Review of Einstein’s Special Theory of Relativity by Rick Dower QuarkNet Workshop August 2002 References A. Einstein, et al., The Principle of Relativity, Dover Pub., Inc. E. F. Taylor and J. A. Wheeler, Spacetime Physics, 2nd ed., W. H. Freeman and Co. A.P. French, Special Relativity, W. W. Norton & Co., Inc. M. Born, Einstein’s Theory of Relativity, Dover Publications, Inc. A. Pais, ‘Subtle is the Lord…’, Oxford Univ. Press

Fundamental Assumptions 1. Relativity: All physics laws remain the same in each inertial reference frame. An inertial reference frame is one in which Newton’s Law of Inertial holds, e.g. a reference frame at rest with respect to the cosmic microwave background. Any reference frame moving at constant velocity with respect to an inertial frame is also an inertial frame.

Fundamental Assumptions 2. Maxwell’s equations are more fundamental than Newton’s Laws. The speed of light in vacuum is a direct consequence of Maxwell’s equations. Thus, the speed of light in vacuum is the same constant value in all inertial reference frames. Since 1983 the speed of light in vacuum has been defined as c = 299,792,458 m/s, i. e. about 3 x 108 m/s.

Lorentz-Einstein Transformations for Space and Time Suppose a Rocket reference frame (R) with x’, y’, z’ axes parallel to Lab reference frame (L) axes x, y, z moves at velocity vr along the x-axis of a Lab reference frame. Also, suppose at time t = t’ = 0 the origins of the two frames coincide. Then the coordinate values of events in L and R are related by the following equations (units for which c = 1): The spacetime interval is invariant: y y’ L R vr x x’

Lorentz-Einstein Transformations for Momentum and Energy In special relativity Maxwell’s equations are invariant, but Newton’s Laws, including F = ma, are not. Expressions for momentum and energy are modified from their classical (Newtonian) expressions. For a particle of mass m moving with speed v in an inertial frame the relativistic expressions are p = gmv and E = gm . (Note: p = vE) The invariant mass (m) of a particle is given by m2 = E2 – p2 . The kinetic energy of a particle is K = E – m . In all these equations the units for mass, momentum, and energy are the same, i.e. E = m for a particle at rest.