17 November 2008

Cat and string :: quantum mechanics and dualities

During the Fall semester of 2007 physics professor at Berkeley, Irfan Siddiqi, asked this question:
If individual atoms always behave according to quantum mechanics, and if all objects are made of atoms, why doesn’t everything behave according to quantum mechanics? Where does classical mechanics come from? I understand what’s quantum. How do you become unquantum? If I were to make Schroedinger’s cat, one atom at a time, would it be quantum mechanical?”
He responded to his own question as follows:
“To date, physicists have reconciled this dilemma by noting that when a quantum object interacts with an uncontrolled environment consisting of many atoms in random states, then any superposed quantum states decay almost instantly. Even if everyday objects could be prepared in a quantum state, as soon as they came into contact with any kind of classical measurement apparatus, they would immediately collapse into a single, definite state perfectly well described by classical mechanics.”
Interestingly at nearly the same time, but at a different location, Prof. Mina Aganagic talked about how she got started in string theory:
“I went to a few talks at Cal Tech colloquia, and one person I admired very much as a teacher was John Preskill. He gave this talk about black holes and information loss and I thought it was fascinating. I walked into John Schwarz’ office and I asked him—I had no idea he was the founder of string theory—and he told me a little bit and he gave me his book about string theory. I opened the first page and I was hooked. What fascinated me about string theory is the kinds of questions people were asking. From the first year of grad school I knew I wanted to do string theory.”
So in a way, it was a profound accident (beings, supposedly composed of atoms, colliding)... and Aganagic went on to explain:
"String theory is the only known solution to the problem at the core of modern physics: the incompatibility of quantum mechanics and gravity. Perhaps the most remarkable thing we know about string theory is that it is a theory with many dualities. Duality means that there can be different descriptions of the same theory, some very simple and classical, and others very complex and quantum mechanical. Dualities have taught us that what originally appeared as distinct superstring theories are in fact weakly coupled descriptions of a single theory.”
Aganagic is working to understand all these dualities which have led to numerous advances in quantum field theory (e.g., the exact solutions of some supersymmetric gauge theories), mathematics (e.g. Calabi-Yau mirror symmetry), and quantum gravity (the counting of black hole entropy). The most important physical principles: gauge theory and general relativity, are predicted by string theory [though the empirical verification of the theory itself may be somewhat problematic]. “Moreover,” she says, “underlying different descriptions of the theory are often different branches of mathematics.” [see her SPIRES HEP papers]

I have always wondered at exactly what scale a classical model must turn to the quantum alternative. Is the demarcation sharp or fuzzy?

So this story about cat and string has a continuation in the tale about how an elephant is described by three blind men (or a group simply called E8 ;)