What is quantum mechanics?

Ha! This is a job for “savagephysics”… so, after I read today some nice and interesting papers (following my own criteria of “nice” and “interesting” , so… things not to be found in PRL, nature or science… :p ) I decided that during this evening I can make some sort of basic introduction of what “quatization” means… I could have said something about “supersymmetrization” but that may be a subject for a future serious paper of mine… about quantization however, unless everybody on earth forgot everything about physics one cannot say many new things… So, quantization: what means “quantizing a theory”? First of all, nature is “quantum”… that is how nature is, we didn’t make it like that… so, when we write “classical” theories we just do something somewhere wrong. Now, there are several aspects where quantization manifest itself but many fields of “research” see only some aspects of it… for example particle physicists working with one or another of the quantum field theories will tell you quantization is all about path integrals… This is quite vague… Feynman path integrals are a form of “quantization” in the sense of constructing the probability amplitudes taking into account the special topology of your problem… in essence this is how you construct a “statistics” and get in the end your probabilities. But before Feynman came with this idea, quantization was done in the old fashion style… like imposing commutation relations on operators and after some time doing second quantization and constructing perturbative theories etc. These methods are generally quite primitive although very much en-vogue today because of two simple reasons: they are suitable for the toy models used in quantum information theory and very few people can control the full strength of path integral quantization… but I am not discussing here about the social issues and lack of education in the western world… back to the point: While doing path integral quantization the Heisenberg relations are encoded in what is known as “time ordering prescription”… (or radial ordering when working on some conformal field theories). Now, because of this one doesn’t need any “operators” anymore but one does have to take into account the fact that in 3 or more dimensions one has fermions and bosons… because of this one has to use special “numbers” (Grassmann variables) in order to encode the quantization of fermions… and here comes the second aspect of “quantization”: symmetry… while the “classical world” doesn’t know what a fermion is, the quantum world behaves quite differently when one deals with fermions instead of bosons. So, dealing with the two of them is the next aspect of “quantization” and it is mostly related to the presence of a… sign… (a special sign in the definition of an algebraic structure)… That sign is very very (very) important and could mean a nobel prize (maybe for me… but I won’t tell more… ) So, this is another aspect of quantization. I will surprisingly not discuss much about the Bohm Aharonov effect or the Wilson loops as they are… not that fundamental.. the basic ideas behind them can be reduced to something I said before. I will also not discuss much now about entanglement mainly because I discussed about it in the posts about holography and it is NOT that fundamental either (it is a simple result of the topological properties of the space used) So, after speaking about topology and fermions what is the third most important thing that defines quantum mechanics? Well, indiscernability of course… It essentially means that one cannot add labels on fundamental particles or at least not as many as one is used to in classical physics. These tree aspects, again: topology, statistics and indiscernability are the 3 most basic constructs of quantum mechanics. All the others can be derived out of them in one way or another. So, whenever we speak about quantum entanglement don’t forget we actually speak about topology. When we speak about supersymmetry and supersymmetrization we speak in fact about the fact that we don’t really deal well with fermions and when we speak about most of the quantum paradoxes known to uneducated quantum foundation people we speak about indiscernability… 

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