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Chapter 1
Relativity
A theory of space, time, and gravity
Relativity is a theory of space and time that provides the foundation for much of physics. It applies to any branch of physics that makes use of the four variables x, y, z, t, where x, y, z are independent spatial coordinates and t denotes time.1 While originating from a reasonable premise (see below), the theory of relativity2 implies conceptions of space, time, matter, and motion vastly different from what our everyday experience of the world leads us to formulate. To understand physics in full, as applied to phenomena beyond ordinary experience, one must study relativity (as well as quantum mechanics); our everyday experience is but a special case of all thatās possible in the universe. Weāll see that relativity consists of two theories: the special theory of relativity (SR) and the general theory of relativity (GR).
1.1The principle of relativity
to vanquish coordinates, transcend them
In broadest terms, relativity holds that the universe doesnāt care what systems of coordinates, or reference frames we use to describe physical phenomena.3 Such a statement hardly sounds revolutionary, yet its implications are far-reaching because in the theory of relativity time is taken as a coordinate in a four-dimensional geometry of space and time, rather than as a parameter in pre-relativistic physics.4 Coordinates are essential for making measurements and performing calculations, yet theyāre not fundamentalāthey donāt exist in natureātheyāre artifacts of our thinking, what we as humans impose on the world. Therein lies the rub. We need coordinates for practical purposes, yet the goal of physics is to formulate laws of nature as manifestations of an objective reality, that which occurs independently of human beings.5 The laws of physics should be expressed in a way thatās independent of coordinate system. Relativity is an outgrowth of a single idea, the principle of relativity, that physical laws be independent of the reference frame used to represent them. Relativity is therefore a law about laws.6 Albert Einstein said: āā¦ time and space are modes by which we think, and not conditions in which we live.ā[2, p81] The program of relativity is to express equations of physics in such a way that, if true in one system of space-time coordinates, are true in any coordinate system, and thereby transcend coordinates. We will travel far in the theory of relativity in pursuit of this goal, which, as weāll see, is achieved by expressing equations as relations between tensors,7 tensors defined on a four-dimensional geometry where time is a dimension.
1.2The Law of inertia: Foundation of special relativity
Motion is ubiquitous, yet learning to describe it correctly took a long time to achieve. Galileo taught, for the purposes of formulating laws of motion, that states of uniform motion are the same as rest,8 when observed from reference frames in which the law of inertia holds, inertial reference frames (IRFs)....
