Albert Einstein Study Guide: Special Relativity

Einstein's third 1905 paper was entitled "On the Electrodynamics of Moving Bodies." Although this paper challenged foundational notions about space and time, each of its parts was simply a response to an important problem facing the physics community of Einstein's time.

One of these three challenges Einstein addresses is the relationship between Maxwell's electromagnetic equations and the mechanical worldview. Scientists in Einstein's day searched for a unifying theory that would explain both electromagnetism and mechanics. Einstein was attracted to this problem because he was troubled by an electromagnetic principle that did not make sense according to the mechanical world view: Faraday's 1831 magnet-coil experiment. In this experiment, a magnet is moved near an electric circuit, and then the circuit is moved near the magnet. According to Faraday, an electric current should be formed whenever there is relative movement, regardless of whether the magnet or the circuit is moving. However, according to Maxwell's equations, an electric current is only induced when the circuit is at rest and the magnet moving. This asymmetrical explanation disturbed Einstein, who was committed to aesthetic principles in his science. In order to resolve this asymmetry, Einstein analyzed the arrangement of magnet and current in terms of relative movement. He proposed that the existence of an electric current depends on the relative velocity of the magnet and circuit with respect to one another. His relativity theory wa s thus the product of his aesthetic discomfort with an asymmetrical explanation.

Einstein was not the first to formulate a relativity theory, however: Galileo had considered the concept in the early seventeenth century. According to Galilean relativity, the laws of mechanics are useless to an observer in a non-accelerating reference frame trying to determine whether he or she is moving with respect to another reference frame. When Newton revisited this problem fifty years later, he attempted to solve it by postulating an "absolute space" eternally at rest, relative to which any reference frame was either at rest or in motion. However, the fundamental pri nciple of relativity remained the same: the laws of mechanics are the same in all inertial (non-accelerating) reference frames, so it is impossible to determine whether an observer in one frame is moving or stationary with respect to another frame of refe rence.

In Einstein's day, physicists questioned whether the relativity principle could be applied to electrodynamic theory as well. Was it also true that the laws of electrodynamics were the same in all reference frames? Physicists were particularly interested in whether the earth's velocity could be detected with respect to the ether, a substance postulated by scientists as a medium through which light waves travel. In the 1880s, the American physicists Albert Michelson and Edward Morley constructed a dev ice called an interferometer to measure the earth's velocity with respect to the ether, but were unable to detect any movement. However, there is no evidence that Einstein was familiar with these results when he dismissed altogether the concept of the et her in his relativity paper. Einstein claimed that it is impossible to detect whether or not one is moving with respect to the ether, rendering meaningless the whole notion of an ether. His dismissal of the ether also meant that every concept involving space and time had to be considered in relative terms, a fundamental challenge to all of nineteenth-century science.

Einstein's relativity theory was presented as a principled, rather than a constructive, theory. A principled theory is one that begins with principles and then uses these principles to explain the phenomena; a constructive theory starts with the observat ions and culminates in theories that explain and reconcile those observations. Einstein's principled account began with the postulate that the laws of science should appear the same to all freely moving observers. In particular, all observers should mea sure the speed of light as the same regardless of how fast they are moving. Thus, there is no "universal time" that all clocks measure; rather, everyone has his or her own personal time. If one person is moving with respect to another, their clocks will not agree. To an observer moving in one frame of reference with uniform velocity relative to a second frame of reference, the clock in the second frame will appear to move more slowly than his own clock. Moreover, since velocity is the measurement of d istance per unit of time, a measuring-stick in the second time frame would appear contracted to the observer in the reference frame. Of course, we do not observe these effects in everyday situations of movement; we do not see a ruler as contracted if we are moving by on a bus. Rather, these phenomena are noticeable only at speeds near the speed of light. Nonetheless, Einstein's relativity paper showed that time and space are not a priori categories of human understanding; rather, they are relative quan tities that are defined operationally.

One implication of relativity is the famous "twin paradox," a hypothetical situation in which one twin embarks on a journey through space while the other twin stays on earth. When the first twin returns home after traveling at a velocity close to the spe ed of light, he finds that he has aged by merely a couple of years, while his brother on earth has been long since dead. This is because the twin on earth has been traveling through space at a constant time (as the earth orbits the sun), whereas the twin in the spaceship has had to decelerate and then accelerate in order to turn back home, so she has not remained in an inertial (non-accelerating) reference frame. This paradox runs counter to our commonsense view of time, but it is a natural consequence of relativity theory.

Einstein's relativity theory also implied the equivalence of mass and energy, as expressed by the famous equation E = mc2. Einstein discovered that electromagnetic radiation, like matter, can carry inertia. A given amount of electromagnetic energy is e quivalent to a certain amount of inertial mass: a little mass is equivalent to enormous amounts of energy. With this equation, Einstein provided a solution to the relationship between the mechanical and electromagnetic world views. He had previously supported the mechanical view alone, but in this paper he showed how mechanical and electromagnetic worldviews could now exist on a n equal footing and inform one another. Thus, yet another central question facing physicists throughout the late nineteenth century was resolved in a single sweep by the young patent officer in Bern.