Everyone is interested in cosmology, right? Well, I’d like to think, anyway, that most people consider the cosmic questions from time to time. How did this all begin and why are things like this, anyway?
Every culture, even every primitive tribe has had its cosmology, its story of The Origin. Then, all the tribe must learn the story by rote. Okay, so God said “Let there be light”, then created the world and all its stuff in the next six days. Makes sense, glad I asked, story over, and now we have to turn to practical stuff, like sharpening our spears for the next mastodon hunt.
No, you don’t need to ask who it was that put God in charge, or to consider possible alternatives. Turtles all the way down? Forget about it.
Over the past 90 years or so, cosmology has become a scientific discipline, part of physics and astronomy. All that we’ve learned in terrestrial labs about the nature of space, time, energy, and the structure of matter applies to what we see in the sky. Physics lets us put together credible, consistent models for the evolution of stars, galaxies, and the expanding universe itself. We have a good story for the synthesis, through astrophysical processes, of the known chemical elements from an initial soup of pure energy. Conversely, because conditions in the very young universe were extreme, with temperatures and densities far beyond what can be achieved in earthly labs, observations of the cosmos yield clues for remaining questions at the very frontiers of ultramicroscopic physics. Cosmology, the study of the biggest know thing, the universe itself, is intimately connected with the study of elementary particles, the smallest known things.
It is a great challenge to write a book to lead the cosmically curious lay reader through the web of observations, theories, and speculations that make up modern physical cosmology. Brian Greene’s The Fabric of the Cosmos is an impressive response to the challenge. It received many laudatory reviews when it appeared last year, without much criticism. In this entry I report a little about my experience with the book and my feelings about it.
As well as challenging the author, any such book poses a challenge also to the interested reader. This isn’t Eden any more, Toto; to achieve enlightenment, we have to try to understand a lot of fundamental physics. We have to be willing to commit some time and effort to it. But still, no matter how curious, as lay readers, we are not able to devote our lives to mastering the subject. We do have other spears to sharpen.
I have a considerable background, a formal education in physics and mathematics, acquired in an era preceding the development of many of the crucial results discussed in this book. So, while very well prepared in fundamentals, my prior knowledge of both cosmology and elementary particles were a couple of decades out of date. After having put considerable effort into reading the book, I’m not totally satisfied with it and wonder how illuminating it might be to readers with much less formal education in math and physics than I have had. I can imagine a typical, intelligent, scientifically aware lay reader, who would be naturally attracted to the subject, but who, on finishing the book, might feel bewildered about what he has read, his head spinning with a sea of terms--entropy, inflation, entanglement, Higgs ocean, strings, branes, super symmetry, broken symmetry, flatness, Calabi-Yau manifolds—but without a satisfying understanding of the logical relationships and mutual implications among them.
I recall that when I read Greene’s The Elegant Universe a few years ago, I was not always happy with his choices of metaphor in presenting quantum ideas. Similarly, with this book, I find some of the metaphors less than congenial, and I think sometimes not well explained. As an example, I’ll look at his metaphor for the all-important hypothesized Higgs field, important both to the fundamental theory of elementary particles, and to explaining inflation, the great new idea of what actually banged in the Big Bang origin of the universe.
Greene’s basic metaphor for a chaotic field in the fantastically hot early universe has a poor, tortured frog frantically hopping on an extremely hot metal bowl, too hot to stand on, while trying to get to his lunch, a pile of worms at the bottom center of the bowl. For the Higgs field, this picture is modified by adding a bump or tower with a plateau at the center of the bowl, with the worms resting on the top.
The important distinguishing characteristic of a Higgs field is that the minimum energy does not occur when the field value is zero, but the significance of this is lost without some discussion of the meaning and use of the field value. If it is not a representation of energy, then what is it.? The meaning of the Higgs field value certainly wasn’t clear to me at the time that he first introduces the metaphor. It has become a little clearer on reading another popularization of the same subject, namely, The Inflationary Universe, by Alan Guth, the actual discoverer of the inflationary theory. I haven’t yet read the Guth book entirely through, but on reading the corresponding sections on Higgs and inflation, which feature diagrams very similar to those in Greene;s book, it seems to make more sense to me than Greene’s presentation, and without having to torture a frog, or harm any other animals in any way.
For one thing, Greene offers the (I think) misleading statement that the frog’s distance from the worms represents the field’s value and the height of the bowl represents the energy. Actually, these diagrams are graphs of the field’s energy density as a function of the field value as independent variable, and in this picture, the field value is a pair of real values, perhaps a complex variable. The magnitude of this complex variable is the radial coordinate in a cylindrical polar coordinate system, so the frog’s distance from the vertical axis of the bowl. (Actually I learn from the Guth book that there must be 24 different Higgs field values).
Further, I think that the pile of worms is a red herring, i.e., a distraction. The frog is not really trying to get to the worms when they are atop the central plateau, but rather, like all systems, he is seeking his minimum energy configuration, which occurs at some distance from the central axis in the case of the Higgs field. Greene uses the worms to cause the frog to hang out a bit on the central peak when he happens to land there by chance in his jumping, after the bowl has cooled a bit. Guth doesn’t need the worms, because he has a little dimple in the energy function at the center of the bowl, invokes supercooling to have the system get trapped there, and invokes quantum mechanical tunnelling to have the system eventually roll down to its minimum energy at a non-zero vacuum expectation value for the the Higgs field, causing the brief but violent exponental inflation of the universe in the process.
Another big problem that I have with The Fabric of the Cosmos is a discussion in Chapter 6, “Chance and the Arrow”, which gives attention to the question of the direction of time-- what, in physics, distinguishes the future from the past? It is not the deterministic laws of simple systems and fields—e.g., Newton’s laws of motion, Maxwell’s equations of the electromagnetic field, the Schroedinger equation in quantum mechanics-- which are all invariant under time reversal. It is only the laws based on statistical approaches to physics that define an arrow of time, in particular, the Second Law of Thermodynamics, which says that the total entropy, or disorder, of the universe only increases in time.
For some reason that I do not yet understand, in Chapter 6, Greene spends a lot of words and a lot of effort arguing for what he admits is a seemingly absurd proposition, namely, that, from any point in time, statistical entropy must increase not only towards the future but also towards the past. In other words, the entropic arrow of time is double-headed. His prime example has you sitting in a bar on a slow Friday night, watching the ice melting in your glass of ice water. At 10:00 PM the bartender served you this glass of water, with a large ice cube. At 10:30, the cube is partially melted, smaller than when you were served it. Now, his proposition is that, based on considerations of probability and mathematics, sitting there staring at your glass at 10:30 you must conclude that the overwhelming odds support the assertion that half-an-hour earlier the ice cube must have been even smaller than now, not larger, notwithstanding your memory, the concurrence of your eqally bored neighbor on the next stool, and the evidence of the tape in the video surveillance device, which all support the opinion that the ice cube was even larger at 10:00 PM than it is now at 10:30.
First, I’m not quite sure why Greene hews to this proposition, except that it seems to have something to do with need to invoke gravitation as the source of the very highly ordered state, a state of lowest possible entropy, which, according to the 2nd Law, the universe must have had at its origin. Gravitation somehow contributes high order, or negative entropy, because of its potential for forming clumps from the high-entropy uniform distribution of energy in the beginning.
Second, I really have not been able to buy the argument for the double-headed entropic arrow of time (which omits any actual demonstration,or even a rough sketch, of the mathematics he is arguing about). It seems to me that it omits a number of considerations that should be relevant, such as the notions of conditional probability, Bayesian probability, and the relations between entropy, information, and ignorance. I’d like to see at least a sketch of the way one would apply the methods of statistical physics to calculate the probabilities in support of Greene’s assertion. I’ve been struggling with using these methods to sketch a contra argument to this assertion.
I’ll post more on this subject later.
It is pretty interesting to compare Greene’s Chapter 6 with an entirely analogous Chapter 15 in Murray Gell-Mann’s book, The Quark and the Jaguar. Which I may also get to soon in this blog.
