# What are the “generations of matter”?

After a series of clicks on New Scientist and Wikipedia, I ended up on the Wiki article for "generations of matter", and I didn't quite understand it. I believe (and this may be wrong) that different generations of matter are divided due to varying energy levels, but that's all I got from the article.

Could anybody please explain to me - in almost-layman's terms (I've basic knowledge of the Standard Model, and therefore quarks, bosons, leptons) - what the term "generations of matter" indicates?

• Have a look at the table of the standard model en.wikipedia.org/wiki/… . the first three columns are the families we have discovered experimentally. the first column/generation is what builds our everyday world to first order. the second and third columns are sequentially heavier and only observed in elementary particle interactions. – anna v Mar 14 '15 at 16:58

The "generations" of matter are mainly based on the electroweak symmetry group $\mathrm{SU}(2)_L\times\mathrm{U}(1)$.

All fundamental quantum fields are either a "singlet" or a "doublet" under the $\mathrm{SU}(2)$ part of this symmetry.

The left-handed fields usually form doublets, and the up- and the down- quark form the first, the strange- and the charm-quark form the second, and the top- and the bottom-quark form the three doublet we have for left-handed quarks. Similarily, the electron and its neutrino, the muon and its neutrino and the tau and its neutrino form the three doublet for the left-handed leptons.

Since there is a gradual progression of masses up->strange->top and electron->muon->tau, we call the fields in the up- and electron-doubles "first" generation, the next heavier ones "second" generation, and the heaviest one "third" generation, also because that is, due to the masses, the order in which we discovered them.

You can get a theory "of Standard Model type" with arbitrarily many generations - you can have $N$ quark doublets and $N$ lepton doublets, but you can't add a single quark (or lepton) that would behave like the others because you need a left-handed $\mathrm{SU}(2)_L$ doublet for the quark to behave like the other quarks (or a lepton to behave like the other leptons). You need to add the fermions in "pairs", either up-/down-type quark pairs or lepton/neutrino-pairs.

So far, there is no indication of more than three generations.

• What's electroweak symmetry? The wiki page tells me about electroweak interaction - which I gather is the interaction between EM force and weak force, but what does the term 'symmetry' indicate? – drunkBrain Mar 16 '15 at 9:42
• @drunkBrain: It's on the page, actually - it's the gauge (symmetry) group for the theory of the electroweak force. Symmetry indicates that these are transformations that leave the action invariant. – ACuriousMind Mar 16 '15 at 10:48
• I don't understand a lot of the vocabulary on the page; my knowledge of quantum physics, as indicated in the original question, is highly limited. So, symmetry is a particular way that a particle bheaves? – drunkBrain Mar 16 '15 at 10:53
• @drunkBrian: No, it has nothing directly to do with particle behaviour. I'm sorry, but one can't explain the meaning of gauge symmetry to someone not familiar with the mathematical formulations of physics in much simpler terms than is done on the Wikipedia pages. Also, particles are not the level at which we look at these symmetries, but the underlying quantum fields, which I ignored in my answer. – ACuriousMind Mar 16 '15 at 11:02
• That's fair enough; I suppose it's not possible to understand this stuff without knowing the basics. In this case, is there any reading you could recommend that would give me an understanding of the concepts/terms used in the Wiki page? – drunkBrain Mar 16 '15 at 11:06

Yes, with energy being mass just to be pedantic.. In practice they are distinguished by their decays and cross-sections for these. Try "clicking" further into Feynman diagrams, this is the most intuitive way of coping with particle physics.

• I don't see how this answers the question. – ACuriousMind Mar 14 '15 at 14:43
• Then maybe I misinterpret the question?: He asks, what the term generations of matter indicates: I answer the generations are distinguished by mass, but in practice it is more convenient to distinguish them by cross-sections for interactions, as these are tied to the energy and mass. – Andreas Gravgaard Andersen Mar 14 '15 at 14:50
• Oh, your "yes" is confusing because the question is not a yes/no question. Additionally, I don't see how Feynman diagrams would tie into the generation distinction. – ACuriousMind Mar 14 '15 at 14:52
• Okay, no problem. I suggest looking at feynman diagrams as these and especially the rules for these gives a more intuitive way of understanding interactions in the standard model, even though the generation differences only appear in the advanced rules and n terms of cross-sections. – Andreas Gravgaard Andersen Mar 14 '15 at 15:00