## Tuesday, 18 June 2013

### N-body wave function has no meaning but shut up and calculate: quantum bayesianism

During my graduate school years I was lucky to be assigned on reporting a technique used in computational quantum chemistry, namely resolution of identity.  It is a simple trick to approximate many integrals with a smaller one. I don't want to discuss about this trick but rather a peculiar idea, if not controversial,  I come up during preparation of that report (here). It is about the legitimacy of wave function in many electron, let's be brave and say N-body, physical systems. Argument is posed by Walter Kohn, Nobel Physicist, in his lecture (here) attributed to Van Vleck:
I begin with a provocative statement. In general the
many-electron wave function $\Psi(r_{1} , . . . ,r_{N} )$ for a system
of $N$ electrons is not a legitimate scientific concept, when
$N \ge N_{0}$ , where $N_{0} = 10^{3}$ .
I believe this argument has a profound implication in interpretation of quantum mechanics. However,  sadly, perception of quantum mechanics in many circles of scientific community is limited to Schrödinger equation and interpretations based on wave function. Specially the concept of wave function collapse. In my view these approaches does not make any sense for macroscopic systems such as, humans. Considering Kohn's statement. I can only see the relevance in quantum computing where really small physical systems are in consideration. (Also see my previous post, pointing out recent works in constructing quantum mechanics without wave function)

One prominent figure in recent times is distinguished Professor Mermin who popularised the short version of Copenhagen interpretation as : 'shut up and calculate' and developer of the ithaka interpretation . Very recently discusses about quantum Bayesianism (here). Again, using Kohn's statement we have to be careful not to extent this concept, again, to macroscopic systems like Humans' or even larger atomic systems, like measurement devices. So, replacing a quantum measurement device with a human observer is a mistake, if not a sin. Doesn't matter even if they have a fancy names like Bob or Alice. Because a measurement device big enough has no defined or meaningful wave function hence any kind of  "quantum probability",  i.e., no superposition to observed systems can be established. Probably, problem lies in the transition from microscopic to macroscopic system. There was a large effort in this direction (here).

What ever you believe and read about quantum mechanics. I can only suggest that your crap detectors must function fully all the time when you hear some one talk about quantum mechanics and its interpretation, including this post. I recommend you Neil Postman's article Bullshit and the Art of Crap-Detection.

PS: Recently, there was an interesting cartoon on xkcd saying that we can safely ignore any phrase that starts with "According to quantum mechanics...".