The SPecial Theory of Relativity
Background
James Clerk Maxwell
Between 1866 and 1870 James Clerk Maxwell developed a theory of electromagnetic disturbances and determined that they travel at a speed very near that of light. Although the speed of light had been experimentally determined prior to Maxwell's work by several scientists, it was in the publication of his book Electricity and Magnetism in 1873 that the four differential equations now known simply as Maxwell's equations first appeared together and presented a unified view of both electric and magnetic fields in space as well as a theoretical value of the speed of light. According to the groundbreaking work of Maxwell, light is nothing more than a particular type of electromagnetic radiation! What his calculations also told him, though, was that electromagnetic waves—visible light included—can never stop or slow down. Light in a vacuum always travels at the speed of light.
...and there was light.
Maxwell, however, lived in a time that saw the beginning of the industrial revolution and his view of a mechanical world in which all motion was determined by prior causes and played out upon an absolute frame of reference was true to his time. He could not understand the propagation of light without a medium to carry the electromagnetic wave nor could he understand how light could always maintain the same speed regardless of an observer's motion relative to the light beam. Additionally, light traveling through a vacuum was as inconceivable as the wake of a boat propagating without water! Hence, the lumeniferous ether was postulated as the medium needed to transport electromagnetic radiation. It was believed to be invisible and massless and pervaded all of space. Its sole function was to carry electromagnetic waves and it very nicely fit with the mechanistic Newtonian view of an absolute coordinate system from which all motion through space could, in theory, be measured.
This Newtonian view of motion had been extremely successful at describing a large number of physical phenomena and could be traced all the way back to Galileo's investigations of inertia. This concept of inertia—incorporated by Newton into his first law of motion—states that every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it. According to this world view, time and space are absolute and there exists some frame of reference (such as the coordinate system needed to identify the position of a desk in a multistory building) that is also absolute. Furthermore, experiments performed are meaningful only to the extent they can be related to the same experiment performed in that absolute coordinate system. According the experiments performed by Galileo, if an observation is made in an inertial reference frame—a reference frame that is stationary or moving at a constant velocity—that observation can be described in another inertial frame of reference by simply adding velocities. A procedure knows as a Galilean transformation.
In an attempt to determine the motion of Earth through the ether, and thus determine its position relative to the absolute reference frame of space and time, the American physicists Albert Michelson and E. W. Morley conducted a series of interferometry experiments beginning in 1887 (see below.)
The experiments were based on the simple concept that light should be affected by Earth's motion through the ether. To understand this, consider what happens to a swimmer who wants to cross a stream that has a swiftly-moving current. As the swimmer starts across the stream, the current will push against her and cause her path to veer downstream instead of straight across the river. This will cause the swimmer to swim more slowly as she battles against the current and swim faster as she swims with the current. Using this reasoning, Michelson and Morley believed that a light beam split by a mirror into perpendicular paths will travel at different speeds since one beam will be impeded by the "current" produced by Earth's drift through the ether. When the two light beams recombined, they hypothesized, the beams would be out of phase due (see figure on right below) to the effect of Earth's motion relative to the ether and an interference pattern would be observed. Even using their very elaborate interferometer, however, the two scientists were unable to detect any movement of the earth through the ether and gradually the scientific community was forced to accept the notion that space and time were not absolutes in any conventional sense and that there is no external standard of rest from which all motion through space can be measured absolutely.
In order to explain the "null" result of the Michelson-Morley experiment, young Irish physicist George FitzGerald hypothesized that the physical dimension of an object is deformed in the direction of motion. Thus, the distance between the mirrors of the experimental apparatus is contracted in the direction of motion by exactly the amount needed to account for the lack of interference of the light beams. The world-renowned physicist Hendrick Lorentz reached the same conclusion, and in an act of almost unheard of generosity, shared credit with the less-well known FitzGerald.
By the end of the nineteenth century, physics was faced with a crisis of immense proportions. Maxwell's equations, which so beautifully combined the equations describing electric fields with those of magnetic fields while theoretically providing a value for the speed of light, produced contradictory results depending on one's frame of reference. If we consider the case of electromagnetic induction—which causes an electric field in a wire loop when a magnet passes through the loop, the accepted view of Maxwell's equations result in a paradox. A moving magnet passing through a stationary wire loop yields a different result than that of a moving wire loop passing over a stationary magnet. The young patent clerk Albert Einstein believed that a single phenomenon—wire loop and magnet approach each other—demanded a single explanation. As far as he was concerned, the vast body of work that was being created on the subject (and was also leading some of the greatest scientific minds down dead-end paths) was simply a misinterpretation of Maxwell's equations based on an erroneous belief in the reality of the luminiferous ether. The solution, according to Einstein, was to give up the concept of the ether and accept the speed of light is constant for all observers.
According to Galileo and Newton, if you speed up, an object's speed relative to you decreases and eventually appears to stand still once you reach the same speed as the object. But, according to Maxwell and countless experiments, light can never stand still.
Einstein realized there was a conflict between the type of relative motion between two inertial frames of reference—called a Galilean transform—and the relative motion between an observer and a beam of light that could only be resolved with a reinterpretation of the type of transform suggested by Lorentz-FitzGerald contraction. In his 1905 paper On The Electrodynamics of Moving Bodies, Einstein resolved the conflict between intuition (based on measurements made in our slow-moving, everyday world) and the measurable properties of light, but the resolution came at a price: Individuals who are moving with respect to each other will not agree on their observations of space and time!
Let's Call The Whole Thing Off...
To understand the implications more fully, consider the following thought experiment courtesy of Brian Greene's book The Elegant Universe.
Imagine two countries that have been at war are sitting down to sign a treaty ending hostilities while traveling aboard a train that is moving at a constant velocity. The catch is that neither country's delegate wants to sign the treaty before the other delegate and thus, a simple system is devised to ensure that both delegates sign the peace treaty simultaneously. The solution involves setting a light bulb at the center of a table in such a way that the light bulb is exactly between the delegate from Forwardland (who is facing the direction the train is traveling) and the delegate from Backwardland (who has her back to the direction the train is traveling). When the light bulbs lights up, that is the signal for both delegates to sign the treaty.
This setup is agreeable to all parties on the train and to both security councils in the countries' respective capitals. Once the bulb lights up and the delegates have simultaneously signed the peace treaty, everyone on the train celebrates the cessation of hostilities, but they are perplexed to discover that fighting has broken out anew between the two countries. The reason given is that the delegate from Forwardland was tricked into signing the treaty before the delegate from Backwardland! How can this be?
The solution lies in the fact that the speed of light is constant for all observers in inertial frames of reference. In this case, one reference frame is the train moving at a constant velocity and the other reference frames are the security councils sitting at their tables in the two capital cities. On board the train, the distance from the light bulb to each delegate is fixed and the light reaches each delegate at the same time. But from the point of view of the two security councils, once the light leaves the bulb, the delegate from Forwardland is moving towards the approaching light at the velocity of the train and it reaches him earlier than the light traveling toward the delegate from Backwardland. This is because the delegate from Backwardland is moving away from the approaching light at the velocity of the train. Because the speed of light is constant, it reaches the delegate from Forwardland first according to the observers on the two security councils! Events that are simultaneous in one inertial frame of reference are not simultaneous in other inertial reference frames!
Page 2 | Page 3 | Page 4 | Page 5 | General Relativity