2: The Ocean Wave …

fn1 I think there is such a quiet spot in my office at CERN which is why, in the birthplace of the world wide web, I still struggle to get on to the internet sometimes. There are just too many waves, arriving at the wrong times, and happening to cancel each other out in the vicinity of my desk.

fn2 I apologise to the seagull. That got unexpectedly violent.

3: … Or Particle?

fn1 This difference spurred the development of quantum mechanics, and inspired a breakthrough result from Albert Einstein, which resuscitated the idea of light as a particle.

fn2 Annalen Der Physik 17 (1905) pp. 132–48. See http://einsteinpapers.press.princeton.edu/

4: Travelling in the Quantum Field

fn1 This is why on some physics wall charts, heavy particles are shown as big blobs compared to smaller blobs for lighter particles such as the electron.

fn2 QED: The Strange Theory of Light and Matter, 1985.

fn3 This is the same effect as minimum height of the land in a valley. On the sides of a valley, adjacent positions have different heights due to the slope, but at the base of the valley – the minimum height – the ground is almost flat and adjacent points have almost the same height. In the same way, paths near the minimum number of turns have a very similar number of turns to each other, so they add up.

5: Atoms

fn1 It is.

fn2 It is tempting to think that these must have been a welcome break from studying the Mancunian weather.

6: Going Subatomic: The Electron

fn1 The magnetic force on a particle depends on both its charge and its speed, whereas the electric force depends only on its charge. So when these are made to be equal, with a bit of algebra the unknown charge can be cancelled out, and the speed can be calculated.

fn2 Knowing the speed is crucial, because that tells you how long the electric force acts on the electrons as the beam passes between the plates. The impulse from the force deflects the beam by an amount depending on the charge (high charge means a larger force, so a larger deflection) and the inverse of the mass (high mass means more inertia, so smaller deflection). The result is that the deflection depends on the ratio of the charge and the mass.

fn3 This is a very painstaking experiment, even more so when carried out with oil drops instead of standard spheres, as it was originally in 1910 by the American physicist Robert Millikan. The experiment is still carried out, largely without success, in far too many undergraduate physics laboratories by squinting and impatient students.

7: Nuclear Options

fn1 The other common forms are beta particles, which are electrons, and gamma rays, which are photons.

fn2 Apparently there’s a good historical raisin for this.

8: The Source of Chemistry

fn1 The equation which describes these waves is the Schrödinger equation. Less famous than his cat but much more useful.

fn2 This unfriendly behaviour is the ‘exclusion principle’ discovered by Wolfgang Pauli, one of the first explorers of our landscape who we will meet again before too long.

fn3 One electronvolt (eV) is the energy of motion that an electron acquires if it is accelerated through one volt of electric potential. So a 12-volt battery can accelerate an electron to an energy of 12 eV. To get to millions of eV would require several hundred thousands of such batteries. Or the nuclear power of one decaying nucleus.

9: Electromagnetism

fn1 Recall that it was by balancing these two forces that J. J. Thomson discovered the electron.

fn2 The original manuscript was submitted in 1864, but, in a situation familiar to scientists everywhere, was then held up in peer review. There’s a letter, dated March 1865, from William Thomson (later Lord Kelvin) saying he was sorry for being slow, that he’d read most of it and it seemed pretty good (‘decidedly suitable for publication’).

10: Invariance and Relativity

fn1 This is the way they appear at the foot of the statue of Maxwell near the Royal Society of Edinburgh.

fn2 This is actually why they save on ink – when we clump the components together into vectors and write the equations that way, the absolute directions of the vectors don’t even appear in the equations. The physics does not depend on them.

11: The Good Ship Dirac

fn1 Energy is equal to the square of the momentum divided by twice the mass, E = p²/(2m), which is equivalent to the possibly more familiar expression for kinetic energy, E = ½mv², where v is the velocity.

fn2 If you want to know, the full expression is E² = m²c⁴ + p²c⁴, where E is the energy, m is the mass and p is the momentum. For zero momentum, this reduces to E² = m²c⁴, and taking the square root of both sides gets us the familiar E = mc². And possibly E = –mc² too (see text).

fn3 This is true in Schrödinger’s equation. But because of the way relativity mixes up energy and momentum (and space and time), the momentum must appear to the same power as the energy. In the Schrödinger equation, the momentum appears squared, which won’t do.

fn4 You don’t need to understand exactly how this works in order to continue our exploration, but if you’d like to see it, here goes. We want an equation like E = Am + Bp, but which is also consistent with E² = m²c⁴ + p2c⁴. If we square the first equation we have to multiply all the terms by each other, so we get E² = A²m² + (Am × Bp) + (Bp × Am) + B²p². Now we have two expressions which ought to both equal E², so they must equal each other: m²c⁴ + p²c⁴ must equal A²m² + (Am × Bp) + (Bp × Am) + B²p², for any values of m and p. If we let A² and B² both be equal to c², that takes care of the terms involving the square of the mass and the square of the energy. But we are left with the other bit (Am × Bp) + (Bp × Am). This can only be zero (for all values of p and m, because we want an equation which works for all particles) if A × B is equal to the negative of B × A. But for all numbers, A × B equals B × A. So A and B cannot be numbers.

fn5 From the point of view of mathematics the numbers can be pretty much anything you like, although if we want to use them to help us understand physics, they take on specific meaning. For example, the numbers in a matrix can encode how the different components of a magnetic field change when we rotate it through some angle about some direction.

The Weakest Force

fn1 Most days except Monday, in fact.

fn2 Though, disappointingly, not in their personal lives.

Planes and Roundabouts

fn1 Newton’s law, F = ma.

Different, Yet Somehow the Same

fn1 An innovation due to Michael Faraday’s very early thoughts about electricity and magnetism.

14: Protons, Neutrons and the Nucleus

fn1 Or to put it another way, they can smash it up.

fn2 G. Allen & Unwin, Limited, a translation of the original “Das Weltbildder neuen Physik” (1929)

15: Hadrons

fn1 As with leptons, this is from the Greek barus (heavy) and meso (intermediate).

16: Quarks and the Strong Force

fn1 Very recently, new structures have been found deep in the interior of the island, with two quarks and two antiquarks (tetraquarks) and four quarks and an antiquark (pentaquarks). Extremely ephemeral, the internal structure of these objects is the subject of ongoing exploration.

18: Flavours and Generations

fn1 The same word is used to describe the different types of lepton – electron, muon and tau.

fn2 Also in Manchester, in 1947 – ten years after the first curry house, according to a report in the Manchester Evening News.

fn3 They have alternative names – beauty and truth – but they are too pretentious for most physicists.

fn4 This peculiar hierarchy of masses may well be one of the biggest clues to what lies beyond the Standard Model – certainly, the top quark plays quite a special role in many speculative new theories.

19: The Weak Force

fn1 Unless and until they meet with a top antiquark and are annihilated.

20: Parity, Helicity and Chirality

fn1 From the same root as ‘helix’. The tip of a spinning arrow will describe a helix as the particle moves along through space.

fn2 Their map of physics should be the same as ours, after all, even if they use different words to describe it.

fn3 Apart from, presumably, saying, ‘See that funny-looking galaxy over there? That’s on our left.’

23: Massless Matter?

fn1 And Swiss. And American.

fn2 He also developed the exclusion principle we discovered in Atom Land.

fn3 Entities must not be multiplied beyond necessity.

24: The Standard Model is Dead – Long Live the Standard Model!

fn1 C₂Cl₄ – two carbons with four chlorines.

25: Neutrino Badlands

fn1 The relevant equations were first written down by Italian physicist Ettore Majorana, and so this kind of particle is often called a Majorana particle, leading to unexpected drug references in many physics presentations.

27: Symmetry and Bosons

fn1 That is, rotations in the U(1) group.

fn2 The ‘S’ means it is a special subgroup of a bigger U(2) group.

28: Virtual Particles and the Defence Against Infinity

fn1 This number characterises the strength of the interaction, and depends on the charge of the electron – if the charge were higher, the number would be higher.

fn2 The proof that this is the case was published by Dutch physicists Gerardus ’t Hooft and Martinus Veltman in 1971.

30: Electroweak Symmetry Breaking

fn1 This is the W boson playing its trick of switching particles around within doublets, which we noted when we first studied the weak force.

fn2 The forces don’t exactly unify (they still come from distinct symmetries, U(1) and SU(2)) but it turns out there is a mixing between the neutral bosons. The photon is not exactly the neutral boson you would expect from U(1), and the Z is not purely from SU(2). They are both a mixture of the neutral bosons one would expect from the two different symmetries.

31: Hunting the Higgs

fn1 This is true for types of materials known as ferromagnets.

32: Why Go?

fn1 Which, as US physicist Lisa Randall has pointed out, would be better named Transparent Matter, really, since it is invisible rather than opaque.

34: Sea Monsters and Dark Matters

fn1 As might be expected, it was large, underground (in the Sanford Underground Research Facility in South Dakota), and made mostly of xenon.

35: Supersymmetry

fn1 The Higgs, which is always special, has to have at least four extra Higgs bosons, as well as superpartners.

36: Into Another Dimension?

fn1 There is no chance that black holes produced this way could destroy the Earth, by the way, otherwise this would have happened, and be happening, already and all over the place, because of the very high cosmic-ray collisions that go on around us.

37: Over the Edge

fn1 The bar is making a half-hearted attempt to be a gastropub, so it has big green olives in a jar, as well as a bottle of balsamic vinegar and some baskets with bread in. The regulars are ignoring all of this and sticking to their drinks and stories, so no one will mind if we use them to try to illustrate sphalerons.

38: A Fifth Force

fn1 In case you were wondering, yes, this is the kind of pub which has jigsaw puzzles on a shelf in the lounge bar, along with backgammon and a Scrabble set with the Q, X and three vowels missing.