It is an extremely well-established experimental fact that the speed of light is the same for all “inertial observers” (those who do not undergo accelerations). The analysis of the consequences of this remarkable fact has forced a complete revision of Newton’s ideas: Space and time are not different entities but are different aspects of one single entity, space-time. Different inertial observers may use different coordinates to describe the points of space-time, but these coordinates must be related in a way that preserves the speed of light. The changes of coordinates between observers form a group, the Lorentz group. To a large extent the mathematics of Special Relativity reduce to the study of this group. Physics appears to respect causality, a strong constraint in the presence of a finite speed of light. We introduce the Poincaré group, related to the Lorentz group. We develop Wigner’s idea that to each elementary particle is associated an irreducible unitary representation of the Poincaré group and we describe the representation corresponding to a spinless massive particle, explaining also how the physicists view these matters.

We introduce the two axioms on which SR is based, namely the Principle of Relativity and the constancy of the speed of light.

This appendix situates quantum technologies as a product of the merger of quantum mechanics, the theory of the very small; and information theory, the theory of how information is communicated and quantified. These intersections of these fields create quantum information science (QIS), provide a basis for understanding quantum sensing, computing, and communication. This appendix explains quantum scale and starts an exploration as to why effects at the quantum scale are so radically different from humans' day-to-day experience.

Einstein’s 1905 special theory of relativity requires a profound revision of the Newtonian ideas of space and time that were reviewed in the previous chapter. In special relativity, the Newtonian ideas of Euclidean space and a separate absolute time are subsumed into a single four-dimensional union of space and time, called spacetime. This chapter reviews the basic principles of special relativity, starting from the non-Euclidean geometry of its spacetime. Einstein’s 1905 successful modification of Newtonian mechanics, which we call special relativity, assumed that the velocity of light had the same value, c, in all inertial frames, which requires a reexamination, and ultimately the abandonment, of the Newtonian idea of absolute time. Instead, he found a new connection between inertial frames that is consistent with the same value of the velocity of light in all of them. The defining assumption of special relativity is a geometry for four-dimensional spacetime.

This chapter covers the Special Theory of Relativity, introduced by Einstein in a pair of papers in 1905, the same year in which he postulated the quantization of radiation energy and showed how to use observations of diffusion to measure constants of microscopic physics. Special relativity revolutionized our ideas of space, time, and mass, and it gave the physicists of the twentieth century a paradigm for the incorporation of conditions of invariance into the fundamental principles of physics.

James Clerk Maxwell’s field theory of electromagnetism had important and previously unrecognized roots in the cable industry of the mid-nineteenth century. When he took up electrical physics in 1854, the subject was permeated by a concern with cable problems. Guided by William Thomson, Maxwell soon adopted Faraday’s field approach, which in 1861 he sought to embody in a mechanical model of the electromagnetic ether. Seeking evidence to bolster the electromagnetic theory of light to which this model had led him, Maxwell joined the British Association Committee on Electrical Standards, which had been formed in 1861 largely to meet the needs of the submarine telegraph industry. Maxwell’s work on the committee between 1862 and 1864 brought home to him the value of framing his theory in terms of quantities he could measure in the laboratory—particularly the “ratio of units”—rather than relying on a hypothetical mechanism. Maxwell’s shift from his mechanical ether model of 1861 to his seemingly abstract “Dynamical Theory of the Electromagnetic Field” of 1864 thus reflected the often overlooked role concerns rooted in cable telegraphy played in the evolution of his thinking.