Chapter I Special relativity a and spacetime Introduction In two seminal papers in 1861 and 1864,and in his treatise of 1873,James Clerk Maxwell(Figure 1.1),Scottish physicist and genius,wrote down his revolutionary unified theory of electricity and magnetism,a theory that is now summarized in the equations that bear his name.One of the deep results of the theory introduced by Maxwell was the prediction that wave-like excitations of combined electric and magnetic fields would travel through a vacuum with the same speed as light. It was soon widely accepted that light itself was an electromagnetic disturbance propagating through space,thus unifying electricity and magnetism with optics. The fundamental work of Maxwell opened the way for an understanding of the universe at a much deeper level.Maxwell himself,in common with many scientists of the nineteenth century,believed in an all-pervading medium called the ether,through which electromagnetic disturbances travelled,just as ocean waves travelled through water.Maxwell's theory predicted that light travels with the same speed in all directions,so it was generally assumed that the theory predicted the results of measurements made using equipment that was at rest with Figure 1.I James Clerk Maxwell(1831-1879) respect to the ether.Since the Earth was expected to move through the ether as it orbited the Sun,measurements made in terrestrial laboratories were expected to developed a theory of show that light actually travelled with different speeds in different directions, electromagnetism that was allowing the speed of the Earth's movement through the ether to be determined. already compatible with special However,experiments,most notably by A.A.Michelson and E.W.Morley in relativity theory several decades 1887,failed to detect any variations in the measured speed of light.This led some before Einstein and others to suspect that measurements of the speed of light in a vacuum would always developed the theory.He is also yield the same result irrespective of the motion of the measuring equipment. famous for major contributions Explaining how this could be the case was a major challenge that prompted to statistical physics and the ingenious proposals from mathematicians and physicists such as Henri Poincare, invention of colour photography. George Fitzgerald and Hendrik Lorentz.However,it was the young Albert Einstein who first put forward a coherent and comprehensive solution in his 1905 paper 'On the electrodynamics of moving bodies',which introduced the special theory of relativity.With the benefit of hindsight,we now realize that Maxwell had unintentionally formulated the first major theory that was consistent with special relativity,a revolutionary new way of thinking about space and time. This chapter reviews the implications of special relativity theory for the understanding of space and time.The narrative covers the fundamentals of the theory,concentrating on some of the major differences between our intuition about space and time and the predictions of special relativity.By the end of this chapter,you should have a broad conceptual understanding of special relativity, and be able to derive its basic equations,the Lorentz transformations,from the postulates of special relativity.You will understand how to use events and intervals to describe properties of space and time far from gravitating bodies.You will also have been introduced to Minkowski spacetime,a four-dimensional fusion of space and time that provides the natural setting for discussions of special relativity. 11Chapter 1 Special relativity and spacetime Introduction In two seminal papers in 1861 and 1864, and in his treatise of 1873, James Clerk Maxwell (Figure 1.1), Scottish physicist and genius, wrote down his revolutionary unified theory of electricity and magnetism, a theory that is now summarized in the equations that bear his name. One of the deep results of the theory introduced by Maxwell was the prediction that wave-like excitations of combined electric and magnetic fields would travel through a vacuum with the same speed as light. It was soon widely accepted that light itself was an electromagnetic disturbance propagating through space, thus unifying electricity and magnetism with optics. Figure 1.1 James Clerk Maxwell (1831–1879) developed a theory of electromagnetism that was already compatible with special relativity theory several decades before Einstein and others developed the theory. He is also famous for major contributions to statistical physics and the invention of colour photography. The fundamental work of Maxwell opened the way for an understanding of the universe at a much deeper level. Maxwell himself, in common with many scientists of the nineteenth century, believed in an all-pervading medium called the ether, through which electromagnetic disturbances travelled, just as ocean waves travelled through water. Maxwell’s theory predicted that light travels with the same speed in all directions, so it was generally assumed that the theory predicted the results of measurements made using equipment that was at rest with respect to the ether. Since the Earth was expected to move through the ether as it orbited the Sun, measurements made in terrestrial laboratories were expected to show that light actually travelled with different speeds in different directions, allowing the speed of the Earth’s movement through the ether to be determined. However, experiments, most notably by A. A. Michelson and E. W. Morley in 1887, failed to detect any variations in the measured speed of light. This led some to suspect that measurements of the speed of light in a vacuum would always yield the same result irrespective of the motion of the measuring equipment. Explaining how this could be the case was a major challenge that prompted ingenious proposals from mathematicians and physicists such as Henri Poincare,´ George Fitzgerald and Hendrik Lorentz. However, it was the young Albert Einstein who first put forward a coherent and comprehensive solution in his 1905 paper ‘On the electrodynamics of moving bodies’, which introduced the special theory of relativity. With the benefit of hindsight, we now realize that Maxwell had unintentionally formulated the first major theory that was consistent with special relativity, a revolutionary new way of thinking about space and time. This chapter reviews the implications of special relativity theory for the understanding of space and time. The narrative covers the fundamentals of the theory, concentrating on some of the major differences between our intuition about space and time and the predictions of special relativity. By the end of this chapter, you should have a broad conceptual understanding of special relativity, and be able to derive its basic equations, the Lorentz transformations, from the postulates of special relativity. You will understand how to use events and intervals to describe properties of space and time far from gravitating bodies. You will also have been introduced to Minkowski spacetime, a four-dimensional fusion of space and time that provides the natural setting for discussions of special relativity. 11