Frame of reference

A reference system is in physics, a spatio-temporal entity that is required to describe the behavior of spatially dependent variables clearly and completely. In particular, the position and movement of physical bodies can only be specified relative to a reference system. It is defined by choosing a reference point and the spatial directions defines and determines a physical process for the time measurement. This is automatically set what is meant by "rest" and " motion ", respectively. This is necessary because different observers describe the same physical action in different ways. For example, could argue that it accommodates a tree, while a pedestrian on the road the situation exactly reversed describes a motorist.

• 3.1 Simple Examples 3.1.1 Which ball abuts the other?
• 3.1.2 At what angle the bullets fly apart?

• 4.1 Mechanics
• 4.2 Electrodynamics
• 4.3 Astronomy and Cosmology

Datums and coordinate systems

As a reference point, a point of a real object is selected frequently, such as " the left front corner of the table ", " the middle of the platform " or " the center of the sun " .. It can also be an imaginary point, such as " the common center of gravity of earth and Moon " or " a freely falling reference system ".

In order to determine the three spatial directions, it still requires at least two other points: Through these three points, a plane is derived. The third dimension, is then obtained, for example, as a normal to said plane. This one has all the requirements for the definition of a coordinate system that can be used to specify points in space. Therefore, the term of reference in the literature also occasionally used as a synonym for coordinate system. Usually, however, the concepts can be distinguished because one and the same frame of reference (e.g., ground) (e.g., Cartesian coordinates and Polar coordinates) can be described by different coordinate systems. It can be converted by a coordinate transformation, the space and time coordinates of any process from one coordinate system to another. Physical formulas that describe the same process in the same reference system, therefore, can still take many different shape for the use of different coordinate systems.

Frequently selected reference systems

Rest frame

The reference system in which, a relevant body is at rest, it's called the rest frame of the body under consideration. He has in this reference system no kinetic energy, either by translation or by rotation, and is in force equilibrium.

Laboratory system

The rest frame of the observer and the apparatus of the considered experiment is called laboratory system. It is usually the most obvious reference to the description of an experiment, but not always the most appropriate. The laboratory system is - if it is on the earth - only approximately an inertial frame.

Center of mass system

In the center of mass system, the focus of a physical system is selected to the origin of the reference system, it "rests" so. For some physical processes, such as the elastic collision, allows the center of mass system, a particularly simple description, because the pulses of the two bodies involved opposite here, by definition, are the same.

Inertial

A reference system rest in the force-free particles, or by running at a constant speed straight paths, ie inertial system. This implies the inertia set. The spatial coordinates of these tracks are inhomogeneous linear functions of time

It is the position of the particle at the time, and its speed. Such reference systems are up to the choice of location and time of origin, the choice of three directions ( " top, front, right") and the choice of a constant speed of the whole reference system ( with respect to another inertial frame ) set. This implies that every system of reference which is at rest relative to an inertial frame or moving at a constant speed towards him, is also an inertial frame.

Accelerated reference system

A reference system is not inertial, ie accelerated reference system.

To explain the difference in the following example is provided:

In an accelerated frame of reference, therefore, move the body, acting on the from the standpoint of the inertial system of any forces, speeds or on curved paths. However, since an acceleration according to the basic equation of mechanics

Is always caused by a force, the observer closes in accelerated reference system to a force that does not exist for the observer in the inertial frame. Such forces are called image forces or inertial forces. For the observer in an accelerated frame of reference they are but, although it can not find the cause for it, just as real as all other forces. Such a body in accelerated system remains only at rest, if there is an opposite to the force of inertia force that keeps the body in balance. In the above example, this means: Someone needs to hold the stroller, otherwise it rolls away.

Rotating frame of reference

A rotating reference system performs compared to an inertial rotational motion. Although in this situation, nothing appears accelerated (when the angular velocity is constant), the rotating reference frame belongs to the accelerated reference systems. A body, which are located outside the axis of rotation, has been in the rotating frame has an outwardly directed centrifugal force. They persist only at rest when simultaneously applying an inward centripetal force on it. Considering from the same position of an inertial system, the centripetal force causes precisely that inwardly directed acceleration, which holds the body in their orbits around the rotation axis ( see, for example chain carousel ).

In addition to the centrifugal force acting on a body, when resting in a not rotating reference system, but moving relative to it, a second Scheinkraft: the Coriolis force. If you stand on a rotating disk, so you can feel only the centrifugal force as a force that always pushes one of the axis of rotation to the outside. If you try to go on the disc, the Coriolis force shall be additional. She is always directed toward the direction of movement sideways and can describe a curve. If one tries, for example, straight to the axis of rotation to go to ( or away from ), you will be distracted. It runs on the plate along a circle relative to the rotational direction around the axis, the Coriolis force of the centrifugal force is directed opposite. If you walk just so fast that one rests viewed from the outside ( from one inertial system off), then you might stay free of forces, because the Coriolis force exactly cancels the centripetal force.

The Earth as a reference body defines a rotating frame of reference. However, the differences from one inertial system can be neglected due to the slow rotation of the earth often, such as in many physical processes in everyday life. In the laboratory, the differences are detectable only with special experiments such as the Foucault pendulum. But large-capacity they have immense influence eg on ocean currents and weather.

Change of the reference system

The detailed description of a physical phenomenon generally depends on the chosen reference system, for example, the observed values ​​for spatial coordinates and times, and so that all sizes formed therefrom, such as speed, acceleration, etc., depending on the reference system appear the observations of the same particular process different so that it different formulas can be read and possibly different conclusions can be drawn about the conduct of the operation or the underlying physical laws.

Variables and mathematical relationships that are invariant under a change of reference system is called invariant.

Simple examples

See also kinematics ( Teilchenprozesse )

Which ball abuts the other?

On a billiard table, that is, in the laboratory system, pushes a red billiard ball centrally against a dormant white and then remains lying. In another reference frame that moves with constant speed so that the red ball rests in it at first, the white ball with the opposite velocity depends on the dormant red ball to bring pressure on them and then left in position while the red ball is now with the initial speed of the white of them moved. In a third reference system, the center of mass of the two balls, both balls move only toward each other, collide, and move away from each other, always at the same speed, which is just half as large as the initial velocity of the red ball in the first reference system. The question of which ball the other triggers, is not physically meaningful question.

At what angle the bullets fly apart?

In the reference system " pool table " the general rule is that for a non- central collision of red move against the dormant white billiard ball, both at exactly 90 ° apart. In the center of mass system, however, make their movement directions after the collision is always an angle of 180 ° (the same as before the collision, only along a different direction). Neither of these two rules is a general law of nature.

Coordinate transformation from one reference system into another

If, starting from a reference system defines a second, then can be by means of a coordinate transformation for each point and each time in force in any reference system coordinates by the coordinate reference system from the other express. In the case of a constant velocity of the reference systems against each other, the Lorentz transformation is applied for Cartesian coordinates. For speeds that are much smaller than the speed of light, it can be approximated by the Galilean transformation, which is not only mathematically simpler, but also with the direct observation tolerated (eg, spatial and temporal distances invariant ). For the same process then belong to the two reference systems, various descriptions, but must match completely after conversion with the correct coordinate transformation.

Principle of relativity

According to the relativity principle, any two reference systems relative to each other in a straight line move uniformly equivalent. That is, there is no physical process in which one besides the fact that the two reference systems ( and the necessary consequences such as Doppler effect) observed a further distinguishing feature between them could move relative to each other. Therefore, the basic physical laws against the exchange between these reference systems must be invariant. Does the law the form of a formula, in which the coordinates of each reference system occur, then the formulas for both coordinate systems need to look exactly the same, and one must arise from the other, if one expresses the coordinates therein by those of the other reference system. Mathematically stated the laws of nature must be invariant with respect to the coordinate transformation. As a result, terms such as " absolute rest " or " absolute motion " physically meaningless because undetectable.

History

Mechanics

In Aristotle, the natural state of a body is the absolute silence. When the body moves, so only through an internal drive or an external constraint. For him, rest and exercise are objectively distinguishable things, so there is in the physics of Aristotle only an objective frame of reference: the Earth.

With the beginning of the modern era, recognized in the 17th century. Galileo Galilei and Isaac Newton, that force-free body does not go by itself in a dormant state, but continue to move in a straight line with their current speed and thus remain in their state of motion. This " inertia " is called inertia and applies equally to stationary and moving bodies. Whether a body moves in a straight line or at rest, therefore, depends only from the standpoint of the observer, ie, away from his frame of reference.

Again in the 17th century. examined Christiaan Huygens, the differences in the descriptions of a simple mechanical process in different reference systems. He described as an elastic collision of two objects from the bank and seen by a passing ship. This served him inter alia to clarify the term " quantity of motion " or pulse.

Until the early 20th century. several key variables were considered to be tacitly invariant under change of the reference system, such as spatial and temporal distances. Einstein postulated in the special theory of relativity in 1905, that all inertial frames are physically equivalent (see relativity principle) and that the speed of light is not depended on the state of motion of the light source. This directly follows the invariance of the speed of light. When the speed of light, however, in contrast to all other speeds in all the reference frames is the same as times and lengths can not be invariant.

Electrodynamics

Until the early 20th century. searched for a medium that allows the wave propagation of light. The inability to detect effects of the movement against this hypothetical ether, led to the preparation of the above-mentioned principle of relativity and the consequent theory of relativity. Accordingly, the notion of the ether had to be dropped. Einstein continued to explain the relationship of electric and magnetic fields, which had already been shown in the Maxwell 's equations in his special theory of relativity. Therefore go magnetic fields from the electric fields produced when changing the reference system, and vice versa.

Astronomy and Cosmology

Aristotle related exclusively to the geocentric reference system and formulated his laws of motion only in relation to this. Ptolemy followed him and created the to the 17th century into the dominant geocentric world view, which was, inter alia, by the Catholic Church strongly defended ( cf. Galilei process). Copernicus described the mid-16th century. the planetary system in the heliocentric reference system. Therein the observer moves with the earth, which in its reference system complicated translucent bow movements of the outer planets find a simple explanation. With the apparatus of Newtonian mechanics, the planetary motions could be very accurately predicted if one took as a point of reference the center of gravity of the solar system. Since this is not too far from the center of the Sun, the heliocentric world view is a useful approximate model.

If we imagine moving away from the Earth, another reference system seems to make sense, depending on the size scale: during the Earth-Moon system, the two celestial bodies move around the common center of gravity. In the reference system solar system, the earth moves on an ellipse around the sun. In the reference system Milky Way, the solar system is moving around the center of the Milky Way. Etc..

According to relativity theory, it is likely to give and no universal reference system for themselves. However, there is only one reference frame in the cosmic background radiation is isotropic. This could theoretically look at the " rest frame of the universe." This changes to the principle of relativity but nothing.