Me and a few friends were wondering about the origin of indistinguishability in QM and thought of the following thought experiment. Consider a toy model of a classical universe which has only one kind of particle(lets call them unons) of some mass m and radius a. Also assume that unons obey newtons laws, and the only interactions between them are elastic collisions. Keeping in mind that there are nothing else in this universe except for unons, I have the following statement and questions
1) If you have a collision between two unons there is no way to observe where the individual unons went.
2) You cannot follow the trajectory of individual unons without disturbing them.
3) 1 and 2 if true would imply that unons have to be indistinguishable to an observer external to the system but still part of the universe ( i.e they too have access to only unons as particles)
4) Would that mean that the equilibrium statistics of unons should not be Boltzmann statistics and should be something like Fermi statistics?
5) Now however if can add another class of point particles to observe unos, then suddenly unons become distinguishable (like in our world) and their statistics become Boltzmann statistics.
6) Thermodynamic properties however are derivable from statistical mechanics and we would expect the same thermodynamics for both 4 and 5, since they should not depend on the point particles. This would be paradoxical if they have different statistics
My gut feeling tells me that 4 is wrong and the systems of pure unons should exhibit Boltzmann statistics as well. Statics of a system should not be Bayesian
However would that mean that indistinguishability is a purely quantum phenomena? Why should that be? After all in my first universe it is impossible to track the trajectories of particles with arbitrary high precision.
Is that because quantum mechanics doesn't exhibit realism? What about (non-local) hidden variable interpretations then? Why would they have indistinguishable particles?