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Overview
Of the four fundamental forces of nature, gravity might be the least understood and yet the one with which we are most intimate. On Gravity combines depth with accessibility to take us on a compelling tour of Einstein's general theory of relativity. A. Zee begins with the discovery of gravity waves, then explains how gravity can be understood in comparison to other classical field theories, presents the idea of curved spacetime, and explores black holes and Hawking radiation. Zee travels as far as the theory reaches, leaving us with tantalizing hints of the unknown, from the intransigence of quantum gravity to the mysteries of dark matter. Infused with Zee’s signature warmth and fresh style, On Gravity opens a unique pathway to comprehending relativity, gravity, spacetime, and the workings of the universe.
Product Details
| ISBN-13: | 9780691202662 |
|---|---|
| Publisher: | Princeton University Press |
| Publication date: | 03/10/2020 |
| Pages: | 200 |
| Sales rank: | 1,061,604 |
| Product dimensions: | 5.10(w) x 8.10(h) x 0.70(d) |
About the Author
Read an Excerpt
CHAPTER 1
A friendly contest between the four interactions
Matter and the forces that move it
To tell the story of gravity waves, let us first go for a quick tour of the universe. Matter consists of molecules, and molecules are built out of atoms. An atom consists of electrons whirling around a nucleus, which in turn consists of protons and neutrons, collectively known as nucleons. The nucleons are made of quarks. That's what we know.
The universe also contains dark matter and dark energy. (More in chapter 18.) Indeed, by mass, the composition of the universe is 27% dark matter, 68% dark energy, and only 5% ordinary matter. To first approximation, the universe may be regarded as one epic cosmic struggle between dark matter and dark energy. The matter we know and love and of which we are made of hardly matters. Unhappily, at present we know little about the dark side.
We know of four fundamental forces between these particles. When particles come into the vicinity of each other, they interact, that is, influence each other. Here is a handysummary of the four forces, known as gravity, electromagnetism, the strong interaction, and the weak interaction.
G: Gravity keeps you from flying up* to bang your head on the ceiling.
E: Electromagnetism prevents you from falling through the floor and dropping in on your neighbors if you live in an apartment.
S: The strong interaction causes the sun to provide us light and energy free of charge.
W: The weak interaction stops the sun from blowing up in your face.
I don't quite remember, but I would suppose that, due to buoyancy, we were not aware of gravity while in our mothers' wombs. But as soon as you entered the world, you knew about gravity, especially if the obstetrician grabbed you by the ankles and hanged you upside down. Then that quick slap on your bottom caused you to cry out and to open your eyes, thus discovering electromagnetism.
Only four forces!
The world appears to be full of mysterious forces and interactions. Only four?
As you toddled, you banged your head against a hard object. What is the theory behind that? Well, the theory of solids can get pretty complicated, given the large variety of solids. But a simple cartoon picture suffices here: the nuclei of the atoms composing the solid are locked in a regular lattice, while the electrons cruise between them as a quantum cloud. A collective society in which all individuality is lost! The atoms no longer exist as separate entities. The arrangement is highly favorable energetically; that is jargon for saying that enormous energy is required to disturb that arrangement. Revolution is costly. It takes quite a tough guy to crack a rock into halves.
So, the myriad interactions we witness in the world, such as solid banging on solid, can all be reduced to electromagnetism. What we see in everyday life is by and large due to some residual effect of the electromagnetic force. Since common everyday objects are all electrically neutral, consisting of equal numbers of protons and electrons, the electromagnetic force between these objects almost all cancels out. Even the steel blade of a jackhammer smashing into rock is but a pale shadow of the real strength of the electromagnetic force.
Just about the only time the true fury of electromagnetism shakes us is when thunder and lightning fill the sky. While we modern dudes have totally enslaved electromagnetism, all ancient people attribute its occasional bursts of temper to the gods.
When you first shook off the ooze, you might have thought that there must be thousands, if not millions, of forces in the world. Thus, to be able to state that there are only four fundamental forces is totally awesome, a feat summarizing centuries of painstaking investigations. For example, realizing that light was due to electromagnetism stands as a towering achievement.
The universe as a finely choreographed dance
While the proverbial guy and gal in the street are plenty acquainted with gravity and electromagnetism, they have no personal experience with the strong and the weak interactions. But in fact, the physical universe is a finely choreographed dance starring all four interactions.
Consider a typical star, starting out life as a gas of protons and electrons. Gravity gradually kneads this nebulous mass into a spherical blob in which the strong and the electromagnetic forces stage a mighty contest.
The electric force causes like charges to repel each other. Thus, the protons are kept apart from each other by their mutual electric repulsion. In contrast, the strong force, also known as nuclear attraction, between the protons tries to bring them together. In this struggle, the electric force has a slight edge, a fact of prime importance to us. Were the nuclear attraction between protons a tiny bit stronger, two protons could get stuck together, thus releasing energy. Nuclear reactions would then occur very rapidly, burning out the nuclear fuel of stars in a short time, thereby making steady stellar evolution, let alone civilization, impossible.
In fact, the nuclear force is barely strong enough to glue a proton and a neutron together, but not strong enough to glue two protons together. Roughly speaking, before a proton can interact with another proton, it first has to transform itself into a neutron. The weak interaction has to intervene to cause this transformation. Processes affected by the weak interaction occur extremely slowly, as the term "weak" suggests. As a result, nuclear burning in a typical star like the sun occurs at a stately pace, bathing us in a steady, warm glow.
Range versus strength
The reason that the proverbial guy and gal in the street do not feel the strong and the weak interactions is because these two interactions are short ranged. The strong attraction between two protons abruptly falls to zero as soon as they move away from each other. The weak interaction operates over an even shorter range. Thus, the strong and weak interactions do not support propagating waves. In this book, we won't talk about these two short range interactions much.
In contrast, the gravity force between two masses and the electric force between two charges both fall off with the separation R between the two objects like 1/R2, the inverse square law celebrated in song and dance. More on this in chapter 2. Gravity and electromagnetism are known as long ranged and thus can and do support propagating waves.
For R large, these forces still go to zero, but slowly enough that we can feel the tug of the sun, literally an astronomical distance away. For that matter, our entire galaxy, the Milky Way, is falling toward our neighbor, the Andromeda galaxy.
Thus, in the contest among the four interactions, brute strength is not the only thing that counts: many phenomena depend on an interplay between range and strength. A case in point is fusion versus fission in nuclear physics. When two small nuclei get together, each consisting of a few protons and some neutrons, the strong attraction easily overwhelms the electric repulsion, and they want to fuse. In contrast, in a large atomic nucleus (famously, the uranium nucleus), the electric repulsion wins over the strong attraction. Each proton only feels the strong attraction of the protons or neutrons right next to it, but each proton feels the electric repulsion from all the other protons in the nucleus. The nucleus wants to split into two smaller pieces, accompanied by the release of energy.
CHAPTER 2
Gravity is absurdly weak
Gravity and the electric force
Gravity is absurdly weak compared to the electromagnetic force.
How do we compare the relative strength between two forces at the fundamental level? First, a reminder of some basic facts.
We learned about Newton (1642–1726/27) and his law of universal gravity in school. It states that the force F of gravitational attraction between a mass M (say, the earth) and a mass m (say, the moon) is equal to a constant G (known as Newton's gravitational constant) times the product of the two masses (namely, Mm) divided by the square of the distance R separating them. Or, in a more concise language, F = GMm/R2.
We also learned about Coulomb's law. It states that the force F of electric repulsion between two charges, one with charge q1 and the other with charge q2, is equal to the product of the two charges (namely, q1q2) divided by the square of the distance Rseparating them. Or, in a more concise language, F = q1q2/R2.
A striking mystery: the fall-off of the force with increasing distance — the 1/R2 inverse square behavior — is the same for gravitation and for the electric force. We will come to the modern understanding of this in due time.
No need to count the number of zeros, we will do it for you
Time out. This is as good a place as any to introduce scientific notation, just in case you do not know it. The ethos behind scientific notation may be expressed as follows: esteemed sir or madam, you don't have to count the number of zeros, we will do it for you. Thus, 100 is written as 102, 1,000 as 103, 1,000,000 as 106, and so on. The number in the exponent, such as 6 in 106, simply indicates the number of zeros when you write out the number 106 as 1,000,000. It follows that a number such as 149 could be written as 1.49 × 102. The multiplication of large numbers is thus rendered easy: the number of zeros simply add. For example, 100 × 1,000 = 100,000 may then be written as 102 × 103 = 102+3 = 105. In this notation, 10 may be written as 101, and 1 as 100 (since it is equal to 1 with no zero following it).
This explains how to write large numbers. Small numbers are written with a minus sign in the exponent. The logic behind this is as follows. Since, as was just noted, 10a × 10b = 10a+b on dividing both sides of this equation by 10a, we obtain 10b = 10a+b/10a and thus, by setting b to -a, we have proved that 10-a = 10a-a/10a = 100/10a = 1/10a For example, let a = 2, and we have 10-2 = 1/102. In other words, we may write 1/100 (which equals 0. 01 in standard nonscientific notation) as 10-2 in scientific notation. As another example, 1/1017 = 10-17 is a very small number, since 1017 is a very large number.
Comparing gravity to the electromagnetic force
After this notational interlude, we are ready to compare gravity to the electric force. To have a fair comparison, let us consider two protons. The gravitational attraction between them is equal to Fgravitation = Gmp2/Ra2/sup>, with mp the mass of the proton. The electric repulsion between them, on the other hand, is equal to Felectric = e2/R2, where e denotes the fundamental unit of charge carried by the proton.
Thus, the ratio of the two forces Felectric/Fgravitation = e2/(Gmp2). Note that the factors of R2 cancel out, so that this ratio is just a number, measured to be about 1036, that is, 1 with 36 zeros after it. This absurdly large number gives precise meaning to the statement that gravity is absurdly weak compared to electromagnetism. Electromagnetism is stronger than gravity by a factor of 10.
Note also that before elementary particles, such as protons, and electrons, were known, any proposed comparison between the strengths of gravity and electromagnetism would have been meaningless. What would you use to do the comparison?
Gravity does not know about yin and yang
That gravity is so much weaker than electromagnetism may surprise the unfortunate who has just had a hard fall. The reason is of course that every atom in the unfortunate's body is being pulled down by every atom in the entire earth. The enormous number of atoms involved more than compensates the teeny number 10-36.
A huge difference, and it is huge, as we will see, is that masses are always positive, while charges can be positive or negative. The electric force between a positive and a negative charge then has the opposite sign, namely, it is attractive rather than repulsive. Likes repel, while opposites attract.
Thus, electromagnetism knows about yin and yang. While yin and yang attract, the electric force is repulsive between yin and yin, and between yang and yang.
In contrast, gravity does not know about yin and yang: everybody is gravitationally attracted to everybody else.
I have already alluded to the reason electromagnetism is well hidden in everyday life: common objects contain equal number of positive and negative charges and so are electrically neutral. Whatever force that exists between them is a residual force, left over after the main electric force — namely, the attraction between the protons and electrons, the repulsion between the protons, and the repulsion between the electrons — has been canceled off. It is as if in a financial transaction involving billions rounded off to the nearest dollar, all we get to see is the rounding error of 23 cents.
What electric and magnetic forces we see in everyday life are just the teeny "round off errors."
A perpetual contest between two forces
An interesting everyday example is the refrigerator magnet. It underlines the enormous strength of the electric force over gravity: the small patch of refrigerator door in contact with the magnet is holding off the entire earth. Furthermore, the magnetic force, caused by the circular motion of the charged particles inside the magnet, is itself much weaker that the electric force.
Once you are alerted to this contest between electromagnetism and gravity, you will start to see it everyday, everywhere. Look at a glass of water. The water molecules hear the incessant siren song of gravity, telling them to lower themselves, to come to the bosom of mother earth. But electromagnetism causes the glass molecules to join hands, forming an interlocking prison through which the water molecules cannot escape. The electric force easily overwhelms the pull of the entire earth.
The escape route is through the top of the glass. Absorbing infrared photons from the environment and hit by air molecules, the water molecules get all agitated and bump into each other in their frenzy. Once in a while, a particular water molecule achieves enough speed — the crowd bumps into him just so — to overcome the downward pull of gravity and shoots to freedom. We call this process evaporation, which leaves us eventually with an empty glass, possibly with some scum in it — the mineral molecules in the scum are too obese to make the getaway.
Or look at a tree. It is desperately pulling up nutrients against gravity. You could surely come up2 with many more examples of this never-ending struggle going on all around us between electromagnetism and gravity.
Newton answers your objection
Let's go back to the refrigerator magnet for a moment. You could have objected that it was not a fair comparison. While the earth is very very large, much of it is also very very far away from the magnet.
Newton was well aware of this problem, and spent almost 20 years proving what he called two "superb theorems." The magnet is being pulled down by the patch of ground beneath your feet, stuff very close to the magnet but composing a small fraction of the entire earth. The rest of the earth, including the enormous amount of stuff on the other side of the world, is far away. Thus, to apply the law F = GMm/R2 to the magnet and the earth, we should mentally cut up the earth into a multitude of infinitesimal pieces, each some distance R from the magnet and each pulling on the magnet, and add up the individual forces.
(Continues…)
Excerpted from "On Gravity"
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Copyright © 2018 Princeton University Press.
Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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Table of Contents
Preface ix
Timeline xiii
Prologue: The song of the universe 1
Part I
1 A friendly contest between the four interactions 9
2 Gravity is absurdly weak 15
3 Detection of electromagnetic waves 25
4 From water waves to gravity waves 31
Part II
5 Spooky action at a distance 37
6 Greatness and audacity: Enter the field 40
7 Einstein, the exterminator of relativity 51
8 Einstein's idea: Spacetime becomes curved 57
9 How to detect something as ethereal as ripples in spacetime 66
Part III
10 Getting the best possible deal 77
11 Symmetry: Physics must not depend on the physicist 88
12 Yes, I want the best deal, but what is the deal? 91
13 The action for Einstein gravity 100
14 It must be 102
Part IV
15 From frozen star to black hole 107
16 The quantum world and Hawking radiation 115
17 Gravitons and the nature of gravity 123
18 Mysterious messages from the dark side 131
19 A new window to the cosmos 140
Appendix: What does curved spacetime mean? 143
Postscript 151
Notes 153
Bibliography 167
Index 169
What People are Saying About This
"On Gravity is a delightful and engaging tour of Einstein’s great triumph—the general theory of relativity—by one of our best tour guides, A. Zee. A fun and fascinating read."—David Kaiser, Massachusetts Institute of Technology"This engaging and enjoyable book focuses on our modern understanding of gravity through general relativity. With an entertaining narrative, Zee examines the development of these concepts and how they mesh with other discoveries in physics. On Gravity makes for compelling reading."—Pedro Ferreira, author of The Perfect Theory"Rigorous and original, On Gravity provides an insightful presentation of the key concepts of gravity and general relativity. This book gives a different and new perspective and will surely generate interest." —Alberto Vecchio, University of Birmingham
