Special relativity - Misplaced Pages

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The special theory of relativity, or SR for short, is the physical theory published in 1905 by Albert Einstein that modified Newtonian physics to incorporate electromagnetics as represented by Maxwell's equations. The theory is called special because the theory applies only to phenomena in which the effects of gravitation can be neglected. General Relativity of course is the theory extended to incorporate gravitation. Before, Hendrik Lorentz and others noted that electromagnetics differed with Newtonian physics in that observations by one of some phenomenon can differ from those of a person moving relative to that person. For example, one may observe no magnetic field, yet another observes a magnetic field in the same physical area. Lorentz suggested a "contraction factor" and a "dilation factor" whereby electromagnetics and Newtonian physics could be partially reconciled. It is this notion of transforming the laws of physics between observers moving relative to one another that gives the theory its name. However, Einstein wanted to know what was invariant (the same) for all observers. His original title for his theory was (translated from German) "Theory of Invariants". It was Planck who suggested "relativity."

SR postulated* that the speed of light in vacuum is the same to all observers, and said that every physical theory should be shaped or reshaped so that it is the same mathematically for every observer. The postulate (which comes from Maxwell's equations for electromagnetics) together with the requirement has several consequences that struck many people as bizarre, among which are: (NB: Lorentz only suggested the Lorentz transformation equations; Einstein derived them from a more fundamental theory.)

Electromagnetism longer requires Lorentz' "fudge" for consistency.
When the velocities involved are much less than speed of light, the resulting laws simplify to Newton's laws.(this is not a consequence that belongs in this list, is it?)
Time is not invariant from observer to another.
Two events that occur simultaneously in different places in one reference frame, may occur one after the other in another reference frame (relativity of simultaneity).
The dimensions (length, e.g.) of an object as measured by an observer may differ from those by another. (This is an obvious difference from Newtonian physics, which showed no such effect.)
The twins paradox is the "story" of a twin who "ages much more rapidly" than the other. (An even more incredible difference.)

Another radical consequence is the rejection of the notion of an absolute, unique, frame of reference. Previously it had been believed that the universe traveled through a substance known as "ether" (absolute space), against which speeds could be measured. However, evidence from the famous Michelson-Morley experiment suggested that either the Earth was always stationary or the notion of an absolute frame of reference was mistaken.

Perhaps most far reaching, it also showed that energy and mass, previously considered separate, were equivalent, and related by the most famous expression from the theory:

E = mc

where E is the energy, m is the mass and c is the speed of light. If the body is moving with speed v relative to the observer, this can be written as:

E = m₀c / √( 1 - v/c )

where m₀ is the mass observed when the relative speed is zero, called the rest mass of the body.

(The term √( 1 - v/c ) occurs frequently in relativity, and comes from the Lorentz transformation equations. It is worth noting that if v is much less than c this can be written as

E ~= m₀c + m₀v / 2

which is precisely equal to the "energy of existence", m₀c, and the Newtonian kinetic energy, m₀v/2. This is just one example of how the two theories coincide when velocities are small.)

At very high speeds, the denominator in the energy equation (2) approaches a value of zero as the velocity approaches c. Thus, at the speed of light, the energy would be infinite, and precludes things that have mass from moving any faster.

The most practical implication of this theory is that it puts an upper limit to the laws (see Law of nature) of Classical Mechanics and gravity formed by Isaac Newton at the speed of light. Nothing carrying mass or information can move faster than this speed. As an object's velocity approaches the speed of light, the amount of energy required to accelerate it approaches infinity, making it impossible to reach the speed of light. Only particles with no mass, such as photons, can actually achieve this speed, which is approximately 300,000 kilometers per second or 186,300 miles per second.

The name "tachyon" has been used for hypothetical particles which would move faster than the speed of light, but to date evidence of the actual existence of tachyons has not been produced.

Special relativity also holds that the concept of simultaneity is relative to the observer: If matter can travel along a path in spacetime without changing velocity, the theory calls this path a 'time-like interval', since an observer following this path would feel no motion and would thus travel only in 'time' according to his frame of reference. Similarly, a 'space-like interval' means a straight path in space-time along which neither light nor any slower-than-light signal could travel. Events along a space-like interval cannot influence one another by transmitting light or matter, and would appear simultaneous to an observer in the right frame of reference. To observers in different frames of reference, event A could seem to come before event B or vice-versa; this does not apply to events separated by time-like intervals.

Special relativity is now universally accepted by the physics community, unlike General Relativity which is still insufficiently confirmed by experiment to exclude certain alternative theories of gravitation. However, there are a handful of people opposed to relativity on various grounds and who have proposed various alternatives, mainly ether theories.