Summary - Relativity

Based only on this principle of relativity, Einstein showed that time and space as seen by one observer would be distorted compared to another observer's perceptions if they were moving relative to each other. This distortion is quantified by the factor

where v is the relative velocity of the two observers. A clock appears to run fastest to an observer who is not in motion relative to it, and appears to run too slowly by a factor of γ to an observer who has a velocity v relative to the clock. Similarly, a meter-stick appears longest to an observer who sees it at rest, and appears shorter to other observers. Time and space are relative, not absolute. In particular, there is no well-defined concept of simultaneity.

All of these strange effects, however, are very small when the relative velocities are small relative to the speed of light. This makes sense, because Newton's laws have already been thoroughly tested by experiments at such speeds, so a new theory like relativity must agree with the old one in their realm of common applicability. This requirement of backwards-compatibility is known as the correspondence principle.

Relativity has implications not just for time and space but also for the objects that inhabit time and space. The correct relativistic equation for momentum is

p = mγv ,

which is similar to the classical p = mv at low velocities, where γ ≈ 1, but diverges from it more and more at velocities that approach the speed of light. Since γ becomes infinite at v = c, an infinite force would be required in order to give a material object enough momentum to move at the speed of light. In other words, material objects can only move at speeds lower than the speed of light. Relativistically, mass and energy are not separately conserved. Mass and energy are two aspects of the same phenomenon, known as mass-energy, and they can be converted to one another according to the equation

E = mc² .

The mass-energy of a moving object is E = mγc². When an object is at rest, γ= 1, and the mass-energy is simply the energy-equivalent of its mass, mc². When an object is in motion, the excess massenergy, in addition to the mc², can be interpreted as its kinetic energy.

Exploring Further

Relativity Simply Explained, Martin Gardner. A beatifully clear, nonmathematical introduction to the subject, with entertaining illustrations. A postscript, written in 1996, follows up on recent developments in some of the more speculative ideas from the 1967 edition.

Was Einstein Right? - Putting General Relativity to the Test, Clifford M. Will. This book makes it clear that general relativity is neither a fantasy nor holy scripture, but a scientific theory like any other.