Relativity: The Special and the General Theory

• 1. Introduction

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  Relativity: The Special and the General Theory began not as a grand treatise but as a short paper, and Einstein wanted the world to read it. He wrote it for people who, in his words, were interested in the theory "from a general scientific and philosophical point of view" but were not conversant with the mathematics of theoretical physics. Published first in German in 1916, it arrived in English translation in 1920, and it has not stopped circulating since.

  Einstein was blunt about what he was attempting. He quoted the physicist Ludwig Boltzmann on elegance, citing Boltzmann's view that matters of elegance ought to be left to the tailor and the cobbler. He made no pretence of having withheld difficulties inherent in the subject. And yet he chose to treat the empirical physical foundations in a, as he put it, step-motherly fashion, so that readers unfamiliar with physics would not feel like a wanderer who could not see the forest for the trees.

  The book is divided into three parts: the first on special relativity, the second on general relativity, and the third on cosmology. What unfolds across those parts is not a simplified digest of the science but a guided tour through the actual reasoning that reshaped our understanding of light, time, gravity, and the structure of the universe itself. The questions it raises are still alive: how can light always travel at the same speed for every observer? Why does a gravitational field behave identically to acceleration? And what does it mean to say the universe might be finite but unbounded?

• 2. The Speed of Light Problem

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  Einstein opens Part I with a principle so old it had become invisible: Galilean invariance, the idea that the laws of physics are the same in every frame of reference moving uniformly relative to another. He illustrates it with two coordinate systems, K and K-prime, moving uniformly to one another, and notes that the mechanical laws of Galileo and Newton hold equally in both.

  Then he introduces the complication. Light in a vacuum travels at 300,000 kilometres per second, and every measurement confirms it travels at that speed regardless of the colour of light. Einstein cites the Dutch astronomer De Sitter, who used observations of double stars to show that the velocity of light cannot depend on the velocity of the body emitting it. This is not a convenient feature of the universe. It appears to directly contradict Galilean invariance.

  To make the contradiction vivid, Einstein uses the image of a railway carriage. If a passenger on a moving train throws a ball forward, an observer on the embankment sees the ball moving faster than the passenger does. Common sense says the same rule should apply to light. But it does not. Both the passenger and the embankment observer must measure the speed of light as identical. Holding both facts together, the constant speed of light and the universality of physical law, forced Einstein to abandon something that had been taken for granted in physics since Newton: the idea that time passes the same way for all observers everywhere.

  H. A. Lorentz had already worked out the mathematical structure that captures this situation. His investigations into electromagnetic and optical phenomena in moving bodies led to what became known as the Lorentz transformation. Einstein presents it here, along with what he calls its nonintuitive consequences, including the slowing of time in a moving frame, a phenomenon known as time dilation.

• 3. Simultaneity and the Shape of Time

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  A lightning bolt strikes point A, and another strikes point B, at opposite ends of a stretch of train track. An observer standing at M, precisely midway between A and B on the embankment, sees both flashes arrive at the same moment and concludes the strikes were simultaneous. An observer at M-prime, sitting on a train moving from A toward B, sees the flash from B arrive before the flash from A and reaches the opposite conclusion.

  Neither observer is wrong. Einstein is explicit: events simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa. Every reference body has its own particular time. There is no meaning in stating the time of an event without also specifying the reference body to which that statement refers.

  Before relativity, physics had quietly assumed that time had an absolute significance, independent of the motion of the observer. Einstein shows this assumption is incompatible with the most natural definition of simultaneity. Once the assumption is discarded, the apparent conflict between the constancy of light's speed and Galilean invariance dissolves. He cites Hippolyte Fizeau's experiment as physical evidence that the speed of light is indeed constant, a demonstration that makes the argument concrete and testable rather than purely theoretical.

  Mass and energy, previously treated as two independent conservation laws, are united into one by the theory. The concept of spacetime, which weaves space and time into a single four-dimensional fabric, enters the discussion here. Einstein attributes this formulation to his teacher Hermann Minkowski, grounding one of the most consequential ideas in modern physics in a specific intellectual relationship.

• 4. Gravity as Geometry

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  Part II begins with a puzzle that Newton's theory of gravity left unanswered. Lead and wood, dropped together in a vacuum, hit the ground at the same time. Every object, regardless of its material or physical state, falls at the same rate in a given gravitational field. This had been known experimentally for centuries. Newton incorporated it into his equations but could not explain why it was true.

  Einstein's key insight is that gravitational mass and inertial mass are equal, and this equality is not a coincidence. To show why, he asks the reader to imagine a large chest floating in empty space, accelerating upward. A person inside, unable to see out, releases an object from their hand. The object drifts to the floor. From inside the chest, the experience is identical to standing in a gravitational field. Einstein asks directly whether we should smile at such a person for concluding they are in a gravitational field. His answer is no. That conclusion violates neither reason nor known mechanical laws.

  Gravity, in this framework, is not a force acting between masses across empty space. It is a consequence of the curvature of spacetime around massive bodies. To describe that curvature mathematically, Euclidean geometry is no longer sufficient. Einstein introduces the thought experiment of an observer on a rotating disk to make the case for non-Euclidean geometry in the description of gravity.

  Newton's theory had long failed to fully account for the precession of Mercury's orbital ellipse, meaning the way Mercury's closest approach to the Sun slowly rotates around the Sun over time. Urbain Le Verrier, who successfully predicted the existence of Neptune by analysing deviations in the orbit of Uranus, tried and failed to explain Mercury's precession using Newtonian mechanics. The observed value was 43 seconds of arc per century. General relativity predicts exactly 43 seconds of arc per century.

• 5. Confirmation and Cosmology

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  General relativity made predictions that went beyond fixing Mercury's numbers. Light, the theory said, should curve as it passes near a massive body. Arthur Eddington confirmed this in 1919, providing the observational evidence that turned the theory into a landmark. A further prediction held that light escaping the gravity of a massive star should lose energy and shift toward the red end of the spectrum. Walter Sydney Adams confirmed this in 1925.

  Part III carries the theory out to the largest possible scale: the structure of the universe. General relativity raises the possibility that the universe is finite but unbounded, a concept that challenges ordinary spatial intuition. In a later appendix, Einstein notes that in 1922 Alexander Friedmann showed the theory's field equations demand an expansion of space. Hubble's observations of extra-galactic nebulae, in which spectral lines showed a red shift increasing regularly with the distance of the nebulae, were interpreted through the Doppler principle as evidence of the expansive motion of stars at large. Einstein writes that Hubble's discovery can be considered to some extent a confirmation of Friedmann's result, and through it, of the field equations themselves.

  The appendices serve the scientifically curious reader who wants more than the main text provides. Appendix One gives a derivation of the Lorentz Transformation. Appendix Two details Minkowski's four-dimensional spacetime. Appendix Three gathers the experimental confirmations. Appendix Four addresses the structure of space. Appendix Five returns to the relationship between relativity and the fundamental concept of space, bringing the book full circle to the philosophical questions raised at the outset.

• 6. Reception and Legacy

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  Abraham Pais, writing about Einstein's publication history, suggests that Hendrik Lorentz may have influenced Einstein to write a popular account of the theory in the first place. Pais describes the original fifty-page account as completed in March 1916 and well-received, with the expanded book finished in December of that year under the German title Über die spezielle und die allgemeine Relativitätstheorie, gemeinverständlich. Demand rose sharply after the eclipse expedition results of 1919 caused what Pais calls a stir.

  A review in Nature framed the book as an answer to a question that thousands had been asking. The reviewer imagined the reader as the man in the street, asking what relativity was, what was wrong with Euclid and with Newton, and what message had come from the stars. Whether a prophet could make his message clear to the multitude, the reviewer wrote, only history could prove.

  The German industrialist and politician Walther Rathenau wrote directly to Einstein after reading the book. He said he had been immersed in Einstein's ideas for weeks, and that he would not have thought it possible to force such a radical rearrangement of ideas through, the way Einstein did, with such simple means and using classical architectonics. That letter is reprinted in the Princeton University Press edition, alongside a page of text in Einstein's own handwriting.

  Martin Rees, Astronomer Royal, has said the book is not only an important historical document but displays the style and clarity of Einstein's thought in a manner accessible to a wide readership. The book has been in print continuously since 1916, through many versions. Princeton University Press issued a 100th Anniversary Edition in 2015 and released it as an e-book in 2019, the centenary of Eddington's eclipse confirmation.