Aberration of light

The aberration of light ( from the Latin aberratio " distraction " ) called in astronomy a small apparent change of place of all the heavenly bodies by the finite speed of light. In addition, theoretical explanation of this effect is of great importance in the history of special relativity.

Types of aberration

This is also referred to as stellar aberration effect influences the star positions in three ways:

There is also a planetary aberration. This is the case if the position and velocity of the measured celestial body during the emission of light are accurately known, as with the planets of the solar system. This can be calculated from the angle of aberration correction, the position and duration of the planet to the time when the light is received by the observer.

Explanation

General aberration

The difference in the propagation direction of light in different inertial is most easily explained with the particle theory of light. The links are here similar to a moving observer, who wants to determine the direction of the onslaught of him raindrops.

Let there be given an inertial frame, in which a light beam emanating perpendicularly from a light source. ( The light source is initially as in this system dormant accepted for reasons of clarity, which corresponds to the circumstances at a light clock or the vertical arm of a Michelson interferometer. ) Dignity in addition to rest a telescope in the same inertial frame, it would have to precisely bring into the perpendicular direction to allow the light source to watch. In contrast, in the event that the telescope moves at a speed, it has to be tilted in the direction of movement in order to keep the beam at its center (left), because the light takes some time to scroll through the telescope. In contrast, in the inertial frame of the observer at the telescope gives the impression that the rays arrive inclined, and the light source ( pictured right) is not in its actual direction, but a small angle of aberration in the direction of the telescope motion moved. The aberration corresponding to the determination of the relative angle with each other inertial motion is derived by application of the relativistic velocity addition (see explanations).

Stellar aberration

The relativistic aberration formula is now generally during the transition from one inertial system to another, regardless of whether the light source at rest in any of these systems or not. For example, in astronomical observations is the light sources as stars or star systems, the exact state of motion is often not known. Because due to the great distance they shrink considerably changing their relative positions in the night sky to very small or even point-like objects whose proper motions are too low ( " fixed stars "). From the perspective of a stationary observer in the sun light from a distant star system would therefore always flow in approximately the same angle. Even large velocities within the observed stellar system ( such as the contrasting movements of double stars ) change in this circumstance anything because here are only those light rays of importance, the straight spread from the binary star system with exactly the angle to reach the observer at all. To determine the direction of a beam so only the relative location of the emission and the location of the receiver play a role. Therefore, the occasional idea is rejected, the angle of aberration from the actual stellar proper motion of the light source depends ( "active aberration "). This fact was pointed out already in 1844 by Herschel and later also by Emden ( 1926) and Eisner (1967).

Critical orbital velocity of the Earth around the Sun is about 30 km / s, which in 6 months, a maximum velocity difference of about 60 km / s is given. Thus, the fixed stars is of the earth as a whole vision in motion. Now it is not possible for the terrestrial observer to decide from a single measurement, whether the beam therefore inclined arrives with him, because a aberration effect is present, or whether the beam was tilted radiated by a star, the rest in the same inertial frame as the observer. Therefore, it is necessary that at a later time a second measurement is carried out, which is compared with the first measurement. The thus-measured annual change in the Aberrationswinkels equivalent (neglecting minor effects such as parallax) the result of relativistic aberration, the rate used is not the relative velocity between the star and Earth, but the relative velocity between the inertial frame in which rests the earth during the first measurement, and the inertia in which it rests in the subsequent measurement in the course of the path around the Sun.

Derivation

In classical mechanics, the velocity components of a beam in different inertial frames are related by the Galilean transformation. A beam, which propagates in an inertial system with exclusively in the y- direction, are obtained in a relatively moving second inertial system with the additional velocity component in the x- direction, while the component in the y direction is the same. The aberration is given by:

This result is only valid as an approximation, because as Albert Einstein showed in 1905, the Lorentz transformation and the relativistic velocity addition must be applied according to the special theory of relativity. As a result, the velocity components of resulting in x-direction and in y- direction, whereby the overall speed of the beam is the same. The correct relativistic aberration formula for this special case is thus:

Where the Lorentz factor. The deviation from the classical formula is so very small at low velocities compared to the speed of light. The same result is also obtained if one considers that light rays or photons have a momentum of (the energy ). Again, results in a transformation in a relatively moving system, a corresponding change in the momentum components according to the relativistic aberration formula.

For the case that the beam is inclined in the two systems, the overall aberration, which can be specified in a number of equivalent variants applies (the first variant is from Einstein, 1905 ):

When the angle in the first system and in a system with moving.

History

The aberration was discovered in 1725 by the English astronomer James Bradley ( and independently later by Eustachio Manfredi in Italy). He actually wanted to measure the annual parallax of the star etamin to finally get an idea about the distances of the stars. But he had the parallax ( well below 0.1 " ) with the means of the 18th century can not prove; this was achieved until 1838 Friedrich Wilhelm Bessel in a nearby star. However, Bradley was capable of the observed spatial shift - which ran at right angles to its expectation - based on Isaac Newton's corpuscular or emission theory by a simple addition of velocities to interpret. While this aberration was largely correct in a vacuum, it was inconsistent with the experiment of François Arago (1810 ), who used a prism to measure deviations from the normal aberration. According to the emission theory a change in angle would have to follow due to the different speeds of light, but no such effect was measured. Above all, however, the emission theory says a source dependence of the longitudinal speed of light ahead of what has been experimentally disproved many times, so that the emission theory is discarded (see corpuscular theory ).

In the 19th century, this statement has been replaced by the assumption that light was not a particle but a transmitted wave in the ether. The aberration ( and later, the Fizeau experiment ) played at the question of the relative motion between matter and ether an important role, because she spoke against a full entrainment of the ether by matter, and seemed to confirm the existence of a stationary or immovable ether. But even this statement had the problem that the wave fronts of the wave fronts actually no aberration should be subject to the ether. Therefore, one had to resort to the concept of energy transfer in accordance with the Poynting vector, so that the beam path is determined. An analogous explanation offered itself, as it was recognized that in the telescope, the wave packets are " cut " by interference from the wave fronts, the aberration could be applied to the wave packets. In addition, there is also the theory of a stationary ether contrary to Arago's null result, since in the media to deviations from the ordinary aberration due to the relative motion of earth - ether ( "ether wind " ) would come. However, Augustin Jean Fresnel was able to fix this problem by assuming that the ether according to the Fresnel osmotic drag coefficient is partially carried with the flow. While this model was mathematically successful, the adoption of a Äthermitführung ( and alternative Mitführungsmodelle as George Gabriel Stokes ) was very problematic and could never be carried out free of contradictions. Ultimately, the idea of an ether as a carrier medium for light had to be discarded because its state of motion could not be measured (see Michelson -Morley experiment).

These statements were eventually replaced in the context of special relativity, and much easier. Here it is irrelevant whether light is seen as a wave or a particle, because the wavefronts are " flipped " for a stationary observer on the Earth due to the relativity of simultaneity and thus result informally, the aberration of light. Similarly, the inclination of the photon path is calculated by the addition of the relativistic speeds. Albert Einstein wrote in 1952 that its direct path to SRT of electromagnetic induction, but also by the aberration of light and the Fizeau experiment was determined. And Robert S. Shankland reports a conversation with Einstein:

" He continued to say the experimental results Which Influenced had him most were the observations of stellar aberration and Fizeau 's measurements on the speed of light in moving water. "They were enough, " he said. "

"He [ Einstein ] continued that the experimental results that had influenced him the most, the observations of stellar aberration and Fizeau's measurements were the speed of light in moving water. "These were sufficient ," he said. "