I recently re-visited a paper written in 2000 by Laughlin and Pines entitled The Theory of Everything (pdf!). The main claim in the paper is that what we call the theory of everything in condensed matter (the Hamiltonian below) does not capture “higher organizing principles”. Condensed Concepts blog has a nice summary of the article.
Because we can measure quantities like and in quantum hall experiments and superconducting rings respectively, it must be that the theory of everything does not capture some essential physics that emerges only on a different scale. In their words:
These things [e.g. that we can measure ] are clearly true, yet they cannot be deduced by direct calculation from the Theory of Everything, for exact results cannot be predicted by approximate calculations. This point is still not understood by many professional physicists, who find it easier to believe that a deductive link exists and has only to be discovered than to face the truth that there is no link. But it is true nonetheless. Experiments of this kind work because there are higher organizing principles in nature that make them work.
If I am perfectly honest, I am one of those people that “believes that a deductive link exists”. Let me take the example of the BCS Hamiltonian. I do think that it is reasonable to start with the theory of everything, make a series of approximations, and arrive at the BCS Hamiltonian. From BCS, one can then derive the Ginzburg-Landau (GL) equations as shown by G’orkov (pdf!). Not only that, one can obtain the Josephson effect (where one can measure ) by using either a BCS or a GL approach.
The reason I bring this example up is because, I would rather believe that a deductive link does exist and that even though approximations have been made, that there is some topological property that has survives to each “higher” level. Said another way, in going from the TOE to BCS to GL, one keeps some fundamental topological characteristics in tact.
It is totally possible that what I am saying is gobbledygook. But I do think that the Laughlin-Pines viewpoint is speculative, radical, and has perhaps taken the Anderson “more is different” perspective too far. It is a thought-provoking article partly because of weight that the authors’ names carry and partly because of the self-belief of the article’s tone, but I am a little more conservative in my scientific outlook. The TOE may not always be useful, but I don’t think that means that “no deductive link exists” either.
I’m curious to know whether you see things like Laughlin and Pines.