WE STAND ON the eastern shore of Bosonia, gazing out at the ocean horizon in front of us and thinking back over the lands we have explored in the preceding expeditions. There is some debate. Should we, can we, continue, or is this the end? Should we put our feet up and stay here? There is a rather nice-looking fish restaurant off the promenade, with a terrace overlooking the beach. We find a table for dinner, and discuss future plans.
Over the aperitif and starters, we relive our recent travels and discoveries. Predicting, hunting and finding the Higgs boson was a singular triumph. A problem in the theory led to the postulation of a qualitatively new and unique object in nature: a fundamental particle with zero spin. Such triumphs occur much more rarely than you might think in physics: Dirac’s prediction of antimatter probably matches it, but not much else comes close.
The Standard Model stands tall, then. The different elements of our map all connect up and fit together self-consistently.
Atom Land has its orderly array of elements, each containing a nucleus surrounded by electrons; quantum particles bound together by the sophisticated road network of electromagnetism.
Those electrons abide on the Isle of Leptons, along with their two easterly allies, Muon and Tau, also connected by road, plus the Neutrino Sector away down to the south and west, accessible only by air, the weak force, which, albeit tenuously, connects all the lands we come across.
East of Atom Land, we entered the nucleus, and Hadron Island. Protons, neutrons and the other hadrons are connected by the sophisticated rail network of the strong force, which also takes us into the Isle of Quarks, with its Down, Strange and the rest, with their primed airports nearby.
And in Bosonia we made sense of the transport networks, and hunted down the Higgs near the Electroweak Symmetry-Breaking Scale.
There might be a bit of a wilderness left over in the Neutrino Sector, but pretty much everything works. Without the discovery of the Higgs, our map would have just been a rough outline, and would definitely have failed around the mountainous Electroweak Symmetry Breaking Scale ridge. With the Higgs, the symmetries hang together, infinities are vanquished, and yet the fundamental particles have mass. With a small number of fundamental objects and principles, the Standard Model describes and predicts an enormous variety of physical phenomena, over energy scales ranging from zero up to several 1012 electronvolts and potentially far beyond, far into the east of our map. There is a mood amongst some of our little band that this is enough. Why explore further?
As the main course arrives, others argue back strongly that we should not be too smug and complacent about the power and subtlety of the Standard Model, and neither should we despair that there is nothing left to discover. There are some important factors to consider. It is worth remembering that our overall map fails entirely to incorporate one of the fundamental forces. As we saw on our digression, gravity is described by the general theory of relativity, and in that context it is a consequence of the curvature of space–time rather than a force like those in the Standard Model, mediated by bosons. For the regions covered by our map, this is good enough. It is even possible to make a quantum theory of gravity that works in these regions, although it is not renormalisable, which as we saw on our last trip means it is not protected against infinity, so we should expect trouble. Far enough east, at high enough energies, trouble does indeed happen.
Because gravity is not properly included in the Standard Model, if we were to go far enough east, there is definitely a distance scale, corresponding to an energy of around 1027 eV, beyond which things definitely go wrong. This is the Planck scale. Gravity at this scale becomes as strong as the other forces. Singularities and infinities break out all over the place, and we have no way of understanding, or predicting, what might happen. This is a very significant failure in the ambition to describe natural phenomena in a single framework. The Standard Model is very clearly not a theory of everything, even if it co-opts General Relativity as a partner.
Worse, even at lower energies, the partnership between the Standard Model and General Relativity is inadequate.
The amazing breakthrough of gravity is that the same theory describes the way objects fall to the ground on the Earth as well as the orbits of the planets and moons in space. This is a classic success of physics – a single set of rules describing a wide range of phenomena. Newton’s gravity was a breakthrough, though you need General Relativity to get the planetary orbits exactly right (and to predict the timing and orbit of a satellite well enough to make the Global Positioning System work accurately).
As accurate measurements of more distant astrophysical objects – stars, galaxies, clusters of galaxies – are made, the expectation is that our theory of gravity should work for them too. Specifically, look at the orbit of stars around the centres of galaxies, compared to the orbit of planets around the centre of the Solar System. For each planetary orbit in the Solar System, there is a predicted speed for the orbit. This has to be the case, because the gravitational attraction between the Sun and the planet has to exactly match the required centripetal acceleration of the orbit. The same applies to stars orbiting the centre of the galaxy. In the Solar System, General Relativity gets it right. But for the stars in the galaxy, the answer does not match the observation. The stars are travelling far too fast – their orbital speeds are too high.
The speed of the stars has been measured accurately using the same technique of spectroscopy encountered in our expedition through Atom Land. Atoms give off, or absorb, light in characteristic patterns, dictated by the jumps in energy that their electrons are allowed to make. These patterns allow us to use spectroscopy to identify the elements in stars, as we saw when exploring Atom Land. But we can also observe that sometimes they are shifted, because the star is either receding or approaching. Just as with the classic example of a passing siren, approaching makes the frequency higher – blue shift, for light – and receding makes it lower – red shift, which is more usual as on average stars are receding. Precise measurements of the rotational speed of galaxies, made by the astronomer Vera Rubin and her team using this technique, convinced people there is a big problem. The stars are going too fast, and the galaxies ought to fly apart.
There are two ways of solving this conundrum. Either our theory of gravity is wrong, or our estimate of the mass of the galaxies is wrong.
If the mass of the galaxies were to be much bigger, by a factor of four or five on average, than the mass of stars and gases that we can see, then the calculations could work again. That would explain the speed of the stars. Though the missing mass, if it is there, doesn’t seem to be made of any known particle in the Standard Model. As a place-holder, we call it ‘Dark Matter’. Whatever the solution, the problem is a good argument to carry on exploring.
Another gravity-related problem is something currently labelled Dark Energy. From measurements of the red shift and brightness of supernovae, it seems that not only is the universe expanding outward from the Big Bang, but that the rate of expansion is increasing. Gravity on its own would slow the expansion, as the stars and galaxies attract each other. So a new ingredient is needed to explain the acceleration. We don’t know what this new ingredient is, but Dark Energy is the name we give to our ignorance. ‘Dark’ presumably comes from analogy with Dark Matterfn1 and ‘Energy’ comes from the fact that it needs to be some form of effective energy density which is constant throughout all space (unlike matter or photons, which get more spread out as space expands). The quantum loops of the Standard Model actually predict the existence of a vacuum energy like this. Unfortunately it gets the answer wrong by a factor of 10120 – ten followed by 120 zeroes, a number so big I am not even going to try to spell it out in words. It is such an enormous number that even some cosmologists have trouble ignoring it. Again, maybe the answer lies to the east.
The discussion continues as we eat, assembling the possible reasons for exploring further east. Another reason for further exploration is brought to the table as the desserts arrive. What about matter and antimatter?
As we explored the Isle of Quarks we discovered that the symmetry between matter and antimatter is broken, meaning there is a real difference between a world made of matter and one made of antimatter. However, the tiny violations of matter–antimatter symmetry that we know of seem far too small to explain the absolutely gross asymmetry we see around us. Matter is common, and antimatter is extremely rare. Expeditions into the Neutrino Sector of the Isle of Leptons may show up a source of matter–antimatter asymmetry that could be fitted within the Standard Model. But unless there is something new going on there, beyond the Standard Model, this source of asymmetry also looks too small. An example of ‘something beyond the Standard Model’ which could be discovered there would be that the neutrinos turn out to be their own antiparticles, a possibility we already discussed on that expedition. Such a discovery would also have implications for the far east of our map, meaning there might be supermassive neutrinos to be found out there.
A final, very general argument is brought up over coffees. It is apparent from our explorations so far that, elegant and economical though it is compared to what went before, the Standard Model contains rather a lot of parameters with seemingly arbitrary, but suggestive, values.
For example, the masses of the particles are distributed over a huge range, from the neutrinos in the west to the top quark in the east (not to mention the massless photon, gluon and possible graviton). Are they really randomly scattered, or is there a pattern in there somewhere? There are some suggestive relationships – for example, the sum or the squares of all the boson masses (Higgs, W, Z) is roughly the same as the sum of the squares of all the fermion masses (quarks and leptons). Is that just a coincidence, or is it a clue?
The Higgs mass is especially troubling. We know all particles get infinite contributions to their masses from quantum loops, and those are removed by inserting the measured mass into the equations, a technique which relies on the symmetry behind the force to protect it from infinities. But with the Higgs boson mass, because of the fact that it has zero spin, the loop corrections are enormous. No infinities, the protection still works, but if you want the Higgs mass to have a reasonable value both at the electroweak scale (which is where it is) and onwards into the east to another energy scale, say the Planck scale, the cancellation of those corrections has to be ridiculously ‘fine-tuned’. It is as though the Higgs balances on a knife-edge over many orders of magnitude, where a slip to either side would make nonsense of the Standard Model. A favourite analogy is a bank account with credits and debits (the quantum corrections) of billions of pounds occurring seemingly randomly throughout the month, yet on the last day of each month the account magically contains exactly £125. This would seem to be too much of a coincidence. There must surely be an accountant paying attention – or, in the case of physics, maybe a bigger theory pulling the strings of the Standard Model.
Even the number of generations of matter looks suspicious. Just the first generation would seem to be perfectly adequate to make up all the elements. As we saw, three is the minimum number to allow a real distinction to be made between matter and antimatter, which seems significant. But perhaps we just haven’t explored far enough east. Maybe there are four, five or even an infinite number of generations?
To the relief of the waiters, we pay our bills and leave the restaurant. But the discussion does not die down as we stroll along the seafront back towards our hotel.