One Ring To Rule Them All: A Visit To The Large Hadron Collider (Part 1.)

I noticed in telling people about visiting the Large Hadron Collider that a surprising number of folks have never heard of it.  In brief, it's the world's largest and most powerful "atom smasher" --a giant ring 27 kilometers in circumference, buried under hundreds of feet of rock, straddling the Swiss-French border.  It was built to probe the fine structure of matter and space-time, by accelerating tiny bits of matter up to very close to the speed of light and then smashing them together (some people say it's rather like throwing a watch against a wall and watching the bits fly out to see how it works, which is not an exact analogy but it gives you the basic idea.)

 If you know that all the matter you see around you is made of atoms, which are in turn made of smaller particles --protons, neutrons, and electrons --and that these particles interact with each other and with fields like the electromagnetic field, you know enough to go on with.

"You don't have anything on your calendar for the first day you're in Geneva," the PR rmanager's email said. "Anything you'd like to do?" "Well," I wrote back, "I've always wanted to visit the Large Hadron Collider."  I meant it as a joke but apparently, she took me seriously.  The visit to the LHC and CERN took place not on my first day there, which was just as well --I had for some reason (and I don't know why, JFK--GVA is a flight I've made more times than I can count, in the line of duty) absolutely crippling jet lag and my first day I couldn't do much more than lie on the bed in my room at La Reserve, feeling bone-crushingly tired and wishing I could sleep, which I couldn't.  It was no fault of the hotel's --La Reserve is located in the Swiss countryside on the shore of Lac Leman, just outside Geneva; it's one of the most relaxing hotels in Europe but I couldn't nod off for the life of me.  Two glasses of wine with dinner didn't do anything but wake me up, and though I'd brought some melatonin with me I decided --rather foolishly --to white-knuckle it through the night.  Melatonin works as far as sedation goes but it also has been increasingly giving me very, very unpleasant dreams and I've been trying to avoid it, though in retrospect I probably should have just knocked myself out.

The next day started early --my hosts on this trip to Geneva were from a small-batch watch company called Roger Dubuis, which makes a few thousand watches per year for the luxury market in a state-of-the-art facility in Meyrin, which is a suburb of Geneva.  Geneva is both a city and a Canton; Meyrin is located in the Canton of Geneva, which makes the watches made by the company eligible for the prestigious Geneva Hallmark.  This is a quality standard granted by the Canton for watches made to a certain level of quality specified by the Geneva Seal criteria.  It's expensive to adhere to the requirements --the cost over making a standard movement is around thirty to forty per cent --but it's one of the company's main selling points; they remain the only company whose production is one hundred per cent Geneva Seal approved.  

I'd long since forgotten that I'd mentioned the LHC to the company's PR manager in New York as I didn't honestly think that touring the LHC was possible, and I hadn't noticed that on my schedule for the day there were 2 hours set aside for "transport to a surprise destination," which I assumed was an off-site facility of some sort --an engraver, an enamelist's studio, a dial factory.  As it turned out, the surprise destination was indeed the Large Hadron Collider.

The LHC is located at the headquarters of the Conseil Européen pour la Recherche Nucléaire,or CERN, which was established in 1957 with 12 member states and now has 20. CERN's purpose was and is to conduct high energy particle physics experiments, and the Large Hadron Collider is the latest and most powerful particle accelerator --an atom smasher, in popular parlance --in CERN's arsenal.  Basically, particle accelerators like the LHC accelerate subatomic particles up to very high speeds --the LHC takes packets of protons up to very close to the speed of light --and smashes them together in order to explore how matter and the structure of space-time as we observe them today, came into existence.

If you observe the Universe today, you can see that it's expanding (this was an unpleasant surprise for Einstein, who favored a static model) and if you run the clock backwards, the Universe gets progressively smaller and denser and hotter.  At time=zero, theory predicts that the very early universe experienced a phenomenon known as the Big Bang, which began as a moment in time when all the matter and energy in the Universe was concentrated in an extremely tiny area --a dimensionless point of infinite energy and density, or singularity.  

The earliest period of the history of the Universe is known as the Planck epoch, after the physicist Max Planck, and lasted for a very short period of time, known as the Planck Time --this is the amount of time it takes for light to travel the Planck Length, which is an extremely short distance; about 1.616 x 10 to the minus 35th power meters. It's impossible to have an intuitive sense for how tiny such a distance is (the Scale of the Universe animation is pretty good though) but it helps to note that it is about 10 to the minus 20th power smaller than the diameter of a proton.  Evidence for the Big Bang is robust --the left-over radiation from the Big Bang has been detected and mapped by deep space microwave radiation telescopes on satellites like the WMAP probe --and though the Big Bang theory is widely accepted, it raises, to put it mildly, a lot of questions.

Most people would like to know where all the matter and energy (we should just say mass-energy, as by Einstein's equation, E=MC^2, we know they are equivalent) came from, which is a highly speculative subject in cosmology.  Part of the problem is that we do not, at present, have the theoretical tools necessary to make mathematically reliable predictions about the earliest stage of the Big Bang, much less answer questions about where all the stuff that became all the stuff we see now came from.  We can reliably date the age of the Universe to a little over thirteen billion years, but the problem with understanding the very early universe is that during the Planck Epoch, the energy density of the universe was so high that the fundamental forces --the electromagnetic force, weak force, strong force, and gravity --are thought to have been unified into a single force.  

Gravity is the odd man out; we have an excellent theory for gravitation --general relativity --and an excellent theory for subatomic particle behavior --quantum mechanics.  However, when you try to make relativity and quantum mechanics play nice together, terrible things happen --the equations begin to generate ridiculous infinities, which scientists take as evidence that neither relativity nor quantum mechanics are complete theories.  What we want is sometimes given the rather Promethean name of a Theory of Everything --a TOE --which would allow us to make sensible predictions about how gravity works at the quantum scale, but so far a good theory of quantum gravity has proven very elusive.  String theory, which postulates that fundamental particles are not point objects, but instead minute strings of mass-energy whose frequency modes correspond to different fundamental particles, is an attempt to cope with the disconnect between relativity and quantum mechanics; quantum loop-gravity theory is another.

The Large Hadron Collider was constructed to help answer questions about conditions in the early universe.  In particular, one of the major unanswered questions it was designed to look into is the mechanism by which particles acquire mass.  The Standard Model of particle physics, which describes the fundamental particles and their interactions (via quantum mechanics) has successfully described all known subatomic particles, as well as the forces through which they interact, and although it is not complete, it's proven pretty solid ever since it got its name in the 1970s.  The Standard Model also predicted the existence of particles which, at the time it was first being formulated, had not yet been observed.  

One reason certain particles --like the so-called "top quark" --had not yet been observed in existing particle accelerators was that such particles are very massive, and thanks to E=MC^2 we know it takes a lot of energy --a very high energy density --to create such particles in the lab.  Such particles also tend to rapidly decay, as they shed energy, into other, more stable particles.  The top quark was finally detected, after a long search, with a machine called the Tevatron --an enormous particle accelerator located at the Fermi National Accelerator Laboratory (Fermilab) in Illinois, USA.  The Tevatron was a colossus --the main accelerator ring was 6.86 kilometers in circumference, and it collided protons and antiprotons together at TeV --trillion electron volt --energies.  Decommissioned in 2011, it was during its operating lifetime the only machine powerful enough to create and observe the top quark.

Despite its success, the Standard Model has some gaps, one of which is a mechanism for describing why particles that have mass, have mass (why a particle should need to "have" something as basic as mass is another question, but suffice to say there are reasons, which is why things like protons and neutrons have mass, and things like photons don't.)  The Higgs boson is the particle --first hypothesized in 1964 --thought to be responsible for giving mass to certain fundamental particles.  

Bosons are one of two classes of elementary particles (the other is the group known as fermions) and for certain reasons they are often force-carrying particles  in the Standard Model --for instance, photons are the force-carriers for the electromagnetic force.  When particles interact electromagnetically, they exchange photons.  The bosons that mediate such interactions are called gauge bosons, and the Standard Model predicted a field --known as the Higgs field --with which elementary particles would interact in order to gain mass (a massless particle like the photon, by contrast, would not interact with the Higgs field.)  The Higgs boson is the gauge particle of the Higgs field, just as the photon is the gauge particle of the electromagnetic field.  The Higgs field, if it exists, would have a non-zero minimum energy in empty space.

Finding the Higgs boson became, after the discover of the top quark, one of the most important remaining goals in confirming the predictive ability of the Standard Model.

The problem, though, is energy.  Nobody really knew exactly how much energy would be necessary to observe the Higgs boson, and theory predicted that the Higgs field emerged about 10 to the minus tenth power seconds after the big bang --many orders of magnitude after the Planck Epoch (whose duration is the Planck Time, remember --about 10 to the minus 44th power seconds) but still so close to time=zero that the energy density of the universe was extremely high.  It was thought possible that Higgs bosons might have been created in very small numbers in accelerators like the Tevatron, but to make them in large enough numbers to be observed with a high enough confidence to confirm the Higgs field's existence --bear in mind that Higgs bosons exist for too short a time to be observed; what scientists would look for are decay products specific to the decay of the Higgs boson --a bigger machine was needed.  And that's where the Large Hadron Collider came in.

Go to part 2

Short Subjects Part VII: S=k x logW

Dramatis Personae: Myself, Oldest Heir

Scene: Walk to school one semi-brisk October morning

OH: . . .So, anyway, I think the way this could work is --theoretically, anyway --you replace each neuron in the brain one at a time with an artificial one.  That way you don't interrupt the continuity of consciousness and you eventually get consciousness in a completely artificial brain.

M: That's an interesting thought experiment.  What about the body?

OH:  Same basic strategy.

M: What about metabolism?

OH:  What about it?

M: Well, I mean --you'd need some sort of energy intake.  You know, an external source of energy.

OH:  Yeah.  I mean, look, what I'm going for here is really total self-sufficiency and physical immortality, OK?

M:  Uh, doesn't the law of entropy forbid that?

OH:  What?

M:  Entropy.  No closed system is a hundred per cent efficient, kinda thing?  So you need some external energy source.  Chemical, nuclear, whatever.

(Pause)

OH:  OK, you know what I'm hearing?  Quitter talk, that's what I'm hearing.

An Inconvenient Truth, Part Deux

"“The luxury industry has changed the way people dress.  It has realigned our economic class system. It has changed the way we interact with others. It has become part of our social fabric. To achieve this, it has sacrificed its integrity, undermined its products, tarnished its history and hoodwinked its consumers. In order to make luxury ‘accessible,’ tycoons have stripped away all that has made it special."


"Luxury has lost its luster."


--Dana Thomas, Deluxe: How Luxury Lost Its Luster

An Inconvenient Truth

"I think most journalists are pretty lazy, number one. A little lazy and also they're spoon-fed information, such as the weapons of mass destruction back in 2003....you have these people who create a package of news, develop it as a story line, a scenario, and they find, as Mailer once said about the press, that they're like a donkey. You have to feed the donkey. The donkey every day has to eat. So [special interests] throw information at this damn animal that eats everything. Tin cans, garbage." --Gay Talese

An Update from "The Science of Scent" --Luca Turin's TED Talk

Thanks to Jon Edwards via Twitter for pointing this out.  Luca Turin's The Science of Scent was the subject of my first post ever on this blog and he's also done a TED talk on his theory and some fascinating subsequent developments.  Love his notion that a theory "is something that lets you do less work."

He is rather entertaining, as organic chemists go.

Gödel, Incompleteness, and an Aging Brain

One of the interesting things about having kids is that they make you learn, re-learn, or realize that you have absolutely no understanding whatsoever of many things that you thought you knew, have forgotten, or prided yourself on understanding (erroneously.) Math, for me, is a biggy. Although I have managed to learn to read, when it comes to math I've always had a combination of genuine fascination with it, and almost totally functional illiteracy, at least when it comes to actually being able to calculate. One subject with which by which I was both intrigued and baffled for years was Gödel's Incompleteness Theorems, which were formulated by Kurt Gödel (left) as a refutation of the idea that mathematics could be put on a rigorously logical axiomatic foundation. He published his paper, which was a fatal torpedo in the side of the Good Ship Certainty, in 1931, under the rather diffident title "On Formally Undecidable Propositions of Principia Mathematica and Related Systems."

Like most people who can't do math but are fascinated by things for which an understanding of math is essential, I had lots of people and circumstances on which I blamed my own incompetence (the usual suspects: the emotional rigors of childhood; indifferent teachers; a disastrously disorganized educational system) but the truth is people who really want to understand math generally find a way to do it, external circumstances notwithstanding.

One of the most conspicuous examples is the Hungarian mathematician Paul Erdös (it is easy to think, considering their names, that an umlaut over a vowel in your name is a sign of predestination to mathematical genius) whose father was in a Russian POW camp for much of his childhood, and whose mother, who had lost Erdös' two older sisters to scarlet fever, kept him home until he was 10 years old, because she feared school was "full of germs" (which, in fact, happens to be true.) Erdös went on to become one of the most prolific mathematicians of all time (neck and neck with the Swiss mathematician Leonhard Euler, who also published around the same number of papers, and who had a considerably more socially developed childhood than Erdös) but in adulthood was also notoriously eccentric --Erdös lived entirely out of a suitcase, never owned a home (or even stayed in one place for very long) and spent his entire very long and productive life staying in a succession of the homes of his colleagues. (He was also an amphetamine addict, and once declared "a mathematician is a machine for turning coffee into theorems" though in his case substituting "dexedrine" for caffeine would have been more candid.)

Gödel was also notoriously eccentric --he was obsessed in his later years with a fear of being poisoned and when his beloved wife Adele died, he essentially starved to death as she was the only person he trusted to prepare his food. If people today know his name it is thanks to his famous Incompleteness Theorem. The Incompleteness Theorem is actually two theorems, which brought to an end a project which had preoccupied mathematicians for some time prior to Gödel's work: the attempt to develop a system of axioms which would form a perfect logical foundation for mathematics. Several such systems were developed, including Peano Arithmetic, something with the exotic name of Zermelo-Frankel Set Theory with Choice (you wouldn't want it without choice, would you?) and finally Bertrand Russel's Principia Mathematica. The idea that mathematics could be placed on firm epistemological ground was articulated probably with the most clarity and determination, at least among Gödel's contemporaries, by David Hilbert, who rejected the maxim ignoramus et ignoramibus ("we do not know, and we will not know") that essentially draws an outline around what is even possibly knowable and says there will always be something outside that line.

Gödel's Incompleteness Theorems are, I've read, very technical, and they have also had the interesting fate, along with the theory of relativity and quantum mechanics, of having had their meaning, or what many of us suppose to be their meaning, extended beyond the domain in which they were intended to function. I read about Gödel for the first time in Douglas Hofstadter's book Gödel, Escher, Bach: An Eternal Golden Braid, which I think I read when I was around twelve and most of which, of course, went rather over my head. Having the book around fed my desire to see myself as a deep thinker, though, and I do remember reading and understanding at least some of it. In particular I recall the bit about the Liar's Paradox ("This sentence is not true") staying with me, and spending a lot of middle school and high school with a constant sense of frustration that mathematical concepts could be so interesting but the actual study of the subject so tedious and humiliating. While Hofstadter, as far as I could, and can, tell, had a perfectly lucid grasp of Gödel's Incompleteness Theorems, I certainly didn't, and the idea that they showed that in general, the universe is a vast unknowable place where there are mysteries which science and reasoning can never unveil seemed to periodically rear its head as the years went by, and I gradually started to think of Gödel's work as implying exactly that --in a fuzzy, unexamined kind of way.

Having a fourteen year old whose math homework I wanted to understand, and help with if I could, made me go back to mathematics after an extremely long hiatus, and not without considerable trepidation. Much to my surprise I found out that after a lapse of some thirty years things like the quadratic formula seemed rather transparently sensible --I wasn't sure quite how, but following a series of clearly articulated steps to find the solution to a math problem no longer evoked a feeling of literally physical anxiety, but instead seemed soothing and actually philosophically reassuring. I still can't calculate worth a damn, really, but I can understand, now, the attraction of mathematics aesthetically. There is something cooly urbane about the formalism of numbers, and I am beginning to suspect that my retreating into books about science as a form of recreation, which was a habit I developed very early in life, stemmed from a sense, even on the low rent linguistic fringes of the actual math that is the real natural language of science, that that stately formalism was there.

Thus, ironically, I got interested in Gödel's Incompleteness Theorem again, and after poking around the offerings on Amazon, bought a couple of e-books to read on the subject, one of which has been providing me not only with a lot of sweat inducing mental exercise but also a realization that Gödel's work tends to get shoehorned into a lot of philosophical discourse where it isn't a particularly good fit. The book is called Gödel's Theorem: An Incomplete Guide to its Use and Misuse, and while it is tough sledding at first (it contains sentences like, "Even if we have no idea whether or not S is consistent, we can prove the hypothetical statement, 'if S is consistent, the consistency of S is unprovable in S" which at first or even tenth reading are clear as mud) it does gradually put together the pieces of Gödel's Incompleteness Theorem in a way that makes both its structure and even the extent of the range of its meaning clear to a non-specialist reader. At least, to this non-specialist reader, after circling around it for thirty-plus years like a nervous fish around a shiny lure.

The Incompleteness Theorems, at least as far as I can summarize them (which is itself doomed to incompleteness --his original paper presented forty six preliminary definitions and several additional preliminary theorems before coming to the point) are as follows:

1. In any formal system S it is possible to make statements that can neither be proved nor disproved in S

2. For any formal system S, the consistency of S cannot be proved in S.

I am, as I mentioned, leaving out a lot --for instance, the stipulation that S must be a "formal system in which a certain amount of arithmetic can be carried out." The specificity of the theorems, though, is what both sets limits on what they themselves set limits on, and what gives them their beauty. To quote An Incomplete Guide:

"It is often said that Gödel demonstrated that there are truths that cannot be proved. This is incorrect, for there is nothing in the incompleteness theorem that tells us what might be meant by 'cannot be proved' in an absolute sense. 'Unprovable' in the context of the incompleteness theorem, means unprovable in some particular formal system."

Gödel rather famously found misunderstandings and minsinterpretations of his work irritating and he took particularly scathing exception to Wittgenstein's dismissal of the theorems as "trickery" (kunststücken) and his claim that the theorems could simply be bypassed; Gödel's response was (and he took a swipe at Bertrand Russel while he was at it):

"Russell evidently misinterprets my result; however, he does so in a very interesting manner. In contradistinction Wittgenstein . . . advances a completely trivial and uninteresting misinterpretation."

If persons of Russell's and Wittgenstein's apparent intelligence and lifelong engagement with the problems Gödel grappled with are capable of finding themselves vulnerable to such rough handling, maybe we can find our own difficulties in understanding his work forgiveable. For me it is just a pleasure --a reassuring pleasure --to find that there is, after all, in Gödel's work the same sort of exactness and splendidly beautiful formal specificity that I found reassuring about science in the first place as a kid . . . and to come a little closer to understanding it on its own terms. It's reassuring to find oneself able to learn, as one gets older. And I find myself delighted to have just a little taste of the same feeling expressed by a much finer mind than my own, that of Paul Erdös:

"I fell in love with numbers at a young age. They were my friends. I could depend on them to always be there and to always behave in the same way."

Perhaps that's exactly the reason I found mathematics so much more congenial the second time around, when life, as middle age looms, seems an increasingly dark business. Even if I'm still barred from citizenship in the metropolis of numbers, it's nice, in a violent and uncertain world, to know it's there.

PS. Erdös had a sense of humor, apparently. He once remarked, "The first sign of senility is that a man forgets his theorems. The second is that he forgets to zip up. The third is that he forgets to zip down."

PPS. One of the most fun things about number theory is how simple the formulations of some of its hardest unsolved problems are. Witness, O Best Beloved, the Collatz Conjecture. It says simply this: take any natural number n. If it is odd, multiply it by 3 and add 1 (n3+1) and if it is even, divide by two. Take the result, and apply the procedure again. No matter what natural number you start with, you will always eventually reach 1 (and, the last three numbers of the sequence are always 4,2,1.) Despite its simplicity, the Collatz Conjecture, proposed by Lothar Collatz in 1937, remains unproven, and no less an eminence than Paul Erdös declared, "Mathematics is not yet ready for such problems." But, you know, knock yourself out.

A Prescient Quote

Two of the most interesting books that I've read in the last few months are Dulles' The Craft of Intelligence, which is on the subject of intelligence gathering and espionage (and which strikes me as something that should be part of any politically engaged citizen's required reading, as the practice of intelligence is such an important part of the formation of public policy) and Bertrand Russel's prescient book length essay from 1922, The Problem of China.

I'd like to write a bit more about both, but here's a quote from the latter:

"Chinese problems, even if they affect no one outside China, would be of vast importance, since the Chinese are estimated to constitute about a quarter of the human race. In fact, however, all the world will be vitally affected by the development of Chinese affairs, which may well prove a decisive factor, for good or evil, during the next two centuries"