From Ethan Siegel: “Ask Ethan: How close are we to a Theory of Everything?”

Ethan Siegel
July 15, 2017

The idea that the forces, particles and interactions that we see today are all manifestations of a single, overarching theory is an attractive one, requiring extra dimensions and lots of new particles and interactions. Image credit: Wikimedia Commons user Rogilbert.

“Those who begin coercive elimination of dissent soon find themselves exterminating dissenters. Compulsory unification of opinion achieves only the unanimity of the graveyard.” -Robert Jackson

Since well before Einstein, it was the dream of those who study the Universe to find a single equation to govern as many phenomena as possible. Rather than have a separate law for each and every physical property the Universe has, we could unify these laws into a single, overarching framework. All the laws of electric charge, magnetism, electric currents, induction and more were unified into a single framework by James Clerk Maxwell in the mid-1800s. Ever since, physicists have dreamed of a Theory of Everything: a single equation governing all the laws of the Universe. What progress have we made? That’s the question of Paul Harding, who wants to know:

“Has science made any progress with regards to the Grand Unified Theory and the Theory of Everything? And could you elaborate on what it would mean if we did find a unified equation?”

Yes, we’ve made progress, but we’re not there yet. Not only that, but it’s not even a certainty that there even is a theory of everything.

The electromagnetic, weak, strong and gravitational forces are the four fundamental forces known to exist in this Universe. Image credit: Maharishi University of Management.

The laws of nature, as we’ve discovered them so far, can be broken down into four fundamental forces: the force of gravity, governed by General Relativity, and the three quantum forces that govern particles and their interactions, the strong nuclear force, the weak nuclear force, and the electromagnetic force. The earliest attempts at a unified theory of everything came shortly after the publication of General Relativity, before we understood that there were fundamental laws to govern nuclear forces. These ideas, known as Kaluza-Klein theories, sought to unify gravitation with electromagnetism.

The idea of unifying gravitation with electromagnetism goes all the way back to the early 1920s, and the work of Theodr Kaluza and Oskar Klein. Image credit: SLAC National Accelerator Laboratory.

SLAC Campus

By adding an extra spatial dimension to Einstein’s General Relativity, a fifth dimension overall (in addition to the standard three space and one time) gave rise to Einstein’s gravity, Maxwell’s electromagnetism, and a new, extra scalar field. The extra dimension would need to be small enough to avoid interfering with the laws of gravity, and the details were such that the extra scalar field needed to have no discernible effects on the Universe. Since there was no way to formulate a quantum theory of gravity with this, the discovery of quantum physics and the nuclear forces — which this attempt at unification couldn’t account for — caused this to fall out of favor.

The quarks, antiquarks, and gluons of the standard model have a color charge, in addition to all the other properties like mass and electric charge. The Standard Model can be written as a single equation, but all the forces within are not unified. Image credit: E. Siegel.

The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth.

However, the strong and weak nuclear forces led to the formulation of the Standard Model in 1968, which brought the strong, weak, and electromagnetic forces under the same overarching umbrella. Particles and their interactions were all accounted for, and a slew of new predictions were made, including a big one about unification. At high energies of around 100 GeV (the energy required to accelerate a single electron to a potential of 100 billion volts), a symmetry unifying the electromagnetic and the weak forces would be restored. New, massive bosons were predicted to exist, and with the discovery of the W and Z bosons in 1983, this prediction was confirmed. The four fundamental forces were reduced down to three.

The idea of unification holds that all three of the Standard Model forces, and perhaps even gravity at higher energies, are unified together in a single framework. Image credit: © ABCC Australia 2015

Unification was already an interesting idea, but models took off. People assumed that at higher energies still, the strong force would unify with the electroweak; that was where the idea of Grand Unification Theories (GUTs) came from. Some assumed that at even higher energies, perhaps around the Planck scale, the gravitational force would unify as well; this is one of the main motivations for string theory. What’s very interesting about these ideas, however, is that if you want to have unification, you need to restore symmetries at higher energies. And if the Universe has symmetries at high energies that are broken today, that translates into something observable: new particles and new interactions.

The Standard Model particles and their supersymmetric counterparts. This spectrum of particles is an inevitable consequence of unifying the four fundamental forces in the context of String Theory. Image credit: Claire David.

So what new particles and interactions are predicted? This depends on which variant of unification theories you go for, but include:

Heavy, neutral, dark-matter-like particles,
supersymmetric partner particles,
magnetic monopoles,
heavy, charged, scalar bosons,
multiple Higgs-like particles,
and particles that mediate proton decay.

Although we can be certain, from indirect observations, that there is some origin to our Universe’s dark matter, none of these particles or predicted decays have been observed to exist.

In 1982, an experiment running under the leadership of Blas Cabrera, one with eight turns of wire, detected a flux change of eight magnetons: indications of a magnetic monopole. Unfortunately, no one was present at the time of detection, and no one has ever reproduced this result or found a second monopole. Image credit: Cabrera B. (1982). First Results from a Superconductive Detector for Moving Magnetic Monopoles, Physical Review Letters, 48 (20) 1378–1381.

This is a pity, in many regards, because we’ve searched, and hard. In 1982, one of the experiments searching for magnetic monopoles registered a single positive result, spawning many copycats which attempted to discover large numbers of others. Unfortunately, that one positive result was anomalous, and no one has ever replicated it. Also in the 1980s, people began building giant tanks of water and other atomic nuclei, searching for evidence of proton decay. While those tanks eventually wound up being repurposed as neutrino detectors, not a single proton has ever been observed to decay. The proton lifetime is now constrained to be greater than 1035 years: some 25 orders of magnitude greater than the age of the Universe.

The water-filled tank at Super Kamiokande, which has set the most stringent limits on the lifetime of the proton. In later years, detectors set up in this fashion have made outstanding neutrino observatories, but have yet to detect a single proton decay. Image credit: Kamioka Observatory, ICRR, University of Tokyo.

This is also too bad, because Grand Unification offers a clean and elegant path to generating the matter/antimatter asymmetry in the Universe. At very early times, the Universe is hot enough to produce matter-and-antimatter pairs of all the particles that can possibly exist. In most GUTs, two of those particles that exist are superheavy X-and-Y bosons, which are charged, and contain both quark and lepton couplings. There’s expected to be an asymmetry in the way the matter versions and the antimatter versions decay, and they can give rise to a leftover presence of matter over antimatter, even if there was none initially. Unfortunately, again, we have yet to find any positive evidence for such particles and/or interactions.

An equally-symmetric collection of matter and antimatter (of X and Y, and anti-X and anti-Y) bosons could, with the right GUT properties, give rise to the matter/antimatter asymmetry we find in our Universe today. Image credit: E. Siegel / Beyond The Galaxy.

Ethan Siegel Beyond the Galaxy

Some physicists contend that the Universe must have these symmetries, and the evidence must simply lie at energies too high for even the LHC to probe.




CERN LHC particles

But others are coming around to a more uncomfortable possibility: perhaps nature doesn’t unify. Perhaps there is no Grand Unified Theory that describes our physical reality; perhaps a quantum theory of gravity doesn’t unify with the other forces; perhaps the problems of baryogenesis and dark matter have other solutions that aren’t rooted in these ideas. After all, the ultimate arbiter of what the Universe is like isn’t our ideas about it, but rather the results of experiment and observations. We can only ask the Universe what it’s like; it’s up to us to listen to what it tells us and go from there.

The Standard Model Lagrangian is a single equation encapsulating the particles and interactions of the Standard Model. It has five independent parts: the gluons (1), the weak bosons (2), how matter interacts with the weak force and the Higgs field (3), the ghost particles that subtract the Higgs-field redundancies (4), and the Fadeev-Popov ghosts, which affect the weak interaction redundancies (5). Neutrino masses are not included. Image credit: Thomas Gutierrez, who insists there is one ‘sign error’ in this equation.

Although we can write the Standard Model as a single equation, it isn’t really a unified entity in the sense that there are multiple, separate, independent terms to govern different components of the Universe. The various parts of the Standard Model don’t interact with each other, as color charge doesn’t affect the electromagnetic or weak forces, and there are unanswered questions about why interactions that should occur, like CP-violation in the strong force, don’t.

When symmetries are restored (at the top of the potential), unification occurs. However, the breaking of symmetries, at the bottom of the hill, corresponds to the Universe we have today, complete with new species of massive particles. Image credit: Luis Álvarez-Gaumé & John Ellis, Nature Physics 7, 2–3 (2011).

It’s the hope of many that unification holds the answer to these questions, and will solve many of the open problems and puzzles in physics today. However, any sort of additional symmetries — symmetries which are restored at high energies but are broken today — lead to new particles, new interactions, and new physical rules that the Universe plays by. We’ve tried to reverse-engineer some predictions using what rules we’d need for things to work out, yet the particles and unifications we were hoping to find never materialized. Unification won’t help you derive emergent properties like chemistry, biology, geology, or consciousness, but will help us better understand the origin of where everything came from, and how.

The cosmic history of the entire known Universe shows that we owe the origin of all the matter within it, and all the light, ultimately, to the end of inflation and the beginning of the Hot Big Bang. Image credit: E. Siegel / ESA and the Planck Collaboration.


Of course, there is the other possibility: that the Universe simply doesn’t unify. That the multiple different laws and rules we have are there for a reason: these symmetries that we’ve invented are simply our own mathematical inventions, and not descriptive of the physical Universe. For every elegant, beautiful, compelling physical theory that’s out there, there’s an equally elegant, beautiful, and compelling physical theory that is wrong. In these matters, as in all scientific matters, it’s up to humanity to ask the right questions. But it’s up to the Universe to tell us the answers. Whatever they are, that’s the Universe we have. It’s up to us to figure out what those answers mean.

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“Starts With A Bang! is a blog/video blog about cosmology, physics, astronomy, and anything else I find interesting enough to write about. I am a firm believer that the highest good in life is learning, and the greatest evil is willful ignorance. The goal of everything on this site is to help inform you about our world, how we came to be here, and to understand how it all works. As I write these pages for you, I hope to not only explain to you what we know, think, and believe, but how we know it, and why we draw the conclusions we do. It is my hope that you find this interesting, informative, and accessible,” says Ethan