Principle of relativity

The principle of relativity states that the laws of nature for all observers have the same shape. Simple considerations show that it is impossible for this reason, to identify a preferred or absolute state of motion of any observer or object. That is, it is only the movements of the body relative to the other articles, but not the movement of the body can be determined relative to a preferred reference system.

In classical physics, as well as in 1905, designed by Albert Einstein special relativity theory (SRT ), this principle was initially given only in inertial frames of reference for the description of uniform and accelerated motion. Although Accelerated reference systems can also be used, but natural laws are not the same simple form as in inertial frames and therefore are not equal with the latter. Therefore, the principle was formally extended to accelerated reference systems in the context of general relativity. According to this modern view is the SRT, the special case of ART, in which the influence of gravity can be neglected, and is now also equally valid for inertial and accelerated reference systems.

Galileo Galilei ( 1632) is considered the first to have formulated this principle. He had only mechanical processes in view and argued that a located below the deck of a ship unaccelerated observer from the events around him can not tell whether the ship is in motion or not. This principle of relativity was used implicitly by Christiaan Huygens in the formulation of the laws of impact.

Classical Mechanics

Isaac Newton following the existence of absolute space was assumed in classical mechanics for centuries. The principle of relativity implicitly contained in this mechanics said that in uniformly moving inertial frames the same laws ( covariance ) of mechanics apply as in absolute space itself, and that it was not possible to determine which system is actually quiet or be moved. That is, the formulas of classical mechanics remain valid when one undergoes a relative to absolute space moving system of the so-called Galilean transformation. Newton wrote in his Principia:

" The motions of bodies in a given space are mutually the same, whether the space is at rest or if he is constantly moving on a straight line. "

In the 19th century, classical physics led after the establishment of Maxwell's theory of electrodynamics in the theory of a stationary ether, which was intended as a transmission medium for the light and eventually became identified with the absolute space of Newton. It was now trying to prove the state of motion relative to the ether of the earth, so also the principle of relativity would have been refuted. However, all remained relevant experiments - such as the Michelson - Morley experiment - unsuccessfully.

Special relativity principle

At the beginning of the 20th century, these unsuccessful experiments led to the principle of relativity ever greater importance was given, which also led to clearer definitions of terms. Henri Poincaré wrote in 1904, for example:

"The principle of relativity, according to which the laws of physical processes for a stationary observer to be the same as for one carried along in a uniform translation, so that we have no means or may have to decide whether we realized in such a movement or not. "

And Albert Einstein defined 1905, the principle of relativity as:

" The laws by which change the states of physical systems that are irrespective of which of two relative to each other located in a uniform translational motion coordinate systems, these state changes are related. "

Hendrik Antoon Lorentz, Poincaré, and Einstein called on the covariance not only the mechanics, but also of electrodynamics. This could be achieved by the Galileo transformation, has been replaced by the Lorentz transformation. The main difference is that in the new transform the velocity of light is an insurmountable limit speed. For velocities that are small compared to the speed of light, the special principle of relativity goes over into that of Galileo. Newton's absolute space is however in contradiction with the principle of relativity. Einstein therefore moved with the special theory of relativity to the conclusion that there is no absolute reference system. This refers to the space and on the time. Hermann Minkowski led this further, by summarizing time and space to four-dimensional space-time.

The relativity principle applies in the SRT initially only in inertial frames, because only in them to take the laws of nature the same simple form. Although the formalism of SRT can be extended beyond, so that accelerated reference systems can be treated, but these systems are not equal with inertial systems.

General Principle of Relativity

In addition to the special principle of relativity led Einstein alleges that in all systems of reference, whether accelerated or not accelerated, the laws must take the same form ( general covariance ). This was motivated by the validity of the equivalence principle, which states that no experiment can determine whether it is located far away in weightlessness masses or in free fall near a mass. Einstein assumed in addition that this is in connection with the mach 'principle, according to which inertia and acceleration only occur relative to the mass of the universe. He wrote in 1916:

" The laws of physics must be such that they apply in relation to any moving frames of reference. [ ... ] The general laws of nature are to be expressed by equations which are valid for all coordinate systems, that is, any substitutions opposite covariant ( generally covariant ) are. "

In fact, general covariance in general relativity is achieved (ART). It was to abandon the idea that the space is Euclidean, because the gravity is understood as a process in the curved space-time, for their description a non-Euclidean geometry must be used. To understand the general covariance, however, the following factors must be considered:

• General covariance can be considered as a mathematical principle, which does not automatically imply a general principle of relativity in the sense of relativity of acceleration by itself. For each theory can be formulated generally covariant with appropriate mathematical effort, such as the SRT and even Newtonian mechanics.

• The equivalence principle is only valid locally due to the occurrence of tidal effects over longer distances. Valid local is therefore also the SRT as a special case of ART in the "flat " or between minkowski spacetime where gravity can be neglected ( "local Lorentz invariance "); That is, in areas where the Riemannian curvature is everywhere zero.

• Also largely matter-free solutions of ART are possible without a single body therefore loses its inertia, making the Mach principle is violated.

Generally speaking, the " Gravito - inertial field ", so the field can be described by the general theory of relativity, both acceleration and gravitational effects, an independent existence of bodies. On the basis of this field can be set, which is now " real" or "absolute" non-uniformly moved by two relatively accelerated observers. However, for complete qualification of the acceleration does not prove the existence of an absolute space, because although the " Gravito - inertial field " as mentioned also exist without matter, it is in the presence of matter still subject to their influence - as opposed to the Newton's absolute space, that of the matter remains unaffected.

Galileo's ship

Here is an excerpt from the description, pp. 197 et seq, of Galileo:

" You Closes in company with a friend in the largest possible space under the deck of a large ship a. Gives you there mosquitoes, butterflies and similar flying creatures; also provides a container with water and small fish in it; also depends on top of a small bucket, which can drop by drop water trickle into a second narrow-necked vessel underneath to. Observed carefully now, as long as the ship stands still, as the flying creatures fly with the same speed in all directions of the room. We will see how the fish without any difference in all directions swim; the falling drops are all placed below in the vascular flow. If your Euerem companions zuwerft an object, so you need not stronger than for the one in the other direction to throw, provided that they are equal distances. If you, as they say, with equal feet makes a jump, you will reach in every direction equidistant. Pay attention to make sure you all of these things carefully, though no doubt prevails that all ships at rest behaves. Now the ship at any speed let move: You will - if only the motion is uniform and not here and there of change - in all these phenomena do not occur see the slightest change. From the same none will be able to refer you if the ship moves or stands still. [...] The reason for this consensus of all phenomena is that the movement of the vessel all, contained therein, and the air, together belongs. That's why I also said that one should go below deck, as above in the open air, which does not accompany the running of the ship, more or less marked differences in some of these phenomena would show. "