John- Thanks for these thoughts.
I'm not an expert in these things, but if quantum gravity sets a minimum distance scale, then there would be a maximum energy density and thus a maximum field. I'm not sure what Motion Mountain is referring to in claiming that there's been an observed field maximum already. I've never heard anyone cite evidence of that sort for any version of quantum gravity. There's an entirely different effect, not involving gravity, which actually limits field strengths. Very high fields cause sparking of the vacuum, i.e. they cause the virtual particle-antiparticle pairs of the vacuum to become real, sort of the way a big field in the atmosphere causes a breakdown of the atmosphere into charged particles. It's hard to imagine how you could get past that process to observe the gravitational effects.
It's great that the Motion Mountain book is free. Despite the acknowledgment, Jon Thaler doesn't recollect any involvement with it. I wrote Baez to ask about his current views on the book, but he says he has not had the time to keep up with the various parts added since he made those initial generally positive comments. Someone submitted this book as a possible "Baloney" candidate, but we didn't put it in that category because we reserve that for cases where there's no ambiguity.
Parts of the book are fun and explanatory. The beginning of the speculations on entropy (equation 112) looks like gibberish because the author seems to be conflating the information content of a message transmission process with the minimum entropy of a physical state, without providing sufficient justification. As I wrote, you shouldn't take my view as gospel.
Following the entropy discussion further, Eq. 113 is presented in a rather elaborate way as a sort of "uncertainty relation". It is in fact just Gibbs' old formula for the mean-square fluctuations of the energy of an object in thermal equilibrium with a heat bath, with one factor in the squared energy fluctuations re-expressed as if it were fluctuations in inverse temperature.* It gives no information at all on a "minimum entropy".
This happens to be a topic I'm familiar with, since as a grad student I measured precisely those fluctuations. ( M. B. Weissman and G. Feher. Observation of energy (thermal) fluctuations in an electrolytic solution. J. Chem. Phys. 63, 586-587 (1975).
also M. B. Weissman and G. D. Dollinger. Noise from equilibrium enthalpy fluctuations in resistors. J. Appl. Phys. 52, 3095-3098 (1981).
) The current we used to make the measurement drove the system slightly out of equilibrium in a way that reduced the fluctuations below the equilibrium value
. In other words, we violated the inequality of Eq. 113.
It's quite possible for a book to be a mixture of good stuff and nonsense. Consider an extreme case- Galileo's Dialogue Concerning the Two Chief World Systems
. The question is whether any
of the new ideas in Motion Mountain are worthwhile, or just some of its energetic presentation of old ideas.
*Technical point. If one were really to define "1/T" by finding the T for which <U> would equal the actual value of U, one would obtain an infinite <Δ(1/T)>, since there's always a non-zero probability of being in the ground state, for which this "1/T" would be infinite. So apparently the author really has done nothing more than re-express ΔU in terms of Δ(1/T) using a linear approximation.
(published on 03/06/11)