On the limitations of quantum mechanics

     Note added: Quantum mechanics can do a lot. It is the basis for understanding lasers, semiconductors, light-emitting diodes (LEDs), most of chemistry and essentially all of electronics (your phone, computer, MRI magnets, etc.).  However, some things elude an understanding starting from the Schrodinger equation. Notably, biological systems and many other complex macroscopic things. Why is that?
    Since most things are made of electrons, protons and neutrons, and the Schrödinger equation* provides the theory of electrons, protons, and neutrons, one might imagine that with hard work and enough computing power one could explain all "everything". That is,  biology, brain chemistry, psychology, etc using quantum mechanics. Indeed many people in the 1950s, 1960s and 1970s thought that it would be possible to explain everything, including life, using quantum mechanics and high-powered computers. Then in 1972 Philip Anderson published a paper called “More is different”**, in which he emphasized fundamental limits to reductionism and argued that due to something called emergence, and emergent phenomena, it is essentially impossible to solve the Schrödinger equation in many complex systems. Thus he argued that although the Schrodinger equation is essentially the theory of everything on earth, it actually tells us very little about most things that we view as important. This latter point was emphasized and elucidated by Robert Laughlin in about 2007 in a paper entitled (ironically) "The theory of everything". (Laughlin is a Stanford physicist who won a nobel prize for his theory of fractional quantization, a phenomena in which two-dimensional electrons lose their fermionic nature and become "1/3" fractional quasiparticles instead. His theory involved a made-up wave-function with exponents of 1/3 where there should have been exponents of 1 or -1 for ordinary fermions.)

Also of interest, Anderson received the Nobel Prize in 1977 for his contributions to the theory of electron localization.  (As you know, electron localization is very important.)


** From wikipedia:  “Anderson has also made conceptual contributions to the philosophy of science through his explication of emergent phenomena. In 1972 he wrote an article called "More is Different" in which he emphasized the limitations of reductionism and the existence of hierarchical levels of science, each of which requires its own fundamental principles for advancement.[16]
A 2006 statistical analysis of scientific research papers by José Soler, comparing number of references in a paper to the number of citations, declared Anderson to be the "most creative" amongst ten most cited physicists in the world.[17]

* When we say Schrodinger equation here, that could really mean Schrodinger or Dirac equation. The Dirac wave equation is the relativistic version of the Schrodinger equation and is is useful and necessary for understanding heavy elements and most of magnetism, which is a relativistic phenomenon.