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8.7 — Beyond the Standard Model
The Standard Model has passed every test for fifty years and everybody working on it believes it is incomplete. Both statements are true, and this chapter explains why, then works honestly through the proposed successors — separating what is established, what is a promising idea with no evidence, and what is currently untestable in principle.
The last distinction matters more than it usually gets. A theory that could be tested and has not yet been is in a different position from one that cannot be tested at all, and both are in a different position from the Standard Model, which has been tested to twelve decimal places.
The problems, ranked
Confirmed observational failures
These are not aesthetic complaints. The Standard Model gives the wrong answer or no answer for something we have measured.
1. Neutrino masses. The theory as written has none. They exist (Chapter 8.5). The mechanism is unknown. This is a confirmed failure.
2. Dark matter. 27 % of the universe's energy, 85 % of its matter, and no Standard Model particle can be it (Chapter 12.7). Confirmed failure.
3. Dark energy. 68 % of the universe, and the theory's own estimate of vacuum energy is wrong by 10^{122} (Chapter 7.9). Confirmed failure, and by the largest margin in the history of physics.
4. Matter–antimatter asymmetry. The universe contains matter. The theory's CP violation is about 10^{10} times too small to explain it (Chapter 7.10). Confirmed failure.
5. Gravity. Not included, and not includable by existing methods. Confirmed gap.
Structural problems
These are not failures — the theory works — but they look like symptoms.
6. The hierarchy problem. The Higgs mass requires cancellation to 34 decimal places (Chapter 8.4).
7. The strong CP problem. QCD permits a CP-violating term with coefficient \theta; the neutron's electric dipole moment says |\theta| < 10^{-10}. Why is a free parameter zero to ten decimal places?
8. Twenty-six free parameters, none explained.
9. Three generations, for no reason.
10. The flavour puzzle. Masses spanning 10^{11}, mixing angles small for quarks and large for neutrinos. No pattern.
Supersymmetry
The idea: a symmetry relating fermions and bosons. Every particle gets a superpartner with spin differing by ½.
| Particle | Superpartner | Spin |
|---|---|---|
| Quark | Squark | 0 |
| Electron | Selectron | 0 |
| Photon | Photino | ½ |
| Gluon | Gluino | ½ |
| Higgs | Higgsino | ½ |
| Graviton | Gravitino | 3/2 |
Why it was so attractive — four independent reasons, which is unusual.
It solves the hierarchy problem. The dangerous quantum corrections to the Higgs mass come from loops. Fermion loops and boson loops enter with opposite signs, so if every fermion has a boson partner of equal mass, the corrections cancel exactly. The cancellation is a theorem, not a tuning.
It unifies the couplings. Chapter 8.3 noted that the three gauge couplings nearly meet at 10^{15} GeV and miss. Adding superpartners changes the running and they meet precisely. This is the single most impressive quantitative argument for supersymmetry.
It provides dark matter. The lightest superpartner, if stable, is neutral, weakly interacting and massive — exactly a WIMP (Chapter 12.7), with roughly the right relic abundance for free. This near-coincidence is called the WIMP miracle.
It is required by string theory.
And it has not been found
The LHC has looked systematically since 2010. Squarks and gluinos would be produced copiously by the strong interaction if they existed below a couple of TeV, and would give distinctive signatures — many jets plus large missing momentum from the escaping lightest superpartner.
Current limits: gluinos above about 2.3 TeV, squarks above about 1.8 TeV, and lighter partners excluded across large regions of parameter space.
This does not rule out supersymmetry, which has over 100 free parameters in its general form and can always be arranged to hide. It does damage the motivation. The hierarchy problem is solved only if the superpartners are near the Higgs mass; at 2 TeV the cancellation is already incomplete, and fine tuning of about one part in a thousand has returned.
The honest assessment: supersymmetry may exist at higher energy, in which case it is not solving the problem it was invented for. The field is markedly less confident than it was in 2008.
Grand unified theories
The idea: the three gauge groups of Chapter 8.2 are pieces of one larger group, broken at high energy.
SU(5), the simplest, proposed by Georgi and Glashow in 1974. It puts quarks and leptons in the same multiplet, which explains something otherwise mysterious: why the electron's charge is exactly -1 and the down quark's is exactly -1/3, with no measured deviation. In a unified theory the ratio is fixed by group theory.
The prediction that killed it: proton decay. If quarks and leptons are in one multiplet, transitions between them are possible:
p \to e^+ + \pi^0
SU(5) predicted a lifetime around 10^{31} years.
Super-Kamiokande looked. With 10^{33} protons in the tank watched for decades, a 10^{31}-year lifetime would give many events per year.
Zero events. The limit is now >2.4\times10^{34} years for this channel.
Minimal SU(5) is dead, killed by an experiment that saw nothing. Larger groups — SO(10), E6 — predict longer lifetimes and remain viable, and SO(10) has the attraction that it naturally includes a right-handed neutrino and hence the seesaw mechanism of Chapter 8.5.
String theory
The idea: the fundamental objects are not point particles but one-dimensional strings, about 10^{-35} m long. Different vibrational modes of the same string are different particles, exactly as different modes of a violin string are different notes.
Why it was taken seriously
It contains gravity, unavoidably. Chapter 7.10 explained that quantising general relativity produces non-renormalisable infinities. Strings remove them, because a string has spatial extent, so interactions are smeared over a region rather than occurring at a point, and the divergences that come from point interactions never arise.
And the graviton is not put in — it falls out. One of the string's vibrational modes is automatically a massless spin-2 particle, which is precisely what a graviton must be. The theory could not avoid gravity if it tried.
Michael Green and John Schwarz showed in 1984 that certain anomalies — mathematical inconsistencies that would kill the theory — cancel exactly, but only for very specific gauge groups. That result set off the "first superstring revolution", and for a few years it looked as though the theory might be essentially unique.
The mathematics, sketched honestly
A point particle traces a worldline through spacetime (Chapter 6.5), and its action is proportional to the length:
S = -mc\int ds
A string traces a worldsheet, a two-dimensional surface, and its action is proportional to the area:
S = -\frac{T}{c}\int dA
This is the Nambu–Goto action. The tension T is the only parameter, usually written through the string length:
\ell_s = \sqrt{\alpha'} \sim 10^{-35}\ \text{m}
close to the Planck length.
Quantising it — requiring the theory to be consistent, with no negative-probability states and no anomalies — produces a startling constraint. The number of spacetime dimensions is not free.
\boxed{D = 26\ \text{(bosonic string)}, \qquad D = 10\ \text{(superstring)}}
The dimension of spacetime is an output, which is unlike anything in the Standard Model.
And it is the wrong answer. We observe four.
Compactification and the landscape
The proposal: six of the ten dimensions are curled up so small that they are invisible. A garden hose seen from far away looks like a line; up close it has a circumference.
The size required is around 10^{-35} m, which is 10^{20} times smaller than a proton and utterly beyond any conceivable probe.
And here is the difficulty that has defined the field for two decades. The shape of the curled-up dimensions determines the physics of the four large ones — the particle masses, the couplings, the gauge groups. Different shapes give different universes.
How many shapes are there? The Calabi–Yau manifolds satisfying the constraints, together with the possible field configurations wrapped on them, give an estimated:
\sim 10^{500}\ \text{possible vacua}
This is the string landscape, and it is a serious problem. A theory with 10^{500} solutions predicts nothing about which one we live in. No principle has been found that selects ours.
The response from part of the field is the anthropic argument: all of them exist somewhere in a multiverse, and we necessarily find ourselves in one compatible with observers. Chapter 12.9 examines whether this counts as physics.
The response from critics, notably Lee Smolin and Peter Woit, is that a framework which accommodates any observation explains none. Their sharpest point is that string theory has, in forty years, made no confirmed prediction that distinguishes it from alternatives.
What string theory has achieved
It is not vacuous, and dismissing it entirely would be wrong. Its real successes are mathematical and conceptual.
Black hole entropy, counted. Strominger and Vafa showed in 1996 that for certain extremal black holes, counting the string states with the given charges reproduces the Bekenstein–Hawking entropy S = A/4 exactly, including the coefficient. Chapter 12.3 explains why that is remarkable: it is a microscopic explanation of a thermodynamic quantity, which is what statistical mechanics did for entropy in Chapter 3.5.
The AdS/CFT correspondence. Maldacena conjectured in 1997 that a gravitational theory in a certain curved spacetime is exactly equivalent to a gauge theory without gravity living on its boundary — a holographic duality, in which a theory in D dimensions equals a different theory in D-1.
This has turned out to be genuinely useful outside string theory. It provides a calculational method for strongly coupled systems where perturbation theory fails, and has been applied to the quark–gluon plasma produced at RHIC — where it predicted a viscosity-to-entropy ratio close to the measured value — and to certain problems in condensed matter physics. Maldacena's paper is the most-cited in high-energy physics.
Mathematical results. Mirror symmetry, discovered by physicists studying Calabi–Yau spaces, solved problems in enumerative geometry that mathematicians had not been able to touch.
What it has not achieved
No experimental confirmation of any kind.
No prediction of the Standard Model's parameters.
No prediction that could distinguish it from anything else at accessible energy.
No unique vacuum.
Supersymmetry, which it requires, has not been found.
The honest position: string theory is a deep and mathematically rich framework that has produced genuine results in mathematics and in calculational technique, and it is not currently a testable theory of nature. Whether it will become one is unknown.
Loop quantum gravity
The alternative approach, and its philosophy is the opposite of string theory's.
String theory quantises matter on a fixed background spacetime. Loop quantum gravity quantises spacetime itself, applying quantum mechanics directly to the geometry of general relativity without adding extra dimensions or supersymmetry.
The central result: area and volume operators have discrete eigenvalues (Chapter 7.5's eigenvalue machinery, applied to geometry).
A = 8\pi\gamma\ell_P^2\sum_i\sqrt{j_i(j_i+1)}
Area comes in quanta, with the smallest unit around \ell_P^2 \approx 10^{-70} m². Space is not infinitely divisible in this picture; it has a granular structure at the Planck scale, described by combinatorial objects called spin networks.
What it offers:
- Background independence — no fixed spacetime is assumed, which is philosophically closer to general relativity's spirit.
- Four dimensions, no extra ones needed.
- No supersymmetry required.
- The Big Bang singularity is replaced by a bounce in loop quantum cosmology, since the discreteness prevents infinite density.
- Black hole entropy is reproduced, though with a free parameter (the Immirzi parameter) fixed by requiring the right answer, which is less impressive than the string result.
What it lacks:
- It does not unify the forces — matter must be added by hand.
- Recovering ordinary smooth spacetime as a limit is not fully established, which is a serious technical gap.
- No experimental confirmation.
A possible test: if spacetime is granular, very high energy photons might travel at slightly different speeds from low energy ones, accumulating a measurable delay over cosmological distances. Gamma-ray bursts have been used to look, and no effect has been found, which constrains some versions of the idea.
Other directions
Asymptotic safety. Perhaps gravity is renormalisable after all, in a non-perturbative way, if the couplings run to a finite fixed point at high energy. Weinberg proposed this in 1979 and there is growing computational evidence. It requires no new particles or dimensions.
Causal set theory. Spacetime is a discrete set of events with a partial ordering, and everything else emerges from that.
Emergent gravity. Gravity is not fundamental at all but a thermodynamic or entropic effect, as Jacobson and Verlinde have argued. Jacobson showed in 1995 that the Einstein equations can be derived from thermodynamics applied to horizons, which is at least suggestive.
Extra dimensions without strings. Large extra dimensions, proposed by Arkani-Hamed, Dimopoulos and Dvali, could lower the true Planck scale to a TeV and make quantum gravity accessible at the LHC. The LHC has looked for black hole production and found nothing, ruling out the most dramatic versions.
What is established, speculative and untestable
Established beyond serious doubt:
- The Standard Model's particle content and interactions, to twelve decimal places.
- Neutrinos have mass and oscillate.
- Dark matter exists as a gravitational effect (Chapter 12.4).
- The universe's expansion is accelerating.
- General relativity is correct in every regime tested.
Well motivated and unconfirmed:
- Some form of dark matter particle.
- The seesaw mechanism for neutrino masses.
- Leptogenesis for the matter asymmetry.
- The axion, for the strong CP problem.
- Grand unification at high energy.
Speculative:
- Supersymmetry.
- Extra dimensions.
- Proton decay at accessible rates.
Currently untestable, possibly in principle:
- String theory's specific compactification.
- The multiverse.
- Physics at the Planck scale, 10^{19} GeV — a collider reaching it would need to be about the size of the galaxy.
What a theory of everything would have to do
If someone claimed to have one, here is what it would need to deliver.
Include gravity quantum mechanically, without infinities, and reproduce general relativity in the classical limit.
Derive the Standard Model — the gauge group, three generations, and ideally the 26 parameters.
Explain dark matter and dark energy.
Resolve the singularities at the Big Bang and inside black holes.
Make a testable prediction that differs from the Standard Model plus general relativity, at an energy someone can reach.
Be unique, or at least explain why our vacuum was selected.
No candidate does all of these. None does more than two or three.
Why the search continues
Because it has worked before, repeatedly. The Standard Model itself arose from exactly this kind of dissatisfaction with a theory that worked. Mendeleev's gaps became germanium and gallium. Gell-Mann's gap became the omega-minus. Dirac's negative energies became the positron. The neutrino was postulated in desperation and found twenty-six years later.
And because the failures are real. Dark matter is not a philosophical worry; it is 85 % of the matter in the universe and we do not know what it is. The matter–antimatter asymmetry is why anything exists, and the theory is off by ten orders of magnitude.
The honest state of play: particle physics is in an unusual position. Its theory is spectacularly successful and manifestly incomplete, and for the first time in a century there is no clear experimental anomaly pointing the way. The muon's magnetic moment, the neutrino sector, and the dark matter searches are where the field is looking hardest.
Where this shows up in your life
Very little of this, directly, and that is worth saying plainly. Supersymmetry, string theory and grand unification have no applications and may never have any.
What does transfer is the technology. The Web, medical accelerators, PET, superconducting magnets, detector technology in security scanners, and grid computing all came out of this field's instrumentation rather than its theory.
And the framework itself is used constantly. Every semiconductor, every laser, every nuclear reactor and every medical isotope depends on the parts of the theory that are settled.
What Part 8 established
Part 8 reduced a hundred particles to seventeen fields.
The quark model explained the zoo, was confirmed by scattering electrons off protons, and predicted the omega-minus before it was found.
Gauge symmetry explains what a force is: demand that a local convention be arbitrary and the force carrier is forced into existence, with the photon's masslessness and hence electromagnetism's infinite range following automatically.
Asymptotic freedom and confinement explain why quarks behave as free particles inside a proton and can never be pulled out of one.
The Higgs field breaks the electroweak symmetry and gives the W, Z and fermions their masses — while accounting for under 2 % of your own.
Neutrinos were postulated to save energy conservation, took twenty-six years to find, and turned out to oscillate, which requires mass, which the Standard Model does not have.
And the machinery — 27 km rings, 1.9 K magnets, 50,000-tonne water tanks a kilometre underground, and detectors that throw away 39,999 events out of 40,000 in real time.
Every prediction the Standard Model has made has been confirmed. It explains 5 % of the universe.
What the next Part fixes
Chapter 8.2's table has quarks and leptons and says nothing about how they assemble into the hundred-odd things you can hold in your hand. Part 9 takes the electron's quantum numbers from Chapter 7.6, adds the exclusion principle from Chapter 7.7, and shows that the entire periodic table — its shape, its row lengths, its chemical families, and the exceptions — follows from counting the orbitals available to an electron around a nucleus. It also works through Rutherford's scattering argument in full, derives Bohr's model and shows precisely where it fails, and takes apart the nuclear binding energy curve that explains both fission and fusion.