For those not versed in the ways of the physics, a neutrino is a fundamental particle. It’s a lepton, the same family of particles as the electron. Unlike the electron, the neutrino has no electrical charge, and so can only interact via the weak nuclear force. That’s how they can travel hundreds of miles through the earth’s crust; they interact with the matter we’re more familiar with (atoms made of electrons, protons and neutrons) only very, very rarely.

That means to detect them you need huge, super-sensitive detectors, typically built deep underground to screen out the signal you would otherwise get from cosmic rays. One is the Super-Kamiokande detector in Japan, which contains 50,000 tons of water. When one of the rare interactions with a neutrino occurs,  the interaction generates a very small amount of light, which is detected and used to infer the properties of the neutrino interaction which caused it.

The OPERA experiment was designed to measure a phenomenon called neutrino oscillation, or neutrino mixing.

There are three types of neutrino: the electron neutrino, muon neutrino, and tau neutrino. The Sun produces a vast number of electron neutrinos as a by-product of the fusion reaction which powers it. When detectors were used to measure the neutrinos being emitted by the Sun, it was discovered that the number was less than would be expected. This became known as the “Solar Neutrino Problem”.

Despite claims to the contrary in certain elements of society and the media, when new evidence is discovered, the theory has to give way. Either the models of what was going on inside the Sun were wrong, e.g. the fusion yield of the Sun was lower that expected, or some aspect of neutrino physics was not properly understood. Cross-checks with other measurements of the Sun indicated support for the Solar models. So the problem was  with the neutrino physics.

It had been assumed that the mass of the neutrino was zero; all measurements made had indicated that it was, at the least, very close to zero. However, if the neutrino had even a very small amount of mass, it would undergo a very peculiar phenomenon due to a quirk of quantum mechanics, called neutrino mixing. Essentially, in the flight from the Sun to the Earth, some of the neutrinos would change flavour, from electron to muon, or tau neutrinos. The “missing” neutrinos were there all along; they just weren’t in the form of electron neutrinos that the detectors were capable of detecting.

The OPERA experiment is designed to more closely measure this process by generating a neutrino beam on demand in an accelerator, and then measuring the mixing that occurred while the beam was in flight.

In doing this, they have apparently detected, to a good degree of statistical significance, that their neutrinos travelled superluminally from the source to their detector. This is well-known to be forbidden by relativity, so if this is a true result, then it will require brand-new physics to explain, and could mark the start of a new era of post-Standard Model physics. It would be one of those fantastic moments where something amazing is discovered by people looking for something else entirely.

That said, it could also be a mistake in their methodology. Relativity has stood unmolested for a century; every experiment concurs with it.

When a supernova occurs, as well as a blinding flash, there is also an extremely intense neutrino pulse. So intense that the even with the rare interaction of a neutrino with the matter we’re made from, the pulse could give you a fatal radiation dose. Knowing how far away the supernova is, the lag time between the observation of the light pulse and the neutrino pulse, and just a dash of astrophysics, you can work out how fast the neutrinos must have travelled, and it comes out subluminal.

So the OPERA guys have done the sensible thing; checked everything they could, and published. It’s very probable that it will turn out to be a complex effect they hadn’t fully considered or was unknown at the time of designing the experiment which will explain the measurements.

The real trouble with these sorts of things is how to manage the media, and how to stop them getting over-excited at things that may well turn out to be nothing, c.f. the hints of the Higgs that melted away in the late Tevatron data.

I actually don’t have much of a point to make about all this, except that the relationship between science, the media, and society, means that there’s really great misunderstanding out there about what’s actually going on. Reading the comments on BBC News, especially the worst-rated ones (thankfully!) does demonstrate the mistrust of science and scientists, and a misplaced belief that science is about arrogance and certainty, when it is really more about doubt, and trusting the weight of the evidence. There’s also a certain group of people who seem to be fully unaware of just how well the world actually is understood these days.

It will certainly be interesting to see what happens if/when these neutrinos are shown to be subluminal!

Then, there’s the wackos, who take any new development as an excuse to just make weird and wacky stuff up. But they’re another story, really.

Apparently you can include math support in a WordPress post now by using the Jetpack plugin. Doesn’t seem to align terribly well on my theme, but I approve!

One of the really weird things about physics as we know it is that the very basic laws are all time-symmetric; they’re indifferent to time going forwards or time running backwards. For instance, the Earth’s motion around the Sun: if time switched direction, the Earth would just go around the other way. The equations would all work and be consistent.

As it happens this isn’t the whole story, as we actually seem to live in a universe in which the laws of physics stay the same if you do something called a CPT transformation: you reverse the direction of time, mirror-flip the entire universe, and then change all the particles for anti-particles. So an electron going right and forwards in time could equally be described as a positron going left and backwards in time, and the physics would all be the same — if you lived in such a universe you wouldn’t notice the difference, you’d think our universe is the crazy flipped one!

The weird and interesting thing is that from our point of view, time obviously has a direction! It marches ever onwards into the future. We remember yesterday, but not tomorrow. It’s blindingly obvious when a piece of film has been reversed, because ludicrous things happen like teacups forming from ceramic shards. That obviously isn’t reversible, so what gives?

Physicists call this problem the arrow of time; why does an arrow, a preferred direction, exist when all the most fundamental laws tell us that the two directions of time should be indistinguishable?

One possible answer is entropy. Broadly speaking, entropy is a measure of disorder in a system. It’s a way of counting how many microscopic ways there are to make a particular macroscopic system. Take for example our smashed teacup. Consider that there are two states that cup can exist in: smashed, and whole. There is only one way for the cup to be whole, so it has a low entropy. There are untold millions of ways that cup can exist as a pile of smashed fragments, so that state has high entropy.

The second law of thermodynamics tells us that, on average, the entropy of a closed system will always increase, based on simple probability – for the cup it is easier to be smashed than to be whole, because there are more ways to be smashed. The laws of physics remain reversible, but the fact that so many more high entropy states exist than low entropy ones mean that playing the odds, you’ll go from low to high entropy.

So cups will always tend to smash rather than spontaneously re-form, energy will tend to turn from ordered forms which we can use (like electricity) into unordered forms, spread through the environment that we cannot use (like heat). There are some pretty compelling thought experiments (see Maxwell’s Demon, for those interested) which suggest that remembering (or more precisely, forgetting) is a process which generates entropy. There’s only one way to remember something, but millions of ways you can forget it.

So maybe that’s why we can remember the past and not the future – our memory works by increasing entropy, and entropy increases into the future. But that doesn’t answer the question as to why entropy appears to have “chosen” a particular direction in which to operate.

Well, consider a universe that starts in an high-entropy state. If that universe is already near or at maximum entropy, then only reversible processes can ever happen, because irreversible processes are the ones which generate entropy. Nothing can live, or die (because death is irreversible). Cups cannot smash, and there is no free energy around with which to do work. Some people speculate that this fate awaits our universe, and it’s called “heat death”. It simply becomes impossible to extract useful energy from the environment because it’s all become useless heat. (The other possible fate is a deep freeze, where the universe spreads out so much that the average energy density of the universe goes to zero. It’s the same problem, a lack of available energy, but much, much colder).

So instead, imagine a universe which starts in a low-entropy state. This universe is then free to be full of entropy-generating events, like smashing cups, machines, and computers (and people!) with memories capable of remembering the past. So maybe the mystery of the arrow of time is solved by our universe beginning in an incredibly unlikely low-entropy state, and evolving towards a higher entropy one, just because higher entropy is more likely than low entropy. The laws of physics all remain fully reversible, it’s just bloody unlikely that our universe started so favourably.

Although, I did have an idea: what if what we think of as the beginning, this low-entropy state, is actually the middle of the existence of a universe? From that point, you could use the laws of physics to extrapolate that universe both forwards, and backwards, but the internally perceived arrow of time, pointing along the direction of entropy growth, would point in different directions in each half of the universe’s history. Furthermore, quantum indeterminancy would guarantee that each “sub-universe” would evolve differently, despite both having come from the same low-entropy seed. Maybe beyond the big bang lies another universe after all.

Isn’t it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too? – Douglas Adams

This post began as a response to Jenny’s article, but it got a little tangential.

I just watched the first in a series of programmes on the history of the Bible, presented by the novelist Howard Jacobson:  “Creation”

I’m wary of entering religious discussions, because they rarely, if ever, go well unless you’re already in agreement with the person with whom you’re discussing.

Nevertheless, I feel, as an atheist, somewhat denigrated by that programme. I feel almost cast as if I was an robotic automaton, in thrall to the iron certainty of my science, of “mere fact”, so blind to art and literature that I would come out of a performance of King Lear and wonder if the man really existed.

They complain about the so-called “New Atheists” campaigning against the straw-men of religious believers; I say that they’re talking about straw-men atheists.

Personally, I love myth, and legend. If we weren’t called atheists, I would love to call ourselves Prometheans, stealing fire from the jealous gods for the benefit of Man. I love reading the modern myths of an author like Neil Gaiman, spinning stories of Dream and Death. I love the musings of Hamlet on death and existence, and I read the philosophy of Sartre and Nietzsche, trying to get to the nature of existence and the human condition.

I see no reason why Genesis should be venerated over and above, say, the Theogony, or the creation tales of the Shintoists, or any other work of literature. The artistry is incredible, but I see no reason why I should be compelled to find truth in it, other than the truths it reveals about the people who wrote these stories.

I find myself most agreeing with the wonderful A.C. Grayling; people wrote these stories to find agency, meaning, in a disordered universe. There’s a good reason most of them start with the division of disorder into order! Jacobson recoils when the ancients were described as ignorant, as if it’s a perjorative; the truth is that they were, they simply did not know then what we know now, after years of struggle and careful experiment. Newton was ignorant of quantum mechanics; that’s hardly a slight on his genius.

As usual, the non-scientist’s misunderstanding of the nature of science is dredged up; that we possess a cast-iron certainty, blind to everything else.

This is bollocks of the absolute highest order. Science is doubt. Science is questioning, science is about looking at the universe and admitting that our understanding of it is fragmentary and incomplete, and that we should rectify that.

Take, for example, particle physics. We have this awesome theory, the Standard Model, that describes to a truely astounding accuracy the behaviour and interactions of every known fundamental particle. It’s a staggering intellectual achievement. We’re not sure about it yet; one component of it (the Higgs particle) is still as yet unobserved, and we know that the theory will break down at higher energy scales.

This isn’t blind certainty, it’s a diligent quest to know and understand more.

What men like Jacobson and his hero, Keats, fear is that all the important things in life lie in the gaps between our knowledge, and that as science carries on it will stitch up those gaps one by one until there is nothing transcendent left in the universe, because something can be transcendent only by being unknown and mysterious, clouded in haze. They fear that the God-of-the-Gaps will be driven out.

One, if your faith is only in a God-of-the-Gaps you deserve to be driven out. What does your faith really mean if it must be constantly modified so that it isn’t obliterated by the encroaches of science? The only way I can see that ending is in a God that has been so declawed as to be nothing more than a vague spirit, not even finding a refuge beyond space and time or after death as he does now.

Two, they ignore the beauty in the truth that science reveals. The inconceivable age of the universe, the bizarre era of the condensed quark-gluon plasma, the last fading microwave echos of the time the universe was opaque, the twisted time and space of a black hole, the wonderful mad complexity of life, the nuclear-powered twisting fury of the Sun, the emptiness in the heart of the atom… the examples of wonderful ideas that come out of science and mathematics are innumerable.

Keats blamed Newton for destroying the poetry of a rainbow by explaining it; I say that a rainbow is still as beautiful today, and I think more so because I understand it; I understand how light is refracted through a drop of water, reflecting off the back surface of the spherical drop. I think that’s beautiful. I think that the solutions of the Maxwell equations of a dielectric interface that describe the reflection of light are beautiful.

Jacobson and Keats would have us give up. To throw our hands in the air, and declare that some things should be unknown, un-sought for. Thank goodness nobody listened to Keats; I dread to think where we would be if Newton’s ideas had been suppressed. This is why we should never, ever give in to irrationality. Some things are far too important.

I think our own origins as creatures who have evolved and transcended our ancestors, who have toiled against the odds to create our civilisation and our knowledge is a far more beautiful story than any that could be told by a religion, and I feel that it is ever the better because it’s what actually happened.

The title of this post is a reference to John Bell’s paper “Against Measurement” which you can read if you happen to be on a University campus. It is a piece of essentially scientific doubt on the admittedly dubious interpretation of the concept of measurement in the foundations of quantum mechanics.

That is something I find absolutely marvellous, that we can measure magnetism on something over 92 million miles away from here, on a surface that’s over 5000 degrees celsius. It’s one hell of a trick, for sure.

It’s accomplished by using a phenomenon called the Zeeman effect, and just a pinch of quantum mechanics. Electrons orbiting the nucleus are only allowed in a set of distinct energy levels, so they can only absorb energy to jump from one level to another. Photons of light have only a certain energy related to their wavelength (or colour); this means that to jump from one given energy level to another, only a very specific colour of light will do.

This means that when certain colours of light hit that atom, they’ll be absorbed and cause electrons to jump into higher energy levels. This causes certain colours of light to be missing when you look at a rainbow (or spectrum) of the light. You can calculate where these lines would be from quantum mechanics. This is how we know what the Sun is made from, for instance.

Now, when you add a magnetic field to the mix, things get a little more interesting. The magnetic field affects the orbit of the electrons, and splits one energy level into many more. This means that there are now more ways for electrons to jump from one level to another, so your neat little spectral absorbtion line will split into many lines: this is the Zeeman effect. You can tell from how much the line has split what the magnetic field strength is.

All these results can be calculated from quantum mechanics, and the Zeeman effect works just as well here on the ground as it does in the Sun. It’s brilliant!

Extra: Spectral lines work in reverse, too. Electrons in higher energy levels in an atom can only lose energy and go into a lower level by emitting a photon of a precise colour. Streetlights, for instance, work by exciting electrons in sodium, which then emit a photon of a very particular orange colour as they drop down into a lower level. This means that streetlights are almost exactly monochromatic (i.e. a single colour).

Some of them have gone well, others not so well, others were going well until I found myself running out of time, started panicing and ignored the obvious answer…

Anyways, all in all, it’s been pretty miserable so far, and it really doesn’t do wonders for morale. I really just want this to be over, because this whole experience is just making me feel like crap, and I’m pretty damned sick of it.

Right now, I’m supposed to be revising Plasma Physics, because the exam’s tomorrow and for the life of me I have no idea what he’s doing using the Bennett relation to derive the Pease-Braginskii current, and I really need this exam to go well. For a whole bunch of reasons.

At least there’s only 4 left! Plasma I think is generally going to go well, then on Friday there’s Comprehensive II, the sequel to the exam that made us all want to commit suicide the first time around, Dynamical Systems & Chaos on Tuesday, which could be pretty unpleasant, and then Foundations of Quantum Mechanics on Thursday which I think will be pretty good too, so should form a pleasant wind-down. Hopefully.

I’m really not looking forward to results day.

Anyways, back to the physics of the Z-pinch…

Since we last met, I attended the Fairtrade Society AGM, at which I failed to get elected as treasurer. I still believe in the cause, though, so I’m actually changing my buying decisions where there is a Fairtrade alternative. Which is actually kinda peculiar! There was also the Fencing annual dinner, proceeded by the shaving of the president, which was pretty funny. Some people weren’t too gentle with the clippers.

The deadline for MSci project bids rolled in, and with any luck my project will be on using a tree code to simulate plasmas in which collisional effects between particles can’t be neglected (e.g. in a very high density plasma) and provides an O(N log N) computation time as opposed to O(N^2) for naive particle-particle interactions. If you didn’t understand what I just said, never mind.

Coming up, my exams start on May 18th, so I basically have to start hitting the revision really hard and cram a whole bunch of knowledge into my head over the next few weeks. It’s going to be quite a ride. Next term there aren’t really any lectures apart from a single revision lecture for each course, so it’s a straight run-up to the exams, and then we’re pretty much free after that. We have to start preparing for a literature review for the MSci project, which I assume translates as “Raid all the books from the library that are relevant to your project, and then read them”.

My family’s going to come up for a day, and we’re going to see We Will Rock You, so that should be an interesting diversion. I should also be Fencing every Wednesday, so that should keep me active.

Then, once that kerfuffle is all over, there’s the Summer Ball, which should be an awesome wind-down to the year. I honestly can’t believe we’re already at this point again. The rapidity of it all is kinda scary, as are some of the implications of this year being over, like a bunch of my friends finishing their degrees. It’s gonna be weird.

My exams are:

• Thermodynamics & Statistical Physics
• Quantum Mechanics
• Applications of Quantum Mechanics & Electrons in Solids
• Fourier Methods, Differential Equations, & Statistics of Meausurement
• Mathematical Methods
• Electromagnetism & Optics

I’ve done one past paper each for the first two, and overall I’m fairly confident, although there are some pretty major gaps in my Thermodynamic knowledge (how do you work out entropy change again?!), which I’m desperately trying to plug. I’ve done some revision in the other areas too, so I’m feeling fairly alright with differential equations, and statistics is just a retread of A Level stats anyway, for the most part.

First exam is on the 28th, so things are moving on.

Went camping last weekend, may or may not do a writeup on that at some point, possibly when I run out of ways to continue procrastinating. Should have struck while the iron was hot.

With thanks to New Scientist for publishing this!

The best part is going through the formulae, as it’s patently obvious that they make no sense at all.

It may sound as a task somewhat obscure, but it’s really not. It governs any kind of potential, like gravitational, or fluid, or electrical, whatever.

Solving the equation in spherical polar co-ordinates gives insight into any problems in which potentials are important in a spherical environment, like the hydrogen atom. As it turns out, the various solutions to this equation are what create the energy levels in atoms, what makes a metal like copper behave differently from a gas like argon. It’s kinda fascinating that you are just going in solving this equation, and this kind of really fundamental stuff just leaps out of the mathematics.

Like the basis of energy levels is that a component of this differential equation has a series solution, a long chain of terms. If this chain of terms is allowed to go off to infinity, it’ll be unbounded – the sum of the series will itself be infinite. So you have to impose an artificial cut-off to the sequence for the solution to exist. The series of terms has to be finite. The really odd part is then this cut-off number, known as L, actually is something physical.

If you ever studied chemistry, you’ll know about s, p, d, and f orbitals, and how different numbers of electrons can fit in each. Well, if an electron is in the p orbital, then the L number I mentioned is 1. d, the L number is 2. You can probably guess what f is!

The reason that chemistry is the way it is all falls out of the solutions to this kind of equations. That really boggles my mind that the way the world is seems to be an inevitable result of the equations that govern it. Amazing.