# It's About Time: Understanding Einstein's Relativity

N. David Mermin
Pages: 208
https://www.jstor.org/stable/j.ctt7t136

Export Selected Citations Export to NoodleTools Export to RefWorks Export to EasyBib Export a RIS file (For EndNote, ProCite, Reference Manager, Zotero, Mendeley...) Export a Text file (For BibTex)
1. Front Matter
(pp. i-vi)
(pp. vii-viii)
3. Preface: Why Another Relativity Book
(pp. ix-xiii)
(pp. xiv-xvi)
5. One The Principle of Relativity
(pp. 1-13)

The special theory of relativity was set forth by Einstein in his 1905 paper “On the Electrodynamics of Moving Bodies.”¹ The term “special relativity” is used to distinguish the theory from Einstein’s theory of gravity, known as general relativity, which he completed ten years later. Except for a glimpse into general relativity in chapter 12, we shall be concerned entirely with special relativity, so from now on I will drop the “special,” with the understanding that “relativity” always refers to special relativity.

Einstein based the theory of relativity on two postulates. The first is now known as the principle of...

6. TWO Combining (Small) Velocities
(pp. 14-18)

In chapter 1 we examined the power of the principle of relativity, deducing the not entirely obvious outcomes of certain collisions by considering other collisions whose outcomes were self evident. But I must now emphasize that besides using the principle of relativity, we repeatedly made implicit use of another rule that enabled us to relate the velocity of a ball in the train frame to its velocity in the station frame. This short chapter gives an explicit statement of this rule.

If, as I hope is the case, the rule strikes you as obvious and therefore uninteresting, please bear with...

7. Three The Speed of Light
(pp. 19-27)

When you turn on a light, how long does it take the light to get from the bulb to the things it illuminates? Galileo apparently tried to answer this by stationing two people with lanterns on top of two mountains, a large distanceDapart. Alice opens her lantern, Bob opens his the instant he sees Alice’s, and Alice notes the timeTthat passes between the moment she opens hers and the moment she sees the light returning to her from Bob’s. To get the speedcwith which the light moves from her mountaintop to Bob’s and back...

8. Four Combining (Any) Velocities
(pp. 28-44)

In chapter 2 we argued that if Alice, a passenger on a train moving atvfeet per second, can throw a ball atufeet per second, then if she throws the ball toward the front of the train, its speedwwith respect to the tracks will be

w=u+v(4.1)

in the same direction as the train.

This is known as the nonrelativistic velocity addition law. It is called “nonrelativistic” because it is only accurate when the speedsuandvare small compared to the speed of light. Evidently it fails to work whenu = c(i.e. if...

9. Five Simultaneous Events; Synchronized Clocks
(pp. 45-57)

The puzzlement we feel at the fact that a given pulse of light has the same speed in both the track frame and the train frame can be traced to a deeply ingrained misconception about the fundamental nature of time. Until we learn otherwise—and prior to Einstein in 1905, nobody had learned otherwise—we implicitly believe that there is an absolute meaning to the simultaneity of two events that happen in different places, independent of the frame of reference in which the events are described. This assumption is so pervasive in our view of the world that it is...

10. Six Moving Clocks Run Slowly; Moving Sticks Shrink
(pp. 58-72)

In chapter 5 we concluded that if two clocks are synchronized and separated by a distanceDin a frame in which they are both at rest, then in a frame in which they move with speedvalong the line joining them, they are not synchronized: the reading of the clock in front lags behind the reading of the clock in the rear by an amountTgiven by

T=Dv/c². (6.1)

We deduced this rule by considering what Alice, who uses the train frame, has to say about the simultaneous reading of two clocks used by Bob, in the...

11. Seven Looking At a Moving Clock
(pp. 73-78)

We have established that in any inertial frame of reference a clock that moves with speedvruns slowly compared with stationary clocks. The slowing-down factor is given by

$s\; = \;\sqrt {1\; - {v^2}/{c^2}}$. (7.1)

One may have the feeling that this is just some kind of trick—a conclusion based on playing intellectual games with the concept of simultaneity. If youactu allylookedat a moving clock would you actuallyseeit running slowly?

The answer is that what yousee depends on whether the clock is moving toward you or away from you. If it moves away from you, you do indeed see...

12. Eight The Interval between Events
(pp. 79-88)

We have identified a variety of things that people using different inertial frames of reference disagree about: the rate of a clock, the length of a stick, whether two events are simultaneous, whether two clocks are synchronized. There are also some things on which people using different frames of reference do agree: people in all frames of reference agree about space-time coincidences—whether two events occur at both the same timeandthe same place. And people in all frames of reference agree, of course, about whether something moves at the speed of lightc.

There are other things that...

13. Nine Trains of Rockets
(pp. 89-101)

In this chapter we shall examine an easy way to explore how a disagreement about whose clocks are synchronized leads to all the relativistic effects we have found: the slowing down of moving clocks, the shrinking of moving sticks, the relativistic velocity addition law, the existence of an invariant velocity, and the invariance of the interval.

We shall do this by examining two frames of reference from the point of view of a third frame in which the first two move with the same speed, but in opposite directions. We take the third frame to be the proper frame of...

14. Ten Space-Time Geometry
(pp. 102-143)

In various figures throughout the book, we have examined different events—things happening at a definite place at a definite time—that occur along a straight railroad track or along a straight line of rockets. Examples of such an event are two rockets and their attached clocks being directly opposite one another, or a signal arriving at the end of a train and triggering the making of a mark on the tracks. In the figures, these events are represented by regions that are small on the scale of the entire figure. In most of the figures, we have taken a...

15. Eleven E=Mc²
(pp. 144-170)

One cannot write a book on relativity without including a chapter onE=Mc², the second most famous equation of all time. I would put ahead of it only the discovery of Pythagoras, which we have also had occasion to use, that the area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the other two side:C²=A²+B². To understand Einstein’s celebrated relation between energy (E) and mass (M), we shall have to examine a third quantity, momentum (P). (Why momentum is always denoted byPorp...

16. Twelve A Bit about General Relativity
(pp. 171-178)

As noted in chapter 2, Einstein was led to his extraordinary insights into the nature of time by his conviction that the laws of electromagnetism ought to be consistent with the principle of relativity, just as the laws of mechanics are. Electric and magnetic forces were not, however, the only forces of fundamental interest in 1905. There was also the force of gravity. Einstein spent another 10 years trying to extend relativity to gravitational phenomena. He succeeded in 1915 with his generaltheory of relativity, which has become of fundamental importance in cosmology, in astrophysics, and even—remarkably for a...

17. Thirteen What Makes It Happen?
(pp. 179-186)

In the end, you may be tempted to regard some of this as intellectual sleight of hand. At the solid, unshakable core of the subject is Einstein’s great 1905 discovery that the simultaneity of two events that happen in different places is not an absolute unconditional relation between those events, but a way of talking about them, appropriate to a particular frame of reference, and inappropriate to frames of reference moving with respect to that particular frame along the line joining the events.

This was known long before 1905 for the spatial relation between two events that happen at different...

18. Index
(pp. 187-192)