Greene seems to ignore an obvious problem. A vessel within which there is a negative pressure tends to shrink. In a sense the universe is a vessel. Why should a negative pressure make it inflate? I think I know the answer and it is a long involved story about how the stress energy tensor can fit into Einstein’s GR equations. It is one of those developments that did not all fit into my head at once when I sort of understood it piecemeal. (Note the use of cause and effect above.) There is another scenario: An ordinary vessel filled with water and mechanisms outside it which pull the vessel boundaries outward. Now we have an expanding region with negative pressure in the context of cause and effect. In the first case the cause is very local; in the second case the cause is global. Greene and I both ignore here the difference between the first and second time derivatives of the volume.
I like Chapter 7 which should be titled “Is This Science?”. Other authors don’t much touch this question except to take sides. Greene supports it’s being science but explores objections well. It prompts me to explain how I lie between these two camps. I believed Newton, and in a sense I still believe him. I believed Maxwell for the reasons that Greene describes well. I warped my head enough to believe Einstein, even his General Relativity in part because I came to believe in the (mathematical) existence of non-embeddable manifolds—even Minkowskian manifolds. I cannot say that I ever believed Schrödinger’s equation or Heisenberg’s formulation. To believe one seemed to preclude believing the other. Von Neumann’s Hilbert space unification was gratifying, but only in a mathematical sense. I don’t believe it either but I sort of understand how to make predictions with it and take it on faith that many such predictions are born out statistically. I can’t find anything there to believe. Incidentally I have never been much impressed with attempts to convince me that the new theory explained all of the successful predictions of the theories being supplanted. I like this quote on quantum mechanics:
Page 170: I agree with Greene’s argument for inclusive concept of reality; I think it can be improved by invoking Ockham. The ‘realists’ against whom Greene argues want to expunge the unobservables. Greene wants to keep some of them to simplify the theory. Which are you to minimize: reality or the elements of the theory? Here these goals are at odds with each other.
I grudgingly support string theory and some of the multiverse models on the bases of potential explanatory power. Part of this is because it is cheap. If I were running a university I would contemplate moving some of those guys into the math department. I believe some of their results like I believe a mathematical theorem, not like I believed Newton. They contribute to our culture the same way math does, and I think that contribution is positive in dollar terms, even worthwhile. Tegmark may yet have the last word.
There is much evidence for the Anthropic Principle besides the value of Λ, the cosmological constant. I was convinced of its explanatory power from about 1953 when my chemistry professor began to enumerate the extraordinary properties of ordinary water and how they bore on college chemistry, not to mention on life. The list has only rapidly grown longer. I am tickled to learn of Weinberg’s 1987 paper predicting a positive Λ on anthropic grounds. I count that as evidence that Λ is positive as a sociological theory rather than a physics theory. The datum is that it was a prediction and Weinberg knows more physics than I.
I understand full well if this leaves you shaking your head. There is no denying that quantum dogma sounds a lot like snake oil.
Page 224: Greene confuses amplitudes, which are complex numbers that the ψ in Schrödinger’s equation denotes, with probabilities. This is going to greatly confuse anyone who attempts to understand this section thoroughly.
Chapter 9 addresses Everett’s multi world interpretation. He addresses the probability question but fails to connect it with the measure problem mentioned earlier in the cosmic landscape area. Some physicists are familiar with how mathematicians solved such problems when the infinite sets were on the real line. Many of the same ideas are applicable under the mathematical term measure theory.
Page 245 stimulated this.
“Duality” and multi “perspectives“ are close to my rejection of “reality”. The creed is that there is no one real thing, no reality.