"In short, Lisi's paper tries to find a mathematical way to unite the interactions of all the particles in the universe, from force-carrying particles called bosons to fermions like electrons and quarks, which combine to make up matter.

The most agreed-upon theory to date — the Standard Model of particle physics — explains the interactions of matter with three of the four fundamental forces of nature: electromagnetism, the strong nuclear force (which binds the parts of a nucleus together), and the weak nuclear force (which allows for the radioactive decay of particles).

Where it's come up short is in explaining the fourth force: gravity. For the 30 years since the Standard Model was proposed, scientists have come up with a number of theories to unite the gravity of Einstein's theory of general relativity with the Standard Model, including string theory, which reduces the forces and matter of the universe to tiny one-dimensional filaments called strings that vibrate in 10 dimensions.

But critics of String Theory, Lisi included, argue it is virtually untestable and bears no resemblance to the world we live in. As Lisi writes in his paper: "A successful description of nature should be concise, elegant, unified mathematical structure consistent with experience."

Lisi's theory attempts to explain the relationship between the particles of the universe with the points on a complex, eight-dimensional mathematical pattern called E8."

"The basic question has to do with the nature of matter, which is of course made up of atoms and molecules, as every freshman probably knows. Your first course in chemistry will probably teach you about how atoms are held together into molecules by electromagnetic forces, chiefly between the outermost electrons of the atom. You will also learn that the center of the atom is the nucleus, which in turn is made up of protons, neutrons, and some other smaller particles which appear only when the nucleus is broken into smaller bits by a fission reaction.

These smaller particles come in hundreds of varieties, but the standard model of particles has shown that all of them can be explained by adding together the properties of only a few. The key particles are the neutrino, the electron, the muon, the tau, and six quarks, which are called top, bottom, up, down, strange and charm. Almost all ordinary matter is made up of the electron and the up and down quarks.

Each of these particles occurs as a triplet. For example, the electron, muon, and tau share many properties, differing mainly in mass. The neutrino comes in three kinds also, called the electron neutrino, the muon neutrino, and the tau neutrino. The quark triplets involve three colors. Each kind of quark can come in red, blue, or green. These are not colors of light, of course, but just a pretty way of doing some accounting.

In addition to the above, each member of every triplet has an antimatter dual. These particles together make up the fermions, particles which ordinarily tend to get as far away from each other as possible. The bosons are a kind of particle which obey another kind of behavior, in which they tend to cluster together.

There are also “particles” which are thought of as carrying forces. The gluon, the photon, and the Higgs are three of these. However, in my opinion, none of these particles is really a particle in the sense we usually think of matter. They do not have mass in and of themselves, but carry the four forces; electromagnetics for the photons, the weak force for the gluons, the strong force and gravity for the Higgs. All of the particles can be thought of as waveforms in some kind of background.

The particles of the standard model have been observed in colliders, and we know of photons directly from light, but the graviton and the Higgs have not been observed, presumably because they require higher energy collisions to become observable. Recall that higher energy collisions happen in smaller spaces. You can think of the Higgs and the graviton as being very small, therefore very high energy particles. Some scientists are hoping that the Higgs and/or the graviton, or maybe even a black hole, will appear in the new generations of colliders, which should be coming on line in the next few years, and which are able to reach energies in the range of one TeV, a tevatron. I think that means a billion electron volts.

All of this is background for the next stage in physics, which is now called, euphemistically, new physics. This forum, Beyond the Standard Model, interests people who want to know why the standard model particles have the mass, charge, and spin, or quantum numbers, that they do, according to measurable physics. String theory can explain the quantum numbers, but it has five different explanations, and it is thought by many that there must be some more basic theory, with only one explanation. M theory has supposedly connected the five stringy theories into one explanation, but no one seems to know what that explanation is. In any case, it leaves unanswered the fundamental question, what is the zero state, the absolute vacuum, the space-time continuum. If there are waves, what is the stuff that is waving? What is it, when it isn’t waving?

Loop quantum gravity, Dynamic Triangulation, and other ideas have been put forward as a means to explore the fundamental question. It largely comes down to a question of geometry. What is the right geometry, the right mathematics, to describe the most fundamental level that underlies all of matter? The fact that the standard model pieces can be hung on the E8 framework is another proposal for a means of investigation of this question. Essentially, it postulates that the particles of the standard model, along with the graviton and the Higgs, must be an emergent effect of the shape of the universe, which exists in higher dimensions than we poor limited humans can perceive.

However, even if we find the answer to the geometry of space-time, there remains the question of what is more fundamental than that? What lies beneath space-time? If the particles can be thought of as being different views of a higher dimensional object, as in the Lisi theory, what is the stuff that causes that higher dimensional object to take the shape it does, and not some other shape?

The stakes are very high. Human culture has entered a cul-de-sac, and we must have some better source of energy than oil if we are to survive as a technological civilization. Atomic energy has given us a clue, but it has some problems, mainly involving the deadly poisonous leftovers of fission. A workable theory of everything may be the key to finding ways to harness energies like the strong force that holds quarks together inside particles, or even the pure energies of mass, and hence gravity, the actual curvature of space-time.

Dr. Lisi’s model may be the best approximation yet to the structure of space-time. Or not. It has the advantage that it can be verified by tests that may be within reach of current technology. Or it can be falsified by those same tests. String, Loop, and Triangulation have suggested no such tests, or at best only a few tests that are not very clear. The Lisi model predicts a few new particles which may soon be within the reach of our technical tools. If these new particles are found, and have the predicted quantum numbers, then the theory will be useful in finding the unification of general relativity with the standard model of particle physics. Lots to look forward to.

Hope this helps. Comments welcome. I am only an independent student, and my understanding is not complete. If anyone here finds I have made a misstatement, I would be very kindly disposed to hear of it."

"Starkind: Yes, you did misspeak on a few points. For example, gluons are the carriers of the strong interaction, not the weak, which is carried by the W+,W-, and Z particles, which are massive. The Higgs is not a gauge boson, and as such is not a carrier of a gauge interaction. It does couple to other particles and gives rise to their masses by virtue of this interaction, but that's not the same as gravity (and has nothing to do with the strong interaction). Gravitons are indeed the carriers of gravity in quantum field theories of gravity, but they're not part of the Standard Model. There are a few other places where I'd question your description of the SM and related matters, but I'll leave it at that."

"My current understanding of E8 is that it is a mathematical object in 234 (IIRC) dimensions. The idea of projecting the object onto a lower dimensional surface is kind of like taking a wire model of a cube, holding it above a sheet of paper in the sun, and tracing the shadows. There are several ways you can turn the wire frame cube to get different patterns on the paper. These are symmetries, all of which are required to get an idea of what the higher dimensional object (in this shadow case, the wire frame cube) actually "looks" like.

Physics isn't about visualization any more. I doubt if humans will ever be able to visualize in much higher than three or four dimensions. Instead, we have to learn the maths. This is hard to do if you are not in a university where such things are taught, but if you are persistant, you can learn a bit on your own. At first, wandering around Wiki is like a maze, but after a while you start to recognise a few things."

"The standard model uses the observable 3 dimensions of space and one of time. The Lisi model does not require extra dimensions of space and time. The dimensions of the E8 system are mathematical, not physical dimensions.

The idea that particles pop in and out of physical space from other dimensions is not really it. One version of QG says we live on a higher dimensional brane (a topological surface) and that some particles, specifically gravitons, move through our brane world, becoming briefly part of it, and then they return to a region called the bulk. The bulk is not space as we know it. This idea is invoked to explain why gravity is so much weaker than the other three forces. Some of the force of the graviton leaks into our world, but most of it goes into the bulk.

String theory uses extremely small Calabi-Yau dimensions, curled up approximately at the Planck scale, to explain this same weakness of gravitation, suggesting that the extra gravitational force goes into the small curled up dimensions. Some other theorists have suggested that there are large extra dimensions, hoping to show an effect on gravitation at small distances, for example less than a millimeter. No such effect has been demonstrated as far as I know.

I don't claim to understand the details of Lisi's idea. But I think I have gotten a pretty good grasp of the dimensions thing. There is commonly a confusion about "higher dimensions" being some kind of 'space' that we just don't see. Physicists don't help clarify this by talking about things like phase space, representational space, momentum space, and so on. These are clearly (I think) not spaces in the sense of a room which you can occupy or not occupy as you so choose. Really a mathematical dimension is any measurement. You can have any number of measurements, or dimensions, but usually physicists like to have as few as is necessary to describe an event. You can describe the shape of any static physical object with three dimensions, the shape of any dynamic object with four dimensions, or maybe five. The one or two additional dimensions are those of time.

But what if you need to describe a system that has charge, mass, spin, and so on, which are not really shapes at all? You need more mathematical dimensions to do that. Lisi's model does describe the quantum numbers, so it needs more dimensions, mathematic dimensions, to do that."