Inertial frame of reference

An inertial frame (from the Latin iners " inactive, sluggish " ) is in physics, a reference system in which force-free body straight, uniform move. In an inertial frame so the Newtonian law of inertia holds in its simplest form, maintained by the force-free body its velocity in magnitude and direction and accelerations calculated proportionally to the applied force. The term inertial system was first used by Ludwig Lange ( 1885).

Different inertial frames move against each rectilinear and uniform. In contrast, rotating or otherwise accelerating reference frames are not inertial. For example, the reference system in which a house on the earth stands still is not inertial. Occur bill forces within him. In an inertial frame no rotation of the fixed stars is observed.

Newton's mechanics

In Newton's mechanics two inertial frames are related by a Galilean transformation.

Galilean transformations form a group. To it a part of the temporal or spatial displacement maps the temporal and spatial origin of a system to those of the other system. Since an inertial system merges with a spatial or temporal shift in an inertial frame, inertial systems are distinguished from no place and no time. The space and time are homogeneous.

For the Galilei group the rotation, the time-invariant part of the reference directions (front, left, top ) of the maps a system to the equally time-invariant directions of the other system. Since an inertial system passes during a rotation in an inertial frame, inertial systems are distinguished from any direction. The space is isotropic.

For the Galilei group is one of the transformation,

With each other at a constant speed moving observer convert times and place names into each other.

Since the laws of Newtonian mechanics are valid in all inertial reference frames moving relative to each other at a constant speed, there is no preferred reference system and no way to measure absolute velocity. This is the principle of relativity of Newtonian mechanics.

Special Theory of Relativity

Instead of the Galilean transformation between inertial frames of Newtonian physics convey in relativistic physics Lorentz transformations and space-time shifts as related coordinates, denoted by which uniformly moving observers, when and where events take place. Together with the spatial and temporal shifts form Lorentz transformations, the Poincaré group.

After following idealized method assigns a uniformly moving observers, such as the radar each event its inertial coordinates: He sends a beam of light to the event and measures with its clock, the start time and the time at which again arrives reflected in event light beam at him. The time at which the event has occurred, it uses the average value

As a distance half the duration of the reciprocating light times the speed of light

In addition, he determined angle between the reference directions, he has chosen, and the outgoing light beam. He assigns the event to the following coordinates:

The reflected light beam is only then returned for each event from the direction of the outgoing light beam, if the observer does not rotate. In this way the observer can distinguish whether it rotates or if it is surrounded by other objects.

General Theory of Relativity

The general theory of relativity is formulated so that their equations are valid in any coordinate system. The world lines of freely falling particles are straight lines (exact geodesics ) of the curved space-time. Gravitational displays in free fall at the tidal effect that neighboring geodesics strive toward or away from one another and can be repeatedly cut. Circling example, two space stations with the same constant distance in various levels the earth, so their trajectories intersect where intersect the orbital planes, then takes her distance until they have gone through a quarter circle, then again, until their train to a semicircle crosses again. This effect of non-uniform gravity ( it acts in different places in different directions or with different strengths ) is called tidal effect. It increases with the distance at small distances. Is it possible to neglect the tidal effect, so in free fall is considered the special theory of relativity.

In general relativity, an inertial frame is described by the Lagrangian formalism: By neglected in the neighborhood of an arbitrary point in space-time curvature of space, is obtained as a local approximation to a Minkowski space, which contains, for a given world line of the inertial system through this point.