The topics of the remaining chapters deal with modern physics, the term used to describe developments that have occured since about 1896, when Roentgen discovered x-rays. The developments of modern physics include, special and general relativity, an understanding of the structure of the atom, quantum mechanics, nuclear physics, particle physics, astrophysics, transistors, and lasers.
Many popular books exist on these topics. Some recent ones accessible to the interested student are:
Albert Einstein is irrevocably linked with relativity. In 1906 he published papers on the special theory of relativity, the focus of most of this chapter, and ten years later on the general theory of relativity, which we will discuss briefly at the end of this chapter. The special theory of relativity, or just relativity for short, knits space and time together into the fabric of our existence. Basic beliefs about time and space must be reexamined in the context of relativity, as well as our concepts of past and future. The general theory builds on the special theory, adding gravity to the mix, resulting in a description of our world where gravity is just a manifestation of the geometry of space. Mass produces a curvature of space, like the way a bowling ball will deform and curve a taught sheet.
Why does relativity force us to rethink our understanding of space and time, and does this mean that all the time spent learning Newton's laws and their consequences was wasted?
I'll answer the second question first. No.
Well maybe a little more explanation is required. The effects of relativity manifest themselves when things move at speeds near to the speed of light, 3×108m/s. Everyday objects on Earth move at speeds much less than the speed of light, so that the difference between the results determined including the effects of relativity and without differ by minuscule amounts. Said another way, the best way to solve problems of falling balls, masses on inclined planes, and pendulums is exactly the way you learned.
Now to answer the first question. Relativity is based on two postulates:
The second postulate is the new element. It's not too hard to see that if the speed of light is the same in all reference systems, then the elapse of time will not be the same. Though it doesn't seem connected, this postulate will eventually lead to that most famous of equations, E = mc².
In order to describe a physical event, it is necessary to choose a frame of reference. For example, for experiments performed on the surface of the Earth can use the local surface as the reference frame. Someone passing by in a fast moving vehicle might choose the vehicle as her reference frame. Would these two see a dramatic difference in an event? Although they may not agree precisely on what occurred, they would both agree that whatever happened followed Newton's laws.
To be more specific, consider a scenario with two observers, one on a fast moving jet aircraft, and the other on the ground. Th observer on the airplane tosses a ball straight upward, and catches it when it falls back down. According to him, the ball moves according to Newton's laws, rising and falling in gravity.
The observer on the ground sees the ball go up and down as well, but according to him, the ball is also moving forward at the same speed as the aircraft, so it follows a parabolic path. Although the path reported is different, both observers agree that the ball moves according to Newton's laws. This is the first postulate of relativity.
What two speed measurements will two observers in relative motion always agree on?
Both will always agree on the speed of light (in vacuum). It is always measured to be c. The second is their relative speed. They must agree on their relative speed, otherwise their would be a difference between their inertial frames.