Thomas D. Le



Einstein's Special and General Theory of Relativity


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Preface

It is called annus mirabilis, the year 1905. An unknown clerk in the Bern Patent Office in Switzerland published a succession of four papers in the prestigious German journal Annalen der Physik, and the world of physics was changed forever.

During this miraculous year, Albert Einstein revolutionized the field of physics with his special theory of relativity, which along with the work of other scientists in the emerging field of quantum mechanics, such as Niels Bohr, Werner Heisenberg, Wolfgang Pauli, and Erwin SchrŲdinger, laid the foundation for modern physics. The emergence of this paradigm shift not only brought about new concepts of the universe but also a counterintuitive view of space and time. Now common sense in scientific investigation was blatantly violated, as scientists grappled with new questions about reality.

Accustomed to Newtonian deterministic laws, physicists were now faced with an array of observations at the microscopic level where only probabilities of behavior made sense. Strange things happened with which Newtonian (classical) physics was no longer equipped to deal, shattering the illusion that after electromagnetism, optics, and mechanics were understood at the end of the nineteenth century, there was not much else left for physicists to do but refine their theories and tie up the loose ends. The dual wave-particle nature of matter, the impossibility of defining both momentum and position of a particle simultaneously, the superposition of quantum states, and other quantum phenomena soon exposed the inadequacy of classical physics and called for a radical view.

While quantum mechanics was raising tough questions, Einstein introduced a concept of space and time that deepened our understanding of the behavior of macrostructures such as the stars, the galaxies, and the universe. Of the four papers Einstein submitted, one described the ejection of electrons by photons, now called the photoelectric effect, which helped build the foundation for quantum theory, and which earned him the Nobel prize for physics in 1921. Another paper determined the sizes of molecules from a study of sugar molecules in a water solution, and the number of molecules in a given mass of a substance. The next paper showed how the irregular, zigzagging movements, called Brownian motions, of particles of smoke provide evidence of the existence of molecules and atoms. But the most important is his paper on special relativity. This seminal work from a patent clerk who had to hide his outside investigation in his office drawer whenever he heard footsteps is nothing short of miraculous. Now we know that neither time nor space is absolute, and that we can only speak of time and space in relation to some frame of reference, and that they differ depending on the frames of reference.

Special relativity, as its name implies, is only a special case of the general theory of relativity, and deals with phenomena that occur in inertial reference frames. The general theory investigates behavior in non-inertial frames. We will examine the theory of relativity in its totality.

The tripartite division of this monograph aims at treating the concept of relativity with the thoroughness that will satisfy the curious as well as the student of relativity.

To fix the theory firmly in the readerís mind, I have included copious examples and problems for practice. Some students of physics may find them useful.

As this year marks the one hundredth anniversary of the special theory of relativity, a review of the theory of relativity is a fitting tribute to the genius who dominated science and popular imagination for much of the twentieth century.

Thomas D. Le
31 December 2005

Contents

Preface

1  Classical Relativity

1.1  Frames of Reference
1.2  The Galilean-Newtonian Relativity Principle
1.2.1  Galilean Velocity Addition
1.2.2  The Galilean Transformation

2   Special Relativity

2.1  Einsteinís Postulates
2.1.1  Einsteinís Two Postulates of Special Relativity
2.1.2  The Lorentz Transformation
2.1.3  Relativistic Addition of Velocities
2.1.4  The Michelson-Morley Experiment
2.2  Simultaneity
2.3  Time Dilation
2.3.1  Time Dilation
2.3.2  The Twin Paradox
2.3.3  Decay of the Muon
2.4  Length Contraction
2.4.1  Length Contraction
2.5  Relativistic Momentum
2.6  Relativistic Mass
2.7  Relativistic Energy
2.8  Relativistic Doppler Effect

3.  General Relativity

3.1  Inertial Mass and Gravitational Mass
3.2  The Principles of Equivalence and Covariance
3.3  Tests of the General Theory of Relativity
3.4  Geometry of Spacetime
3.5  Einsteinís Curvature of Spacetime
3.6  Black Holes

4.  Problems

References

Internet Resources

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