I keep hearing that one shouldn’t, so soon afterwards, speak of the implications of the Virginia Tech tragedy for certain political positions. But shouldn’t we be outraged by this horrific event? And if there’s an elephant in the room, why should we ignore it?

Now, I have no problem with hunting, and don’t want to ban guns entirely. But there is plenty to agree with in Elayne Boosler’s furious rant over at The Huffington Post. You don’t have to buy it all - I don’t - to feel that there is something right about this kind of outrage. Why isn’t the mainstream media, instead of repeating the same grisly facts over and over, exploring the implications of

The number of children under the age of 17 shot by guns in America every year is greater than the gun-related deaths of children in all the industrialized nations of the world COMBINED.

and

3,300 Americans have died in Iraq and Afghanistan in the last four years. 120,000 Americans have been shot to death in America in the last four years. Where is the outrage? If we can elect a new congress based on its commitment to end the war overseas, we can elect a congress committed to end the war here at home. End both wars.

Boosler ties her piece up by anticipating the associated hypocrisy we might see when the President responds to today’s Supreme Court decision that refuses women a medical procedure even in the case that it may be life-saving.

“Today’s decision affirms that the Constitution does not stand in the way of the people’s representatives enacting laws reflecting the compassion and humanity of America. This affirms the progress my administration has made to defend the “sanctity of life”.

Thanks for the outrage Ms. Boosler - you’re not alone.

SEED has come out with it’s latest Cribsheet, this one on String Theory. The Cribsheets are very handy one-page summaries of some fascinating science issue. The latest one is pretty good; it only refers glancingly to the anthropic principle, which is a much more accurate view of the state of discussion about string theory than one would get by reading blogs. Clifford was apparently a consultant. You can see it in gif or as a pdf.

Previous Cribsheets include:

1. Stem Cells
2. Climate Change
3. Avian Flu
4. Hybrid Cars
5. Nuclear Power
6. Hurricanes
7. Extinction
8. The Elements

With the latest one, we seem finally to have escaped the tyrrany of the mesoscopic. I predict that the next one will involve cosmology or astrophysics. Unless they are going to count The Elements, whose origin does after all take place in the sky. Perhaps some day we will get quantum mechanics.

It’s still National Poetry Month! Today we transgress the “National” by including a Canadian; this is by Sonnet L’Abbé.

The vocabulary of desire
is incomplete, a word is missing.

My tongue searches
for your body in language
and finds you in every word.

I thought this was a small thing, a stone
in the palm I could offer you,
my body in darkness a simple gift
casual as a pebble.
As if touching were easier than speaking,
as if this poem did not prove you
inside me already, as if asking
meant I still had the power to invite.

But you make me aware of breathing,
of the awesome fact
that each particle of air
has been taken at least once
into every lung.
Suddenly I have no boundaries
and to kiss you seems to drink up the sky,
slip it from my tongue into your mouth.

Our bodies just our hearts’ clothing,
and I came to you so shabbily dressed.
Maybe I thought that for one night
I could wear your beauty through closeness
and for a few hours believe myself
splendidly arrayed.

But you know all the lyrics
to rejection.
My body, your exquisite voice’s
shattered glass.

And here’s another one: Theory My Natural Brown Ass.

John Edwards wants to simplify the way some people pay taxes. In particular, he has noticed that about 50 million Americans have very simple tax returns — so simple, that the IRS already has all of the necessary information to just go ahead and calculate their taxes for them. Obviously this won’t work for self-employed people or anyone with an interesting set of deductions, but there are plenty of people not in that category.

So Edwards is proposing Form 1, a short form that the IRS will fill out and send to those who qualify, so that they can look over it and make sure it all seems correct. (Via Neil the Ethical Werewolf.) If so, just sign and return it and you’re done. Not only will it greatly decrease the burden both on taxpayers and the IRS, it will also benefit the millions of low-income workers who are eligible for the Earned Income Tax Credit but might not realize it.

It is, in other words, one of the most obviously good ideas to come out of a Presidential candidate in a long time. But wouldn’t you know it, readers of the National Review don’t agree.

Basically they have a single objection, phrased in multiple ways: if we decrease the pain involved in paying taxes, people won’t mind as much. And then they won’t agitate as vociferously for tax cuts. That’s basically it. Some get overly enthusiastic and start griping about employer withholding more generally, suggesting that every taxpayer should be forced to save up money and file quarterly tax reports. That would truly drive home the pain.

And all I want to say is: I really hope this becomes a major talking point among Republican candidates. More pain at tax time! I’m sure voters will appreciate the shrewd calculation underlying this enlightened policy. And as a benefit, since Republican voters are unenthusiastic about the current Presidential field and have already begun to long for a novelty candidate to swoop in and shake up the race, this opens the door for the perfect nominee!

If the Terminator can become governor of California, I don’t see why Clubber Lang can’t run for President. The Mr. T Doctrine is as well-thought-out as what we currently have.

Once per year, I spend a morning visiting a local high school to discuss physics with a class of talented seniors. This is a program organized by a wonderful teacher - Ranald Bleakley - who I met through the Saturday Morning Physics program that I have run at Syracuse for the last five years.

Ranald spends the entire school year teaching physics to these students, covering the classic subjects - mechanics, electricity and magnetism, etc. - and trying to connect these ideas to frontier topics in modern physics. Because these are all bright, motivated and college-bound students, they generate a large number of questions, many of which Ranald handles. Nevertheless, a pile of unanswered questions inevitably accumulates, and it is my job to try to get through some of these during my visit.

Although I didn’t attend high school in the U.S., there are enough similarities to the British system that I always find it strangely nostalgic to walk the corridors again after all these years. There is a certain smell, and a certain atmosphere of restrained mayhem that one can just sense as soon as one walks through the doors.

The students in Ranald’s class are always a great deal of fun - smart and curious and easy to interact with after the first few minutes when they’re first getting used to speaking to me. So, what was the number one question they had? “We’ve heard a lot about this thing called string theory - what’s it all about?” It doesn’t matter where you go - people are talking about it!

I was able to give them a little review of the regimes of validity of General Relativity (GR) and Quantum Field Theory (QFT), talk about physical situations where both theories seem to be needed, and hence discuss the problems that their incompatibilities present. I then sketched out what string theory is, and why we think it is attractive - namely that it seems to provide a consistent theory of quantum gravity. This discussion also allowed me to make some useful distinctions between Theories (with a capital “T”, if you like) such as GR and QFT, which have made numerous verified predictions, and theories (with a small “t”), such as string theory, which many scientists find extremely attractive, for good reasons, but which have yet to confront experiment.

A second question was a standard one I get in public lectures, although these students seemed to have more background than the general public, - “We know that the universe is expanding; do we know if it is infinite in size or not, and whether it will expand forever or eventually recollapse?”

This is an interesting question, to which cosmologists for a while often gave a set of technically wrong answers. What we think we measure, through combining results from a number of experiments such as the WMAP satellite and the Hubble Space Telescope, is the local spatial geometry of the universe (the geometry of spatial slices). This is determined by the local energy density in the universe.

If the matter in the universe consisted only of regular matter (dark matter, baryons, and radiation) for all time, then one could indeed infer the ultimate destiny of the universe from such measurements, since positive spatial curvature implies more than a critical density and hence ultimate collapse, while flat (which seems to be what we measure) or negatively curved spatial geometries imply eternal expansion. However, the possibility of a cosmological constant (which may be causing cosmic acceleration) ruins this connection, meaning that one could, in fact, live in a positively curved universe that expands forever.

Furthermore, our measurements of the local spatial geometry tell us nothing about the topology of the universe - i.e. its connectedness, and whether it is finite. For example, there actually exist so-called compact hyperbolic manifolds, which are homogeneous and everywhere negatively curved, but in fact are of finite volume. One can construct these in analogous ways to making a torus from an infinite flat plane (and this means also that if the universe is flat, we also don’t know if it is finite or infinite).

One can, of course, perform measurements to see if the universe is finite on a given scale (because if so there would be correlations in light coming from beyond that distance on very different parts of the sky. The furthest away light we have is the CMB, and current tests have not revealed the telltale signs of cosmic topology in it. Therefore, our best knowledge of the universe is that, even if it were negatively curved, it could be finite or infinite, but if finite, then only on so-far unobserved scales.

Later questions included

• “I understand that when some stars die they end up as neutron stars, and others end up as black holes. What’s the difference?” This allowed me to discuss some quantum mechanics - the Pauli exclusion principle and degeneracy pressure.
• “How do astronomers measure distances?” This gave me a chance to talk about the cosmological distance ladder, parallax, cepheid variables, type Ia supernovae, and much more.
• “Why do you spend your time studying these things?”

This last question led into a discussion of what an academic’s life is like, and then a chat about what kinds of other careers open up to you when you have a physics degree, with the associated critical thinking and problem solving skills.

This type of public outreach is extremely rewarding and requires basically no preparation. Most cosmologists and particle physicists can provide coherent answers to the questions above straight off the tops of their heads. The students seem to enjoy the time, get their questions answered, and provide good donuts by way of thanks.

And another thing - it’s worth commenting on the makeup of the class this year. I counted around fifteen students, only three of whom were men. I don’t know whether this was anomalous, and I certainly don’t want boys to be discouraged from taking physics, but it was wonderful to see so many young women enthusiastic about science.

The annual April meeting of the American Physical Society is currently underway. This meeting brings together thousands of physicists, from all branches except condensed matter. The condensed matter types have their own meeting (in March), which dwarfs ours. For the next few days, there will be a flurry of press releases originating in Jacksonville, Florida. Although I have been missing the action down south, there is one press release which was conspicuous in its absence. A measurement of frame dragging was not announced by the Gravity Probe B satellite (affectionately known as GP-B), as originally planned. Instead, NASA issued an Interim Report summarizing the state of the data analysis thus far. The press release is here.

GP-B is probably the oldest space experiment alive. The mission was first proposed in 1959, and funding began in 1964 (Francis Everitt, the Principal Investigator, has been involved from the very beginning). The science goal is eminently worthwhile: to measure the Lense-Thirring precession (also known as frame dragging) due to the Earth’s rotation. In general relativity a rotating mass will drag space along with it, leading to effects which would be completely absent in Newtonian gravity. For example, a gyroscope in polar orbit about the Earth will show an extra precession due to the Earth’s one-revolution-per-day spin. One of the problems with general relativity is that gravity is much too weak. Every time we come up with some cool effect (gravitational waves, frame dragging, time dilation), it turns out that it’s almost impossible to see the effect. Frame dragging is no exception. If we were near a rapidly rotating black hole, frame dragging would jump out at us: a gyroscope would wobble all over the place. But the Earth’s frame dragging, for an object in orbit 650 km up, adds up to a miniscule 39 milli-arcseconds per year (mas/yr). For some sense of how small this is, consider your average visible, bright star. For generations we’ve considered the stars to be fixed on the sky. As we now know, this isn’t entirely accurate, and the stars do indeed move. The record-holder is Barnard’s star, which moves by 10,000 mas/yr. Typical stars have proper motions closer to 100 mas/yr. In comparison to the effects of frame-dragging, the “fixed” stars are moving all over the place, which emphasizes the difficulty of measurement. GP-B monitors the orientation of the spin axis relative to a particular star (IM Pegasi). This star was specifically chosen because it is bright in both optical and radio, allowing its motion (against a background, fixed frame of distant quasars) to be exquisitely well-measured using radio telescopes (through Very Long Baseline Interferometry, incorporating data from the VLA). (If you’re wondering about GP-A, it was launched in 1976. It carried an atomic clock, and directly measured the time dilation due to the gravitational redshift, confirming relativity at the 0.01% level.)

If the only precession came from frame-dragging, the experiment might be somewhat more straightforward. The problem is that there are other physical effects which cause precession, and which completely overwhelm the signal of interest. The Earth is not a perfect sphere; it is squashed, being 43 km fatter around the equator than around the poles. This provides a convenient handle upon which gravitational tidal forces of the Moon and Sun pull, leading to a precession of 50,000 mas/year. There is also geodetic precession, which is a general-relativistic effect due to the curvature of spacetime about the Earth (and which would be present even if the Earth were not rotating). Geodetic precession is also comparatively large (6,600 mas/year), and is by now well established. It will need to be understood to an unprecedented degree before a measurement of frame-dragging is possible. The two main science goals of GP-B are the precision determination of both geodetic precession and frame dragging. Yesterday they announced a measurement of the former to 1%. A pretty picture from the GP-B website summarizes:

One major development in the intervening 40 years since GP-B was initially funded has been the use of the LAGEOS satellite system to independently measure frame dragging. These satellites were designed to be orbiting “test particles”, to enable geodynamic measurements of the Earth. They are nicely round and reasonably uniform, completely passive, and each is covered with 426 cube-corner retroreflectors. A retroreflector is just a box with mirrors on the inside walls, and one wall missing: a light ray coming in through the missing wall is bounced back in the direction it came from. (Commonly found in reflectors along highways, or reflecting tape in clothing/bags/shoes.) Apollo astronauts left some large retro-reflectors on the moon. One can shoot laser pulses at these, detect the returning photons, and precisely measure the position of the Moon (to better than a cm!). These lunar-ranging experiments turn out to be an important constraint on alternative theories of gravity. Similarly, the positions of the LAGEOS satellites can be precisely monitored, and the orbital evolution of two of the satellites can be used to accurately measure the precession. In this case, rather than using the spin of the satellite (or a gyroscope within it) as a reference, one uses the orbital plane of the satellite motion. [In the interest of full disclosure, it should be mentioned that my first refereed paper was an analysis of the effect of the Earth’s gravitational and magnetic field on the spin of the LAGEOS satellites. There are a number of important systematics which depend crucially on understanding this spin.] To use the LAGEOS satellites to measure frame dragging, the full gravitational field of the Earth needs to be accounted for (in particular, the mass multipoles due to the non-sphericitiy of the Earth). As it happens, the GRACE and CHAMP experiments have recently provided unprecedented maps of the Earth’s field. Incorporating these results into an analysis of the orbits of LAGEOS, a measurement of the Earth’s frame dragging was accomplished by Ciufolini and collaborators, at the level of ~10%. (Due to subtleties in the analysis there is some debate as to the ultimate precision of the measurement; but a confirmation of frame dragging is generally agreed upon.)

When GP-B was first proposed, measuring frame dragging seemed like a great idea. However, as the decades went by and GP-B was still far from launch, and as the price for the mission broke the $0.5 x 10⁹ barrier, enthusiasm for the experiment started to wane. In addition, general relativity has been tested in many independent ways at this point, and LAGEOS has confirmed that frame dragging is consistent with general relativity at the ~10% level. This is not to say that it’s not worth precisely measuring frame dragging; it’s just perhaps not the first thing on our list of worries. A number of review panels have been convened over the decades to evaluate the mission’s fate, and each time the mission has squeaked by. A study of the politics behind this mission would be quite interesting. My principal worry about GP-B is that there are essentially two possible results: either GP-B confirms general relativity (in which case everyone says great, and continues to do what they were doing), or GP-B claims a result inconsistent with relativity (in which case everybody questions the result). This is an extremely difficult experiment, and there are many ways for things to go wrong. And, for better or worse, nothing like GP-B will be done again in the near future, and so it will be highly non-trivial to independently test its results.

After many difficult years, the GP-B satellite was finally launched on April 20, 2004. The satellite is an amazing feat of engineering. This is truly a precision science experiment, but one that is being flown in the harsh environment of space rather than being lovingly tended to in a lab in the basement. The gyroscopes are superconducting spheres; the most perfectly engineered spheres ever produced (equivalent to a spherical Earth with no mountain (or valley) higher (or deeper) than 2.4 meters). The spins of the four independent gyroscopes, cooled to 1.8 Kelvin, were monitored for over a year. Although the satellite is still in orbit, at this point the liquid helium which cooled the gyroscopes has boiled away (by design), and the satellite is no longer taking precision data. At this point it remains to analyze the data sent from the satellite, and announce whether or not general relativity is correct.

Originally, yesterday was going to be the big press release circus where NASA announced the results of the mission. But the analysis has run into a number of snags. Even though the gyroscopes are very close to perfect spheres, tiny imperfections cause electrostatic patches on the surface of the spheres (and housing). This breaks the spherical symmetry, and causes a polhode motion. Although this effect was anticipated, it was thought that it would remain constant through the life of the mission. This has not turned out to be the case, and the time variation needs to be understood and accounted for in the analysis. In addition, the surface electrostatic patches interact with the rest of the spacecraft, causing miniscule torques (which vary with the relative alignment of the entire spacecraft about the axis of rotation). Until these effects are well under control, a definitive measurement of frame dragging is impossible. Yesterday’s announcement was that the geodetic precession has been measured to better than 1%, and agrees with the predictions. Although this is indeed an important measurement, it is not what everyone has been waiting for.

After over four decades, it is not unreasonable for the GP-B team to ask for a little extra time to check and double-check their results. It is to their credit that they are being deliberate and meticulous in their analysis. The final results are to be announced this coming December, hopefully leading to yet another important observational test of general relativity. And a conclusion to one of the most technically ambitious experiments ever launched into space.

Things to gawk at on the internets:

• Remember the String Kings? Then you’ll love the Director’s Cut, brought to you by Steven Miller.
• Remember that the cell is like Tron? There’s a Director’s Cut of the Inner Life of a Cell video as well, with commentary and all that. (Thanks to many people for letting me know.)
• Construct a Heptadecagon with nought but compass and straightedge! That’s a seventeen-sided polygon, for those of you keeping score at home. Wikipedia shows you how.

Today at Fermilab, the MiniBooNE experiment announced to a packed auditorium their long-awaited results looking for neutrino oscillations. Below is a guest post from Dr. Heather Ray, a scientist at Los Alamos National Lab, who has been working on the experiment for several years. I have known Heather since she was a graduate student on the CDF experiment at Fermilab, when she was at the University of Michigan. To the right is a photo of her with her significant other, Ivan Furic.

MiniBooNE Neutrino Experiment Results

by Dr. Heather Ray, Los Alamos National Lab

Neutrinos, a fundamental particle of nature, are believed to oscillate, or change from one type to another. In the long list of experiments which have claimed an observation of neutrino oscillations, one stands apart : LSND. The LSND result doesn’t fit in with our picture of oscillations from other experiments, and as such is highly controversial. The MiniBooNE experiment was designed to explore the LSND result, to conclusively prove or disprove the claimed oscillations. MiniBooNE announced it’s first results today (April 11th, 2007). The illustrious rulers of the Cosmic Variance blog have asked me to write a bit about this result. So, let the amazing neutrino story begin!

In the Standard Model of physics there are three main categories of fundamental particles: quarks, leptons, and gauge bosons, or force carriers. The leptons are the electron, muon, and tau, as well as their partner neutrinos : ν_e, ν_μ, and ν_τ. Neutrinos in the Standard Model have no charge and are massless. Imagine for a minute that neutrinos do have mass. If they have mass then they are able to oscillate, or change type. Neutrinos have definitively been observed changing from one type into another, yet the Standard Model of physics says that neutrinos do not have mass. The simplest solution to this conundrum is to allow the neutrinos to have mass.

In more technical terms we say that the weak eigenstates ( ν_e, ν_μ, and ν_τ) are made up of a combination of mass eigenstates. For example, in a two-neutrino scenario, at the time of creation the muon neutrino is a combination of the two mass eigenstates :

|ν_μ(0)> = -sin θ |ν₁> + cos θ |ν₂>

where the probability for two-neutrino oscillations is given by :

P_osc = sin²(2θ) * sin²[ (1.27 * Δm² * L) / E ]

The probability has two terms which are constrained by the design of the experiment (L, the distance from the neutrino source to the detector, and E, the energy of the neutrino beam), and two terms which are fit for when performing a two-neutrino oscillation analysis (Δm² and sin²(2θ), where θ is the mixing angle between the two neutrino states and Δm²_ab = m²_a - m²_b).

Neutrino physicists illustrate the current status of neutrino oscillations using a two dimensional plot that is the function of the two fit parameters. Oscillation results from the solar and atmospheric sectors (the tiny red and blue dots) have been observed and confirmed by several experiments. The set of several independent measurements allows us to constrain the range of fit parameters for those oscillations. The LSND result, which spans the upper third of this plot, has a large allowed region in parameter space.

In the Standard Model there are only three neutrinos, all of which interact with matter. The Δm² is the mass squared difference between the two neutrino states. These three results represent three differences, or splittings, between the mass states. If the Standard Model of physics is correct and there are 3 and only 3 neutrinos, a summation law should exist : Δm²₁₃ = Δm²₁₂ + Δm²₂₃. You can see that even at LSND’s lowest allowed Δm² point the summation law does not hold.

If LSND’s observation is found to be a true fact of nature, the Standard Model of physics cannot fully accommodate/explain neutrino interactions! This “breaking” of the Standard Model is very exciting to physicists, and indicates there is new physics that we haven’t previously thought possible. Many things could be true - there could be new allowed interactions for neutrinos (Lorentz Violation, CP/CPT violation, the list goes on!), or there could be additional particles - sterile neutrinos, which don’t interact with other matter but only can been seen through mixing with other neutrinos.

To properly explore the LSND signal we need an experiment that has the same experimental constraints (L/E, from the oscillation probability formula), so that the entire allowed region of LSND can be explored. The follow-up experiment also should have more events (smaller statistical errors), and a different signal signature, backgrounds, and sources of systematic errors. This experiment is MiniBooNE.

MiniBooNE is located at Fermi National Accelerator Laboratory, in Batavia, IL. To produce our neutrino beam we start with an 8 GeV beam of protons from the Booster. The proton beam enters a magnetic focusing horn where it strikes a beryllium target. The interactions of the protons+Be produce positively and negatively charged mesons (pions and kaons). The positively charged mesons will decay to produce a neutrino beam, while the negatively charged mesons will decay to produce an anti-neutrino beam.

There are still a lot of mysteries surrounding the interactions of neutrinos. We don’t yet know if neutrinos mix with the same probability as anti-neutrinos. Therefore, the LSND result, which claims observation of anti-ν_μ → anti-ν_e oscillations, needs to be explored using both neutrinos and anti-neutrinos. For the first check of LSND we chose to focus the positively charged mesons, which means we’re looking for ν_μ → ν_e oscillations. This choice was solely dictated by physics : the proton + Be interactions produce far more positively charged mesons. This means the rate of collection for our neutrino sample is much higher than our rate of collection for an anti-neutrino sample. We chose to collect the quick data set first, and then proceed with analyzing that data while collecting the anti-neutrino data set.

The mesons decay in flight into the neutrino beam seen by the detector : K⁺ / π⁺ →μ⁺ + ν_μ, where the ν_μ comprise the neutrino beam seen at MiniBooNE. These mesons decay in flight in our vacuum decay region. Following the decay region is an absorber, put in place to stop any muons and undecayed mesons. The neutrino beam then travels through approximately 450 meters of earth before entering the MiniBooNE detector.

MiniBooNE is a 12.2 meter diameter sphere. The detector is filled with pure mineral oil and lined with photomultiplier tubes (PMTs). PMTs work like a reverse light bulb - instead of putting in electricity to produce light the PMTs collect light from neutrino interactions in our detector and output an electrical pulse. There are two regions of the MiniBooNE detector : an inner light-tight region and an optically isolated outer region known as the veto region, which aids in vetoing cosmic backgrounds.

Neutrinos interact with material in the detector. It’s the outcome of these interactions that we look for. These neutrino interactions in the MiniBooNE detector leave a distinct mark in the form of Cerenkov and scintillation light. Cerenkov light is produced when a charged particle moves through the detection medium with a velocity greater than the speed of light in the medium (v > c/n). This produces an electro-magnetic shock wave, similar to a sonic boom. The shock wave is conical and produces a ring of light which is detected by the PMTs. We can use Cerenkov light to measure the particle’s direction and to reconstruct the interaction vertex. This effect occurs immediately with the particle’s creation and is known as a prompt light signature.

Charged particles moving through the detector also may deposit energy in the medium, exciting the surrounding molecules. The de-excitation of these molecules produces scintillation light. This is an isotropic, delayed light source, and provides no information about the track direction. We can however use the PMT timing information to locate the point, or vertex, where the neutrino interaction occurred.

We can use the patterns of light seen in our PMTs to determine what type of neutrino interacted in our detector. In the charged-current quasi-elastic events, a neutrino interaction in the detector will produce the lepton partner of the neutrino. For example, an electron neutrino interaction will produce an electron, and a muon neutrino interaction will produce a muon. Electrons travel for only a very short time before their velocity falls below the Cerenkov threshold. They multiple scatter along the way, as well. This leaves a fuzzy Cerenkov ring in the detector. Muons tend to travel for a much longer distance. As they travel through the detector they lose energy, and the angle at which the Cerenkov light is being emitted shrinks. Muons also emit scintillation light. The signature of a muon in the detector isn’t one of a ring, as in the case of an electron. It is instead a filled in circle of light. Neutral pions decay into two photons, which then pair produce. The electrons from this pair production each create a ring in the detector.

MiniBooNE is performing a blind analysis. This means that we can either :

• see some of the information in all of the data : we can check the charge per PMT as a function of time, to verify our detector isn’t failing,
• see all of the information in some of the data : we are able to select data sets which will have no oscillation events present, if we assume maximal allowed oscillations from LSND. We can use these data sets to then tune and verify our Monte Carlo simulation.

but we can’t see all of the information in all of the data. Having access to all of the information in all of the data is unblinding. Prior to unblinding we had to have all components of the analysis completely fixed. We aren’t allowed to go back and change event selection cuts or error estimates once we unblind.

Our oscillation analysis can be boiled down to this simple algorithm : determine a set of event selection cuts which will isolate the electron neutrino events but remove the majority of all other events. There are a certain amount of electron neutrino events inherent in the beam, which come from kaon decays. There are also a small amount of other types of events (delta decays, pi0 events) which will pass the electron neutrino cuts, but which are not from true electron neutrino events. The sum of the estimated intrinsic electron neutrino events plus the fake events is the total number of events we expect to see, if no oscillations are present. We compare the number of events observed in data to the number expected, as a function of the reconstructed neutrino energy in these events. If we observe oscillations we should see an excess of data events over the expectation, whose shape will change as a function of the oscillation parameters.

This plot shows the MiniBooNE final sensitivity, compared to the prediction from our 2003 Run Plan. Curves are shown overlaid on the allowed LSND region.

This plot shows the final result from the likelihood analysis. Data points are the black dots. The expected event spectrum is shown in red, and is broken down into the intrinsic electron neutrino and fake event shapes in the green and blue.

We have two separate analyses that are used in the oscillation search : one which depends on likelihood variables, and one which depends on a boosted decision tree. These two analyses have a small overlap in event composition, and provide a good check of each other. We have complete confidence in our analysis if these two analyses find the same result. Before we unblinded our data we had to decide which of the two analyses we would call our primary analysis, for the purpose of quoting numbers in publications. We made this decision based on the expected sensitivity found using Monte Carlo. The sensitivity is the amount of parameter space allowed by the LSND result that we expect to be able to probe. Our sensitivity studies showed that with the likelihood analysis we were able to achieve a sensitivity which agrees quite well with the sensitivity MiniBooNE was designed for. This is something to be quite proud of! We also agreed that the final result quoted for the two neutrino oscillation search would be from 475 MeV to 3 GeV, based on the LSND best fit region.

MiniBooNE unblinded on Monday, March 26th, 2007. When we opened the box we found no evidence for an excess of events over the background prediction. The MiniBooNE neutrino data set agrees with the no neutrino oscillation hypothesis, in the range of reconstructed neutrino energy from 475 MeV to 3 GeV. The probability that MiniBooNE and LSND both are due to two-neutrino oscillations is only 2%. The likelihood and the boosting analyses also agree quite well in measured excess events.

I’m sure by now you’ve noticed that MiniBooNE observes an excess of events in the low energy region. We first saw this excess two weeks ago, when we unblinded. At that point we began working like madmen to determine what those events could possibly be. We’re rechecking our detailed understanding of various low energy background events: interactions in the dirt surrounding the detector, radiative delta decays, low energy neutral current events, you name it, we’re exploring it. Obviously, we don’t want to make any additional comments about this excess until we’re certain that we’ve performed all possible checks on our event predictions in that region. We’re hoping to have this excess mystery resolved in the next few months.

MiniBooNE’s neutrino oscillation analysis was the first of two analyses needed to conclusively explore the LSND result. An anti-neutrino oscillation analysis will also need to be performed. At MiniBooNE it would take many more years to accumulate the data set needed to perform this anti-neutrino analysis. Instead, I’m hoping that we can continue this exploration at the Spallation Neutron Source, at Oak Ridge Laboratory in TN. The SNS is designed to be a world-class neutron facility. One of the side-effects of the process which produces the neutrons is that you get an amazing neutrino beam for free! Funding permitting I’m hoping we can begin taking data at the SNS within 3 to 4 years. At the SNS we could perform neutrino and anti-neutrino measurements simultaneously (no need to switch the horn polarity!), look for oscillations, sterile neutrinos, and look for CP/CPT violation in the neutrino sector.

References

• S. Ahmed et al. [SNO Collaboration], Phys. Rev. Lett. 92, 181301 (2004), arXiv.org/nucl-ex/0309004
• G. Fogli et al., Phys. Rev. D 67, 093006 (2003), arXiv.org/hep-ph/0303064
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• http://www-boone.fnal.gov
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Each year, John Brockman’s Edge asks a collection of deep thinkers a profound question, and gives them a couple of hundred words to answer: The World Question Center. The question for 2005 was What Do You Believe Is True Even Though You Cannot Prove It? Plenty of entertaining answers, offered by people like Bruce Sterling, Ray Kurzweil, Lenny Susskind, Philip Anderson, Alison Gopnik, Paul Steinhardt, Maria Spiropulu, Simon Baron-Cohen, Alex Vilenkin, Martin Rees, Esther Dyson, Margaret Wertheim, Daniel Dennett, and a bunch more. They’ve even been collected into a book for your convenient perusal. Happily, these questions are more or less timeless, so nobody should be upset that I’m a couple of years late in offering my wisdom on this pressing issue.

Most of the participants were polite enough to play along and answer the question in the spirit in which it was asked, although their answers often came down to “I believe the thing I’m working on right now will turn out to be correct and interesting.” But to me, there was a perfectly obvious response that almost nobody gave, although Janna Levin and Seth Lloyd came pretty close. Namely: there isn’t anything that I believe that I can prove, aside from a limited set of ultimately sterile logical tautologies. Not that there’s anything wrong with tautologies; they include, for example, all of mathematics. But they describe necessary truths; given the axioms, the conclusions follow, and we can’t imagine it being any other way. The more interesting truths, it seems to me, are the contingent ones, the features of our world that didn’t have to be that way. And I can’t prove any of them.

The very phrasing of the question, and the way most of the participants answered it, irks me a bit, as it seems to buy into a very wrong way of thinking about science and understanding: the idea that true and reliable knowledge derives from rigorous proof, and anything less than that is dangerously uncertain. But the reality couldn’t be more different. I can’t prove that the Sun will rise tomorrow, that radioactive decays obey an exponential probability law, or that the Earth is more than 6,000 years old. But I’m as sure as I am about any empirical statement that these are true. And, most importantly, there’s nothing incomplete or unsatisfying about that. It’s the basic way in which we understand the world.

Here is a mathematical theorem: There is no largest prime number. And here is a proof:

Consider the list of all primes, p_i, starting with p₁ = 2. Suppose that there is a largest prime, p_*. Then there are only a finite number of primes. Now consider the number X that we obtain by multiplying together all of the primes p_i (exactly once each) from 2 to p_* and adding 1 to the result. Then X is clearly larger than any of the primes p_i. But it is not divisible by any of them, since dividing by any of them yields a remainder 1. Therefore X, since it has no prime factors, is prime. We have thus constructed a prime larger than p_*, which is a contradiction. Therefore there is no largest prime.

Here is a scientific belief: General relativity accurately describes gravity within the solar system. And here is the argument for it:

GR incorporates both the relativity of locally inertial frames and the principle of equivalence, both of which have been tested to many decimal places. Einstein’s equation is the simplest possible non-trivial dynamical equation for the curvature of spacetime. GR explained a pre-existing anomaly — the precession of Mercury — and made several new predictions, from the deflection of light to gravitational redshift and time delay, which have successfully been measured. Higher-precision tests from satellites continue to constrain any possible deviations from GR. Without taking GR effects into account, the Global Positioning System would rapidly go out of whack, and by including GR it works like a charm. All of the known alternatives are more complicated than GR, or introduce new free parameters that must be finely-tuned to agree with experiment. Furthermore, we can start from the idea of massless spin-two gravitons coupled to energy and momentum, and show that the nonlinear completion of such a theory leads to Einstein’s equation. Although the theory is not successfully incorporated into a quantum-mechanical framework, quantum effects are expected to be unobservably small in present-day experiments. In particular, higher-order corrections to Einstein’s equation should naturally be suppressed by powers of the Planck scale.

You see the difference, I hope. The mathematical proof is airtight; it’s just a matter of following the rules of logic. It is impossible for us to conceive of a world in which we grant the underlying assumptions, and yet the conclusion doesn’t hold.

The argument in favor of believing general relativity — a scientific one, not a mathematical one — is of an utterly different character. It’s all about hypothesis testing, and accumulating better and better pieces of evidence. We throw an hypothesis out there — gravity is the curvature of spacetime, governed by Einstein’s equation — and then we try to test it or shoot it down, while simultaneously searching for alternative hypotheses. If the tests get better and better, and the search for alternatives doesn’t turn up any reasonable competitors, we gradually come to the conclusion that the hypothesis is “right.” There is no sharp bright line that we cross, at which the idea goes from being “just a theory” to being “proven correct.” Rather, maintaining skepticism about the theory goes from being “prudent caution” to being “crackpottery.”

It is a intrinsic part of this process that the conclusion didn’t have to turn out that way, in any a priori sense. I could certainly imagine a world in which some more complicated theory like Brans-Dicke was the empirically correct theory of gravity, or perhaps even one in which Newtonian gravity was correct. Deciding between the alternatives is not a matter of proving or disproving; its a matter of accumulating evidence past the point where doubt is reasonable.

Furthermore, even when we do believe the conclusion beyond any reasonable doubt, we still understand that it’s an approximation, likely (or certain) to break down somewhere. There could very well be some very weakly-coupled field that we haven’t yet detected, that acts to slightly alter the true behavior of gravity from what Einstein predicted. And there is certainly something going on when we get down to quantum scales; nobody believes that GR is really the final word on gravity. But none of that changes the essential truth that GR is “right” in a certain well-defined regime. When we do hit upon an even better understanding, the current one will be understood as a limiting case of the more comprehensive picture.

“Proof” has an interesting and useful meaning, in the context of logical demonstration. But it only gives us access to an infinitesimal fraction of the things we can reasonably believe. Philosophers have gone over this ground pretty thoroughly, and arrived at a sensible solution. The young Wittgenstein would not admit to Bertrand Russell that there was not a rhinocerous in the room, because he couldn’t be absolutely sure (in the sense of logical proof) that his senses weren’t tricking him. But the later Wittgenstein understood that taking such a purist stance renders the notion of “to know” (or “to believe”) completely useless. If logical proof were required, we would only believe logical truths — and even then the proofs might contain errors. But in the real world it makes perfect sense to believe much more than that. So we take “I believe x” to mean, not “I can prove x is the case,” but “it would be unreasonable to doubt x.”

The search for certainty in empirical knowledge is a chimera. I could always be a brain in a vat, or teased by an evil demon, or simply an AI program running on somebody else’s computer — fed consistently misleading “sense data” that led me to incorrect conclusions about the true nature of reality. Or, to put a more modern spin on things, I could be a one of Boltzmann’s Brains — a thermal fluctuation, born spontaneously out of a thermal bath with convincing (but thoroughly incorrect) memories of the past. But — here is the punchline — it makes no sense to act as if any of those is the case. By “makes no sense” we don’t mean “can’t possibly be true,” because any one of those certainly could be true. Instead, we mean that it’s a cognitive dead end. Maybe you are a brain in a vat. What are you going to do about it? You could try to live your life in a state of rigorous epistemological skepticism, but I guarantee that you will fail. You have to believe something, and you have to act in some way, even if your belief is that we have no reliable empirical knowledge about the world and your action is to never climb out of bed. On the other hand, putting aside the various solipsistic scenarios and deciding to take the evidence of our senses (more or less) at face value does lead somewhere; we can make sense of the world, act within it and see it respond in accordance with our understanding. That’s both the best we can hope for, and what the world does as a matter of fact grant us; that’s why science works!

It can sound a little fuzzy, with this notion of “reasonable” having sneaked into our definition of belief, where we might prefer to stand on some rock-solid metaphysical foundations. But the world is a fuzzy place. Although I cannot prove that I am not a brain in a vat, it is unreasonable for me to take the possibility seriously — I don’t gain anything by it, and it doesn’t help me make sense of the world. Similarly, I can’t prove that the early universe was in a hot, dense state billions of years ago, nor that human beings evolved from precursor species under the pressures of natural selection. But it would be unreasonable for me to doubt it; those beliefs add significantly to my understanding of the universe, accord with massive piles of evidence, and contribute substantially to the coherence of my overall worldview.

At least, that’s what I believe, although I can’t prove it.

The LHC has just passed a major milestone, by cooling one eighth of the machine to 1.9 K. Given that the temperature of outer space is about 3 K (the temperature of the cosmic microwavve background radiation), that makes the LHC very very cool indeed. The cold sector is 3.3 km long, and has over 200 of the big 2-in-1 superconducting dipole magnets in it. These are the magnets that will keep the particles going in a circle 27 km in circumference. This cooling operation has taken several months, starting in January, with many successful checks and tests along the way.

Bravo!