DomDominate said:
Why do we even need to invent this concept of spin to explain this phenomenon?
The troublesome part to understand is
fermionic spin right? If we can't understand it as a "spinning top" - is there another way to understand it beyond that "it works"?
Here is a simple personal reflection explain in simple terms, I made decades ago when examining the handwaving arguments going from KG to Dirac equation in class. A common argument is to just then postulate the linear dirac equation, rather than trying to related solutions in KG space with dirac space.
But suppose instead we have a spin 0 "particle" that we expect to comply to SR, so we naively expect it to comply to the klein gordon equation.
Then lets supposed we have an observer, we let processes inputs of hte KG solution space, and then we ask the agent to make a guess what's in there? Does anyone think the agent will come up with the idea that we have a system of spin 0 particles, that moreoever does not seem to nserve probability?? Possible yes, but not very likely.
It may be a more likely guess that we have a system of fermions in here.
But the two explanations seems mathematicall related, just like the KG and dirac equations and it's components are related via the pauli transformations. But do we postulate them, or can we motivate them?
Are these "apparent" fermions related to the initially naively assume spin 0 bosons? Could it simply be that, from the perspective of inference, a system of spin 0 bosons and a system of fermions are dual descriptions, but that the fermionic description simply is more stable? Is the reason we have not observed the supersymmetric partners, if they exist, maybe becase even if we did, the preferrable abduction would be the fermionic dual? After all, a model failing to preserve probability is NOT an "inconsistency" per see - it's just STRANGE and by definition a bad explanatory model. But I think when it comes to inference, one should not confuse bad or unfit with "forbidden"? This may be another loose way to consider a "spontanously broken symmetry" in terms of inference.
For me at least, this is my best conceptual intutitive picture of what a "fermion is", it can be seen as a "transformation of something else", fermion or boson is in the eye of the beholder. Works for me.
/Fredrik