Physicist Amok

(I’m posting a lot of things that fell through the cracks, beginning with this. )

CERN had an open day for the Large Hadron Collider before they turned it on. A group of us, biologists all except for me, headed out bright and early on Sunday morning from Lausanne to see the great machine, along with 15,000 other people.

The primary attractions were of course the detectors and a tour of the tunnels, but by the time we arrived at the Meyrin site at about 11:00, there was at least a four hour wait to get a ticket, assuming there were any tickets left at that point. This didn’t stop us: CERN had arranged many other attractions. There were demos of superconductivity and superfluidity, the requisite freezing of things in liquid nitrogen and shattering them for the children, and a display of artwork inspired by the LHC. I didn’t see any of this.

I dragged the unfortunate biologists who accompanied me to the magnet factory, to the magnet testing center, and to the prototype of the linear collider that will succeed LHC. They were good sports, even as I quizzed them on the discoveries of the famous physicists whose names the streets bear.

One thing that astonished them was the amount of prefabricated construction. The buildings aren’t pretty. I explained that this is a working lab: the buildings have to go up fast, and if you need a hole in the wall, you can’t wait for approval. You just grab a drill. Under these conditions, prefab is the best option.

CERN put an enormous amount of effort into this open day. The magnet factory had magnets in various stages of construction set up throughout the room, and the engineers of the facility giving tours in English, French, and German. We were lucky enough to get a tour by one of the head engineers of the division, who gave us a wonderfully detailed description of the construction process.

In any circular accelerator, you have to bend the beam, accomplished with magnetic dipoles, and you have to focus it, using quadrupoles. The LHC ring consists of a series of 50m long dipoles with smaller quadrupoles of 6m interspersed. Protons traverse narrow tubes through the length of these magnets. The magnets look almost straight, but the accelerator is a circle. They must be curved. But if you do the calculation for an accelerator 27km in diameter, a proton only has to shift 7mm to the side in a 50m tube.

Actually, the quadrupoles are straight. The dipoles are ever so slightly curved: the physicists insisted that the beam could deviate no more than 1mm, not 7mm, from the center of its containing tube all the way along the accelerator. Our guide recounted a scene anyone who has dealt with physicists will find familiar:

“We need 1mm precision the whole way.”

“Impossible.”

“1mm.”

“Alright, it’s possible, but it will be enormously expensive.”

“1mm.”

To curve them, they string the plates that form the magnets on the beam tube, put the whole thing in an enormous press, forcefully bend it, then weld it in that shape.

How do they know they have met their required precision? They transfer the magnet to a sealed room where they use a laser/reflector system to measure the geometry to a fraction of a millimeter precision.

Once it has passed that test, the magnet is transferred to the testing facility, which we also visited. Here they seal the magnet into its insulating jacket, insert the tubes that carry liquid helium to cool the coils of the magnet, and check that it’s air tight.

The coils are superconducting. This is one of the most important facts about LHC: it’s what makes the machine possible. A superconducting wire can carry seven hundred times the current of a copper wire of the same cross section. A comparable magnet made with superconducting wire is 25 times smaller than its copper counterpart. LHC’s coils are a few cm across. In copper they would be almost a meter. In the tight spaces of LHC’s underground tunnels, this is a vital concern.

The superconductors carry a price though: NbTi, the only one commercially viable when LHC’s development began, isn’t superconducting above a couple degrees above absolute zero. The only practical coolant at these temperatures is liquid helium. Making and distributing that much liquid helium demands cryogen facilities as expansive as the magnets themselves.

The test facility has a direct link to the tunnels. When a magnet is declared complete, it is lowered 100m to the tunnels and slowly, carefully dragged to its final position. The pit was closed to prevent anyone falling in it, but they had a movie of the magnets being hauled at 2km/h through the tunnels, with a selection of charmingly incongruous background music along the lines of ‘Carmina Burana’ or the closing march from ‘Star Wars.’

All of this occupied our afternoon, after we had eaten lunch at a nearby Indian restaurant, and half our party (including a nine and ten year old boy) had departed. Before lunch was the hilight of the day: CLIC, the Compact Linear Collider, or rather its prototype. LHC smashes protons together. Protons are heavy, which makes it easy to reach high energies, but they consist of three particles. Making sense what happened when two protons, six particles, smashing into each other is difficult. LHC gets us to high energies to see what’s there. Then we need a collider that uses truly elementary particles — in this case electrons and positrons.

The day of circular electron collider is over. Electron radiate their energy as X-rays when dragged in a circle, and it swiftly becomes impractical to push energy in faster than it radiates. Modern facilities using electrons are straight, but unlike in circular accelerators where you can increase the energy just a bit with every circuit, all the energy must be given in one pass. As the energy grows, the distance you need to do this gets longer and longer.

CERN’s cost constraints dictate an accelerator no longer than 50km, but you can’t get close to the target energy of 3TeV in this distance. CLIC’s designers have found an incredibly clever solution.

Instead of accelerating one electron to 3 TeV, accelerate a thousand in a bunch to 3 GeV, which is perfectly possible in a reasonably sized linear collider. How does this get us closer to 3 TeV? It’s only the energy of individual particles that count, not the combined energy of all of them.

Someone person figured out how to build a device, two specially shaped metal chambers connected by a mass of fiber optic cable, that saps 96% of the energy from those thousand electrons as they fly into one chamber, and transfers it all to one electron just entering the other chamber. That single electron goes flying out at the required 3 TeV. The technical difficulties are enormous, but suddenly a sub-50km, 3 TeV collider seems possible.

It was a lovely day. My biological colleagues learned something about smashing very small things, and I relived my childhood dreams of building particle accelerators. And I bought a t-shirt with the Lagrangian of the standard model on the front.

I found myself in need of a rough form for the -decay spectrum, so I went and fetched Fermi’s Nuclear Physics from the library. I thought I would share a passage which suddenly made a lot of things go click for me:

According to the relativistic theory of the electron, an electron has energy . This equation permits negative energy values.

In Dirac’s theory, practically all negative states are filled at all points in space. A vacuum is then a sea of electrons in negative energy states. The presence of this charge is not observed because it is uniformly distributed.

A photon of sufficiently high energy may lift an electron from a negative energy state. The energy threshold for the photon is , since for a free electron there are no states between and . Physically, this means that the photon must supply enough energy to create two particles of mass . Momentum must be conserved and this requires either that the negative energy electron be near a nuclear or an electron, i.e., not free, or that two photons coming from different directions coalesce and lift an electron from a negative energy state. If the electron is near a nucleus it may occupy discrete states just below . These are within a few eV of 510,000eV. Strictly, then, the threshold for pair formation near a nucleus is . This is of no importance because binding energy and because transitions from negative energy states to the discrete part of the spectrum are improbable and not yet observed.

I’ll get around to quantum mechanics eventually. Bear with me.

Biology is autonomous from physics. Any change to quantum mechanics will have at most cosmetic implications for biology. Quantum mechanics contributes nothing more than the existence of atoms and molecules, which are necessary for the lossless transmission of information. However, anything that replaces present day quantum mechanics must also predict atoms and molecules. The interactions between the two subjects a minimized because their interface is pinned by experiment.

Within physics, thermodynamics, fluid mechanics, elasticity, and the other macroscopic theories bear the same relation to quantum mechanics. The interfaces between the subjects are experimentally pinned.

A similar pattern appears within biology. Population genetics is built on molecular biology, but their interface is pinned by the existence of genes. We can replace our understanding of an allele’s molecular character, but that allele’s propagation in a population isn’t going to dramatically change.

This pinning is a form of damage control. All fields of science depend on other fields to be able to bootstrap themselves. The only way to keep the structure from falling to shreds is to pin the interfaces. A particle physicist uses macroscopic equipment, which experimentally obeys classical mechanics and electromagnetism. If the relation between his equipment and what he studies weren’t experimentally fixed in the intervening scales, his experiments would be impossible.

It is worth keeping your field as self contained as possible. Black boxes that reach into the heart of entirely different fields are a recipe for disaster.

This is why I dislike the Copenhagen interpretation of quantum mechanics. It posits an observer, whose observation collapses the wave function to an eigenstate of the observation in question. In so doing, it reaches directly to the heart of neuroscience, and builds quantum mechanics on the hardest, most central questions of an even larger area of science.

If the neuroscientists come up with the answer that consciousness isn’t anything special, just a pattern of spikes in neurons, then we have an insoluble problem. Further, there isn’t likely to be a physically robust structure of these firings which is consciousness, so what’s to stop other random patterns of particles from observing and collapsing wave functions? These difficulties are so great, that any interpretation — that is, a connection of the undisputed mathematical structure to reality — which is properly pinned at its boundaries are immediately preferable.

Yet most physicists aren’t willing to accept a new interpretation which requires conceptual gimmicks. Visualizations are tools with local use, not integral parts of theories. Since Heisenberg, we want our theories only to relate observable quantities, not enforce a particular picture. This was the great downfall of the Bohm-de Broglie pilot wave mechanics.

Thankfully, there is an interpretation which is both properly pinned and satisfies the Heisenberg aesthetic. There’s a beautifully written, absolutely simple book on it (Consistent Quantum Mechanics by Robert Griffiths). The book is available for free online.

Physics Musings points to a Physics Today article about common misconceptions of quantum mechanics students. This is a topic dear to my heart, as I hope someday to teach the subject myself.

I have a lot of ideas about what to include and how to present it, but I’ll save them for another time. My principal complaint is that there’s not enough relation to reality. Quantum mechanics is fundamentally about what happens when you go into a laboratory and start messing with stuff (said the theorist).

Most quantum mechanics books today are watered down versions of Schiff’s classic text. A few have departed from that path, notably Feynman (volume 3 of the Lectures), Schwinger (a fascinating, if idiosyncratic, book), and Sakurai (insert obligatory gripe over the scattering chapter he didn’t write here).

Let us remember the origin of Schiff. It was based on Oppenheimer’s lectures on quantum mechanics, which were given to graduate students who needed the theory in their work. The experimental motivation for the abstract mathematics was obvious: it was why they were bothering in the first place.

The situation has changed. Now this approach is being used for undergraduates with little experimental background, who have not already mastered the classical eigenfunction techniques in electromagnetism or the Hamiltonian formalism that motivated Schrodinger’s wave mechanics