# Why are stable fundamental particles fermions?

Within the Standard Model, any particle decay eventually terminates at the same stable fundamental particles, i.e. u- and d-quarks, the electron and neutrinos (let's forget about neutrino oscillations for now), or the respective antiparticles. Those are fermions. Is there a (simple) answer why? Could one, in principle, make a consistent model where the stable fundamental particles are bosons?

• Is the photon not a stable decay product? – gj255 Feb 17 '17 at 18:21
• Everything is stable, unless there are lighter particles it can decay to. Boson number is not conserved, therefore a single one can decay. However, the photon is the lightest of them all, so that would be stable. The lightest single fermions cannot decay, however. So perhaps the question should rather be: “Why is there only one stable boson but multiple stable fermions (proton, electron)?” – And I would not call the up and down quarks stable, there are no asymptotically free states with them, they are always bound. – Martin Ueding Feb 17 '17 at 18:56
• @MartinUeding "there is only one stable boson" seems not to be quite precise. Photons are a class of particles with different energy content and THE photon doesn't exist. Isn't this a little bit a weakness of teaching the standard model and not explaining that the fermions all unique and indistinguishable (all protons are the same) but photons are not all the same? – HolgerFiedler Feb 18 '17 at 6:51
• @HolgerFiedler: All particles can exist in different states of energy, so your comment doesn't make much sense. – Ben Crowell Jul 26 at 12:42
• @BenCrowell Under equal conditions (altitude to a gravitational source, velocity in relation to another particle) particles are the same; a proton is still a proton, the energy content is due to kinetic or potential energy. Not so the photons. Their energy content is independent from altitude and they all are moving with c. So the question is, how they differ to obey different energy content. I think that electric and magnetic fields as well as photons are composed of more elementary particles. Read my tracts, the conclusions are interesting. – HolgerFiedler Jul 26 at 18:21

The standard model evolved to fit measurements and observations. The observations have an axiomatic position in any model designed to fit the observations.

Mathematics allows to pick different sets of axioms, making theorems into axioms and former axioms provable as theorems. In a similar way the postulates which tie a subset of mathematical relations to describe the measurements can be changed, and new , mathematically simpler postulates replace them, but the observational ones are still there to be proven from the postulates. In other words in a physics model there are always statements that are axiomatic, connected with observations. A final un-peeling of the onion , asking "why", will at the end hit a "because that is what is observed".

So the "why are fundamental particles fermions" hits on baryon number conservation as a validated hypothesis, and the observation that the proton has spin 1/2 as well as the electron has spin 1/2, and both are stable.

From these three observations/measurements and conservation laws, the complexity of particle interactions, starting from scatterings of protons, electrons and photons, have disclosed the number of fundamental particles in the table: Conservation laws, also basic and axiomatic from observations, of momentum, energy, and angular momentum have led to this table , so that a mathematically consistent model, the standard model could fit and thus encapsulate the plethora of data.

Thus it is the two everyday stable particles of protons and electrons that are underlying the spin determinations of all the elementary particles in the table using consrvation laws. It so happens that it is only the photon that is a stable boson, but the "happens" is a physical observation.

In other words, thinkers did not sit and think " let us assume that most stable particles are fermions and see if this fits the data, if there exists a stable world". The mathematical model evolved to fit the data.

Could one, in principle, make a consistent model where the stable fundamental particles are bosons?

If you are asking about the world we live in, the answer is no: because the stability of matter as we know it depends a lot on the Pauli exclusion principle, also an observational postulate.

• Thanks for your comment. Still, dare to express a slight discomfort with it: it is quite natural that a consecutive chain of asking 'why ist that?' questions about our physical models sooner or later ends with '... because we made the model to meet our observations'. I would like to make one step backwards and understand, why only (if so) the assumption of a fermionic elementary particle collection (leaving the gauge bosons aside) makes sense within our QFT framework, or equivalently, which problems would arise elsewise. – G. Rosenzweig Feb 21 '17 at 21:10
• without the Pauli exclusion there are no atoms as we know them and thus no chemistry. Every negative charge around a positive charge would decay down to the ground level because there would be no limit to how many would be in the ground level, so all would. – anna v Feb 22 '17 at 4:39

Within the Standard Model, any particle decay eventually terminates at the same stable fundamental particles, i.e. u- and d-quarks, the electron and neutrinos.

Not true - decay chains can also end in stable photons, and at temperatures high enough to create quark-gluon plasmas, they can also end in quarks or gluons. In general, particles decay into lighter particles whose total decay products have the same total conserved quantum numbers of color charge, weak isospin, electric charge, weak hypercharge, baryon number, electron number, muon number, and tau number. (Neutrino oscillations allow interactions that violate electron, muon, and tau number individually, but preserve their total "lepton number.")

Think it by the way that the stability of the properties of the subatomic particles in our surrounding allows us to find the same conditions around for life. A knife would be a knife in Africa as well as in Australia as well as in the Space station.

There are some moments which are important:

1. If the energy exchange between the subatomic particles would be binary - means it would only exist photons of one energy content - the electrons in atoms would be only in two states, excited or not, and this would be a very poor world. So the bosons are a class of very important particles.
2. Photons have both oscillating electric and magnetic dipole moments. But only two photons - of the same energy - can have a symbiotic state (photon bunching), bigger clusters (connected through their magnetic and electric dipole moments) are not possible.
3. The above mentiond stability of our surrounding is a local property only. Near conglomeration of matter, much larger in relation to our sun, the gravitational potential transforms the accustomed world. Electrons or protons no more exist, only neutrons. Under higher gravitational potential neutrons no more exist, only gluon-quark plasma. In Black holes - to be speculative - perhaps even the photons are smelted in constituents.

What the science has done is the classification of the founded elementary particles into the Standard model and the division of this particles into matter constituents and exchange (of energy) constituents.

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