Space and Spaces

This is the title of a talk given today by Graeme Segal at Oxford’s Mathematical Institute. He gave this same talk last year as the Presidential Address for the London Mathematical Society, which means there’s a nice written version online here. I mainly mention this with the hope of one day understanding it properly, so forgive the sparsity of details.

One of the key ideas of the talk was to explain why we observe particles in nature, even though our best description of (most of) fundamental physics, quantum field theory, says that fields are the fundamental physical objects. To answer this question, one needs to think about the relevant spaces of states and observables, and one sees that noncommutative geometry enters essentially. The following nice quote touches on this:

In one way quantum field theory is enormously simpler than its classical counterpart, for there are no particles: the manifold of configurations is simply a space of smooth fields on M. In exchange for this simplification, the state-space can no longer be interpreted as an ordinary space: it is an object of non commutative geometry, and that is why when we look at the world we sometimes see particles and sometimes see fields.

To really understand what’s going on, it seems that some reasonably high-level mathematics is needed—Segal had hoped to formulate an explanation for non-mathematicians, but he couldn’t come up with one. A key result seems to be a theorem—a generalisation of the Stone-von Neumann theorem—that explains why we sometimes see particles and not waves: the theorem says that the algebra of observables on the state space of fields contains an algebra isomorphic to the observables on the tangent bundle of the configuration space of a collection of particles. I don’t understand the proof or surrounding discussion well enough to explain it further, so I won’t try, but merely plan to try sometime in the future. There’s much more in the paper about the notions of physical and mathematical spaces from the algebraic topologists perspective, but that’s even farther outside of my understanding.


Before, behind and beyond the discovery of the Higgs boson

This is the title of a conference run by the Royal Society in London that I spent today and yesterday attending. Overall, there wasn’t anything particularly new or controversial said, and the level was mostly non-technical. Nevertheless, there were many good talks, albeit with plenty of overlap; I’ll quickly mention just a few.

The first talk, by Tom Kibble, was a lovely 40 minute recounting of the birth of the idea of spontaneous symmetry breaking in gauge theories from his perspective as one of its founders and as a member of Abdus Salam’s group at Imperial College. Another interesting talk was by Mikhail Shaposhnikov on his Higgs inflaton model of cosmology, which uses the Higgs field to drive inflation and incorporates scale symmetry. In addition, there were several experimental talks, including one by Fabiola Gianotti and Tejinder Virdee (former spokespersons for ATLAS and CMS, respectively) on the Higgs discovery/measurement and there were several other talks on searching for new physics at the LHC. One interesting fact from Chris Llewellyn-Smith in his talk on the genesis of the LHC—with apparently more such stories contained in his upcoming book—is that the LHC magnet casings are, because of him, coloured Oxford blue, which is, he remarked, unfortunately quite similar to Cambridge blue… 

Arkani-Hamed Oxford talks

Nima Arkani-Hamed was in Oxford two weeks ago giving two lectures for the philosophy of cosmology conference “Anthropics, Selection Effects and Fine-Tuning in Cosmology.” He also gave two talks in the maths department on scattering amplitudes and a talk in the physics department about building a 100 km circular collider. I think that similar versions of all these talks can be found online, so I’ll just give a broad outline and some nice quotes.

In his first conference talk, “Naturalness and It’s Discontents: Why Is there a Macroscopic Universe?,” he talked mostly about naturalness in relation to the cosmological constant and hierarchy problems, stating that “naturalness problems are not an inconsistency of physics—rather, they’re a guide for what to expect,” and “that something big and structural is needed to remove the cosmological constant problem”. He said, “the broad idea of naturalness is being put under more pressure by the LHC, but I’m not more worried than pre-LHC since people already had to make excuses.” However, “it’s a little disquieting.” He mentioned that nothing else new at the LHC would represent a 1% fine-tuning for the weak scale, which has happened before in physics e.g. the moon eclipsing the sun and the low quadruple of the CMB. However, if it goes to a 1/10,000 tuning, “it would make the Higg’s much more special that these crappy examples.” On the multiverse: “Asking if we’re part of a multiverse isn’t a theory but a caricature of what a future theory might look like.” In response to a question at the end he said: “the manifold structure [of spacetime] is all in our heads–it’s better to phrase things in terms of high-energy scattering amplitudes.”

His second conference talk, “Space-Time, Quantum Mechanics and the Multiverse,” was about the physics motivation for considering a multiverse. Basically, “it’s the only scientific approach to the cosmological constant problem and it happens in some theories e.g. chaotic inflation, string theory, simple toy models.” He said that he suspects that making sense of the multiverse will require equally as radical a step as going from classical to quantum physics. He thinks this will involve getting rid of space-time and thinking carefully about what are the precise observable: “the really big mysteries are cosmological observables.”

He gave a talk in the maths department on the Amplituhedron. He started with a long discussion about how gravity implies the lack of local observables (except at infinity). He then talked about how the least action formulation of classical mechanics helped connect to the next level of description of (quantum) physics and how something similar will probably be needed to get rid of space-time. This is linked to the idea that scattering amplitudes written in terms of Feynman diagrams are made to have manifest locality and unitarity, which requires incorporating gauge redundancy, but in the alternative approach scattering amplitudes for a particularly symmetric (N=4 SYM) theory come out more simply as the “volume” of some region in some space, which means that unitarity and locality are derived. He then spent quite some time defining the amplituhedron idea as a generalisation of the inside of a triangle. (There was a follow-up technical talk the next day that I didn’t attend.)

His collider talk, “Motivations for 100 km collider,” began with: “every physics point in this talk is obvious,” with his view that the main motivation for building a collider being that it’s the obvious future of the field. He said, “we’ve never had a consistent theory valid up to exponentially higher energies–this is a qualitatively different scenario from what we’ve seen in the past,” but that in every scenario he can imagine we will need a 100 TeV pp machine–there are deep structural issues in QFT at stake in finding out if the weak scale is natural. If we don’t find anything more at the LHC, there’ll be a 10% tuning and we’ll want to know if it’s more (the tuning goes as the square of the machine energy) since it’s significant to say that the weak scale is 100 times more tuned than other examples. He also said that he thinks that the Higgs find is undersold: a light Higgs boson means that our vacuum is qualitatively different to a random condensed matter system (“it’s not some crappy metal”). When talking about the 1% tuning in the fact that neutrons don’t bind he said that when he tried to learn nuclear physics as graduate student he found it really confusing. He also talked about his visit to China to discuss building a 100 km collider there and about the new centre for future HEP being set-up in Beijing, which he’s going to spend 2-3 months at every year for the next two years. He thinks there’s a greater than 1% chance that they’ll actually build it, which is why he’s spending that much time there. He noted that a good thing about building the next large collider under an authoritative regime is that you only have to convince a few people (unlike in the US). He also mentioned that he had a one hour conversation with Al Gore in which he apologised for the SSC cancellation (he was largely responsible for that). In response to a question about split-SUSY (I think), he said: “the psychological thing with model building is that you have to believe it’s right at the time so you’re motivated to work out its consequences, and when you’re done you forget about it. I wish I didn’t need these psychological crutches, but life is hard.”

NZ government funds new Science Centre

The University of Canterbury (UC), my undergraduate institution, is struggling financially following the 2010/11 Christchurch earthquakes that left the university with damaged infrastructure and reduced student numbers.

The government recently made some announcements that they will give much-needed financial support to UC to build a $212m “Canterbury Regional Science and Innovation Centre” and to upgrade its engineering facilities. The Science/Engineering bias is in accordance with government agenda and any support for other areas will have to come from funding within the university.

I was asked by the UC media consultant to answer some questions relating to this announcement. I tried to be optimistic about the support for science, whilst emphasising that it’s important that other academic areas are supported in the university–lest UC becomes a technical institute.The resulting article is here, but I’ll paste my full answers below:

How exciting this is for the future of UC Science–and why? How this will really raise the value, integrity and status of UC Science?

This is tremendously exciting for the future of UC Science. If post-quake UC is to be a competitive science research and teaching institution that attracts students and leading researchers, then it needs upgraded infrastructure and a distinctive brand.

There is a unique opportunity for us to learn from our earthquake experiences and to plan strategically for the future as we rebuild; the proposed Canterbury Regional Science and Innovation Centre (CRSIC), which is made possible due to this government support, is representative of the type of ambitious long-term thinking that UC and Canterbury needs.

However, it is important to remember that people are a university’s most valuable asset. New infrastructure alone does not create a thriving university, although it can certainly help to attract world-class academics and foster research. In addition, a healthy and diverse intellectual climate requires that we give adequate support to non-STEM subjects.

How exciting this is for prospective UC students–and why?

Future students can look forward to having modern, open science facilities. Well-designed spaces can make a huge difference to one’s university learning and social experiences—something I have recently experienced first-hand at Oxford in the vibrant atmosphere of the new Mathematics Institute. Such spaces also encourage collaboration and the transfer of ideas through casual interactions amongst academics and students, both within and across disciplines—such interdisciplinary collaboration will be needed to solve complex problems such as climate change. The new science facilities should help to improve students’ learning experiences and to equip them to tackle such important future problems, as well as to thrive in modern collaborative workplaces.

How this will help attract Year 12 and 13 high school students to UC?

Modern facilities will naturally attract students, but also the improved outreach ability that UC Science will have will strengthen connections with local schools. Hopefully this will expose some young people to the excitement of science when they might not have had the opportunity otherwise, and perhaps it will even encourage them to pursue science at university.

How this proposal will help graduating Science students get jobs?

[I don’t really have anything meaningful to say here.]

The new facilities will be designed to encourage collaboration with industry. This will be an important component of making graduates more employable and fostering innovation in the region.

Any over overall comments would be great.

Overall, the type of support that the government is giving UC Science is vital if we are to be globally relevant in science education and research in the future. It is important that we not only invest in long-term structural foundations, but that we leverage this financial support to attract and retain leading researchers so that we can move forward also on a strong intellectual foundation.

Book Review: Nobel Dreams

Nobel Dreams, by Gary Taubes, is the story of CERN’s Super Proton Synchrotron (SPS) particle accelerator–the predecessor to the Large Hadron Collider, which contained the world’s first proton-anti-proton collider–as it was operated in the early 80’s. The star of this book is Carlo Rubbia, the experimentalist who headed the Underground Area 1 (UA1) collaboration, an experiment attached to the SPS.

In the first half of the book, Taubes recounts how Rubbia’s talent for electronics, his cutthroat personality, and his intense politicking saw him become the most powerful person at CERN. Rubbia used his influence to get the SPS adapted to collide protons with anti-protons–a radical idea at the time–in hopes of reaching high enough energies to discover the W and Z bosons, the mediators of the weak force. In 1983 UA1 did discover the W and Z bosons, although Rubbia claimed a discovery before this was statistically warranted–a move that ensured glory for his team over UA2, a competing experiment attached to the SPS. This work promptly and predictably resulted in Rubbia and the accelerator physicist Simon van der Meer being awarded the Nobel prize in 1984.

The second half of this book gives a detailed account of some of Rubbia’s and UA1’s subsequent work: the search for supersymmetry from September 1984 until March 1985. Following the discovery of apparent anomalies in the data in the form of monojets and dijets, Rubbia claimed prematurely that UA1 had discovered “new physics,” to be sure that another team wouldn’t beat him to a discovery. This signal was found by the data analysts and theorists to be nothing more than background, despite great resistance from Rubbia who badly wanted a second trip to Sweden.

The second part of the book is a tad boring at times since it recounts in detail events and conversations as they happened, which is not always interesting to read. It does, however, give an insight to academic politics, the daily workings of forefront researchers, and the dangers of seeing patterns where there are none.

The final paragraph is a conversation between Taubs and Alvaro de Rujula, a CERN-based theoretical physicist, which is rather telling given the unhealthy dominance that string theory research has had in theoretical physics during recent decades, so I’ll reproduce it here:

On August 4th, 1985, I sat in the cantina at CERN drinking beer with Alvaro de Rujula. We talked about whether the demise of the monojets had created a corresponding lull in the supersymmetry work. Or whether the theorists were so hot on superstrings that they would continue on supersymmetry undeterred as well. De Rujula predicted that 90 percent of the theorists would work on superstrings and the connection with supersymmetry, because it was fashionable. When he intimated that this was not a healthy state, I asked him what he would prefer to work on. rather than answer directly, he digressed.

“It must be remembered,” de Rujula told me, “that the two people most responsible for the development of superstrings, that is to say, Green and Schwarz, have spent ten to fifteen years systematically working on something that was not fashionable. In fact, they were ridiculed by people for their stubborn adherence to it. So when people come and attempt to convince you that one must work on the most fashionable subject, it is pertinent to remember that the great steps are always made by those who don’t work on the most fashionable subject.”

“The question then,” I said, “is what do you work on instead? What will your next paper be on?”

“That’s a question for each theorist to ask himself,” he replied. “And it depends on whether you want to survive as a theorist, or you have the guts to think that pride in your own work is more important than the momentary recognition of your fashionable contribution. that’s for each person to decide by himself, depending on his level of confidence in his own genius.”

“So,” I repeated, “what is your next paper going to be on?”

“I’m trying to tell you,” de Rujula said, “that I have no idea.”


Good scientists expect that their students will exceed them. Although the academic system gives a successful scientist many reasons to believe in his or her own authority, any good scientist knows that the minute you succumb to believing that you know more than your best students, you cease to be a scientist.

-Lee Smolin

Einstein in one sentence

This is a neat article by John Baez and Emory Bunn which discusses the geometrical meaning of Einstein’s equations. It includes this characterization of Einstein’s equations in one plain English sentence:

Given a small ball of freely falling test particles initially at rest with respect to each other, the rate at which it begins to shrink is proportional to its volume times: the energy density at the center of the ball, plus the pressure in the x direction at that point, plus the pressure in the y direction, plus the pressure in the z direction.