It's a Small World

Built up over the last 70 years, the Standard Model is the most successful attempt yet to create a single theory describing the forces and particles that make up our universe. The Standard Model describes all the elementary particles as well as the strong, weak, and electromagnetic forces.

The Standard Model explains all the hundreds of particles and complex interactions using only 17 particles:

The Elementary Particles

All elementary particles are either fermions or bosons. The particles which form matter are called fermions. These may be either quarks (pronounced "kworks") which combine to produce protons and neutrons in the atomic nucleus, or leptons (such as electrons). A proton is composed of two "up" quarks and one "down" quark, and a neutron is composed of two "down" quarks and one "up" quark:

The particles which carry the fundamental forces are called bosons (sometimes referred to as exchange particles). For example, the gluon is the boson which holds the quarks together to form protons and neutrons (we'll hear more about gluons when we consider the strong nuclear force later):

Fermions and bosons behave differently. Fermions (such as electrons) do not like to occupy the same states, so keep away from one another (due to the Pauli Exclusion Principle). This antisocial behaviour of fermions is what gives atoms their shape, and prevents matter from collapsing down into a featureless blob. However, bosons (such as photons) are quite happy to congregate in the same state. They can gather together in a cooperative fashion to create laser light, for example.

For every type of particle there also exists a corresponding antiparticle. Antiparticles have opposite charges, for example, a proton has positive electric charge whereas an antiproton has negative charge. The existence of antiparticles makes possible the creation of antimatter, composed of atoms made up of antiprotons and antineutrons in a nucleus surrounded by positrons. When a matter particle and antimatter particle meet, they annihilate into pure energy.

This neat chart from Scientific American shows all 17 particles in the Standard Model, together with their masses:

The Four Fundamental Forces

There are four fundamental forces of nature. At the microscopic level, these four forces are not forces in the usual sense of the word. Forces are now considered to be produced by an exchange of boson force particles. These bosons are exchanged between fermion matter particles.

Here are the four fundamental forces:

The Electromagnetic Force

The force between electrically-charged particles, and magnetism. The force is carried by photons. The quantum approach to this force is called quantum electrodynamics (or QED for short).

For example, electrically charged particles (such as electrons) might be attracted or repulsed from each other due to the electromagnetic force. What actually happens is that when an electron repels or attracts another electron, photons are transferred between them. Photons are the carriers (or mediators) of the electromagnetic interaction. The "force" emerges as the interacting particles change their speed and direction of travel as they absorb or release the energy of the photon.

The diagram below is a Feynman diagram of two electrons interacting via the electromagnetic force, passing a photon between them:

(For a decoding of the letters used to denote particles in these Feynman diagrams, see the standard model chart at the top of this page)

The Weak Nuclear Force

The force behind beta radioactive decay (see here). This force is carried by the W and Z bosons.

The diagram above shows beta radioactive decay. A neutron is transformed into a proton, giving off an electron and an antineutrino. The down quark from the neutron changes to an up quark producing a W boson, the mediator of the weak nuclear force. The W boson then decays into an electron and an antineutrino.

This force has been unified with the electromagnetic force to form the electroweak force, i.e., they are the same force behaving in two different ways at our everyday low energies. If it is hot enough (for example, the unimaginably high temperatures reached in the first moments after the Big Bang) then the electromagnetic force and the weak force would merge into a single electroweak force. The difference in strength of the electromagnetic and weak forces is due to the difference in mass between the W and Z bosons and the photon: the weak force is mediated by the massive W and Z bosons and is therefore weak and short range, whereas the electromagnetic force is mediated by massless photons and is therefore long-range (can bring us light from the stars, for example).

The theory of electroweak unification predicts another key particle, the Higgs boson. The role of the Higgs boson is to give mass to the W and Z bosons, but not to the photon (the mechanism by which this imbalance occurred is called symmetry breaking). The Higgs boson has not yet been detected in experiments, but it is hoped the 27 km-long Large Hadron Collider at CERN will have sufficient energy to produce the massive Higgs boson. But if the Higgs boson gives mass to other particles ... what gives mass to the Higgs boson?!

The Strong Nuclear Force

The force which holds protons and neutrons together within the nucleus (see here). Needs to be strong to hold a nucleus together against the enormous forces of repulsion of the protons. This is the force behind alpha radioactive decay (the ejection of a helium nucleus - two protons and two neutrons - from a larger atomic nucleus).

The force is created by pion exchange. A pion is composed of two quarks - see the diagram below which shows a proton changing to a neutron and vice versa via pion exchange. It is this pion interaction which holds the atomic nucleus together:

In the diagram above, the pion is composed of an up quark and a down antiquark.

As quarks are held together in protons and neutrons by gluons, it is the gluons which mediate the strong nuclear force. The theory of interacting quarks and gluons is called quantum chromodynamics (or QCD for short).

Gravity

Gravity is not incorporated into the Standard Model.

"There is nothing new to be discovered in physics now. All that remains is more and more precise measurement." - Lord Kelvin (in 1894)

Quantum Field Theory

At the end of the nineteenth century it was believed that all of the big problems in physics had been solved. All of physics, it seemed, could be explained in terms of particles (the atoms) and fields (which spread through space, invisible to our eyes, able to exert force on particles at a distance). However, the discovery of quantum mechanics and relativity soon shook that cosy worldview. It was discovered that light was composed of packets called photons (see back to the page Quantum Mechanics: An Introduction). As it was known that light is an electric field (Maxwell's theory of light), this suggested that fields were not continuous but could, in fact, be quantized into particles. In 1927, Paul Dirac published a paper combining quantum mechanics with Maxwell's theory of light to give a quantum theory of the photon: a relativistic quantum field theory.

This idea of the electromagnetic force being composed of billions of force-carrying photons was explained in the section on the electromagnetic force above. The theories of the three fundamental forces incorporated in the standard model - the electromagnetic force, the weak nuclear force, and the strong nuclear force - are quantum field theories and show that a field is really composed of billions of force-carrying bosons, such as the photon and gluon, spread through space. Relativistic quantum field theory completely eliminates the distinction between particles and fields.

In the 1940s, Richard Feynman developed a new method for calculating particle interactions in quantum fields. This involved his famous Feynman diagrams (considered earlier). The Feynman diagram method works by calculating all the possible ways in which two particles can interact and then adding them up. In fact, there are an infinite number of different ways in which these interactions can take place, and an infinite number of different paths that a particle can take between two points. It emerges that the probability of a particle appearing at a certain position is based on the sum of all possible paths that the particle can take from point A to point B (as seen in the discussion on quantum mechanics, a particle's position should be considered as the quantum superposition of many possible positions, so it makes a kind of sense that a particle's motion path should be a quantum superposition of all possible motion paths).

Quantum field theory is plagued by problems which emerge when considering such infinite possibilities. Mathematical methods have been developed to avoid the problems by the rather unsatisfying technique of renormalization. This has been called mathematical butchery, however the predictions of quantum field theory have been verified experimentally and shown to be extraordinarily accurate.

String Theory

String theory can avoid the infinities of renormalisation by treating particles as little loops of energy rather than points of infinitely small size. These loops trace out very small tubes in space when they move. The loops have a tension which increases at low energies making the loops tighter and more pointlike. Particle interactions are described by tubes joining and splitting (see diagram above) in a smooth process which avoids the undesirable infinities.

The downside of string theory is that the equations only work in 10 or 11 dimensions of space (the extra dimensions are understood to be curled up very small). As a result, string theory remains rather speculative and controversial.

The Tower of Turtles

An effective theory is a theory which is built-up on deeper theories, i.e., its inputs are the outputs of a deeper theory. For example, in nuclear physics one takes the mass, charge, and spin of the proton as inputs. In the Standard Model, one can calculate those quantities, using properties of quarks and gluons as inputs. Nuclear physics is an effective theory of nuclei, whereas the Standard Model is the effective theory of quarks and gluons.

From this point of view, every effective theory is equally fundamental - that is, not truly fundamental at all. Will the "ladder" of effective theories continue?

There's a famous story: a lecturer was presenting a lecture on astronomy. At the end of the lecture, a little old lady got up and said: "What you have told us is rubbish. The world is really supported on the back of a giant turtle." The scientist gave a superior smile before replying, "What is the turtle standing on?" "You're very clever, young man", said the old lady, "but it's turtles all the way down."

The lady was clearly aware of the principle of infinite regression (see here). The tower represents the chain of explanation (Paul Davies's term). As Steven Weinberg has said: "I have to admit that, even when physicists will have gone as far as they can go, when we have a final theory, we will not have a completely satisfying picture of the world, because we will still be left with the question 'why?' Why this theory, rather than some other theory?" (see here).

In his book The Goldilocks Enigma, Paul Davies suggests that science will always have to accept some turtle (positioned at a relatively low position in the tower of turtles) as the fundamental, bottom turtle: the "Super Turtle". That is their starting point: The equations must be accepted as 'given', and used as the unexplained foundation upon which an account of all physical existence is erected." Many string theorists would position the multiverse interpretation as their Super Turtle - the fundamental base layer. Though, as explained in the page on The Anthropic Principle, the multiverse interpretation only pushes the problem back to a deeper layer, and you end up having to posit a ladder of multiverses! Turtles upon turtles.

Does this mean our attempts to plough ever deeper into the world of particle physics is futile? Well, if we are truly living in a universe of infinite regression at the microscopic scale then by delving deeper and deeper we are in fact NOT even revealing more fundamental aspects of the universe: one step forward on an infinite path leaves you no nearer the destination. If we are truly living in an infinite-regression universe then it would appear that our experimental tools such as particle accelerators are not suited to the task of revealing fundamental truth - there will always be a deeper layer to be uncovered.

Here are some speculative thoughts about how to do away with the idea of a Super Turtle:

Imagine we live on a hypothetical flat surface, trapped in two dimensions, and all our experimental results travelling down the ladder of effective theories are the equivalent of travelling about that surface - learning a bit more about the surface on which we live. But that surface is an infinite plane: we can keep walking forever. What we really need is some way of getting "up in the sky" - movement in a third dimension - so we can look down, and then we could clearly see the infinite plane on which we live. We could see the infinite chain of turtles. We could capture the truth of our situation. What we're missing is that "big picture". How might we get it?

Well, particle accelerator experiments aimed at finding more fundamental effective theories might be considered analogous to determining more decimal places of pi: no matter how many decimal places you calculate, you will never possess the actual value; you can never get to that ultimate truth. In this respect, we could imagine successive digits as representing a deeper effective theory:

However, pi can also be expressed as an infinite series:

Here's the key: it is then possible to express that series in compact form:

So it is possible for the representation (i.e., the equation as written directly above) of an infinite tower of turtles to take a finite, compact form (without the need to introduce series-ending Super Turtles). And that entire form can be viewed and comprehended (even by the minds of mere mortals - something not possible with the original infinite tower). But it has to be more than just a mathematical formula: it's an all-encompassing comprehension of reality, not founded on some arbitrary Super Turtle (for example, deciding to consider the multiverse as fundamental, equivalent to stopping the calculation of pi after an arbitrary 2 million decimal places and saying "That's it"). This could be considered the "God's-eye" view of the infinite tower of turtles: the ability to see an infinite chain in a finite form. This is the "big picture" of reality we are seeking.

This is a similar notion to Cantor's Absolute Infinity. John D. Barrow from The Infinite Book: "Cantor could build up a never-ending tower of larger and larger infinities from below but he realised that that infinity could not be approached 'from above'. There was no God's-eye view of the tower that was available to us. Cantor used the name Absolute Infinity for the totality of everything. It is something that is beyond mathematical determination or representation. It can only be comprehended by the mind of God."

Maybe Cantor underestimated humanity; maybe we could comprehend that God's-eye view as long as it was presented in a compact form. (It's interesting to note how in the latest computer simulation "God games" such as The Sims "the game is observed from an aloft, elevated perspective" - see this Wikipedia article. This is considered in the page on The Big Brother Universe).

"To my mind there must be, at the bottom of it all, not an equation, but an utterly simple idea. And to me that idea, when we finally discover it, will be so compelling, so inevitable, that we will say to one another: 'Oh, how beautiful. How could it have been otherwise?'" - John Wheeler

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Andrew. Just curious. What is your academic background? - Tim Clark (Assoc. Prof.), 26th July 2007

Hi Tim, I studied physics as an undergrad at Edinburgh University. My background is really in computing, though. I just have a fascination with these fundamental theories, and have pursued them as a hobby in my spare time. I think there's a thirst out there in a lot of people wanting to know the answers to the "big questions". - Andrew Thomas, 26th July 2007

Hi Andrew, loving this site. It does appear you have a particular bias against particle accelerators. You mention in several articles that we seem to be wasting our time with them and that they're fundamentally trying to measure the wrong thing. Did you have a bad experience with one as a child? :D :D I'm mostly kidding, but partly serious. What do you think we should be doing instead? Thanks!!!! - Mike Pinkerton, 9th September 2007

Oh dear, I had better be careful what I write! As you suggest, I can't help feeling there's a certain futility about the current work with particle accelerators. I presume you're aware of this notion of a vast "Great Desert" in energy values between what current accelerators can achieve and the energy required for unification of the fundamental forces, a desert which, it seems, we will never be able to cross. This quote I found on the internet says it well: "Theorists do expect novel higher-energy phenomena, but only at absurdly inacessible energies. Proton decay, if it is found, will reinforce the belief in the great desert extending from 100 GeV to the unification mass of 10^14 GeV. Perhaps the desert is a blessing in disguise. Ever larger and more costly machines conflict with dwindling finances and energy reserves. All frontiers come to an end." See: http://math.ucr.edu/home/baez/week131.html Also, most interesting recent results in particle physics seem to have come from astronomy, not accelerator experiments: dark matter, for example. That's not in the Standard Model!

So what should we be doing instead? Well, maybe we should be looking at the stars more. And maybe a more honest discussion about the limitations of our experimental methods would be welcome, perhaps together with less talk of achieving grandiose "theories of everything" in the near future. Or maybe we should just take a step back, take stock, and have a think. Thinking is free.

Thanks very much for your comment. - Andrew Thomas, 10th September 2007