip to the West Coast, here are some accumulated things that may be of interest:

  • One thing I didn’t do while there was attend the 2020 Breakthrough Prize symposium. For videos of three talks about supergravity, see here. At the time of the award I wrote here about why a \$3 million prize for a failed idea about particle theory was a bad idea. Listening to the talks, I think an even worse idea is telling the public that this is a great example of why they should trust science.
  • For another dubious idea from the West Coast, in January the KITP is bringing high school teachers to Santa Barbara to teach them about Spacetime, Holography, and Entanglement. Most of the programs the KITP has run for teachers (see here) have been devoted to explaining important, solid science. Back in 2001 when they promoted string theory I thought that was a bad idea, this latest one isn’t much better. Again, when the credibility of science is under attack, why go to the public (or, in this case high school teachers) to promote a highly speculative research program? Is it really a good idea for high school teachers to be exposed to this kind of hype, presumably with the hope that they’ll somehow transmit it to their students?
  • On the evergreen topic of bad multiverse science, Scott Alexander here defends multiverse speculation, responding to Jim Baggott’s article. He and the authors of the more than four hundred comments debate at length a red-herring issue. Alexander writes:

    My understanding of the multiverse debate is that it works the same way [as respectable paleontology]. Scientists observe the behavior of particles, and find that a multiverse explains that behavior more simply and elegantly than not-a-multiverse.

    Yes, if theorists had a simple, elegant multiverse theory with lots of explanatory power, you could get into interesting arguments about its testability and whether the idea was solid science or not. The problem is that no such multiverse theory exists. If you want to talk about the MWI multiverse, your problem is that solving the measurement theory problem by just saying “the multiverse did it” may be “simple” and “elegant”, but it’s also completely empty. If instead you want to talk about the cosmological multiverse, the problem is that you don’t have a theory at all (and the actual fragments of a theory you do have are complicated and ugly). For more about this, see my posting and article on Theorists Without a Theory.

For something more positive, while traveling I noticed two quite interesting articles which explain in a detailed technical way approaches to two of the great unsolved problems of our time, while carefully discussing why the approaches have not (yet?) worked, leaving the great problems unsolved.

  • For mathematics and the Riemann Hypothesis, see Alain Connes and Caterina Consani’s article The Scaling Hamiltonian, about the attempt to understand the zeros of the Riemann zeta function in terms of the properties of a specific Hamiltonian operator, which in some sense is a generator of a group of scaling transformations.
  • For physics and quantum gravity, see Donoghue’s A Critique of the Asymptotic Safety Program, which has a detailed discussion of the problems with making sense of both quadratic gravity Lagrangians and the idea of a non-trivial fixed point gravity theory theory. I was interested to see that he has a lot to say about the Lorentzian vs. Euclidean signature issue, something often ignored.

Finally, I recommend reading Elizabeth Landau’s interview at Quanta with astronomer Virginia Trimble and Trimble’s excellent advice to us all:

Pay attention. Someday, you’ll be the last one who remembers.

Update: Two more math-related items well worth a look:

Update: Yet another blog entry from Scott Alexander about the multiverse, with more hundreds of comments. What is it with the fascination for this empty argument?

At BBC Science Focus, more multiverse promotion from Sean Carroll. He does end though by getting to the real point (note that when theoretical physicists say a question is “hard to answer”, it means they have no idea how to answer it):

Many-Worlds is a lean and mean theory, but it’s possibly too lean and mean; there is very little structure to rely on, so questions like “Why do probabilities behave the way they do?” and “Why is classical mechanics such a good approximation to the world we see?” are hard to answer.

This is exactly the problem that those arguing over this at Slate Star Codex and elsewhere don’t seem to understand: saying “all is the Schrodinger equation” doesn’t tell you how to connect the theory to the world we observe. Adding in an ontology of multiple universes does nothing at all to solve this problem.

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Today’s Hype

Hype about string theory and fundamental physics seemed to have been dying down recently, with only three editions here so far in 2019 of This Week’s Hype. Today however brings a bumper crop of the highest quality, with new examples from a few of the world’s most prominent theoretical physicists. Today’s hype neatly exemplifies the two main current genres of hype about string theory and supposed new fundamental physics. The first is the old-school genre of string theory hype we’ve now been seeing for 35 years: “string theory makes a testable prediction” (no, it doesn’t). The second is the new, post-modern variety: no actual theory, just a grandiose claim that space and time have been replaced, although it’s unclear by what.

Trend: Cosmic Predictions from the String Swampland

In the subtitle of this APS Physics piece from Cumrun Vafa, we learn that the string swampland has “led to testable predictions about dark energy.” If you read the article trying to find the testable predictions of string theory, you’ll get to Figure 3, where the caption says “The colored curves are string theory predictions for dark energy for different values of c.”

The problems with this include:

  • This is based not on a theory or calculation, but on a conjecture (see e.g. here) that consistent string vacua have certain properties.
  • Many experts disagree with this conjecture. In particular it would imply that the well-known supposed metastable string vacua of KKLT are inconsistent, and that is a matter of controversy.
  • This conjecture is not the sort of thing that can be proved one way or another, since it is not about something well-defined. The non-perturbative formulation of string/M-theory necessary to get a well-defined answer to such questions about string vacua remains unknown. You can make various conjectures about the behavior of this unknown theory, but then your swampland conjecture is a conjecture about a conjecture.
  • The conjecture involves an unknown constant “c”. Unless you know what “c” is, you don’t actually have a prediction.

In his conclusion, Vafa writes:

In the next 5–10 years, we may know, for example, whether dark energy is constant or not. If it is, that could pose a serious blow to string theory. But if dark energy is found to be changing, could that observation be the first experimental evidence for ideas emanating from string theory?

The most likely possibility over the next 5-10 years is that measurements continue to be compatible with constant dark energy. I don’t believe for a minute that 10 years from now after that result is in you will see Vafa or anyone else giving up on string theory or even admitting it has suffered a “serious blow”. On the other hand, if there is any evidence for a varying dark energy, Vafa or others will surely claim it as “evidence for string theory”, which it will not actually be.

Over the last 15 years I’ve often written here about this “Swampland philosophy”, which never made much sense to me. I didn’t understand back in 2005 and still don’t understand now why conjectures that behavior you don’t observe in the real world might be inconsistent with some other conjectures about an unknown M-theory are supposed to be of interest. The sociological motivation here is rather clear though: the KKLT-based “anthropic landscape” philosophy has not worked out well for the field, and the hope is to disentangle the subject from that morass. A good explanation of what is going on is provided by this (stolen from Will Kinney, who also has a lot to say about the whole swampland business):

Cosmic Triangles Open a Window to the Origin of Time

This is a different sort of hype, with no direct relation to string theory. In this genre of hype, you don’t have any connection between your calculation and either experiment or a fundamental theory, but this doesn’t stop you from making grandiose claims. What’s behind this particular article is this paper, which develops a nice calculational method exploiting conformal symmetry. What’s not made clear in the Quanta article is that this has no connection to anything measurable. As the authors of the article explain:

In this paper, we have worked under the lamppost of weakly broken conformal symmetry. This has allowed us to derive particularly clean insights into the analytic structure of inflationary correlators. However, it also restricts the strength of the couplings between the inflaton and additional massive fields. This makes the observational challenge to detect these effects enormous.

In other words, this is about speculative models in which the observable effects described at length in the Quanta article would be unmeasurably small.

The post-modern hype come into play with the argument that these conformal-symmetry based calculations somehow tell us how to replace space and time.

This suggests that the temporal version of the cosmological origin story may be an illusion. Time can be seen as an “emergent” dimension, a kind of hologram springing from the universe’s spatial correlations, which themselves seem to come from basic symmetries. In short, the approach has the potential to help explain why time began, and why it might end. As Arkani-Hamed put it, “The thing that we’re bootstrapping is time itself.”

If you’re trying to understand the origin of this particular dollop of hype, it’s a good idea to keep in mind something Arkani-Hamed said at a talk about Lance Dixon’s work back in 2013:

… I AM an ideologue. In my defense at least I can say that I’m a serial ideologue, in the sense that I’ll take totally different ideologies and drop the last one without thinking about it, but it’s very important for me personally to be an ideologue when I’m working on something…
So, usually I’ll get up when I talk about scattering amplitudes and give a long introduction about how spacetime is doomed, we have to find some way of thinking about quantum field theory without local evolution in space time and maybe even without a Hilbert space and blah-blah-blah. This is all very high-falutin stuff, this is stuff that Lance wouldn’t be get caught dead saying. I think none of these guys would ever say something that sounds so pretentious, but I have to say it, you know I have to say it, because this is the only way I can get up in the morning, and like “I suck again, OK, here we go, I’m doing it because spacetime is doomed, I swear to God, right”.

I’m actually rather sympathetic to the “bootstrap” philosophy in some general sense, which I’d interpret as “all is unitary representation theory of the conformal group”, i.e. that constraints of conformal symmetry, analyticity and unitarity are almost enough to determine a fundamental theory. The 1960s version of this, trying to get strong interaction physics purely from such general principles, didn’t work out, but I’ve become more and more convinced that representation theory and fundamental quantum field theory are very deeply intertwined. I do think though that to get anywhere you’re going to need to either work top-down (i.e have an actual fundamental theory and derive its implications) or bottom up (i.e. use observations to find the route to better theory).

Will head out soon for a short vacation in Northern California (if it hasn’t burned to the ground). I had thought about stopping by the 2020 Breakthrough Prize Symposium, but decided listening to talks about why supersymmetry/supergravity got a $3 million award would not be good for my blood pressure.

Update: Those interested in KKLT vs. Swampland debates might be interested in the latest from Tom Banks. He makes a detailed case against KKLT/eternal inflation/Landscape models, which string theory Swampland enthusiasts may find appealing. They should however note what he has to say about string theory itself:

A more sensible attitude, which I share, is to accept that string theory defines some models of quantum gravity, but obviously not the one that corresponds to the real world.

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John Tate 1925-2019

John Tate, who was responsible for some of the most important developments in number theory and arithmetic geometry during the second half of the twentieth century, has passed away at the age of 94. Tate was a faculty member in the Harvard math department when I was an undergraduate there, moving on to UT Austin in 1990, then retiring from there in 2009.

The work that Tate is famous for includes “Tate’s thesis”, his 1950 doctoral thesis, which may be the most influential doctoral thesis of modern mathematics. For a book-length explanation of Tate’s thesis, see Ramakrishnan and Valenza’s Fourier Analysis on Number Fields. The later generalization of the GL(1) case of Tate’s thesis to the non-abelian GL(n) case is one of the founding pillars of the Langlands program.

Tate was the Abel Prize laureate in 2009, and one can learn a lot more about him from an interview conducted around the time of the award. For an extensive discussion of Tate’s mathematical work, see this article from James Milne, or this review by Milne of Tate’s Collected Works.

From Milne’s web-site, some stories about Tate:

A mathematician was explaining his work to Tate, who looked bored. Eventually the mathematician asked “You don’t find this interesting?” “No, no” said Tate, “I think it is very interesting, but I don’t have time to be interested in everything that’s interesting”.

As a thesis topic, Tate gave me the problem of proving a formula that he and Mike Artin had conjectured concerning algebraic surfaces over finite fields. One day he ran into me in the corridors of 2 Divinity Avenue and asked how it was going. “Not well” I said, “In one example, I computed the left hand side and got p13; for the other side, I got p17; 13 is not equal to 17, and so the conjecture is false.” For a moment, Tate was taken aback, but then he broke into a grin and said “That’s great! That’s really great! Mike and I must have overlooked some small factor which you have discovered.” He took me off to his office to show him. In writing it out in front of him, I discovered a mistake in my work, which in fact proved that the conjecture was correct in the example I considered. So I apologized to Tate for my carelessness. But Tate responded: “Your error was not that you made a mistake — we all make mistakes. Your error was not realizing that you must have made a mistake. This stuff is too beautiful not to be true.”

During a seminar at Harvard, a conjecture of Lichtenbaum’s was mentioned. Someone scornfully said that for the only case that anyone had been able to test it, the powers of 2 occurring in the conjectured formula had been computed and they turned out to be wrong; thus the conjecture is false. “Only for 2” responded Tate from the audience. [And, in fact, I think the conjecture turned out to be correct except for the power of 2.]

Tate’s father, John Torrence Tate Sr., was a physicist, editor of the Physical Review between 1926 and 1950. In one famous story, Tate Sr. stood up to Einstein by insisting that one of his papers be refereed in the usual way. Einstein was outraged (but it turned out the paper was incorrect). A few years ago I was at a talk here in New York at the Simons Foundation, during which the speaker put up a slide referring to Tate (Jr.)’s work, with a picture of Tate. After a moment, from the back of the room we heard “that’s not me, that’s my father!”.

Update: Kenneth Chang has an obituary of Tate at the New York Times.

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Foundations

Some links related to the foundations of math and physics:

  • Kevin Hartnett at Quanta has a long article on Jacob Lurie and his work on infinity categories. Unfortunately Lurie didn’t participate in the article himself, so comments are only from others. The article does a good job of giving at least a vague sense of what these very abstract foundational ideas are about, as well as examining the math community’s struggle to absorb them. Lurie’s work on this is spread out over more than 900 pages here and more than 1500 pages here. Recently he has been putting together an online textbook/reference version of this material as Kerodon, which is modeled after and uses much of the same software as Johan de Jong’s Stacks project.
  • At Mathematics without Apologies, Michael Harris has some comments on a recent discussion of the Mechanization of Math, held here in New York at the Helix Center. A video of the discussion is available here.
  • In the new (November) issue of the AMS Notices John Baez has a review of a recent collection of articles about the foundations of mathematics and physics. The book, Foundations of Mathematics and Physics One Century After Hilbert, contains contributions about both math and physics, although in his review Baez concentrates on issues related to physics. He notes “The elephant in the room is string theory.”
    The same issue of the Notices contains an informative long article about Michael Atiyah and his career, written by Alain Connes and Joseph Kouneiher (Kouneiher is the editor of the book reviewed by Baez).

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2019 Physics Nobel Prizes Announced, John Horgan Wins

The 2019 Physics Nobel Prizes were announced this morning, half going to Jim Peebles for his work on big bang cosmology, half to Michel Mayor and Didier Queloz for discovery of an exoplanet.

You can read elsewhere more details about the prize winners and their work, but I do want to point out that this announcement means (since there will be no further Physics Nobel Prize awards before the start of 2020) that John Horgan has won his 2002 bet with Michio Kaku, with \$2000 going to the Nature Conservancy. The winning prediction from Horgan was:

By 2020, no one will have won a Nobel Prize for work on superstring theory, membrane theory, or some other unified theory describing all the forces of nature.

If one looks at the comments back then, Gordon Kane signs on to an even stronger variant of the Horgan/Kaku bet:

By 2020 there will be a Nobel Prize for a string- or unification- or supersymmetry-based theory or explanation or experimental discovery.

Luckily for him he doesn’t seem to have put up any money for this, since he has now lost this bet.

For my own comments at the time, see here (this was a couple years before this blog was started). As I explained there, I was willing to sign up on Horgan’s side of the bet if the “other unified theory” clause was eliminated. Unlike Horgan, I’m not a sceptic at all of the existence of a unified theory, or of humanity’s ability to find it. My argument (which I think has held up well) was that we’re not going to get there by pursuing superstring theory or anything like it. In a better world, the LHC would have found not a vanilla Higgs, but something unexpected that gave us a new idea about electroweak unification, one that pointed to a successful new idea about a fully unified theory. I didn’t think this was likely, but I thought it was possible, and I wasn’t interested in betting against the possibility I would most like to have seen.

What shocks me about where we are now that Kaku and Kane have lost their bets is not that they lost, which was to be expected, but that this loss seems to have had zero effect on their behavior. Kane’s endless replacement of failed predictions by new ones is a well-known story. For Kaku, one can get some idea of his current point of view from this interview:

Yahoo News: So tell us about your work in string field theory. You’re trying to finish Einstein’s equation?

Michio Kaku: That’s right. We want to find the “God Equation” — the ultimate theory that explains the entire universe. We want an equation that’s maybe 1 inch long that would allow us to “read the mind of God” — those are Einstein’s words.

Yahoo News: And how’s it going?

Michio Kaku: We think we have it! It’s called string theory. It’s not in its final form, and it’s not testable yet, [but] we have the Large Hadron Collider outside Geneva.

We’re testing the periphery of the theory, but the theory itself is a theory of the universe — so it’s very hard to test. But we physicists are optimistic. We think we will be able to test the theory. And we think it is the final theory. So physics ends at that point. Another era opens up, but one era ends when we finally prove this is the Theory of Everything….

If string theory is correct, it means that all the subatomic particles — the electrons, the protons — are nothing but musical notes on a tiny vibrating rubber band. So that physics is nothing but the harmonies of the vibrating rubber bands. Chemistry is nothing but the melodies you can create from the vibrating strings. The universe is a symphony of strings.

And the mind of God is cosmic music resonated through hyperspace.

Kaku also appears in this recent story, which Sabine Hossenfelder refers to as “math fiction”. For this kind of phenomenon I prefer Horgan’s version: “science fiction in mathematical form”.

I don’t know of other bets on string theory, but there were quite a few bets about SUSY. I assume David Gross has now paid off his lost bets on SUSY, haven’t heard though anything about that. At the Copenhagen SUSY bet event, the losers (Arkani-Hamed, Gross and Shih) showed no signs that losing a bet on a scientific outcome had any effect at all on these scientist’s views on the issue they were willing to bet on.

Update: Horgan has posted his own take on this here.

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