Principle of relativity

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Relativity: The Special and General Theory

A principle of relativity is a criterion for judging physical theories, stating that they are inadequate if they do not prescribe the exact same laws of physics in certain similar situations. These types of principles have been successfully applied throughout science, whether implicitly (as in Newtonian mechanics) or explicitly (as in Albert Einstein's special relativity and general relativity).

1 Basic relativity principles
2 Special principle of relativity
- 2.1 In Newtonian mechanics
- 2.2 In special relativity
3 General principle of relativity
- 3.1 General relativity
4 See also
5 References and links
6 External links

[edit] Basic relativity principles

Certain principles of relativity have been ubiquitously assumed in most scientific disciplines. One of the most ubiquitous is the belief that any law of nature should be the same at all times; and scientific investigations generally assume that laws of nature are the same regardless of the person measuring them. These sorts of principles have been incorporated into scientific inquiry at the most fundamental of levels.

In theoretical physics, a result called Noether's theorem states that the statement "The laws governing forces are the same at all times" is equivalent to the law of conservation of energy, and the principle of "The laws governing forces are the same at all places" is equivalent to the law of conservation of momentum. In such contexts, relativity principles are more than just prescriptions for how natural laws should be phrased -- they are descriptions of symmetries which the scientific community believes that nature has.

[edit] Special principle of relativity

The special principle of relativity states that physical laws should be the same in all inertial reference frames, but that they may vary across non-inertial ones. It has been used in both Newtonian mechanics and Special relativity; for the latter, its influence was so strong that Max Planck named the theory after the principle.

The principle forces physical laws to be the same in any vehicle moving at constant velocity as they are in a vehicle at rest. A consequence is that an observer in an inertial reference frame cannot determine an absolute speed or direction of their travel in space; they may only speak of their travel relative to some other object.

The principle does not extend this property to noninertial reference frames because those frames do not, in general experience, seem to abide by the same laws of physics -- for example, people often feel fictitious forces when their reference frames accelerate.

[edit] In Newtonian mechanics

Main article: Galilean relativity

The special principle of relativity was first explicitly enunciated by Galileo Galilei in 1639 in his Dialogue Concerning the Two Chief World Systems, using the metaphor of Galileo's ship.

Newtonian mechanics added to the special principle several other concepts--various laws and an assumption of an absolute time. When formulated in the context of these laws, the special principle of relativity states that the laws of physics are invariant under a Galilean transformation.

[edit] In special relativity

Main article: Special relativity

In the late 19th century, Joseph Larmor and Hendrik Lorentz discovered that Maxwell's equations, the cornerstone of electromagnetism, were invariant under a Lorentz transformation, but not under a Galilean transformation. This left a large amount of confusion among physicists, since a theory which did not obey the Galilean transformation either violated the prevailing notion of absolute time or the special principle of relativity. Many physicists, including both Larmor and Lorentz, discarded the special principle of relativity in favor of a luminiferous aether -- a single monolithic reference frame which electromagnetic effects propagated within.

Albert Einstein discarded these in his 1905 paper "On the Electrodynamics of Moving Bodies." Einstein elevated the principle of special relativity to an axiom of the theory, and discarded the notion of absolute time. He replaced the Galilean transformation with the Lorentz transformation in general, and required the speed of light in a vacuum to be the same for all observers, regardless of their motion or the motion of the source of the light. The latter was demanded by Maxwell's equations, which imply the general invariance of the speed of light in a vacuum.

The strength of special relativity lies in its derivation from simple, basic principles, including the invariance of the laws of physics under a shift of inertial reference frames. (See also: Lorentz covariance.)

[edit] General principle of relativity

The general principle of relativity states that physical laws should be the same in all reference frames -- inertial or non-inertial.

Physics in non-inertial reference frames was historically treated by a coordinate transform, first, to an inertial reference frame, performing the necessary calculations therein, and using another coordinate transform to return to the non-inertial reference frame. In most such situations, the same laws of physics can be used if certain predictable fictitious forces are added into consideration; an example is a uniformly rotating reference frame, which can be treated as an inertial reference frame if one adds a fictitious centrifugal force and Coriolis force into consideration.

The problems involved are not always so trivial. Special relativity predicts that an observer in an inertial reference frame doesn't see objects they'd describe as moving faster than the speed of light. However, in the non-inertial reference frame of Earth, treating a spot on the Earth as a fixed point, the stars are observed to move in the sky, circling once about the Earth per day. Since the stars are light years away, this observation means that, in the non-inertial reference frame of the Earth, anybody who looks at the stars is seeing objects which appear, to them, to be moving faster than the speed of light.

Since non-inertial reference frames do not abide by the special principle of relativity, such situations are not self-contradictory. However, they do provide a strong motivation to look for a set of physical laws which are constant in all reference frames -- inertial or non-inertial.

[edit] General relativity

Main article: General relativity

General relativity was developed by Einstein in the years 1907 - 1915. General relativity postulates that the global Lorentz covariance of special relativity becomes a local Lorentz covariance in the presence of matter. The presence of matter "curves" spacetime, and this curvature affects the path of free particles (and even the path of light). General relativity uses the mathematics of differential geometry and tensors in order to describe gravitation as an effect of the geometry of spacetime. Einstein based this new theory on the general principle of relativity, and he named the theory after the underlying principle.