Explaining the Higgs Mechanism

(by rknop) Oct 12 2012


There's a fair amount of bruhaha in the popular press what with the announcement of the discovery of what is probably the Higgs Boson at CERN last summer. In describing why the Higgs Boson is so important, you will read that the Higgs Boson "gives other particles mass". This is the so-called Higgs Mechanism, and is an esoteric thing arising from the mathematics of Quantum Field Theory (QFT) that's very difficult to understand at a popular level. You can find a number of analogies out there, such as the description of the famous actor walking through the crowd at a Hollywood Party, and acquiring inertia (i.e., mass, i.e., resistance to being accelerated) as a result. (You can find that description here at the Exploratorium's site, along with a brief mention of the W and Z bosons, a description of whose properties is what led to the Standard Model of Particle Physics predicting that the Higgs Boson must exist.)

I have to admit, this analogy has always left me cold. Part of the reason is that my familiarity with QFT (remember, that acronym stands for Quantum Field Theory) is quite shaky, and I didn't really know how the Higgs mechanism worked. This analogy didn't give me, as a physicist, any insight into the actual Higgs mechanism. It's still on my list to become much more conversant with QFT. After all, QFT and GR (General Relativity) are the two most fundamental theories of reality that we've got, and while most physicists don't actually work with them on a daily basis (they're either working with more complicated and practical things like solids or fluids, or, as with this year's Nobel Prize Winners, they're working on fundamental physics in a manner that is adequately, and more easily, described with the non-relativistic version of quantum Mmechanics).

In this post, I'm going to try to describe, at a popular level, the view of reality that QFT gives us, and then, using only one equation (and it's one you've seen before, many times), try to tell you how it is that the existence of the Higgs Boson leads to other particles having mass. here are the sections below:

  • Fields in Physics
  • The Magnetic Field
  • The Photon, and the Electromagnetic Field
  • Fields and Particles in General, and an Analogy to a Lake
  • Energy in QFT
  • Massive Fields
  • The Higgs Field and Mass Terms in QFT
  • Pithy Summary

Fields in Physics

One of the problems in physics (or nearly any other technical area of study, including, unfortunately, law) is that there is a lot more new vocabulary than there are new words. That is, there are words with everyday definitions that are different from the technical definition in physics. One of the most common ones you hear is "theory", which is used in everyday parlance to mean "speculation", but is something very different in science. In physics, we talk about "fields", and it often sounds very scary and esoteric. However, the basic definition of a field is actually fairly straightforward:

field, n.: something that has a value everywhere in space

That's it. I'll give you a few examples of fields below, including everyday things you can understand, physics things you've heard of before, and esoteric physics things that might surprise you. Here's a physics example: a temperature field. Look around the room you're in. Imagine putting spatial coordinates on that room. That is, in one corner, draw three axes. Label the two on the ground the x and y axes, and label the one sticking up the z axis. Now, at any point in your room, in principle you could measure the temperature, with a thermometer or some other device. If, say, you've got a hot plate (or, equivalently, a computer) running in your room, just above it the temperature will be higher than it is somewhere else in the room. That is, the temperature has a different value everywhere in the room. You can just talk about the temperature at one point, but if you talk about all of the values of the temperature everywhere in the room, you could call that the "Temperature Field", and even give it mathematical notation, T(x,y,z), and then deal with it conceptually and mathematically as if it were one thing— albeit one thing that's got different values at different places.

The Magnetic Field

One physics field you've almost certainly heard mentioned is the magnetic field. Consider, for example, a bar magnet. There's a magnetic field around it, and you may have seen it visualized similar to the following:

Magnetic Field
A magnetic field. Image by Wimkimedia Commons users lscha1, Mirek2.

A magnetic field is a little different from a temperature field. A temperature field's value is just a single number, with temperature units. A magnetic field has both a strength and a direction. The arrows in the picture above tell you the direction of the field; the strength is weaker the farther away you get from the magnet.

This magnetic field can interact with other things. You could, for example, hold the magnet near a nail on a table, and pull the magnet; if you're careful, the nail will be dragged along behind the magnet. (If you're not careful, the nail will jump and stick to the magnet, or you'll get the magnet too far away and the field won't be strong enough to overcome friction from the table.) There are two jargon terms I want to introduce here: interaction and coupling. The magnetic field is clearly interacting with the nail. How strong the pull of the field on the nail is depends on how strong the iron in the nail couples to the magnetic field.

Indeed, there's another coupling going on here that I want to draw your attention to. There's also iron (or some other sort of atom) inside the bar magnet, which is itself coupling to the magnetic field. Wait! Did you notice what I just did there? The word "the" in "coupling to the magnetic field" is very important. Previously, I'd been saying "a" magnetic field, as if the magnetic field from the Earth and the magnetic field from the bar magnet were two different things, so that each one is just a magnetic field. However, really, each point in space has a magnetic field strength, whatever it was that gave rise to it. So, really, there is just one magnetic field, which is everywhere in space. If you go to a very empty part of space, the value of the field might be zero everywhere nearby, but you can still describe the field there, just by saying what the value (even if zero) is everywhere in space. In this way of looking at it, the iron atoms in the bar magnet have properties that couple them to the magnetic field in such a way that the strength of the magnetic field around the bar magnet takes on certain specific values.

The Photon, and the Electromagnetic Field

Two new concepts here. The first new concept is the electromagnetic field. Just as there is a non-zero magnetic field around a bar magnet, there is a non-zero electric field around a charged object, such as an electron, or a Van de Graaff machine that you've charged up.

An electromagnet. Image: Gina Clifford.

Way back in the 19th century, physicists figured out that the electric and magnetic fields are in fact two aspects of the same thing, which today we call the electromagnetic field. If you've ever built an electromagnet, say, by wrapping a wire around a nail many times and connecting the wire to a battery, you've been playing with the unification of the electric and the magnetic fields (albeit mediated by the moving charges in the wire). The different voltage on the two terminals of the battery create an electric field, which pushes around the charges in the wire, and the current (which is the moving charges in the wire) gives rise to a magnetic field.

In fact, you don't need charges there at all. If you have a varying electric field, it automatically gives rise to a magnetic field, and vice versa. The classical physics of this is described by Maxwell's Equations. Indeed, Maxwell's Equations show that you can get waves in the electromagnetic field, and that these waves will freely propagate through space. We call such a wave an electromagnetic wave, although you probably more often call it by its more common name, light. Light that you see, the "heat" that you feel radiating off of a burner (which isn't really heat in the physics sense), the ultraviolet radiation that gives you sunburns, the microwaves produced by a cellphone or a microwave oven, and radio waves are all the same physical phenomenon: electromagnetic waves. Another couple of vocabulary words here: these electromagnetic waves represent a disturbance, or an excitation of the electromagnetic field. If there's a light wave passing by, the electromagnetic field doesn't just have a zero (or even a constant non-zero) value, but it's got some wiggly business going on.

Classical physics allows a disturbance of any size in the electromagnetic field. In particular, the energy in an electromagnetic wave can be arbitrary small. Have an electromagnetic wave with a certain amount of energy? Divide all the strengths of the electric and magnetic fields, and the energy in that wave goes down by a factor of four, but everything still solves the equation. This is what happens in classical field theory.

Here's the next new concept. Quantum field theory (QFT), on the other hand, only admits quantized excitations of the field. With the electromagnetic field, a disturbance of a given frequency (which we would see as a given color, if it were a frequency in the range that our eyes can detect) can't have any old energy. Rather, it must come in quantized steps of energy. There's a minimum energy that you can have in a light wave of a given color, and the total energy you have must be an integer multiple of that minimum energy. When you have an excitation of the electromagnetic field that has this minimum energy, we call that excitation a photon.

You've probably heard the photon described as "the particle of light", and this is an accurate description. However, when we say "particle" in quantum field theory, what we really mean is a disturbance of a field. So, a better way to describe a photon is to say that it is a disturbance of the electromagnetic field, or an excitation of the electromagnetic field. The field's natural state, or vacuum state, is no electric or magnetic field anywhere. If there is any light propagating, it must come the form of these quantized excitations of the field, that correspond to some multiple of the energy that one photon represents.

Fields and Particles in General, and an Analogy to a Lake

So, great. We've got the electromagnetic field. It may be a newish concept, although almost certainly you've heard the word "electromagnetic" before; but, at the very least, you've heard about magnetic fields. And, we've got the idea that light is a wave propagating through this field, and that we might describe that as a "disturbance" or "excitation" of the field. And, we have the concept of the photon, as the minimal allowed disturbance (at a given frequency) of the electromagnetic field. We also will sometimes refer to this minimal disturbance as a particle, and thus call the photon the particle of light.

Let me give you another example of a field, that has a disturbance in it: the surface of the water on a lake.

The surface of a lake represents a height field. Image: Kenneth Allen.

Here, the field is a height field. Rather than having a value everywhere in three-dimensional space, it have a value everywhere in two-dimensional space. That is, you could draw x and y axes on the surface of the lake to represent a coordinate system to figure out where you are on the lake. For every value of (x,y)— that is, everywhere on the lake— the water level has a height above its average height. I chose this image because the field value is zero most places on the lake. You can see that it's very still water, and the height field of the lake is undisturbed.

However, over on the left of the lake, you can see a localized disturbance. There are ripples propagating through the height field represented by the surface of the lake. In QFT terms, we'd say that this excitation of the field would represent the presence of a fair number of "lakeon particles" in that general area of the lake, just as a disturbed electromagnetic field represents the presence of photons. With a nod to Heisenberg's Uncertainty Principle, you can't figure out exactly where the lakeon particles are. Indeed, you could view the height field of the lake as being some sort of abstract thingy that you could use to figure out a probability density for there being a lakeon present. Where there's some wiggly business going on, as is the case on the left side of the lake, there's a non-zero probability that you'd find a lakeon at that spot were you hypothetically able to pinpoint the lakeon.

Here's the fun thing: in QFT, everything is described by fields. The photon is the particle of electromagnetism, but rather than being what you'd think of as a particle (a little spec), in QFT it's really a disturbance of the electromagnetic field, some wiggly business that propagates around like wave. Well, everything else is the same way. You might be used to thinking of particles like electrons as little specs the same way you might talk about particles of dust. That's not how our most fundamental of theory describes them. Rather, there is an electron field, a field that is a weird and abstract thing that's much harder to visualize than the height field of a lake or even the electromagnetic field. However, it is in fact a field in the physics sense of the word, in that it has a value everywhere in space. If you disturb this field, and get a wave moving through it, that excitation of the field is what an electron is. Or, to be more precise, the minimal allowed disturbance of that field would be an electron; a larger disturbance would represent a larger number of electrons.

Energy in QFT

Physicists are obsessed with energy. Isn't everybody? It turns out, though, that when people talk about energy in popular parlance, they are talking about something vaguer, that incorporates aspects of both energy and entropy (and maybe perhaps your force of will and current capacity for focused cognitive activity). But that's neither here nor there.

In physics, identifying the energy in a system is often a very useful thing to do, because energy is conserved. Saying that "energy is conserved" is very different from the popular parlance version of "energy conservation", which is about keeping energy in a useful form. In physics, energy is neither created nor destroyed, so there's no need to try to conserve energy; it just happens, always. That fact, plus a whole lot of math, allows us to make all kinds of predictions about how physical systems will behave.

In QFT terms, there are a few ways that energy can arise. There is the self-energy of a field. If you've got an electric field in space, there's an energy density associated with that field. (I say "energy density" rather than just "energy", because the field isn't all at once place, but is distributed through space. So, within a given volume, there will be a certain amount of energy; energy within a volume divided by that volume gives you energy per volume, or energy density.) There is also the energy of interaction between fields. So, because a charged particle like an electron can interact with the electromagnetic field, there is an energy associated with the interaction of the electron field and the electromagnetic field. How much energy depends on the values of the two fields— that is, how probable it is that there are one or more electrons or photons at various points in space— and the coupling strength between those two fields. Another kind of particle, the neutrino, has no electric charge; it does not interact with the electromagnetic field at all, and so we would say that it does not couple with the field, or equivalently that the coupling strength the neutrino field and the electromagnetic field is zero.

For the electromagnetic field, that's basically all you have to worry about: the self-energy of the field, and the energy that comes with coupling from other fields.

Massive Fields

Many of the fields in QFT, on the other hand, are massive fields. These are fields like the electron field, the quark field (quarks being the particles that make up protons and neutron), and several other of the fields we know about. A massive field is a field such that if you have an excitation of that field— that is, a particle— that particle has mass associated with it. The mass of the electron is not zero, nor are the masses of quarks zero. There are a couple of massless fields in QFT, such as the electromagnetic field— photons have zero mass.

It turns out that mass is just another form of energy. If you have something with mass m, it has energy E just as a result of its mass; the amount of mass-energy E that you've got when you have something of mass m is given by the most famous equation in all of physics:

E = mc2

In this equation c is the speed of light. The equation is just the conversion factor between mass and energy; it tells you how much energy there is associated with a particle of mass m. Among other things, this means that it's possible to create mass "out of nothing", although you're not really creating it out of nothing, you're just converting other forms of energy into mass energy. If two photons with the enough energy come together and interact in just the right way, it's possible that they'll disappear and create two particles, a positron and an electron, the positron being a antimatter particle that's sort of like the opposite of an electron. The mass of the positron is exactly the same as the mass of the electron.

Pair Production
Pair production: two gamma ray photons come in, interact, and out comes a positron (e+) and an electron (e-).

Notice that before, you had two photons, and zero mass; after you have mass. If you've taken a chemistry class, you may have learned about the law of "conservation of mass". This law is in fact not strictly correct. For chemical reactions, the amount of mass that gets converted to energy and back is typically about a billionth the amount of mass present, so it's correct to very good approximation. But, when we're talking particle physics, it's not true at all. You can convert mass energy to and from other forms of energy.

This means that when you're writing down the energy expressions in QFT, you have to include not only the self-interaction of fields, and the coupling of fields to other fields, but also the mass energy associated with the particles of that field. Unfortunately, the way that you add this mass energy in QFT is rather ad-hoc. The coupling of the fields together come in a fairly elegant way (although the actual coupling strengths are arbitrary, and as of right now we have to take them as "just the way nature is" rather than determining them from fundamental principles). However, the mass terms show up in an ugly and tacked-on way.

The Higgs Field and Mass Terms in QFT

And so, finally, we come to the Higgs field. Now, if you've been paying attention, by introducing the "Higgs field", I'm saying that there's a new kind of particle, which we'd call the "Higgs particle". In fact, you hear it called the "Higgs boson", because physicists categorize things (for reasons that aren't important here) as either fermions or bosons. Electrons, for instance, are fermions, while photons are bosons. The Higgs field is predicted by the standard model of particle physics in a fairly esoteric way. Suffice to say that the part of the standard model of particle physics that predicts the Higgs field also predicts other things that had previously been measured in physics experiments. That is, we have a theory that predicts various things, and some of the predictions of that theory had been validated. So, we had reason to take this theory seriously. The theory also predicted that there would be this Higgs field, and that it would be a massive field. In other words, there was a prediction for a new field, and excitations of that new field would show up as a massive particle. The mass of the particle is still tiny tiny tiny compared to everyday masses, but it's huge compared to the masses of the other fundamental particles we know about. As such, it took accelerators that were able to accelerate other particles to very high energies before there was enough energy to create this new massive particle.

The Higgs field, however, has a key difference from the other fields. Above, I talked about the analogy to the surface of a lake. The "vacuum state", that is, the natural, undisturbed, zero-energy state of the field was a field with a zero value everywhere— a level lake everywhere at its average height. Fields don't necessarily have to be this way. For instance, it would be entirely possible to have an electric field that is doesn't have any waves moving through it, but that is constant everywhere in space. The electric field inside some kinds of capacitors is very much like this. This electric field would have energy associated with it though (which is why capacitors work!), and so we wouldn't call it the vacuum state of the field. The vacuum state of the electromagnetic field is in fact a field value of zero.

The Higgs field is different. It's vacuum state is in fact not a field value of zero. This has consequences. One consequence is that when you figure out the interaction of the Higgs field with other fields, you get an additional energy term in the equations of QFT describing the energy of everything. The neat thing is that that extra energy term resulting from the non-zero vacuum value looks exactly like the mass-energy term of the other field. Consider, for example, the electron field. Where we used to have an ad-hoc mass term, we now just have another elegant field coupling term with the Higgs field, but that term looks, mathematically, just like the mass term. The energy we would have called the mass energy of the electron is in fact something that arises with the interaction of excitations of the electron field with the vacuum state of the Higgs field.

Notice that this doesn't mean that the Higgs boson gives particles their mass. In the "star walking through a crowed in a party in Hollywood" analogy, you might be tempted to think that all the people in the room represent Higgs bosons. They do not. The sea of people, as it were, together represent the vacuum state of the Higgs field. Even though there aren't any actual Higgs bosons tooling around, the interactions of other fields with the field of which the Higgs boson is an excitation is what gives rise to the mass energy terms in the QFT equations.

So what about photons and other massless particles? They don't couple to the Higgs field; they ignore it, and so no mass-like terms show up in the equations for them. The different masses of all the other particles arises because of the different coupling strengths between those particles and the Higgs field.

Pithy Summary

The mass energy of particles in quantum field theory is in fact the result of interaction of the fields associated with these particles as they couple with the non-zero vacuum state of the Higgs field.


5 responses so far

A muddled article on Relativity in the Oberlin alumni magazine

(by rknop) Aug 24 2012

My wife graduated from from Oberlin college in 1992, and as such she gets the Oberlin alumni magazine. The summer 2012 issue includes a one-page article entitled "The Entirety of Relativity", which I find to be a very unfortunate presentation of Relativity. (As a pedantic point, it's only talking about Special Relativity (SR), and doesn't address General Relativity (GR) at all, but that really is a pedantic point. When a physicist says "Relativity", she likely means GR (especially given that SR is a subset of GR, so nothing is lost), but when presented publicly we often use "Relativity" as a shorthand for SR.)

The basic problem with the article is that it presents the theory as if its nature were the way that SR has been taught to students for a long time. The article starts with three things that are correct as far as they go: moving clocks run slow, a moving rod is short, and moving clocks aren't synchronized. Where the article loses me, however, is on point number 4, "That's All There Is To It.".The brief text after this says that the first three points are the basis of relativity, and the rest of the article claims that all of SR is a consequence of these three points. This is at the very least a perverse way of describing the theory.

A lot of texts at both the high school and college level present Relativity by first presenting these three points. You're given formulae for each of these consequences; parts of them resemble each other, but they're each presented as if they were a fundamental formula that couldn't be derived from anything else, for you to memorize (or, in a more modern way of thinking about it, look up) and use. However, this is a back-assward way of presenting SR, and I would argue that stating that the rest of SR is a consequence of these three observations is not just back-assward, but in fact wrong.

In fact, these three points are themselves consequences of the theory of Relativity. The formulae for them can be derived from more fundamental considerations. They're no more fundamental than all of the various kinematic formulae you memorize or look up (such as da2) when you do a non-calculus Newtonian mechanics class; those kinematic formulae themselves are just results of the definition of velocity and acceleration as, respectively, the rate of change of position and the rate of change of velocity, together with Calculus. Those definitions are the fundamental thing, not all the various kinematic equations you learn to use if you take a non-Calculus physics class. I could start with da2, take a couple of derivatives, and say, "hey, acceleration is the rate-of-change of the rate-of-change of position, and that's a consequence of this kinematic equation". That would be back-assward and indeed wrong, and it's just as wrong to say that everything else in Relativity is a consequence of moving clocks running slow, separated moving clocks not being synchronized, and moving rods being short.

Special Relativity itself starts with just two very simple postulates— "simple" in the sense of "not complex", not in the sense of "easy to understand". Those postulates are:

  • The laws of physics are the same for every freely-falling observer
  • The speed of light is one of those laws of physics; every freely-falling observer will measure the speed of light in a vacuum to be 2.998×108 meters per second.

Everything else in SR— including moving clocks running slowly, separated moving clocks not being synchronized, and moving rods being short, as well as other things (such as the Doppler shift, focusing of light emitted by a moving object in the direction of motion, an apparent rotation of a moving object) are consequences of these two postulates.

I should note that both of these postulates do require more explanation to be truly precise. For the first postulate, you have to carefully define "freely-falling observer". You get it basically right if there are no net external forces other than gravity acting on that observer. (However, if you allow gravity to be around, things can get a little subtly complicated. It doesn't ruin the postulates, but you have to be careful in treating the consequences.) For the second postulate, in fact it's not the speed of light that's absolute, it's the speed of any object that both carries energy and is massless. Light just happens to be the thing that we think about the most that works like this, and thus we call the cosmic speed limit "the speed of light", even though we really ought to call it "the speed of spacetime" (at least in the context of Relativity).

One of the most interesting consequences of these two postulates it that you have to change the way you think about time. Most of us live our lives with a Galilean/Newtonian view of time: it's an absolute, that advances at the same rate and is the same for everybody. However, you can't maintain that idea and have the speed of the same bit of light be measured at the same rate by everybody regardless of how they're moving. Galileo and Newton would say that the latter is wrong; Einstein's postulate, from which all of Relativity springs, was that in fact it's this speed of massless objects that is absolute, and as such we just have to give up on the idea of absolute time. Some of the consequences of this are that separated moving clocks aren't synchronized and moving clocks run slow... as well as other things.

I'm fond of the way that Thomas Moore's Six Ideas That Shaped Physics presents Special Relativity. (This is the book series that I currently use when teaching introductory calculus-based physics.) His Book R of the series is written for college-level physics who have had Calculus (and indeed have had some Calculus-based Newtonian physics). It presents SR not in the old-fashioned and unfortunate pedagogical way that the Oberlin article does— by starting with the consequences such as time dilation and with their formulae, and only later getting to the fundamental structure of spacetime implied by Einsteins postulates— but rather by starting with the fundamental structure of spacetime implied by Einstein's postulates, and then developing the consequences out of that

Yes, it's easier to just learn the formulae and do calculations about time dilation and so forth, and presents fewer difficult abstract conceptual challenges to students coming across this for the first time. However, if you learn it this way, you're given a warped perspective of what the theory of Special Relativity really is. My beef with this Oberlin alumni article is that it presents Relativity as if the theory itself is based and structured in the way that it has often been taught.

6 responses so far

When Andrew Hacker asks "Is Algebra Necessary?", why doesn't he just ask "Is High School Necessary?"

(by rknop) Jul 29 2012

Yes, I admit, the editorial at the New York Time entitled "Is Algebra Necessary?" pushes my buttons. Hacker makes some valid and relevant points, and I'll get back to that. However, the core of his argument is the ultimate in anti-intellectualism. What's worse, it's the kind of anti-intellectualism that you get from intellectuals, the sort of thing that sprouts from those on the math-ignorant side of the "two cultures" identified by C. P. Snow.

Andrew Hacker's argument against making algebra necessary for high school and college students is essentially: Math Is Hard. Having to do it gets in the way of people who could be amazing at other things, because they will drop out of high school because Math Is Hard. So, rather than stop them from achieving all that they might achieve, we should just remove algebra from the high school curriculum. He points out that failing math is one of the main reasons students leave school. Now, I might think that this is a reason to look at our educational culture, at how math is taught, at the fact that it is somehow deemed acceptable and indeed normal to find basic math impenetrable. But, if you're on the other side of the two cultures, evidently this means that we as a society should just give up on the general teaching of basic algebra. Evidently, it's OK that the elites who understand the simplest things about science become that much more separated from the general educated public, and that the generally educated public know that much less about them.

There's one particular part of the argument I want to highlight:

Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job. John P. Smith III, an educational psychologist at Michigan State University who has studied math education, has found that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” Even in jobs that rely on so-called STEM credentials — science, technology, engineering, math — considerable training occurs after hiring, including the kinds of computations that will be required.

So, because algebra isn't what's needed in jobs, we shouldn't be teaching it. This is absolutely the wrong way to think about a lot of education.

If you accept that argument, we need to reevaluate the entire high school curriculum, and the entire core curriculum of all colleges and universities. I think most people would agree that you need to be able to read and write in order to function in today's society. Do you really need to be able to interpret themes in literature, however? Honestly, is anything that you do in high school or college English classes really necessary in the workplace, any more than algebra is? The kind of reading and writing that most people need is something that students should already know by the time they're out of middle school. Likewise, history, biology, all the rest: everything that they study in high school is not going to be necessary for their jobs. And, really, if the purpose of high school and college is to train people to function like good little Betas and Gammas within our economic system, why is Andrew Hacker singling out algebra for attack? If we're going to dumb down the curriculum because we don't like that right now some people aren't mastering it, why don't we just dumb it down all the way?

The simple fact is that a college or university education is not job training. In recent decades, it's become conflated with job training, at least in North America, and this is too bad. A liberal arts education is all about expanding your mind, all about being able to think. It's not about gaining skills that you are then going to use in a job. Too many of us professors tend to not have any clue what somebody is supposed to do to earn a living after a liberal arts education other than go to graduate school (so that your liberal arts education is "training" for what you do next). That's because that was our own life trajectory, and it's what we know. Liberal arts education is to make people into good citizens, not into good workers. They are to acquaint you with the intellectual achievements of humankind. That is why we read the Iliad, why we watch a performance of Hamlet, why we learn about the history of ancient Greece, and, yes, why we study algebra. Because we want people to be educated so that they understand the intellectual achievements that have made our society what it is today, and that will drive our society in the future. We're training people to be members of civilization, not employees.

I will say that Hacker makes some good points. There are other kinds of quantitative reasoning, which too many of those coming into college and too many in our society completely don't grasp, that people should learn. A better understanding of basic statistics may at this point be more important to the citizen of a democracy than an understanding of algebra. So, yes, I would agree that we could and perhaps should de-emphasize algebra in favor of making time for statistical awareness, and perhaps in filling in the basic number sense that students failed to get out of elementary school. However, to me this is a bit of a red herring. Yes, we should always be evaluating what the subject matter of mathematical high school education is. But, right now, the problems are bigger than that. That so many people through high school without basic quantitative reasoning skills is not a reason to throw out algebra. We do, however, have to figure out why it is somewhere around fifth grade that individuals and society both get the "Math Is Hard" meme so firmly embedded. Why it becomes normal not to "get" math and indeed a little weird to actually understand and like those classes. Why it becomes OK to not like and not try at math and just do what's necessary to get by without actually learning anything. I strongly believe that there are serious problems with a lot of the math education that's done at the later elementary, middle school, and high school level. But that's not a reason to give up. We might as well point at various studies of how little so many people know about the state of the world to say that teaching geography and international history just isn't worth doing any more.

Perhaps the problem, or part of the problem, is that we have conflated vocational and liberal arts education. Anybody who is interested in a liberal arts education does not deserve a degree if they are completely ignorant of algebra, and any society that values liberal arts education cannot neglect algebra. However, perhaps not everybody needs such a liberal education. If we have the problem right now of too many people failing out, it may be that we're pushing them through the wrong kind of education. This does not mean that a liberal arts education needs to jettison those parts of it that are hard for people on the wrong side of C. P. Snow's divide!

Algebra is fundamental to nearly all of "higher math". Even if you want to do more than the most basic of things with statistics, you need to know some algebra. To give up on that would be right on par with the giving up on the teaching of history as anything other than memorizing the occasional date, and to give up on the teaching of English literature as anything other than being able to read a short document for simple surface content and to put together a simple declarative sentence. If you want people to be educated beyond elementary school and beyond "job training", then algebra is one of the intellectual foundations of our civilization that simply cannot be neglected.

75 responses so far

The Higgs Boson and Statistics

(by rknop) Jul 06 2012

GUILDENSTERN: ...Four: a spectacular vindication of the principle that each individual coin spun individually is as likely to come down heads as tails and therefore should cause no surprise each individual time it does.

   —"Rosencrantz & Guildenstern Are Dead" by Tom Stoppard

There has been a lot of bru-ha-ha over the last few days about the much anticipated discovery of what looks to be the Higgs Boson at CERN. Among many other things that you have probably read is the statement that the confidence that the signal is real is 99.9999%. You might be wondering, why so many 9's? That is, they had a signal a while back that was already 99% or thereabouts certain. If I had 99% confidence in winning the lottery I would go out right now and spend $1000 on lottery tickets. Why was a 99% confidence limit not good enough to indicate discovery? Indeed, the announced discovery, with 99.9999%, is at the statistical confidence level that is considered the minimum for a particle physicist to announce a discovery. Why do they have to be so damn confident?

Rather than talking about the energy spectra of interaction cross sections, let's talking about flipping coins. At the opening of Tom Stoppard's play Rosencrantz & Guildenstern Are Dead, the two courtiers are flipping coins (and have been doing so for some time). They are approaching a streak of 100 flips of heads in a row. Rosencrantz (who wins a coin each time it comes up heads) is not concerned about this, but Guildenstern is so disturbed by the seeming violation of the laws of probability that he philosophizes at length about what it is that's going on. (The real thing that's going on is that he's a character in a play, not a real person.) Let's keep it more modest, though.

Suppose I were to walk up to you with a quarter, and flip it six times in a row. If the quarter is normal, and if I'm not cheating, the probability that all six flips of the quarter will come down heads is about 1.5%. In other words, if I do flip six heads in a row, you can be 98.5% sure that it was not due to random chance, that I must have been cheating somehow. (Ask me to show you this sometime.) You're not 100% confident, because there is a small chance that six heads will come up in a row just randomly, but it is a very small chance... and so you would be well within your rights to think that something was probably up. It may not be good enough to convict somebody in a courtroom, but it's certainly good enough to bet on.

Suppose instead, however, that 30 people come up to you, and each one of them flips six coins in a row. The probability that at least one of those people will flip six heads in a row is 38%. So, while it won't happen every time this crowd of coin-flippers accosts you, you shouldn't be particularly surprised that somebody flipped six heads in a row if a whole bunch of people tried it. Even though it's extremely unlikely that any given coin flipper will flip the coin six times, the probably that somebody somewhere will is entirely reasonable. Lightning has to strike somewhere. (See Randall Munroe's much more concise take on this, and on overreactions to it.)

This same principle applies to particle physics. The particle physicists looking for the Higgs Boson were not sure at exactly what energy the particle would show up. Here's one of the plots from the CMS collaboration:

From the 2012 July 4 CMS Higgs Seminar; (c) CERN

The signature of the Higgs Boson is the extra bump of events at an energy of 125 GeV. There are lots and lots of events at all energies in the plot; there's a little something extra there, which indicates that something is going on there, and that something is probably the production of a short-lived Higgs boson. But they didn't know before they found it to look right at 125 GeV; it could have been at other energies, too. If all they were after was finding something that was "a little extra" at 95% confidence, they could have found it lots of places; indeed, there's a data point hanging out there at a bit over 135 GeV that is that far away from the background. But since there's 30 data points in the plot, I'm not the least bit surprised to see that. Randomly, you'd expect to see at least one of those more than 3/4 of the time somebody showed you a plot like this with 30 data points, even if there are no new particles.

The physicists in these collaborations were doing the equivalent of looking at a whole bunch of people flipping coins, and trying to find somebody who was flipping more heads than tails. If you look at 30 people who flip 6 coins and you find one person who has flipped 6 heads in a row, you have no right to declare that you've found a person who is cheating at flipping coins; the chances of that happening randomly are too high. Similarly, if you look at a whole bunch of different energies, and you see a single place where more is going on to 99% confidence than you'd expect from random fluctuations, you don't have much confidence that you've really found anything... because if you look at enough different energies, you will eventually find the unlikely random fluctuation. This is why for a particle physicist to be confident that she really has discovered something, she needs six nines in her confidence.

As for why the Higgs field (the "same thing" as the Higgs Boson... it's complicated) gives particles mass... that I really don't understand.

16 responses so far

Neil deGrasse Tyson isn't the only black astronomer

(by rknop) Jun 29 2012

I have noticed a tendency recently for people to mention Neil deGrasse Tyson when talking about black people doing science, and doing astronomy in particular. There's absolutely nothing wrong with this; deGrasse Tyson is, in fact, black, and is, in fact, an astronomer. Indeed, as somebody who's caught the attention of the media and who evidently has the charisma to hold it, he's the closest thing we have to a modern-day Carl Sagan. So, go on celebrating him!

However, I am brought to mind this XKCD comic, in which Zombie Marie Curie comes back to take people to task for always mentioning her, and only her, when trying to convince people that women can do science.

There are actually lots of black astronomers out there, and I don't know who most of them are. (Just because I don't know who most of all astronomers are.) Yes, blacks do remain an underrepresented minority in astronomy, but that shouldn't take anything away from the individuals out there who are doing solid astronomy. I will mention two I have personally worked with. (There are more famous ones than these two, but my point is just to give a shout-out to a couple of good folks.)

Lou Strolger is an associate professor at Western Kentucky University. I met him in 1999 when I was a post-doc at LBNL and he was a graduate student at Michegan (although in residence in Chile) working with Chris Smith. In fact, Lou was a member of the other team; I was in Saul Perlmutter's supernova cosmology project, and Lou was in Brian Schmidt's team. However, in 1999, Saul's gang collaborated with Chris and Lou (and some others) on a search for "nearby" supernova. (Things less than a billion light-years away. You know, backyard stuff.) Lou went on to be a post-doc working with Adam Reiss (the third guy to share the Nobel Prize with Saul and Brian), and after that to WKU. Had I stayed at Vanderbilt, almost certainly I'd be collaborating with him now. My post-doc, Rachel Gibbons, and I talked to Lou about some collaborative ideas a year or so before I left Vanderbilt. Lou still works on supernovae and cosmology.

Jedidah Isler is a graduate student in astronomy at Yale— or, at least, she was last time I checked. It's possible she's graduated in the last year. I knew her when she was a master's student at Fisk University in the Fisk-Vanderbilt Bridge Program. Although I wasn't her advisor, I did interact with her, and worked with her on one project (that, sadly, didn't end up going anywhere, although she did come along to Chile with me and another graduate student on an observing run). Instead of continuing on at Vanderbilt, Jedidah had the opportunity to go work with Meg Urry at Yale; Meg Urry is one of the uberpundits of active galactic nuclei. (In an example of "small world" syndrome, one of Meg's post-docs, Erin Bonning, is going to be teaching physical science at Quest this coming year.) Last I talked to Jedidah, she was not sure she was going to continue in astronomy after graduating, but was considering going into public policy. We'll see what happens!

3 responses so far

Comments on old posts disabled (with an aside about plasma cosmology)

(by rknop) Jun 28 2012

Fairly frequently I get an e-mail message letting me know that there's a new comment, a screed from somebody who is put off by my telling the world the truth about the nature of Plasma Cosmology in my post How I Know Plasma Cosmology Is Wrong. This is an ancient post, and the truth is that I don't really have the time or inclination to engage with the true believers on the matter; this is why I haven't been approving those comments. (They weren't ones I wanted to let pass without comment.) However, rather than just disable comments on that post, I realized it made sense to disbale comments on all old posts that I wasn't going to engage on any more.

I left all posts from 2012 still able to comment. It's kind of depressing how few there are.

By the way, in case you thought you were missing something, the comments on the "Plasma Cosmology" that I didn't approve for the most part made one of two points:

  • I was unprofssional and behaving badly by calling Plasma Cosmology a crackpot theory. Why can't I just engage the theory on its own merits? My tone was perhaps a little bit to dickish; I'll apologize to Phil Plait, at least, if not to the actual plasma cosmologists themselves. Because, the actual truth is that Plasma Cosmology is a crackpot fringe theory, and to call it anything else would be little different from saying that creationism or intelligent design are "viable scientific alternatives" to evolution. The widespread acceptance of standard cosmology is not because those of us in the mainstream are too afraid to look at the evidence and speak out against the unthinking consensus. The widespread acceptance of standard cosmology is because there is a lot of evidence for it, and there's not evidence for the alternative proposed by the plasma cosmologists.
  • There is no good evidence for the Big Bang model, Dark Matter, etc. These statements are just flatly incorrect. There is a tremendous amount of evidence for dark matter. I have covered that elsewhere, and a casual browse through Ethan Siegel's blog, among several others, can give you an introduction to all of that. (Humorously, the "bullet cluster" is one thing that can be identified as the "smoking gun", but it's just one piece of evidence amongst a large number of pieces of evidnece.) As for the Big Bang itself, I point you to my podcast at 365 Days of Astronomy from last year entitled On the success of Big Bang Cosmology.

22 responses so far

Same Old Story : Too Many Graduate Students

(by rknop) Jun 16 2012

Via Slashdot, I saw this report from the NIH advisory committee. The summary of the problem: there are too many graduate studnets produced in biomedical fields for the number of academic positions that will be available for them in the future. Quotes include:

NIH should create a program to supplement training grants through competitive review to allow institutions to provide additional training and career development experiences to equip students for various career options, and test ways to shorten the PhD training period.

Of course, earlier there is the statement of purpose:

Attract and retain the best and most diverse scientists, engineers and physicians from around the world to conduct biomedical research as well as increase the number of domestic students from diverse backgrounds who excel in science and become a part of the Science Technology Engineering and Mathematics (STEM) workforce

This is a decades-old story at this point. I remember my junior or senior year of college (back in 1989 or thereabouts) hearing news stories about how there was going to be a "shortage of scientists", because all of those who rushed into science after Sputnik were going to be retiring. BS, of course, because during the intervening decades they all groomed multiple replacements for themselves, but they're only retiring once.

In my very early years of graduate school (1990-1992 or thereabouts), there was a statistical continuum of letters to the editor to Physics Today talking about the sea of physics post-docs out there: PhDs who could get a temporary post-doc position, or two, or three, but who couldn't find permanent positions. The astronomy journal club (I believe it was) at Caltech dedicated one of their meetings to talking about this issue. And, the professors there all gave lip service to "training students so that they can go into other careers." But I could practically hear each and every professor there thinking "but not my students— they will be the ones who get the coveted academic positions." (Some may even have been generous enough to think "Caltech" students.)

The sad truth is that those professors were probably mostly right, although not entirely. Of the three PhD students who worked with my advisor, Tom Soifer, when I was there, we're all in faculty positions. James Larkin is at UCLA and Tom Murphy is at UCSD. I'm the odd one out, teaching at a teaching-focused small liberal arts college rather than at a prestigious research Unviersity, but still I've got one of those rare and coveted professor positions. In Physics, professor positions everywhere are heavily dominated people with degrees from the top handfull of schools... yet they are all themselves still training graduate students, with graduate training programs designed to produce more academic researchers.

Socieites and meetings and focus groups will meet every so often and wring their hands about the problem, and give lip service either to increasing the number of staff scientists and decreasing the number of graduate students, or give lip service to "training graduate students for other careers". But little has changed despite this hand-wringing in the last twenty years, and I don't expect it to change any time soon. The professors, the ones in position of power, are the rare few who got the desired positions, so they aren't feeling the pain, and thus have little incentive to change it. Meanwhile, funding agencies keep talking about "attracting the best scientists", which leads to university administrations talking about "improving the graduate program", which inevitably leads to trying to attract more graduate students. It's a vicious cycle that's not going to end.

(And even if you do get into a scientific research position, you're still screwed. At least in astronomy, funding has gone completely into the toilet. Last I heard, NSF astronomy was granting only about 1/8 of the proposals it received, which is even worse than when I was failing to get NSF grants in the 00's. Also, national observatory facilities are being eviscerated on the altar of ausperity and gigantic projects. Not only are there too few research science positions for the graduate students we're producing, there are too many research science positions for the amount of science that our society is willing to support! It's bad all around.)

What you should do about it is be open and honest to any young people you know. Warn them that going into an academic PhD program is a trap. You will be enticed with the promise of an intellectually fulfilling job as a research scientist, once you put up with the years of hazing you undergo as a grad student. Only, at the other end, statistically you won't be able to find a job. I wrote about this back in January in my post Why go to graduate school in Physics?. The short version is that there's only one reason: because you want to be a physics graduate student for six years, and it's worth it to you to take six years out of your life to do that. Yes, if you want to be a professor, you have to get a PhD. Similarly, if you want to win the lottery, you have to buy lottery tickets. but the competition is intense.

You will also spend much of your graduate school career frustrated as you will see that everybody around you knows that the system is broken, that academic PhDs are being vastly overproduced... but that nobody is willing to do anything about it.

So do something about it yourself. Don't let yourself into the trap unless it's not a trap for you, but an interesting diversion for your life.

18 responses so far

Intelligent Design is Scientific Fraud AND It's Bad Religion

(by rknop) May 28 2012

I'm posting this just to make sure the record is clear: I don't like Intelligent Design. The people who push it are culture warriors with a religious agenda that involves the denial of science. People who believe it are either confused and have been sucked in by those with an agenda, are cynical culture warriors who want to see science attacked, or are legitimate honest backers who really don't realize that by backing Intelligent Design, they're rejecting the fundamental basis of science.

I hope that's clear.

The reason I say this is that there is a post on the Intelligent Design blog "Uncommon Descent" that includes a quote from an earlier post of mine that appears to be supporting their argument. I reject their argument, and I reject the Intelligent Design behind them. The basis of their argument is that the "Darwinists" (a bad term, as it conflates science and religion) themselves can't agree about whether relgion is consistent with science, and so therefore you can't trust that it is. This, of course, has no logical basis. Hell, look at me and look at Uncommon Descent: thesists also disagree! What does that tell you about the issues behind them? Not very much. Trying to figure out what is true based on finding subsets of those who argue about it who have one thing in common but disagree on something else doesn't tell you a whole hell of a lot.

Looking at the post my quote is from, in retrospect, worrying that the ranting frothing of New Atheists is going to hurt free software is silly (Oracle, the closed gardens being built by the likes Apple and Facebook, the patent lawyers at Google, Samsung, Apple and others in the smartphone business, the MPAA and RIAA, and rhetoric over cyberterrorism don't need help from any form of atheists). However, I do stand by my rejection of the position on science and religion held by the New Atheists— those atheists who insist that modern acceptance of science requires atheism, and that having any form of religion is inconsistent with it. Not all atheists think that.

Any more than all Christians think that the Bible must be read literally, or any more than all Christians think that you must reject biological evolution.

So do NOT take my quote in the "Uncommon Descent" blog in support of what they're saying as any kind of support whatsover for the position taken by that blog.

Evolution is extremely well-established science. It is one of the cornerstones of biology. You can reject it, but in so doing you're rejecting the basic methodogy and mode of sciecne. And, I think that the evidence around us, the many huge successes science has had in describing our world and allowing us to manipulate it, makes rejecting science as a way of constructing reliable knowled rather absurd. New Atheists are sometimes befuddled by theists like myself who believe that there is wisdom in the Bible but reject things like the creation story as literal truth; how can you "pick and choose" is usually the sophomoric comment made in blog comment threads. Part of the reason of that is that in the intellectual mode of thought represented by science, you can't pick and choose. You can, and all of us are, be more convinced by some lines of evidence than others. Dark Matter is assuredly real, for instance, but Dark Energy, while I think it is probably real, may instead be a pointer to cracks in our theories. But you can't reject some lines of science because you don't like the results philosophically, if the scientific evidence is there. And the evidence for evolution is there, completely and overwhelmingly. Reject evolution, be it by being a classical creationist or by being an Intelligent Design supporter, and whether you know it or not you are rejecting science itself.

As for why I say it is fraud, that is well documented. While there are trained scientists out there who believe in Intelligent Design, honest ones who've managed to confuse and convince themselves that there's something to it, that's not where Intelligent Design came from. This has been well documented, in the case of the Dover trial and elsewhere. The lobbying organizations who push Intelligent Design and those behind the movement aren't scientists who beleive that they have a better theory, or even highly confused pseudoscientists like the backers of Plasma Cosmology, but they are (at least in the USA) Christians who think that science is a threat to their form of their religion. Intelligent Design was cleverly designed as a strategy to package creationism in such a way that it might be able to slip into school science curriculums where raw creationism was not able to. This is the way in which it is scientific fraud.

As for why it's Bad Religion— I covered that five years ago in my post Intelligent Design: a trap for Christians. Precisely because it's designed to sound scientistic, it allows Christians who think that accepting Christianity means that you can't accept modern science, including Evolution, to think that they're accepting science without having to reject their Christianity. But it's a trap, because as I've already said, it's not only bad science, it's fradulent science.

The real truth is that you can do what I have done, what Guy Consalmango (the Vatican Astronomer) does, what Ken Miller does, and what all the signers of the Clergy Letter Project do: accept modern science for what it is! Yes, some put an interpretational spin on it— evolution, you might say, may be part of God's engine of creation or some such. The difference, though, is that you don't have to deny the utterly rock-solid scientific truth of biological evolution, of mutations mediated by natural selection leading to change in species and the development of new species over time. Yes, you will find lots of Christains out there who say that you're fooling yourself by thinking you're still Christian (or a follower of whatever other religion— again, I talk from my point of view). Yes, you will find New Atheists out there who will hurl all sorts of insults at you about being intellectually dishonest because you haven't accepted the one true religion of atheism in your heart. (And you will be a bit struck by how the similar the fundamentalist atheists and fundamentalist Christians sound. Indeed, look at that Uncommon Descent post I linked to— they're agreeing with the more annoying and frothy New Atheists such as the Jerry Coyne that things like Evolution Sunday and the Clergy Letter Project are no good. There's more common ground between the New Atheists and Uncommon Descent than there is between me and Uncommon Descent!) But there are lots of us out there— probably not a majority, given how sadly strong the right-wing religion movement in the USA is today, but probably a plurality!— who are in the same position, the position of fully accepting modern science while recognizing that one may be an atheist or one may be a theist at the same time.

If you're Christian, do not fall for the trap of Intelligent Design.

And if you're atheist, don't fall for the trap of New Atheism.

And, in any event, don't take my arguing against Intelligent Design as evidence that I'm a New Atheist or that I hate religion, and don't take my arguing against New Atheism as evidence that I'm in any way, shape, or form accepting of Intelligent Design.

10 responses so far

"Of the Wonderful Kind", a play by Claire Hately

(by rknop) Apr 05 2012

You wanted to see a picture of me in a onesie, riding a unicorn and weilding a light sabre? Why, yes, I can accommodate that:

One of the fun things about being at Quest University is the diversity of student "majors". Students don't actually have majors; instead, they choose a "Question" that they focus much of their last two years on. Most of the students I have working with me have a Question that's focused somewhere in the physical sciences, although some are a bit more diverse. One of the ones that is entirely out of the physical sciences is Claire Hately's question, "How Can We Keep Creativity Alive?" For her keystone project (the project that all students do by the end of their tenure here), she wrote and is now producing a play entitled "Of the Wonderful Kind". The one performance is tonight.

The play takes place in two locations: first, in the bedroom of an 8.5-year-old boy who's created a startling and potentially world-changing invention for the next day's school science fair. Second, inside the mind of that boy, as his confused imagination tries to deal with growing up. The play is quite funny and lasts about an hour.

And, yes, I play the 8-1/2 year old boy. Everybody else in the play is a Quest student, and is 24 years old or younger (mostly 4 or so years younger). So, naturally, I was the obvious choice to play the little boy...! Claire herself plays the role of my little sister, and various other students play my mother, the Nymphs of the Night (faeries who carry on like drug dealers), Jesus, as well as various characters in my imagination including a train conductor, the psychotic favorite doll of my little sister, a couple of cats, a foul-mouthed and wryly philosophical toad, a bevel of hard-drinking poker players, a kindly old train conductor and his assistant who turn evil, and, of course, Cowboy Bill, the flying cowboy who does nice things for people but never stops to ask for any thanks.

Sadly, I've had a cold since last week, so I've sort of lost my voice. But, I'll make it through.

One response so far

Neutrinos don't travel faster than light

(by rknop) Mar 18 2012

Last September, those who pay attention to discoveries in physics were rocked by an experimental result that suggested that neutrinos had been observed moving faster than the speed of light. Neutrinos produced at CERN in Switzerland (not at the LHC, but at another accelerator there) were detected at Grand Sasso in Italy by the OPERA experiment. The result only showed them moving a couple hundredths of a percent faster than light. That doesn't sound like much, but Special Relativity, one of the pillars of modern physics, indicates that the speed of light is an absolute limit, and that it takes an infinite amount of energy for a massive particle to reach that limit. As such, if a particle is going even a little bit faster— and the reported uncertainties on the reported result were much less than the difference between the measured speed and the speed of light— it would be an important result, indicating that in at least some regimes, Special Relativity breaks down.

Most physicists were dubious of the result. Special Relativity (SR) has withstood a lot of experimental tests. As such, any result that indicates that it isn't absolutely true is going to be subject to a lot of scrutiny, and is going to require robust reproduction before we really take it seriously. Also, the press reports and popular perception of the result missed one of the most important points. "Was Einstein wrong?" was the question asked. There were statements or implications that SR would have to be thrown out. The thing is, even if we'd seen a case where SR was violated, all the other experiments that show that it works still stand. It would only mean that SR isn't an absolute theory, that it's an approximation that works frequently but not always. We have many other theories like that. Newton's theory of gravity is a great theory that we use for a lot of things, but we know that there are situations where it isn't quite right (black holes, gravitational lensing of light, the precise orbit of Mercury, the precision required by the GPS), and we have to go to another theory (Einstein's General Relativity).

As I said, though, most of us suspected that the results from the OPERA experiment indicating neutrinos moved faster than light weren't correct. There was no scientific fraud involved, nor did anybody at OPERA do anything wrong from a moral or professional point of view. What they did was exemplary science. And, the rest of us, in doubting their results and wanting confirmation, also behaved as scientists are supposed to. We suspected that there would be some sort of systematic error that explained the apparent detection of faster-than-light neutrinos. It wouldn't be easy to find, because if it were, the scientists at OPERA would have already found it and would never have reported their result. Indeed, a few weeks ago there were reports that a loose cable, as well as possible shortcomings in corrections to GPS timings, may have been the source of the measured too-short travel time for the Neutrinos from CERN in Switzerland to OPERA in Italy.

However, even if the systematic error were never identified, for scientists as a whole to take the result seriously, there would need to be an independent verification by other scientists using separate techniques and separate equipment. A couple of days ago, a report from the ICARUS team indicated a failure to reproduce the OPERA results. This team was looking at the same source of neutrinos at CERN as the OPERA team, but it was a second team using a different detector. This is exactly what we needed. If they had come up with a measurement consistent with OPERA's measurement (and if the OPERA team hadn't identified the likely culprit systematic), then the scientific community would have to start taking faster-than-light neutrinos seriously. (It would be nice to reproduce the result also with a different source, in case there was some systematic involved with the timing on that side that would affect both results, but this would already be enough that we'd have to sit up and pay attention.) However, the ICARUS team reports timings that are entirely consistent with neutrinos moving at the speed of light. (In fact, they aren't moving at the speed of light. However, because their mass is so low, at the energies of these neutrinos they are moving a tiny, tiny fraction slower than the speed of light, a difference small enough that the experiment wouldn't be able to detect it.)

The story isn't completely over. Because SR is one of the foundations of modern physics, it's always worth testing its fundamental postulates. We'll keep pushing at it and looking for cracks in the theory, trying to see if it breaks down in places where we hadn't yet looked. However, at the moment, there's no indication that the theory breaks down anywhere. The brief suggestion that neutrinos might somehow be able to violate SR (which would have lead to all sorts of potentially cool consequences) has passed, as most of us suspected it would.

2 responses so far

« Newer posts Older posts »