Chapter 1
A Brief Stroll in Special Relativity
Abstract This chapter is a short review of what students generally encounter in a
modern physics course: a discussion of time in a universe with a constant velocity
of light, and the important consequences of the relativity of time such as length
contraction and time dilation.
1.1 The Trouble with Absolute Time
The story of the discovery of special relativity is one of the most interesting in physics,
and is covered in many books, including several by Einstein (Einstein 1923, 1934;
Bergmann 1942; Rindler 1969; Weaver 1987). Accordingly we will here discuss only
very briefly the ideas which led Einstein to special relativity.
In the late nineteenth century the two great theories of physics were Newton’s
mechanics and gravitational theory, and Maxwell’s electromagnetism. It was widely
believed that there might be no more basic physical theories to be discovered:
quantum mechanics was of course decades in the future. However there was a flaw
in the combination of these two theories, inherent in the classical concept of time.
Mechanics was based on absolute time; as Newton phrased it in the Principia, “Absolute, true, and mathematical time, of itself, and from its own nature, flows equably
without reference to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or
unequable) measure of duration by the means of motion, which is commonly used
instead of true time; such as an hour, a day, a month, a year.”
The transformation between Cartesian reference frames in uniform motion, called
the Galilean transformation, is based on the notion of absolute time, and was universally accepted in the nineteenth century. For motion along the x direction the situation
is shown in Fig. 1.1; the primed system moves past the unprimed system at velocity
v, with the origins coinciding at time zero.
The Galilean transformation between the two systems is
x
= x − vt, y
= y, z
= z, t
= t = absolute time.
(1.1)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. J. Adler, General Relativity and Cosmology, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-61574-1_1
3
A Brief Stroll in Special Relativity
Abstract This chapter is a short review of what students generally encounter in a
modern physics course: a discussion of time in a universe with a constant velocity
of light, and the important consequences of the relativity of time such as length
contraction and time dilation.
1.1 The Trouble with Absolute Time
The story of the discovery of special relativity is one of the most interesting in physics,
and is covered in many books, including several by Einstein (Einstein 1923, 1934;
Bergmann 1942; Rindler 1969; Weaver 1987). Accordingly we will here discuss only
very briefly the ideas which led Einstein to special relativity.
In the late nineteenth century the two great theories of physics were Newton’s
mechanics and gravitational theory, and Maxwell’s electromagnetism. It was widely
believed that there might be no more basic physical theories to be discovered:
quantum mechanics was of course decades in the future. However there was a flaw
in the combination of these two theories, inherent in the classical concept of time.
Mechanics was based on absolute time; as Newton phrased it in the Principia, “Absolute, true, and mathematical time, of itself, and from its own nature, flows equably
without reference to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or
unequable) measure of duration by the means of motion, which is commonly used
instead of true time; such as an hour, a day, a month, a year.”
The transformation between Cartesian reference frames in uniform motion, called
the Galilean transformation, is based on the notion of absolute time, and was universally accepted in the nineteenth century. For motion along the x direction the situation
is shown in Fig. 1.1; the primed system moves past the unprimed system at velocity
v, with the origins coinciding at time zero.
The Galilean transformation between the two systems is
x
= x − vt, y
= y, z
= z, t
= t = absolute time.
(1.1)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. J. Adler, General Relativity and Cosmology, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-61574-1_1
3