I think the basic answer is that your question “why does statistical mechanics actually work?”, actually remains unresolved. There are a number of distinct approaches to the foundations of the subject, and none is completely satisfactory.
Personally, I have never found maximum entropy approaches very satisfying.
An alternative approach, pursued in a lot of the literature on this topic, is to seek a mathematical reason (e.g. in the Hamiltonian dynamics of typical systems statistical mechanics is applied to) why measured quantities at equilibrium take values as though they were averages over the whole phase space with respect to the microcanonical measure (even though they clearly aren’t, because typical measurements are too fast—this can be seen from the fact that in systems that are approaching equilibrium, measurements are able reveal their nonequilibrium nature). This program can pursued without any issues of observer-dependence arising.
It’s good to know that I’m not going crazy thinking that everyone else sees the obvious reason why statistical mechanics works while I don’t but it’s a bit disappointing, I have to say.
Thanks for the link to the reference, the introduction was great and I’ll dig more into it. If you have any ways to find more work done in this area (keywords, authors, specific university departments) I would be grateful if you could share them!
I think the basic answer is that your question “why does statistical mechanics actually work?”, actually remains unresolved. There are a number of distinct approaches to the foundations of the subject, and none is completely satisfactory.
This review (Uffink 2006), might be of interest, especially the introduction.
Personally, I have never found maximum entropy approaches very satisfying.
An alternative approach, pursued in a lot of the literature on this topic, is to seek a mathematical reason (e.g. in the Hamiltonian dynamics of typical systems statistical mechanics is applied to) why measured quantities at equilibrium take values as though they were averages over the whole phase space with respect to the microcanonical measure (even though they clearly aren’t, because typical measurements are too fast—this can be seen from the fact that in systems that are approaching equilibrium, measurements are able reveal their nonequilibrium nature). This program can pursued without any issues of observer-dependence arising.
It’s good to know that I’m not going crazy thinking that everyone else sees the obvious reason why statistical mechanics works while I don’t but it’s a bit disappointing, I have to say.
Thanks for the link to the reference, the introduction was great and I’ll dig more into it. If you have any ways to find more work done in this area (keywords, authors, specific university departments) I would be grateful if you could share them!