# Why bosons have integer spin and fermions have half-integer ones?

Due the fact that the fermions are the "block particles" and the bosons are the "carriers" I just came out with the question that, why the "block particle" have half-integer spin and the "carriers" have an integer spin?

• Yes, i know... But what does it have to do with their interaction? – Oriana L. Aug 30 '17 at 23:24
• @Mithoron The value of the spin does not provide a definition for bosons and fermions. – Diracology Aug 30 '17 at 23:29
• Yes, It's true, but is curiouos that the fermions the "blocks of the matter" and the bosons "the carriers of the forces" have this difference. And I wonder why it is so. – Oriana L. Aug 30 '17 at 23:36
• Related: physics.stackexchange.com/q/13787/2451 and links therein. – Qmechanic Aug 31 '17 at 4:36

The fact that bosons have integer spin whereas fermions have half-integer is actually a result from the so-called spin-statistics theorem.

The definition of bosons and fermions is not in terms of spin, it is in terms of symmetry of the wave function under exchange of particles. The spin-statics theorem says that the wave function of an integer spin identical particles' system is symmetric under exchange of particles and therefore those are bosons. On the other hand the wave function of an half integer identical particles' system is antisymmetric under exchange of particles and thus they are fermions.

If you are interested in knowing why force carriers are bosons you can check this: Why are all force particles bosons?

why the "block particle" have half-integer spin and the "carriers" have an integer spin?

Everything of coursed is based on observations and measurements, which define your "block" particles particularly. Chemistry is an old science and it depends crucially on "block" particles. The existence of nuclei also is based on "block" particles . The existence of spin states is an observational fact.

The mathematical model that fits this contains the Pauli exclusion principle which led to the spin statistics theorem imposed on the quantum mechanical solutions for atoms.

Without the Pauli exclusion principle there would be no chemistry, no nuclei and thus the universe as we know it.

Bosons are an observational fact also, because photons are bosons. (Please note that all particles can be carriers of dp/dt in loops in Feynman diagrams as long as quantum numbers are conserved) . But if the carriers of the simplest interaction in lowest order , electron electron scattering for example, would not be bosons the quantum number exchanges would not be conserved. Thus the gauge theories which developed to explain observations have bosons as carriers of the simplest, lowest order, interactions between elementary particles, describing the different fundamental forces.

• I am sorry, I disagree with your statement. The only observational input is the fact that all observed particles come in two classes: totally symmetric or totally antisymmetric representations of the permutation group. The rest is the content of the spin-statistics theorem, and not just some empirical fact. – user178876 May 10 '18 at 22:07
• @marmot so then you are one of the platonists, "mathematics defines reality". It is the way many theorists view the world. In my view , there is a huge number of mathematical possibilities that never manifest in reality. It is the observation of a symmetry/behavior of matter in reality that chooses the mathematical model that fits it. And spins are measured quantities, in real numbers. – anna v May 11 '18 at 4:22
• I do not consider myself a platonist. Would you say that charge conjugation is just an experimental fact or the consequence of a symmetry? I'd like to argue that it is the latter, and similarly the spin-statistic theorem tells us that the statistics is a consequence of other things. But I also do not want to start a discussion. – user178876 May 11 '18 at 4:27
• In my view the mathematics imposes consequences in the analysis of the data, not on reality. Reality is what it is and one chooses mathematical models that fit it and are predictive of new situations (othewise it would be a mapping). For example I see many here really believe that space is filled by the fields of the elementary particles in the standard model and that is the ultimate level of reality, not the particles and the data that describe them. But yes, it is not worth it to discuss as each has a fixed pov. – anna v May 11 '18 at 4:52

I think as follows: 1. The de Broglie waves of multiple particles moving in a single orbit and having same spin quantum number are connected in series. 2. The de Broglie wave shift msλ at the joint. (ms:spin quantum number, λ:de Broglie wave length) Then, the connected waves of Fermions interfere destructively and the connected waves of Bosons interfere constructively. Therefore, we can explain Pauli exclusion principle. And we can say that the connected n electro-magnetic waves correspond to a harmonic oscillator which has energy nℏω in a black body.

• What does "connected in series" mean in point #1? – Kyle Kanos Apr 30 '19 at 14:56
• I think that symmetric and anti-symmetric wave functions are false. Because, these functions may not be the eigenfunctions of the system composed of plural identical particles. Please think about the system composed of two electrons. One is in a hydrogen atom. Another is in a helium ion He+.H1=(p1^2)/(2m)-(e^2)/(4πε0 ❘r1-rA❘ ), H2=(p2^2)/(2m)-(2e^2)/(4πε0 ❘r2-rB❘ ), H1φA(r1)=EAφA(r1), H2φB(r2)=EBφB(r2). The wave function ψ=φA(r1)φB(r2)-φA(r2)φB(r1) is not the eigenfunction of operator H1+H2. (H1+H2)ψ≠(EA+EB)ψ. Please calculate it. – OKAYASU May 2 '19 at 7:50
• Then, I tried to explain Pauli exclusion principle by interference of de Broglie wave. – OKAYASU May 2 '19 at 7:55
• Please remember Black body radiation. I think that the connected electromagnetic waves in a black body correspond to a harmonic oscillator which has energy nℏω. – OKAYASU May 2 '19 at 11:11