# Relativity, Special Theory of

# Relativity, Special Theory of

The Special Theory of Relativity describes the way in which an observer's experience of time and space is interrelated, while the General Theory of Relativity addresses the interrelationships among mass, space, gravity, and motion. Motivated by his concerns about problematic features of electro-magneticism—especially the relationship between electric and magnetic fields—Albert Einstein (1879–1955) proposed the Special Theory of Relativity in 1905. However, since most of the character and consequences of Special Relativity can be more easily developed in the arena of kinematics (the description of motion), this entry will focus on the ways in which motion influences the outcome of measurements regarding space and time.

## Inertial reference frames

The term *reference frame* ordinarily refers to a *coordinate system* (like the Cartesian system with three mutually perpendicular axes labeled *x, y,* and *z* ) in which the location and motion of an object can be conveniently described, along with a set of synchronized clocks with which to determine the time at any location in that coordinate system. Given such a reference frame, one can specify the coordinates of any event *E* by stating its location (*x, y, z* ) and the time (*t* ) of its occurrence in the notation: *E* (*x, y, z, t* ).

Of all possible reference frames, Special Relativity is concerned only with *inertial reference frames* —reference frames in which Newton's First Law (sometimes alled the Law of Inertia) holds. It can be shown that any reference frame that moves with constant velocity (constant speed and direction) relative to an inertial frame is also an inertial reference frame.

## Postulates

Einstein's Special Theory of Relativity proceeds from two fundamental postulates regarding the results of comparing the observations of physical phenomena (sets of events) by observers in two or more inertial reference frames. These two postulates may be stated as follows: (1) The speed of light is the same in all inertial reference frames, independent of the motion of the source; and (2) The form of all physical laws (not only those pertaining to mechanics) is the same in all inertial reference frames. The first postulate represents a break from the common expectation that the speed of light relative to its source would be fixed, as would be the case for a bullet fired from a gun. The second postulate represents a significant extension of the classical principle of relativity that applied only to the laws of mechanics.

## Predictions

From these two postulates a number of fascinating predictions can be deduced.

**The relativity of simultaneity.** The *Lorentz transformation,* named after Dutch physicist Hendrik Anton Lorentz (1853–1928), is a set of equations that allows the calculation of event coordinates in one reference frame from the coordinates of the same event in another frame. Suppose that in reference frame *S* an observer notes two events that occur at different locations, but at the same time. The *S* observer says that these two events occurred simultaneously. Then consider another reference frame S ́ that is moving at a constant velocity relative to *S.* Applying the Lorentz transformation to the event coordinates in *S* to obtain the coordinates for the same two events in S ́ leads to a remarkable result. Observers in S ́ would say that these two events occurred at different times. That is, events that appear simultaneous in one inertial reference frame would not be observed as simultaneous in any other inertial frame. The amount of time separation would depend on the relative speed of the two frames. Simultaneity is not absolute, but is dependent on the observer's reference frame. In other words, there is no universal time on which all observers can agree.

**Length contraction.** Consider a meter stick oriented parallel to the *x* axis of a references frame *S* that is moving at speed *v* along that same *x* axis. Let S ́, consider a clock that is at rest in S ́. Relative to any observer at rest in *S,* that S ́ clock is moving at speed *v.* As it moves, it passes numerous *S* clocks that are distributed throughout reference frame *S.* Suppose that the S ́ clock was synchronized to display exactly the same time as one particular *S* clock at the instant the S ́ clock passed it. Now suppose that at some later time, the display of the S ́ clock is compared with a second *S* clock as it passes it. Once again, applying the Lorentz transformation to predict the coordinates of this second clock-passing event leads to a surprising result: The S ́ clock will lag behind the second *S* clock. A moving clock (the S ́ clock is moving relative to reference frame *S* ) records less elapsed time than do stationary *S* clocks. This is the phenomenon called *time dilation.* Numerous empirical tests have affirmed this peculiar effect.

There is a symmetry that must be acknowledged in regard to the time dilation phenomenon. Comparing equivalent observations by observers in two different reference frames, each would say (with justification) that the clocks of the other were running slowly. That symmetry has led some persons to question the idea of twins with differing motion histories actually achieving different ages. The standard scenario for the so-called twin paradox posits a pair of twins with a keen interest in testing relativity theory. While one of the twins stays at home, the other takes off in a rocket and travels at a substantial fraction of the speed of light for a few years, as measured on his own calendar watch, and then turns around to reverse the trip. Upon reunion with his twin, how will the age of the traveler compare with the stay-at-home sibling? From the viewpoint of the homebody, the traveler's clocks have been running slowly for most of the trip, both outbound and inbound (the direction of travel is irrelevant). So, it would seem that at the reunion, the traveler would be younger than his homebound twin. However, what about looking at things from the standpoint of the traveler? Would it not be the case that the homebody's clocks were running slowly so that the homebody would be the younger sibling at reunion? That's the usual presentation of the twin paradox—conflicting conclusions flowing from the symmetry of the time dilation phenomenon.

It turns out, however, that there is no actual paradox, no conflicting predictions. The traveler really is the younger at reunion. There was no effective symmetry in the motion histories of the twins. One stayed in a single reference frame the entire time; the other accelerated from one frame to another several times. The amount of time elapsed between the twins' separation and reunion events will be different for each as a consequence of differing histories of motion. Strange, perhaps, but apparently true.

**The mass-energy relationship.** If there is one mathematical relationship that best characterizes the popular conception of special relativity it would have to be the equation *E* = *mc* 2*;,* where *E* represents energy, *m* represents mass, and *c* is the speed of light. But what does this familiar equation actually signify? In very general terms it signifies that mass is one particular form of energy and that it could, given suitable circumstances, be transformed into other forms of energy. Nuclear reactors, for example, provide the circumstances for a controlled transformation of some of the mass-energy of selected radioactive nuclei into heat, which is then used to drive conventional electrical energy generators. In a similar way, a coal-fired power plant accomplishes the same transformation of mass-energy into heat by means of chemical rather than nuclear reactions.

There is more, however, in the familiar *E* = *mc* 2*.* The mass, *m,* that appears in this equation is the *relativistic mass,* whose value depends on the speed of the object under consideration. In fact, as an object's speed, *v,* approaches the speed of light, the value of its relativistic mass approaches infinity. In effect, that means that it would require an infinite amount of energy to accelerate an object to the speed of light. With only finite amounts of energy available, the speed of small objects (such as atomic constituents) can be increased (in a particle accelerator device) to a value approaching the speed of light, but never equaling or exceeding it. Nothing having mass can be given a speed relative to a local observer that is equal to or greater than the speed of light. This is a speed limit that is enforced not by legal decree, but by the very nature of the universe itself—specifically the relationships among space, time, motion, and energy.

This speed limit applies only in a localized region of space. If one is considering the motion of extremely distant objects, say billions of light-years away, another factor must be included—the expansion of space itself. In the language of General Relativity, space is not merely a nothing in which things may be placed, but a specific something that has properties and is able to act and be acted upon. One of the things that cosmic space is doing, apparently, is expanding. Distant galaxies are observed to be receding from the Earth because the space between them and the Earth is expanding. The motion of distant galaxies that can be attributed to this spatial expansion phenomenon is not restricted by the speed of light limitation just discussed.

## Implications for religious thought

The theory of relativity must be clearly distinguished from what is ordinarily denoted by the word *relativism.* Moral relativism, for instance, presumes that there are no universal standards of right and wrong behavior. Likewise, epistemic relativism presumes that there are no observer-independent standards for objective knowledge. As noted above, however, the special theory of relativity entails no denial of standards for comparing the observations of various observers. On the contrary, relativity theory specifies those standards with great clarity. Relativistic mechanics differs from classical mechanics not by abandoning standards, but by offering a specific and new set of standards that bring predictions and observations into agreement.

Another feature of Special Relativity theory that suggests an application to religious thought is its demonstration of the fact that common sense sometimes needs to be corrected. Most people have common sense notions of space and time that function perfectly well as they go about their daily routines of life. People use these notions as they plan their travels from place to place and as they proceed throughout the course of a day. These common sense notions include the following:

- All impartial observers should agree on the time interval between two events.
- All impartial observers should agree on the distance between two points.
- Things can always be made to go faster.
- Twins remain equal in age no matter what they do.

However, each of these expectations turns out to be incorrect, and concepts of space and time must be modified in order to comprehend what careful observations and measurements have revealed.

The origin of such shortcomings in common sense notions of space and time is easy to identify: These notions are based on limited experience. Until physicists performed observations and measurements on particles moving at speeds approaching the speed of light, the shortcomings of human concepts of space and time could not be detected. Extending human experience with space, time, and motion into new speed regimes revealed those shortcomings and inspired modifications of the sort proposed by Lorentz and Einstein. The lesson is evident: Epistemic dogmatism (I have the complete and final understanding of *X* ) must often be replaced with epistemic humility (what I now think I know may someday need to be modified in response to an expansion of experience). This is not to despair and claim no knowledge whatsoever. This is rather to remain open to correction, even while celebrating the knowledge of the day. On these matters theology and science enjoy full agreement.

*See also* Einstein, Albert; Relativity, General Theory of; Space and Time

*Bibliography*

adams, steve. relativity: an introduction to space-time physics. london: taylor and francis, 1997.

eisntein, albert. the meaning of relativity (1921). princeton, n.j.: princeton university press, 1966.

harrison, edward r. cosmology: the science of the universe, 2nd edition. new york: cambridge university press, 2000.

mcfarland, ernie. einstein's special relativity: discover it for yourself. toronto: trifolium, 1998.

mermin, n. david. space and time in special relativity. prospect heights, ill.: waveland press, 1989.

moore, thomas a. a traveler's guide to spacetime. new york: mcgraw hill, 1995.

rindler, wolfgang. introduction to special relativity, 2nd edition. oxford: clarendon press, 1991.

taylor, edwin f., and wheeler, john a. spacetime physics: introduction to special relativity, 2nd edition. san francisco: w. h. freeman, 1992.

howard j. van till

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