Warped Passages - Lisa Randall [47]
Special relativity is important both because it was a dramatic deviation from classical physics and because it was essential to the development of general relativity and quantum field theory, both of which play a significant role in more recent developments. Because I won’t use specific special relativity predictions when I discuss particle physics and extra-dimensional models later on, I’ll resist the urge to go into all the fascinating consequences of special relativity, such as why simultaneity depends on whether an observer is moving and how the sizes of moving objects are different from when they are at rest. Instead, we’ll delve into another dramatic development, namely general relativity, which will be critical when we consider string theory and extra dimensions later on.
The Principle of Equivalence: General Relativity Begins
Einstein wrote down his theory of special relativity in 1905. In 1907, while working on a paper that summarized his recent work on the subject, he found himself already questioning whether the theory could apply to all situations. He noticed two major omissions. For one thing, physical laws looked the same only in certain special inertial reference frames—those that moved at fixed velocity with respect to each other.
In special relativity, these inertial reference frames occupied a privileged position. The theory left out any reference frame that was accelerating. If you pressed the accelerator while driving your car, you would no longer be in one of the special reference frames where the laws of special relativity apply. That’s what’s “special” in special relativity: the “special” inertial frames are only a small subset of all possible reference frames. For someone convinced that no one’s reference frame is special, it was a big problem that the theory singled out inertial reference frames.
Einstein’s second misgiving concerned gravity. Although he had figured out how objects respond to gravity in some situations, he still hadn’t come up with formulas for determining the gravitational field in the first place. The form of the gravitational force law was known in some simpler settings, but Einstein wasn’t yet able to deduce the field for every possible distribution of matter.
Between 1905 and 1915, in a sometimes grueling exploration, Einstein addressed these problems. The result was general relativity. He centered his new theory around the equivalence principle, which states that the effects of acceleration cannot be distinguished from those of gravity. All the laws of physics would look the same to an accelerating observer as they would to a stationary observer placed in a gravitational field that accelerates everything in the stationary frame with an acceleration of the same magnitude—but in the opposite direction—as the original observer’s acceleration. In other words, you wouldn’t have any way of distinguishing uniform acceleration from standing still in a gravitational field. According to the principle of equivalence, there is no measurement that would distinguish between these two situations. An observer could never know which situation he was in.
The equivalence principle follows from the equivalence of inertial and gravitational mass, two quantities that in principle could have been different from each other. Inertial mass determines how an object will respond to any force—how much the object would accelerate if you applied that force. The role of inertial mass is summarized in Newton’s second law of motion, F = ma, which says that if you apply a force of magnitude F to an object with mass m, you will produce an acceleration a. Newton’s famous second law tells us that a given force produces smaller acceleration on an object that has bigger inertial mass, which is probably very familiar to you from experience. (If