In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.
For example, in the framework of special relativity the Maxwell equations have the same form in all inertial frames of reference. In the framework of general relativity the Maxwell equations or the Einstein field equations have the same form in arbitrary frames of reference.
Certain principles of relativity have been widely assumed in most scientific disciplines. One of the most widespread 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.
Any principle of relativity prescribes a symmetry in natural law: that is, the laws must look the same to one observer as they do to another. According to a theoretical result called Noether's theorem, any such symmetry will also imply a conservation law alongside.[1][2] For example, if two observers at different times see the same laws, then a quantity called energy will be conserved. In this light, relativity principles make testable predictions about how nature behaves.
According to the first postulate of the special theory of relativity:[3]
Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.
—Albert Einstein: The Foundation of the General Theory of Relativity, Part A, §1
This postulate defines an inertial frame of reference.
The special principle of relativity states that physical laws should be the same in every inertial frame of reference, but that they may vary across non-inertial ones. This principle is used in both Newtonian mechanics and the theory of special relativity. Its influence in the latter is so strong that Max Planck named the theory after the principle.[4]
The principle requires physical laws to be the same for any body moving at constant velocity as they are for a body at rest. A consequence is that an observer in an inertial reference frame cannot determine an absolute speed or direction of travel in space, and may only speak of speed or direction relative to some other object.
The principle does not extend to non-inertial reference frames because those frames do not, in general experience, seem to abide by the same laws of physics. In classical physics, fictitious forces are used to describe acceleration in non-inertial reference frames.
Newtonian mechanics added to the special principle several other concepts, including laws of motion, gravitation, and an assertion of an absolute time. When formulated in the context of these laws, the special principle of relativity states that the laws of mechanics are invariant under a Galilean transformation.
The principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation; so that we have not and could not have any means of discerning whether or not we are carried along in such a motion.
In their 1905 papers on electrodynamics, Henri Poincaré and Albert Einstein explained that with the Lorentz transformations the relativity principle holds perfectly. Einstein elevated the (special) principle of relativity to a postulate of the theory and derived the Lorentz transformations from this principle combined with the principle of the independence of the speed of light (in vacuum) from the motion of the source. These two principles were reconciled with each other by a re-examination of the fundamental meanings of space and time intervals.
The strength of special relativity lies in its use of simple, basic principles, including the invariance of the laws of physics under a shift of inertial reference frames and the invariance of the speed of light in vacuum. (See also: Lorentz covariance.)
It is possible to derive the form of the Lorentz transformations from the principle of relativity alone. Using only the isotropy of space and the symmetry implied by the principle of special relativity, one can show that the space-time transformations between inertial frames are either Galilean or Lorentzian. Whether the transformation is actually Galilean or Lorentzian must be determined with physical experiments. It is not possible to conclude that the speed of light c is invariant by mathematical logic alone. In the Lorentzian case, one can then obtain relativistic interval conservation and the constancy of the speed of light.[6]
All systems of reference are equivalent with respect to the formulation of the fundamental laws of physics.
—C. Møller The Theory of Relativity, p. 220
That is, physical laws are the same in all reference frames—inertial or non-inertial. An accelerated charged particle might emit synchrotron radiation, though a particle at rest does not. If we consider now the same accelerated charged particle in its non-inertial rest frame, it emits radiation at rest.
Physics in non-inertial reference frames was historically treated by a coordinate transformation, first, to an inertial reference frame, performing the necessary calculations therein, and using another 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 does not see objects he would 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.
General relativity was developed by Einstein in the years 1907 - 1915. General relativity postulates that the globalLorentz 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.
↑ Poincaré, Henri (1904–1906). "The Principles of Mathematical Physics". Congress of arts and science, universal exposition, St. Louis, 1904. Vol.1. Boston and New York: Houghton, Mifflin and Company. pp.604–622.
↑ Yaakov Friedman, Physical Applications of Homogeneous Balls, Progress in Mathematical Physics 40 Birkhäuser, Boston, 2004, pages 1-21.
Living Reviews in Relativity— An open access, peer-referred, solely online physics journal publishing invited reviews covering all areas of relativity research.
In classical physics and special relativity, an inertial frame of reference is a frame of reference not undergoing any acceleration. It is a frame in which an isolated physical object—an object with zero net force acting on it—is perceived to move with a constant velocity or, equivalently, it is a frame of reference in which Newton's first law of motion holds. All inertial frames are in a state of constant, rectilinear motion with respect to one another; in other words, an accelerometer moving with any of them would detect zero acceleration.
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein's 1905 treatment, the theory is presented as being based on just two postulates:
The laws of physics are invariant (identical) in all inertial frames of reference.
The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer.
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur.
The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.
Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames of reference. Galileo Galilei first described this principle in 1632 in his Dialogue Concerning the Two Chief World Systems using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer below the deck would not be able to tell whether the ship was moving or stationary.
In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws. While this concept is exhibited by general relativity, which describes the dynamics of spacetime, one should not expect it to hold in less fundamental theories. For matter fields taken to exist independently of the background, it is almost never the case that their equations of motion will take the same form in curved space that they do in flat space.
In theoretical physics, an invariant is an observable of a physical system which remains unchanged under some transformation. Invariance, as a broader term, also applies to the no change of form of physical laws under a transformation, and is closer in scope to the mathematical definition. Invariants of a system are deeply tied to the symmetries imposed by its environment.
In physics, Albert Einstein derived the theory of special relativity in 1905 from principle now called the postulates of special relativity. Einstein's formulation is said to only require two postulates, though his derivation implies a few more assumptions.
The history of special relativity consists of many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einstein and subsequent work of Max Planck, Hermann Minkowski and others.
What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which marked the end of the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century.
In theoretical physics, a preferred frame or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different (simpler) from those in other frames.
In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame. This possibility was raised by mathematician Henri Poincaré in 1900, and thereafter became a central idea in the special theory of relativity.
Albert Einstein presented the theories of special relativity and general relativity in publications that either contained no formal references to previous literature, or referred only to a small number of his predecessors for fundamental results on which he based his theories, most notably to the work of Henri Poincaré and Hendrik Lorentz for special relativity, and to the work of David Hilbert, Carl F. Gauss, Bernhard Riemann, and Ernst Mach for general relativity. Subsequently, claims have been put forward about both theories, asserting that they were formulated, either wholly or in part, by others before Einstein. At issue is the extent to which Einstein and various other individuals should be credited for the formulation of these theories, based on priority considerations.
The moving magnet and conductor problem is a famous thought experiment, originating in the 19th century, concerning the intersection of classical electromagnetism and special relativity. In it, the current in a conductor moving with constant velocity, v, with respect to a magnet is calculated in the frame of reference of the magnet and in the frame of reference of the conductor. The observable quantity in the experiment, the current, is the same in either case, in accordance with the basic principle of relativity, which states: "Only relative motion is observable; there is no absolute standard of rest". However, according to Maxwell's equations, the charges in the conductor experience a magnetic force in the frame of the magnet and an electric force in the frame of the conductor. The same phenomenon would seem to have two different descriptions depending on the frame of reference of the observer.
In physics, the principle of covariance emphasizes the formulation of physical laws using only those physical quantities the measurements of which the observers in different frames of reference could unambiguously correlate.
In physics, a covariance group is a group of coordinate transformations between frames of reference. A frame of reference provides a set of coordinates for an observer moving with that frame to make measurements and define physical quantities. The covariance principle states the laws of physics should transform from one frame to another covariantly, that is, according to a representation of the covariance group.
There have been various formulations of special relativity over the years which differ from Einstein's theory. While some are mathematically equivalent to Einstein's theory, others aim to revise or extend it.
When using the term "the speed of light" it is sometimes necessary to make the distinction between its one-way speed and its two-way speed. The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed from the source to a mirror and back again to detector. Albert Einstein chose a synchronization convention that made the one-way speed equal to the two-way speed. The constancy of the one-way speed in any given inertial frame is the basis of his special theory of relativity, although all experimentally verifiable predictions of this theory do not depend on that convention.
Criticism of the theory of relativity of Albert Einstein was mainly expressed in the early years after its publication in the early twentieth century, on scientific, pseudoscientific, philosophical, or ideological bases. Though some of these criticisms had the support of reputable scientists, Einstein's theory of relativity is now accepted by the scientific community.
There are many ways to derive the Lorentz transformations utilizing a variety of physical principles, ranging from Maxwell's equations to Einstein's postulates of special relativity, and mathematical tools, spanning from elementary algebra and hyperbolic functions, to linear algebra and group theory.
This page is based on this Wikipedia article Text is available under the CC BY-SA 4.0 license; additional terms may apply. Images, videos and audio are available under their respective licenses.
