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 ;)

Parallel worlds :: Mark | Hugh EVERETT

... incredible documentary from Mark Everett, frontman of the EELS (an alternative rock band best known for its first record Beautiful Freak and its melancholy follow-up Electro-Shock Blues), on his journey to understand his father Hugh Everett III, the quantum physicist who opposed Bohr's Copenhagen interpretation by developing the theory of parallel multiple worlds.

Hugh Everett's 1957 Ph.D. dissertation at Princeton was followed by a paper in the same year entitled "'Relative state' formulation of quantum mechanics", Rev. Mod. Phys. 29: 454–462. The documentary uncovers passages from a draft which were not included in either formal publications, but are nonetheless interesting for intuitively grasping a difficult idea:

'[O]ne can imagine an intelligent amoeba with a good memory. As time progresses the amoeba is constantly splitting, each time the resulting amoebas having the same memories as the parent. Our amoeba hence does not have a life line, but a life tree. The question of identity or non identity of two amoebas at a later time must be rephrased. At any time we can consider two of them, and they will have common memories up to a point (common parent) after which they will diverge according to their separate lives after this point. It becomes simply a matter of terminology as to whether they should be thought of as the same amoeba or not, or whether the phrase "the amoeba" should be reserved for the whole ensemble.

We can get a closer analogy if we were to take one of these intelligent amoebas, erase his past memories, and render him unconscious while he underwent fission, placing the two resulting amoebas in separate tanks, and repeating this process for all succeeding generations, so that none of the amoebas would be aware of their splitting. After awhile we would have a large number of individuals, sharing some memories with one another, differing in others, each of which is completely unaware of his "other selves" and under the impression that he is a unique individual. It would be difficult indeed to convince such an amoeba of the true situation short of confronting him with his "other selves".

The same is true of [sic] one accepts the hypothesis of the universal wave function. Each time an individual splits he is unaware of it, and any single individual is at all times unaware of his "other selves" with which he has no interaction from the time of splitting.

We have indicated that it is possible to have a complete, causal theory of quantum mechanics, which simultaneously displays probabilistic aspects on a subjective level, and that this theory does not involve any new postulates but in fact results simply by taking seriously wave mechanics and assuming its general validity. The physical "reality" is assumed to be the wave function of the whole universe itself. By properly interpreting the internal correlations in this wave function it is possible to explain the appearance of the world to us (classical physics, etc.), as well as the apparent probabilistic aspects.'

Hugh Everett's theory was generally rejected by the physics community for decades. A typical critique invoked subjective experience; for example, Bryce DeWitt had claimed that since he could not feel himself split as in the amoeba metaphor, the theory could not be true. Everett replied in his letter to DeWitt that when Copernicus made his radical assertion that the Earth revolved around the sun instead of the converse, critics rejected Copernicus because they could not feel the Earth moving.

Everett's famous footnote in the Reviews of Modern Physics paper summarized his many-worlds theory where the Schrödinger equation holds for both the quantum and Newtonian worlds:

'In reply to a preprint of this article some correspondents have raised the question of the "transition from possible to actual," arguing that in "reality" there is—as our experience testifies—no such splitting of observer states, so that only one branch can ever actually exist. Since this point may occur to other readers the following is offered in explanation.

The whole issue of the transition from "possible" to "actual" is taken care of in the theory in a very simple way—there is no such transition, nor is any such transition necessary for the theory to be in accord with our experience. From the viewpoint of the theory all elements of a superposition (all "branches") are "actual," none any more "real" than the rest. It is unnecessary to suppose that all but one are somehow destroyed, since all the separate elements of a superposition individually obey the wave equation with complete indifference to the presence or absence ("actuality" or not) of any other elements. This total lack of effect of one branch on another also implies that no observer will ever be aware of any "splitting" process.

Arguments that the world picture presented by this theory is contradicted by experience, because we are unaware of any branching process, are like the criticism of the Copernican theory that the mobility of the earth as a real physical fact is incompatible with the common sense interpretation of nature because we feel no such motion. In both cases the argument fails when it is shown that the theory itself predicts that our experience will be what in fact it is. (In the Copernican case the addition of Newtonian physics was required to be able to show that the earth's inhabitants would be unaware of any motion of the earth.)'

So what are the main points? Human consciousness does not collapse the wave function. Everything that is possible does happen (in some branch of the multiverse).