Hardcover
-
PICK UP IN STORECheck Availability at Nearby Stores
Available within 2 business hours
Related collections and offers
Overview
Originally published in 1989.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Product Details
| ISBN-13: | 9780691633848 |
|---|---|
| Publisher: | Princeton University Press |
| Publication date: | 04/19/2016 |
| Series: | Princeton Legacy Library , #952 |
| Pages: | 220 |
| Product dimensions: | 6.30(w) x 9.30(h) x 1.00(d) |
Read an Excerpt
Science à la Mode
Physical Fashions and Fictions
By Tony Rothman
PRINCETON UNIVERSITY PRESS
Copyright © 1989 Princeton University PressAll rights reserved.
ISBN: 978-0-691-08484-8
CHAPTER 1
THE GARDEN OF COSMOLOGICAL DELIGHTS
(WITH G. F. R. ELLIS)
1. FAIRY TALES
Recently, at a New York cocktail party, a young physicist was asked how he made his living and he replied that he was by specialty a cosmologist. While it might be debated whether cosmology constitutes a "living," his host remained undeterred and immediately inquired if it would be possible to make an appointment for a manicure and a haircut. The physicist explained that cosmology is the study of the large-scale structure of the universe and that he — alas — knew very little about nail polish, split ends, and all those other things a cosmetologist presumably deals with. Both the physicist and his host had a good laugh, after which the host meekly retired with a faint "oh," apparently convinced that cosmology was incomprehensible.
A complementary but equally dismissive view was once expressed in a lecture by Nobel laureate Hannes Alfven who remarked that present cosmological theories have "the character of ancient Indian myths, with turtles standing on elephants standing on. ... Very beautiful fairy tales."
The cocktail party host and Alfven expressed two views that characterize quite accurately the nonspecialist's view of cosmology and the theory on which it is based — general relativity. Either it is the most grandiose enterprise imaginable, combining supreme chutzpah and unintelligible mathematics, or it is not physics at all but rather esoteric mythology.
It strikes us that there is some truth in both the Cocktail Party View and the Indian Mythology View, but that the discipline of cosmology really falls somewhere in between. Because cosmological theories make many predictions that are not yet testable by experiment (and may never be), they are by their very nature highly conjectural and a fertile ground for speculation. Yet, in some areas, our present theories make remarkably good predictions and are so esthetically pleasing that it is difficult to believe there is not some truth in them.
In this article we are going to speculate. Too often, in the free press, all attention is devoted to the so-called "standard cosmological model" with the tacit assumption that the standard model is correct and we know everything there is to know about the universe. Here, we are going to ask the question, "What if the standard model is wrong? Are there any alternatives?" Indeed there are. Even if there weren't, the case for the standard model would be logically much stronger if we could show that all the alternatives were incorrect. After all, you can't logically conclude the standard model is the model if it is the only model you've invented. In fact, this is one of the most important reasons for examining other possibilities. But before we tackle these difficult "eccentric" models, let us start the reader on the beginner's path with a review of the old standby, standard Big Bang cosmology.
2. THE STANDARD MODEL: "DULL AS DISHWATER"
We should first explain what a model is. Einstein's equations do not specify the universe; rather, they may be considered a general framework within which you can construct many different model universes. These model universes may have absolutely nothing to do with the real one — and usually they don't — but ideally they should represent the large-scale distribution of matter in our universe and the curvature of spacetime caused by that matter. Such curvature is, for instance, manifested in the famous bending of light around the sun and other celestial objects like black holes. (See "Demythologizing the Black Hole" by R. Matzner, T. Piran, and T. Rothman in Frontiers of Modern Physics, Dover, 1985). In addition, the model should also describe the history or evolution of the matter in the universe and hence the history of the universe itself. Now, which model is "correct" can be determined only by self-consistency and comparison with the real universe, and this is where experimentalists come in. In our field, experimentalists are usually called astronomers. Of course, you are quite at liberty to throw out Einstein's equations and write your own — some people do — and this procedure brings about the proliferation of even more models.
For about the last twenty years, one cosmological model has carried the title "standard." It also goes by the name of the Friedmann cosmology, or the Robertson-Walker cosmology, and often the Friedman-Robertson-Walker cosmology and occasionally the Friedmann-Lemaître-Robertson-Walker cosmology, depending on which nationalities are disputing priority. (Friedmann was Russian, Lemaître French, Robertson American, and Walker English.) In any case, the FLRW cosmology is the model popularly known as the Big Bang. There are, in fact, any number of Big Bangs, so we will stick with the acronym FLRW when speaking of the standard Big Bang.
Before tearing apart the standard model, it is only fair that we explain why most cosmologists are its ardent supporters. First of all, the FLRW Big Bang is the simplest of all Big Bangs and physicists are highly attracted to the Principle of Simplicity. We will explain exactly what we mean by "simplicity" a little later; but because the concepts involved are somewhat abstract, let us start with the more famous and concrete successes of the standard model.
The FLRW cosmology has made two startling predictions. The first of these is that the light isotopes, most importantly helium and deuterium (heavy hydrogen), were formed roughly three minutes after the Big Bang when the universe was extremely hot. You must keep in mind that in the Big Bang picture the universe cools as it expands, somewhat like the expanding freon that cools your refrigerator. When the universe was three minutes old it was cool enough so that neutrons and protons could stick together to form deuterium (at higher temperatures the neutrons and protons merely bounced off each other) but hot enough so that helium-forming reactions could take place. This occurred at a temperature of about one billion degrees, much hotter than the center of the sun. When the temperature dropped far below one billion degrees this "primordial nucleosynthesis" stopped and, according to the standard model, we should be left with roughly 25% helium by mass and 2 × 10-5 parts deuterium.
It may seem like a miracle that astronomers in fact do measure about 25% helium in the real universe, but it is a miracle squared that they also measure something like 2 × 10-5 parts deuterium. This must be counted as a great success of the standard model.
The second prediction of FLRW is that there should exist relict radiation left over from the cosmic fireball, just as gamma rays are left over from a nuclear explosion. For technical reasons the radiation actually seen comes from about 100,000 years after the Big Bang, when the universe became transparent; but, in any case, the radiation also cooled as the universe expanded and should be observable today not as gamma rays or even visible light but as lower-frequency microwaves. Indeed, in 1965 the famous "cosmic microwave background radiation" was discovered by Arno Penzias and Robert W. Wilson at Bell Labs and explained by Robert Dicke's group at Princeton.
Because these two predictions are so decisive, they are often used to compare one cosmological model to another and we will refer to them frequently. Actually, it is so difficult for a model to predict both the light isotope abundances and the cosmic microwave background that most alternative models have been of the Big Bang type. This fact will become more evident as we go along.
Now, we mentioned that the FLRW was the simplest Big Bang model. In order to do useful work, the physicist must translate words like "simple" into mathematical concepts. We will now explain what simple means to a cosmologist. These concepts are, unfortunately, more abstract than helium and microwaves, and the reader is advised at this point to mix a vodka tonic. Lime, please.
The FLRW assumes that at some finite time in the past, the universe started to expand from a singular state of infinite temperature and density. Furthermore, the density of material (say, neutrons, protons, electrons, photons, etc.) is assumed to have been uniform throughout the universe and the expansion of the universe is taken to be homogeneous and isotropic. Let us illuminate some of these terms. A singularity is a point of spacetime where some quantity becomes infinite. In the FLRW universe — alas — virtually everything becomes infinite at the instant of the Big Bang itself, which is thought to have occurred between 10 and 20 billion years ago. If you think a singularity must be a breakdown of sorts, you are absolutely correct. We will have more to say about this later.
The term "isotropic" refers to a system that looks the same in all directions or, in technical language, is "rotationally symmetric." You might imagine yourself standing at the edge of the Grand Canyon and turning around. The abyss before you does not look like the desert behind you, so the area surrounding the Grand Canyon is certainly not isotropic. On the other hand, if you stood like a lizard in the middle of the desert, it might very well look the same in all directions, so we would say the desert is isotropic.
By contrast, the term "homogeneous" refers to a system that looks the same at any point or, technically speaking, is "invariant under translations." For instance, if the Grand Canyon were idealized as being very straight and of uniform width, we could walk along it and at any point it would look exactly as it had a moment before. We could not tell we had moved. Yet, we could still turn around and see the desert, which appears very different from the canyon. So here we have a situation which is an isotropic but homogeneous. Since these terms are very important in cosmology, it is best to remember them: homogeneity means no change in landscape when one walks; isotropy means no change when one spins. See Figure 1.1 to understand that isotropy everywhere implies homogeneity but not vice versa. (Philosophical exercise: is life homogeneous?)
Thus, as foretold, the FLRW cosmology is about as simple as one can get. We may visualize the universe to be filled with radiation such as photons, quarks, and neutrinos, as well as more ordinary matter such as protons and neutrons. This material is absolutely uniform everywhere and in all directions, that is, homogeneous and isotropic. Furthermore, the requirements of homogeneity and isotropy ensure that the universe is expanding at equal rates in all directions and that annoying things like bumps and shock waves do not exist.
Observationally, we cannot actually verify that the universe is homogeneous simply because we cannot travel very far from earth. Even if we could travel 1,000 light years we would still be seeing everything from the same region in our galaxy. Isotropy implies that we cannot point in any particular direction and say "we have seen the center of the universe over there," which is the same as saying, "the universe is very different that way." This isotropy seems to exist approximately in the real universe if we ignore irregularities such as mere galaxies and only consider size scales of galactic clusters and above.
Any cosmological model must predict that the currently observed universe is approximately isotropic. However, we do not call this a "success" of the standard model since it was assumed to be isotropic from the very beginning.
We are going to start multiplying now. The FLRW model itself comes in several styles. The Einstein equations predict the universe is either expanding or contracting and observations of the redshifts of distant galaxies indicate that the universe is presently expanding. (Light becomes redder when emitted from an object moving away from us and bluer when emitted by objects moving toward us. Hence, galactic redshifts indicate the universe is expanding.) The Einstein equations, however, do not specify the amount of radiation or matter present in the model, and these must be determined by direct astronomical observation or other theoretical considerations. If the matter or radiation content of an FLRW universe is below the so-called "critical density," the model will keep expanding forever. In other words the universe is "open." Most evidence indicates that the real universe belongs to this "no frills attached" variety. There are, however, available extras. Massive neutrinos may exist, as well as photinos, gravitinos, Higgsinos, and a host of other new exotic particles which we fortunately cannot discuss here. (Physics has gotten out of hand.) If these particles contribute a sufficient mass density to the universe, the expansion of the universe will eventually halt and the universe will recollapse. Such a universe is often termed "closed."
It is time to ask a stupid question: why is the universe expanding at all? A satisfactory philosophical answer probably can't be given but a physical one can: the universe was born with a certain amount of kinetic energy (energy of motion) and potential energy (gravitational energy). Like a ball being thrown into the air, the universe initially has most of its energy in kinetic energy, but gradually more and more is transferred to potential energy until the ball stops. The ball then has no kinetic energy and falls back to the ground. This is like a closed universe. If, however, the ball has sufficient amounts of kinetic energy, it will reach escape velocity and never fall back to the earth. This is like an open universe.
For the moment, these are all the details we need of the standard model before tearing it apart.
Perhaps the first point that should be made about that standard model is that sixty years ago it would not have been considered standard at all. For philosophical reasons Einstein originally felt that an ideal universe should be neither expanding nor contracting but static, and his first cosmological model of 1917 was exactly that. Now, in order to produce a static model of the universe from his equations, Einstein was forced to add the famous "cosmological constant." This constant may be thought of as adding a term to the potential energy of the universe equivalent to a repulsive force or pressure. Einstein chose a value for the constant that added just enough so that the kinetic energy of the universe was zero. The ball always "hovered" at the top of its flight. (A more accurate analogy would be a pencil balanced on its point.) Such a situation may seem impossible, and indeed Eddington showed in 1930 that a static universe was unstable and tended to contract or expand. In any case, by that time evidence for the expansion of the universe had been discovered, and in 1931 Einstein dropped the cosmological constant as the "biggest blunder" of his life.
Recently, models with cosmological constants have come back in vogue (see Section 5 of this essay) and are now classed as nonstandard models. So the moral of the story is that, like Tchaikovsky and high heels, cosmological models come in and out of fashion. This is the theme of our essay: one should be careful what one calls standard, for tomorrow there may be a replacement. Therefore, the reader would be wise not to forget cosmological constants.
There are more serious objections to the standard model than changing fashion. We mentioned that the FLRW cosmology begins with a singularity. This is a much more serious breakdown than a flat tire or a cracked engine block. It is, in fact, a physical impossibility — a region where the laws of physics break down altogether and even spacetime itself comes to an end. To avoid the singularity is probably the main reason cosmologists search for other models.
There are other conceptual problems with the FLRW Big Bang. Recall that we said it was exactly homogeneous and isotropic. Physicists who follow the Principle of Simplicity are attracted to this model because it is indeed the simplest conceivable cosmology. On the other hand, physicists who rely on the Principle of Greatest Probability (also known as the Principle of Minimum Serendipity) are disturbed. Just how likely is it that the universe was created in an exactly uniform fashion with strict homogeneity and isotropy? Such a birth seems at best implausible but this is exactly what FLRW claims. Doubts such as these led to the creation of anisotropic and inhomogeneous models which we will discuss in Section 3.
(Continues...)
Excerpted from Science à la Mode by Tony Rothman. Copyright © 1989 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
Table of Contents
- FrontMatter, pg. i
- CONTENTS, pg. v
- PREFACE, pg. vii
- 1. E GARDEN OF COSMOLOGICAL DELIGHTS, pg. 3
- 2. METAFLATION ?, pg. 29
- 3. Geodesics, Domes, and Spacetime, pg. 51
- 4. The Evolution of Entropy, pg. 75
- 5. A Memoir of Nuclear Winter, pg. 109
- 6. Genius and Biographers: The Fictionalization of Evariste Galois, pg. 148
- NOTES, pg. 195
- INDEX, pg. 201