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Everything that exists in our Universe, as far as we understand it, is made up of particles and fields. At a fundamental level, you can break everything down until you reach the limit of divisibility; once things can be divided no further, we proclaim that weve landed upon an entity thats truly fundamental. To the best of our current understanding, there are the known elementary particles those represented by the Standard Model of elementary particle physics and then there are the unknowns: things that must be out there beyond the confines of the Standard Model, but whose nature remains unknown to us.

In the latter category are things like dark matter, dark energy, and the particle(s) responsible for creating the matter-antimatter asymmetry in our Universe, as well as any particles that would arise from a quantum theory of gravity. But even within the Standard Model, there are things for which we dont quite have an adequate explanation. The Standard Model consists of two types of particles:

While theres only one copy of each of the bosons, for some reason, there are three copies of each of the fermionic particles: they come in three generations. Although its long been accepted and robustly experimentally verified, the three-generational nature of the Standard Model is one of the great puzzles of nature. Heres what we know so far.

On the right, the gauge bosons, which mediate the three fundamental quantum forces of our Universe, are illustrated. There is only one photon to mediate the electromagnetic force, there are three bosons mediating the weak force, and eight mediating the strong force. This suggests that the Standard Model is a combination of three groups: U(1), SU(2), and SU(3).

Although the Standard Model possesses an incredibly powerful framework leading to, by many measures, our most successful physical theory of all-time it also has limitations. It makes a series of predictions that are very robust, but then has a large number of properties that we have no way of predicting: we simply have to go out and measure them to determine just how nature behaves.

The particles and forces of the Standard Model. Any theory that claims to go beyond the Standard Model must reproduce its successes without making additional predictions that have already been shown to not be true. Pathological behavior that would already be ruled out is the largest source of constraints on beyond-the-Standard Model scenarios.

But what the Standard Model doesnt tell us is also profound.

All of these things can only, at least as we currently understand it, be measured experimentally, and its from those experimental results that we can determine the answers.

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Fortunately, were good enough at experimental particle physics that weve been able to determine the answers to these questions through a series of both clever and brute-force observations and experiments. Every single one of the Standard Models particles and antiparticles have been discovered, their particle properties have been determined, and the full scope of what exists in the Standard Model three generations of fermions that are all massive and where quarks of like charges and the massive neutrinos all mix together is now unambiguous.

The rest masses of the fundamental particles in the Universe determine when and under what conditions they can be created, and also describe how they will curve spacetime in General Relativity. The properties of particles, fields, and spacetime are all required to describe the Universe we inhabit, but the actual values of these masses are not determined by the Standard Model itself; they must be measured to be revealed.

The two major ways that we know there are three generations no more and no less of fermions are as follows.

1.) The Z-boson, the neutral but very massive weak boson, has a series of different decay pathways. About 70% of the time, it decays into hadrons: particles made up of quarks and/or antiquarks. About 10% of the time, it decays into charged leptons: either the electron (1st generation), muon (2nd generation), or tau (3rd generation) flavor, all with equal probabilities. And about 20% of the time predicted to be exactly double the frequency that it decays to a charged lepton it decays into neutral leptons: the neutrinos, with equal probability for each of the various flavors.

These neutrino decays are invisible, since it would take about a light-year worth of lead to have a 50/50 shot of detecting your average neutrino. The fact that the fraction of Z-bosons that decays into invisible constituents (i.e., neutrinos) is exactly double the fraction that decays into the known charged leptons tells us that there are only three species of neutrinos that are below half the mass of the Z-boson, or around 45 GeV/c. If there is a fourth generation of neutrino, the lightest massive particle in each of the three known generations, its more than a trillion times more massive than any of the other neutrinos.

The final results from many different particle accelerator experiments have definitively showed that the Z-boson decays to charged leptons about 10% of the time, neutral leptons about 20%, and hadrons (quark-containing particles) about 70% of the time. This is consistent with 3 generations of particles and no other number.

2.) The presence of neutrinos that were created in the early Universe, during the first ~second of the hot Big Bang, imprints itself onto other observable cosmic signals.

In addition to the constraints on neutrinos, there are no additional charged leptons or quarks at masses at or below 1.2 and 1.4 TeV, respectively, from experimental constraints at the Large Hadron Collider (and the fact that probabilities must always add up to 100%).

All told, this strongly disfavors the existence of a fourth (or higher) generation of particles.

If there were no oscillations due to matter interacting with radiation in the Universe, there would be no scale-dependent wiggles seen in galaxy clustering. The wiggles themselves, shown with the non-wiggly part (blue, top) subtracted out (bottom), is dependent on the impact of the cosmic neutrinos theorized to be present by the Big Bang. Standard Big Bang cosmology with three neutrino species corresponds to =1.

With the exception of the neutrinos, which appear to be just as stable in the electron species as they are in either the muon or tau species, the only stable charged particles (including neutral composite particles with charged, fundamental constituents) in the Universe are made out of first-generation quarks and leptons. The muon is the longest-lived unstable particle, and even it only has a mean lifetime of 2.2 microseconds. If you have a strange (or heavier) quark, your lifetime is measured in nanoseconds or less; if you have a tau lepton, your lifetime is measured in fractions-of-a-picosecond. There are no stable species that contain second-or-third generation quarks or charged leptons.

There are no hints in the decays of the most massive particles the W, the Z, the Higgs or the top quark that there are any particles in additions to the ones we know. When we look at the mass ratios of the different generations, we find that the four separate types of particles:

all have significantly different mass ratios between the generations from one another. In addition, although quarks mix with one another and neutrinos mix across the generations, the ways in which they mix are not identical to each other. If there is a pattern or an underlying cause or reason as to why there are three generations, we havent uncovered it yet.

Instead of an empty, blank, three-dimensional grid, putting a mass down causes what would have been straight lines to instead become curved by a specific amount. In General Relativity, we treat space and time as continuous, but all forms of energy, including but not limited to mass, contribute to spacetime curvature. The deeper you are in a gravitational field, the more severely all three dimensions of your space is curved, and the more severe the phenomena of time dilation and gravitational redshift become. It is not known if there is a connection between the number of spatial dimensions and the number of fermionic generations.

One of the ideas thats sometimes floated is really just a hint: we have three generations of fermionic particles, and we have three spatial dimension in our Universe. On the other hand, we have only one generation of bosonic particles, and one time dimension in our Universe.

Could this be a potential link; the number of spatial dimensions with the number of generations of fermions, and the number of time dimensions with the number of generations of bosons?

Maybe, but this line of thought doesnt provide any obvious connections between the two. However, pursuing it does help us understand what similarly-minded connections arent present. Particles dont have different spins or spin-modes across generations, indicating that intrinsic angular momentum is simple and unrelated to either generations or dimensions. There is CP-violation in the (weak) decays of heavy quarks, and that requires a minimum of three generations, but we still dont know why theres no CP-violation in the strong decays.

If youre looking at 3 as though its a mysterious number, you might note:

but none of them have any known connection to either the number of spatial dimensions or the number of generations. As far as we can tell, its all just coincidence.

The difference between a Lie algebra based on the E(8) group (left) and the Standard Model (right). The Lie algebra that defines the Standard Model is mathematically a 12-dimensional entity; the E(8) group is fundamentally a 248-dimensional entity. There is a lot that has to go away to get back the Standard Model from String Theories as we know them, and there are numerous ways to recover three generations based on how the various symmetries are broken in String Theory.

Perhaps. By adding in additional symmetries and by considering larger gauge groups, its possible to come up with a rationale for why there would be three, and only three, generations of particles. Indeed, thats not too far fetched. In supersymmetry, there would be more than double the number of particles than are present in the Standard Model, with an additional fermion for every boson, an additional boson for every fermion, and multiple Higgs particles as well as supersymmetric Higgsinos that would exist.

In string theory, were required to go to even greater states of symmetry, with larger gauge groups that are capable of admitting the particles of the Standard Model many times over. It is certainly possible, with such a wide set of variables to play with, to choose a way that these very large gauge groups might break to not only give rise to the Standard Model, but to a Standard Model that has three identical copies of its fermions, but no additional bosons.

But, again, theres no reason that we know of that dictates why this ought to be the case. When you strike a pane of glass with a rock, its possible that the glass will shatter in such a way that youll wind up with three specific shards that are identical; thats a plausible outcome. But unless you can predict those shards in advance, the idea doesnt have any predictive power. Such is the case with string theory at present: it could lead to three generations of fermionic particles, but theres no way to predict such an outcome.

A geometrical interpretation of the Koide formula, showing the relative relationship between the three particles that obey its particular mathematical relationship. Here, as was its original intent, its applied to the charged leptons: the electron, muon, and tau particles.

Back in 1981, physicist Yoshio Koide was looking at the then-known particles of the Standard Model and their particle properties, and took particular notice of the rest masses of the electron, muon, and tau particles. They are:

Although it might appear that theres no relationship at all between these three masses, his eponymous Koide formula indicated differently. One of the rules of quantum physics is that any particles with the same quantum numbers will mix together. With the exception of lepton family number (i.e., the fact that theyre in different generations), the electron, muon, and tau do have identical quantum numbers, and so they must mix.

What Koide noted was that mixing would generally lead to the following formula:

where that constant must lie between and 1. When you put the numbers in, that constant just happens to be a simple fraction that splits the range perfectly: .

The Koide formula, as applied to the masses of the charged leptons. Although any three numbers could be inserted into the formula, guaranteeing a result between 1/3 and 1, the fact that the result is right in the middle, at 2/3 to the limit of our experimental uncertainties, suggests that there might be something interesting to this relation.

But even with all that said, theres no underlying reason for any of this; its just a suggestive correlation. There may be a deep reason as to why there are three generations no more, no less of fermionic particles in the Standard Model, but as far as what that reason might be, we have no indicators or evidence that are any better than these tenuous connections.

The experimental data and the theoretical structure of the Standard Model, combined, allow us to conclude with confidence that the Standard Model, as we presently construct it, is now complete. There are no more Standard Model particles out there, not in additional generations nor in any other yet-undiscovered place. But there are, at the same time, certainly puzzles about the nature of the Universe that require us to go beyond the Standard Model, or well never understand dark matter, dark energy, the origin of the matter-antimatter asymmetry, and many other properties that the Universe certainly possesses. Perhaps, as we take steps towards solving those mysteries, well take another step closer to understanding why the Standard Models particle content is neither greater nor lesser than it is.

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Why are there exactly 3 generations of particles? - Big Think