Special relativity

The special theory of relativity (short SRT) is a physical theory of the motion of bodies and fields in space and time. It extends the original in mechanics discovered Galilean principle of relativity to the special relativity principle. The special principle of relativity, according to not only the laws of mechanics, but all the laws of physics in all inertial systems have the same shape. So the speed of light has the same value in any frame of reference. Moreover, it follows from the principle of relativity, that there is no absolute space and absolute time. Instead, hang lengths and times from according to the Lorentz contraction and time dilation of the movement of the viewer. Another important consequence of the SRT is the equivalence of mass and energy.

As birth of special relativity is the article " On the Electrodynamics of Moving Bodies " viewed, Albert Einstein published in 1905, following preparatory work by Hendrik Antoon Lorentz and Henri Poincaré. Since the theory is concerned with the description of relative motion and frames of reference with the relativity of time durations and lengths, they soon became known as " Theory of Relativity". In 1915 she was renamed by Einstein in Special Relativity, when he published his General Relativity (GR ). This includes different than the SRT also gravitation.

The SRT is confirmed by some classic experiments such as the Michelson -Morley experiment or the Kennedy - Thorndike experiment, as well as a range of modern tests.

• 3.1 Aberration
• 3.2 Doppler effect
• 3.3 Lorentz force
• 3.4 Indirect effects

• 4.1 Classical Mechanics
• 4.2 General Theory of Relativity
• 4.3 Quantum Theory
• 4.4 aether theories

Introduction

The laws of classical mechanics have the special property, in any inertial frame, ie unaccelerated in any moving system to apply equally ( principle of relativity ). This fact makes it possible to also drink ICE at full speed, for example, a coffee without the speed of 300 km / h has not any effect. The transformations ( conversion formulas ) which in classical mechanics from one inertial system to another is converted, hot Galilei transformations, and the property that the laws do not depend on the inertial frame ( So do not change at a Galilei transformation ) are called according to Galilean invariance. The formulas for a Galilei transformation follow immediately from the classical idea of ​​all the events underlying three-dimensional Euclidean space and one of them independent ( one-dimensional ) time.

End of the 19th century was however recognized that Maxwell's equations, which describe the highly successful electrical, magnetic and optical phenomena are not Galilean invariant. This means that the equations change in shape when a Galilean transformation is carried out in a system moving relative to the starting system. In particular, the speed of light from the reference system would depend if you looked at the Galilean invariance as fundamental. Maxwell's equations would thus be in a single reference frame is valid, and it should be possible by measurement of the speed of light to determine its own speed relative to this system. The most famous experiment, which sought to measure the velocity of the Earth relative to this excellent system is the Michelson -Morley experiment. However, no experiment could detect a relative movement.

The other solution of the problem is the postulate that the Maxwell equations are unchanged in each reference system and instead the Galilean invariance is not universally valid. Then enters the Lorentz invariance In place of the Galilean invariance. This postulate has far-reaching implications for the understanding of space and time, because the Lorentz transformations which leave Maxwell's equations unchanged, pure transformations of space (such as the Galilean transformations ), but rather this change space and time together. Same time, the basic equations of classical mechanics must be reformulated because they are not Lorentz - invariant. For low speeds, however, Galilei transformations and Lorentz transformations are so similar that the differences are not measurable. Therefore, the validity of classical mechanics at low velocities of the new theory does not contradict.

The special theory of relativity thus provides a broader understanding of space and time, according to which even the electrical dynamics no longer depends on the reference system. Their predictions were experimentally verified in many cases successfully and confirmed with high accuracy.

Lorentz transformations

The invariance of physical laws under Lorentz transformations is the central claim of the theory of special relativity. Therefore, in this section the physical effects of Lorentz transformations are clearly explained.

Since the laws of electrodynamics in each reference system apply equally unchanged, in particular also applies to their prediction of a constant vacuum speed of light. The light is so equally fast in each reference system. This follows directly from the Lorentz invariance, and it is often regarded as the most important property of the Lorentz transformations that they let the speed of light unchanged.

Einstein's thought experiment

To illustrate the various aspects of the Lorentz transformations, we use in the following a thought experiment, which goes back to Albert Einstein: A train passing through a station with speed. On the platform and in the train are different observers whose observations and measurements to be compared. They have watches and standards, as well as flashing lights, which light signals can be exchanged. We call the front in the direction of travel of the train " Zuganfang " and the other we call " end of train ". The Zuganfang first reached that end of the platform, we " rear " refer to as the. Later, he comes to the " front " at the end.

For the Zugpassagier it looks as if he would rest and move the platform with the speed and towards the rear of the train. According to the principle of relativity, his perspective is as accurate as that of the observer who is standing on station. Both reference frames are inertial and thus physically equivalent.

It is very important to note that each observer can make direct statements only about events that take place directly in place. However, he wants to know when an event has taken place at a different location, he can only rely on light signals which were sent out of this place. He can about the distance and the light transit time then infer the time of the event, because the speed of light is the same in all inertial frames.

Simultaneity

A major difficulty in understanding the effects of the Lorentz transformations, the concept of simultaneity. Therefore, to understand it is important to make clear that simultaneity of events at different locations is not defined a priori. To define simultaneous use is made of the speed of light, since this is the same in all reference frames. The light signals of two simultaneous events will reach an observer at different times when the events differently occur far away from the observer. When an observer, however, is equidistant from two events and reach light signals from these it simultaneously, it is called the two events themselves simultaneously.

This definition of simultaneity appears clearly understandable, but, together with the Lorentz invariance to a paradoxical effect: the simultaneity of two events at different locations depends on the state of motion of the observer.

This fact can be understood immediately with the thought experiment described above:

In the middle of the platform is a lamp. For an observer standing on the platform, is immediately clear: When the lamp is turned on, then the light reaches both ends of the platform at the same time: It has indeed to cover the same route in both directions. Now consider the situation from the perspective of a passenger of the train: The platform now moving with constant velocity v to the rear. The light, however, also opposite the train in both directions, the velocity c. At the time of sending both web Soaring are the same distance from the lamp. Thus, the front end of the platform is against the light beam, so that the forward running light covers a shorter distance until it reaches this end of the platform. Conversely, the rear end of the platform moves toward the trailing him light so that the light must travel a slightly longer path here until it has reached that end. Therefore, the light will reach the front end of the platform earlier than the rear, and thus the two ends of the platform can not be achieved simultaneously.

The observer on the platform and the observer on the train so do not agree on the question whether the two events "the light reaches the front end of the platform " and "the light reaches the rear end of the platform " are the same. However, since both observers moving uniformly, neither system is excellent: The perspectives of the two observers are therefore equivalent. Simultaneity is actually different for the two observers.

The simultaneity of events whose location changes only perpendicular to the direction of movement in both reference systems the same: If the lamp hanging halfway up the train, the light is the same for both the observer on the platform as well as for the observer on the train the sub- reach and top of the train -.

Lorentz contraction

From the relativity of simultaneity results in a different, paradoxical acting effect: Assume that the beginning of the turn (see Einstein's thought experiment ) triggers when passing through the front panel Growing a flash of light and the end of turn triggers just such a flash of light at the rear end of the platform from. The observer in the middle of the platform looks at the passage of the train both flashes simultaneously. Thus he notes that at the same moment at which the front of the train passes through the front end of the platform, and the rear end of the train passes through the rear end of the platform. He concludes that train and the platform at the current speed are equal.

For an observer in the middle of the train, the situation but is somewhat different: the flash of light from the beginning of the train reached him sooner than the flash of light from the rear end of the train, because he - from the perspective of the platform - runs counter to the front light flash and simultaneously removed from the rear light flash. Since the "back " event happened ( the pulling end, the rear end of the platform ) for him is later than the "front" ( the Zuganfang happens, the front end of the platform ), he concludes that the train is longer than the platform, because after the end of the train was still not arrived at the platform, as the Zuganfang has left him again.

Thus, for the observer on the train platform of the shorter and longer than the train for the observer on the platform. The principle of relativity states again that both sides are right: When is shortened from the perspective of Zugfahrers the (moving ) platform, then also from the perspective of the platform observer of the (moving ) train to be shortened. Lorentz contraction is only valid in the movement direction, since the direction perpendicular to the movement matches the simultaneity of events in the two reference systems. Both observers so agree, for example, about the height of the contact wire.

An indirect proof of length contraction also results from the problem of the electromagnetic field of a moving at high speed electric point charge. The electric field of this object is at zero or low compared to the speed of light speed just the Coulomb field of the charge, ie with a uniform distribution of the radial direction and having an electric field strength E = Q/R2, where Q is the charge strength and the distance R from the particles. With increasing proximity to the speed of light to focus on the other hand - because of the distance contraction in the direction of movement - increasing the electric fields in the transverse directions to the movement. Additionally now occur in addition to electric fields also ( asymptotically equally strong ) magnetic fields, which circle the axis of movement.

Time dilation

As distances of observers in different inertial frames are determined differently, the relative velocity of inertial systems must also be considered for comparison of time periods: The observer on the train (see Einstein's thought experiment ) stand at the rear of the train and at each end of the platform was a clock. The clock on the front end of the platform is set in motion when the beginning of the turn it happened, and the clock at the far end of the platform, when the end of the train it happens. As the train for the observer on the platform as long as the platform, the clocks are started simultaneously so after his term simultaneity. The clock on the front end of the platform is stopped when the rear end of the train it happens.

The observer on the train continues its clock in motion when it passes through the rear end of the platform, ie simultaneously with the start of the local Station Platform, and it stops when it passes through the front end of the platform, simultaneously with stopping the local Station Platform. After his term simultaneity, the clock is going on at the front end of the platform opposite of the rear end of the platform and thus also towards his clock, because according to his concept of length of train is longer than the platform. The amount of time that it measures for its journey from the rear to the front end of the platform, so is less than the duration of which is indicated by the clock at the front end of the platform when it passes them.

The observer on the platform so looking at the displays of watches that the observer in the train measures a shorter period of time than he did, since after his simultaneity refers to the start and stop times of the clock of the observer in the train and the clock at the front end of the platform are the same, are the time periods of equal length after his term simultaneity. He therefore concludes that the clock of the observer is going to slow the train. After the simultaneity concept of the observer on the train, however, the start times of the clocks do not coincide, so that he does not make this observation.

This observation can be reversed even by one each clock at the beginning and at the end of the train mounts and starts at the same time after the simultaneity concept of the observer on the train, if the beginning of the train passing through the front end of the platform. From the perspective of the observer in the train results then that time passes more slowly on the platform as the train.

Again, it can not decide which of the two has observer right. Both observers move unaccelerated relative to each other and are therefore equal. Periods are different for the two observers, and for both observers, time passes in their respective rest system the fastest, while they slowly passes in all relatively moving systems. This effect is called time dilation. The time which reads each observer on its own clock, is called closing time. This measured with a " entrained clock " time always results in the shortest time possible, unchanging value among all time periods measured for two at a short distance consecutive events in inertial frames with different relative velocities. All other values ​​were defined as' dilated time ".

Concretely: The entrained Watches "tick" for train passengers quickly (ie show a greater time ) on similar station clocks, where the train rushes past with velocity v. If increased its speed, and the (generally very low ) dilation of time indicated by the station clock time is getting bigger, while the train from measured time ( the proper time ) always remains the same. In contrast to this time dilation is a measure of length from the perspective of train passengers has the value L, as seen from the station clock, and shortening (length contraction, see above) appears. The effects are enormous: small: Namely, an interval dτ the proper time compared to the time period dt, which is indicated by the station clock, only a little smaller ( applies more precisely, the train speed is ( for example, 80 km / h), c the other hand, the extremely much higher speed of light ( ~ 1 billion km / h).

The proper time is, moreover, " the " fundamental invariant for the change of coordinates given above ( Lorentz transformation → Lorentzinvariante ).

An immediate consequence of time dilation is that the elapsed time depends on the chosen path. Suppose someone gets into the train and moves to the next station. There, he gets into a train, which travels back to the starting point. Another observer has been waiting in the meantime there on the platform. After returning comparing their clocks. From the perspective of the observer remained at the station, the traveler now has experienced a time dilation both on the outward journey and on the way back. Thus, the clock of the traveler goes from the perspective of waiting by now. From the perspective of the traveler, however, the waiting experiences a time dilation, so now need to assess at first glance, the clock of waiting from the perspective of the traveler. This paradox is called twin paradox. In this case, however, the situation is not symmetric because the traveler is switched, has so changed his frame of reference. Thus, in contrast to the observer on the platform, the traveler is not in an inertial system. Therefore, the clock of the traveler actually goes by.

A version of this paradox was actually demonstrated in an experiment to check the special theory of relativity. The measured time periods of two atomic clocks were compared, one of which in an aircraft orbited the Earth, while the second remained on the clock start and destination airport. The " residual " clock showed a small but accurately measurable speed increase. (see Hafele - Keating experiment)

Relativistic velocity addition

If now in the train the conductor at a constant speed forward running ( see Einstein's thought experiment ), its speed for an observer on the platform according to classical mechanics is simply defined as the sum of the running speed and the speed of the train given. In relativity theory, such a simple addition does not produce the correct result. From the platform looking at the time, for example, from a car needs the conductor to the next, because of the time dilation is longer than for the train passengers. In addition, the car itself is seen from the platform Lorentz shortened. Added to this is that the conductor runs forward, so the event " reaching the next car " earlier takes place in the train: Due to the relativity of simultaneity, this means that the event for the observer on the platform is later than for the train passengers. Overall, therefore, all these effects result that the speed difference of the conductor to train for the observer on the platform is less than for the observer on the train. In other words: The conductor is seen from the platform slow road as it would result saw the addition of the speed of the train and the speed of the conductor from the train. The formula with which to calculate this velocity, ie relativistic addition theorem for velocities.

The extreme case occurs when one considers a current forward light beam. In this case, the slowing effect is so strong that the beam of light from the platform again has the speed of light. The constancy of the speed of light is indeed the basis of the theory of relativity. This also ensures that the conductor on the platform always slower than the speed of light moves from the perspective of the observer, if its running speed in the rest frame of the train is less than the speed of light: Suppose the conductor holds a flashlight at a mirror at the end of the car and runs slower than light. Then, viewed from train from the light beam is reflected and hits the guard before he reached the end of the car. If now its speed perceived from the platform as superluminal, so the conductor would reach the end of the car in front of the light beam and thus not held the meeting with the light beam. Such a meeting at the same place at the same time, however, observers independently and thus results in a contradiction. So the relativistic addition of two speeds below the speed of light always produces a result below the speed of light.

Now the conductor can also run in the train not only forward but also backward. In such event, the event " reaching the next car " later in the train instead and thus " premature" for the platform - observer relative to the train passengers, while the other effects still act " slowing down ". The effects cancel each other out just when the conductor at the same speed runs in the train backwards as the train travels: In this case, the theory of relativity came to the conclusion that the conductor is at rest relative to the platform. For higher speeds, the observer now looks back at the platform a higher speed than it would be expected according to classical mechanics. It goes back to the extreme case of the rearward light beam which in turn is also seen from the platform exactly traveling speed of light.

Momentum, mass and energy

In the station (see Einstein's thought experiment ) there is also a games room with pool tables. On one happened when the train goes by, just following, from the perspective of the observer described on the platform: Two billiard balls, each having the same absolute speed as the train, but to move perpendicular to the track one another, encounter completely elastic together, and in such offset so that they move after the collision parallel to the track, the red in the direction of the train ( and in the reference system at rest ), the blue in the opposite direction.

In classical mechanics, the momentum of an object is defined as the product of mass and velocity of the object. The total momentum, which is obtained by simply adding the individual pulses, is a conserved quantity. In fact, the above impact of the so- defined pulse from the platform view is obtained: As the balls move even after the collision with the same speed against both before, is the so- defined pulse before and after the collision is zero.

Seen from the train roll the balls before the collision at an angle toward each other: parallel to the track, both have the speed of the platform ( since they move along with the platform ), and perpendicular to the track, they have opposing speeds ( this component is based on the movement of the balls relative to the platform perpendicular to the train ). The total momentum of the two balls perpendicular to the track is therefore zero, parallel to the track of the total momentum of ball mass is twice times the platform speed.

After collision, the red ball now has the speed - and hence the pulse - zero ( from the platform point of view it is with train speed in the direction of pull was on the way), so now the blue ball has to bear the entire pulse. To determine the speed of the blue ball, but looked at in the previous section relativistic velocity addition must now be used, and - as stated above - a lower speed than twice the speed of the platform has this ball now ( = train speed ). It is thus clear that the classical momentum conservation is no longer valid. To produce the conservation again the relativistic impulse is used which increases more than linearly with speed. For the same reason, the kinetic energy at high speeds must increase faster than it does according to classical mechanics.

The equivalence of mass and energy states that one can read the rest energy of each particle, body or physical system to its mass. The rest energy is proportional to the mass. The factor which connects these two values ​​is the square of the speed of light:

Because you can see from the mass the rest energy, you will understand why in radioactive decay or nuclear fission, the daughter together have less mass than the original Core: Part of the initial rest energy is optionally converted into kinetic energy of the daughter particles and other radiation.

Suction. relativistic mass and rest mass

Assigns one by

The velocity-dependent energy of a particle or body in motion also calculated a mass, it is called relativistic mass. It is not independent of the reference system fixed property of the particle, but depends on its speed (or the observer ) from. In the rest frame coincides with the mass, which is therefore sometimes referred to as rest mass. With sufficiently strong approaching the speed of light is arbitrarily large. With the relativistic mass, the relativistic momentum in Newton's mechanics as being a " mass times velocity ". The fact that the momentum of a particle to grow indefinitely, while its speed is limited by the speed of light upwards, is effected in this image by the relativistic mass correspondingly increasing. In the field of relativistic velocities a particle to a force perpendicular to its direction of flight reacts so that after the Newtonian mechanics just have to write the relativistic mass him. For a force in the direction of the velocity, however, one would again take another mass, and for other directions, the acceleration is not even parallel to the force.

The term relativistic mass is therefore avoided in modern physics from these and other reasons. So you can not measure with a scale in the gravitational field of its value. Finally, one has for the relativistic mass up to the constant factor has the name power. The term mass is used to refer, as in Newton's physics, a property of the particle, body or physical system, which is independent of the reference system, unlike the parameters speed, momentum and energy.

Of time and space for space time

Given the above relativistic effects naturally arises the question of how these effects are to be interpreted. Looking at the time as a fourth dimension to, can be seen along with the three dimensions of space, the four-dimensional space-time, but does not provide the four-dimensional Euclidean space, but the so-called Minkowski space The difference arises from a mathematical peculiarity of the metric ( better pseudo - metric ) of Minkowski space - they can have both signs. This results in the difference of rotations in four-dimensional Euclidean space and the below " rhombohedral " Coordinate transformations of the four-dimensional space-time. At the same time still results in such a way that in the theory of relativity is a difference between space-like and time-like or - at Zeitartigkeit - may remain between " past" and "future", depending on the sign of the metric of the point in Minkowski space or by the sign of its time coordinate (see also: light cone ).

The motion of an observer is reported in this four-dimensional space-time to a curve ( the so-called world line of the observer ) and leaves in Minkowski diagrams. Here, one sees that the present change of the reference system in any case ( both mechanically and classically - relativistic ) is accompanied by a " tilt" the time axis. This describes the " relativity of GleichORTigkeit ": But while the observer finds in the train, for example, that his case remains on him in the luggage rack all the time in the same place, it is clear to the observer on the platform that the same case with the train moved, consequently therefore just does not stay in the same place. What distinguishes the Minkowski space theory of relativity Newton's space and time, is the fact that for each other moving frames of reference, the simultaneity is relative, as described above. This means that according to the theory of relativity (as opposed to classical mechanics ) along with the time axis the spatial axis is tilted.

A well-known movement in the two coordinate axes to be changed, the rotation in space. The picture illustrates the difference between the known rotation and the specified reference system convertion: While in rotations in space both axes are rotated in the same direction, rotated in a reference system converting spatial axis and time axis in opposite directions: From the original square creates a surface equal rhombus, with the condition of the surface equals the constancy of the speed of light corresponds. The long diagonal ( an angle bisector of the axes, called the first median) remains unchanged. But just describes the path of light, their increase is the speed of light. The immutability at reference system change so just means that the speed of light is constant.

From these considerations it follows that it is useful to consider space and time as a unit, such as length, width and height form a unit, namely the three-dimensional space. The four-dimensional unit of space and time is called space-time. It is therefore no longer possible, independent of the observer to specify a particular direction as the direction of time, just as in space no unique ( independent observer ) "Front" is. So run, for example, both the black and the yellow timeline " rolling " time axis in the direction of time. However, it is - in contrast to the normal space - in space-time is not possible to rotate the time direction to the direction in space, or even the time " to turn ", ie to exchange past and future. Due to the constancy of the diagonals of the limited areas of the diagonals are always converted to yourself. This corresponds to the area of equality of the drawn network segments.

On closer inspection of the rotation (left picture) you can see that each coordinate square is again converted into an equal square ( the rotated square is top right of the origin hatched in the figure). In addition, the intersection of the rotated y- axis (yellow line ) to the intersection of the rotated first parallels the x-axis (light brown line ) equidistant from the origin as the non-twisted intersection. The y value of this intersection point is, however, smaller than for the non-rotated intersection. This leads to the phenomenon of foreshortening when the line is viewed from the x-direction.

Turning now to the right analog image so you can see that also here the coordinate square is converted into an equal area, but the new surface is no longer square, but rhombohedral. This has the effect that the intersection of the "rotated " time axis ( yellow) with the next parallels the rotated axis in space (light brown) higher, ie later than in the untwisted case. Suppose now that the space axes are " set " at each tick of a clock, one sees immediately that the clock in the "rotated " coordinate system, ie relative to the observer moving clock, apparently goes slower ( between two ticks more time passes the observer ). From the analogy to the rotation is also clear that it is also this is just a " perspective " effect. This explains quite naturally the apparent contradiction that both observers see the clock of the other run slower. The foreshortening is mutually perceived, without that this would lead to contradictions.

A major difference of the reference system change for rotation, however, is that for the variable " time " instead of shortening an extension ( elongation: time dilation ) is perceived. This can be readily seen by the above comparison: With the rotation in the space of intersection of the yellow and light brown line moves down ( foreshortening ), while the reference system converting upwards.

Effects

The already declared effects of the Lorentz transformations can be partially observed directly. In particular, the time dilation has been confirmed by many experiments. This increases the lifetime of unstable elementary particles in particle accelerators, which was mainly detected in the relatively long-lived muons. In addition, an atomic clock remaining on the ground watches was analogous to the twin paradox placed in an airplane and a very small, but measurable retardation compared with observed.

However, the special theory of relativity also has consequences that are not so obvious consequences of the Lorentz transformations. Some of these effects are shown here.

Aberration

When an observer moves faster and faster, the light beams similar to raindrops come to him more and more opposed from the beginning. It changes the angle at which a light beam is incident on a moving observer. Originally explained this phenomenon, the aberration of light, Newton's corpuscular theory of light with just as with raindrops. In the special theory of relativity is replaced by the now classical relativistic velocity addition. It follows that a moving observer watching after the corpuscular another angle of aberration as by the special theory of relativity and would measure different speeds of light of the incident light, depending on the speed of movement.

After the observation that light like a wave ( wave theory ), but you could not understand the aberration. When a light wave the wave fronts would not be changed when the observer moves in the Newtonian physics. Only in the special theory of relativity, the wave fronts change due to the relativity of simultaneity as particle trajectories, and aberration is understandable, whether it occurs in waves or particles.

Doppler effect

For waves that propagate in a carrier medium such as sound waves, it is used for a movement of the source or the receiver with respect to the carrier medium to a change of the measured frequency. In this case, the effect is different, depending on whether the source or the receiver is moved relative to the carrier medium. In general, the frequency is greater when moving the source and receiver to each other, because then more peaks are detected by the receiver in the same time. Accordingly, the frequency becomes smaller as the source and receiver move apart. This frequency shift is called the Doppler effect. For sound waves, the receiver can be faster than the waves and escape them altogether, and the source can be ahead according to their own signal, resulting in the sonic boom.

For light waves, in a vacuum there is no relative movement to the carrier medium can be measured, because the vacuum speed of light is the same in all inertial systems. , The Doppler effect of the light may thus depend only on the relative velocity of the source and receiver, that is, there is no difference between the movement of the source and the receiver. Since relative motion is not faster than light in a vacuum speed possible, there is no light in the vacuum phenomenon analogous to the sonic boom. In media such as water, where the propagation speed of light is less than that in vacuum there with the Cherenkov effect on the sonic boom similar phenomenon.

It is clear that the time dilation has an influence on the frequencies that measure two relatively moving observer. Therefore, the light is also a Doppler shift occurs, when the observer is moving perpendicular to the direction in which the source is located. This effect is called the transverse Doppler effect. It must be noted that the definition of the angle of incidence is dependent on the observer due to the aberration. Therefore, occurs depending on where the reference system the light is incident perpendicular to an increase in the frequency ( blue shift ) or a decrease ( red shift ).

From the perspective of the rest system of the receiver, the time in the system of the source passes slower due to the time dilation. This means that he in his system a lower frequency measures as an observer at rest relative to the source, so it measures a redshift. This effect is referred to as transverse Doppler. The stationary source to observer explains the effect so that the receiver does not move vertically at the time of receiving the direction of the source, but away from the source. The light beam hits the receiver in his view, from behind which he explains the redshift.

From the perspective of the rest system of the source passes according to the time in the rest frame of the receiver slowly. Therefore, the receiver measures a higher frequency, that is, a blue shift, when the light is in the rest system of the source to the moving direction is perpendicularly incident to the receiver. The beneficiary shall certify this blue shift again different, because in his view it is not true of the light beam at a right angle, but obliquely from the front. So he will explain the blue shift by approaching the source.

Lorentz force

Normally, it is assumed the theory of relativity would only relevant at very high speeds. The explanation of the Lorentz force is an example of that already can result from low speeds visible differences to classical physics.

An electron is moving parallel to a laboratory at rest and charge neutral wire in which an electric current flows, the electrons move inside the wire at the same speed in the same direction as the single electron outside. By the current, the wire has a magnetic field. Since the electron moves perpendicular to the magnetic field, it is attracted by the Lorentz force to the wire, as the picture shows.

In the rest frame of the electron, the conductor, a magnetic field has indeed still (because its electron rest, but for the positively charged residue moves from atomic cores themselves ), but since the electron relative to itself, of course, rests, it experiences no Lorentz force. So there is apparently no explanation for the acceleration of the electron, which would be contrary to the principle of relativity.

However, considering the statements of the theory of relativity, it is found:

• The electrons are moving in the rest frame of the wire, so lorentzkontrahiert. That is, in the " wire - frame of reference " in a given volume of more electrons than the " electron - reference ."
• In the atomic cores, it is just the reverse: In the " Electron- reference system " are in a given volume more atomic cores to find than in the " wire frame of reference ", since the ions rest in the latter.

In the electron reference system are therefore per volume less electrically negative electrons and electrically more positive atomic cores than in the wire - frame of reference. There was but the same amount available from both the wire - reference system (the wire was yes, by assumption, a total of uncharged), outweighs the electron - reference system, the positive charge, ie, the wire is positively charged. Since positive and negative charges attract each other, it is clear that the electron is attracted to the wire.

This observation shows that are transformed by Lorentz transformations magnetic fields partially in electric fields. That allows to return the Lorentz force to electrostatic attraction. This effect has a measurable impact even for small speeds - the average electron velocity in the wire direction is typically less than a millimeter per second, which is much smaller than the speed of light.

Indirect effects

The indirect effects of the detection time dilation of the so-called " Myonenschauern " include muons have an average life of Δτ ~ 2:10 -6 s, are generated in about 30 km altitude of the cosmic radiation in large quantity and reach in just such amount of the earth's surface, although they - even if they are moving at the speed of light - after a few miles, almost all decay need to be. This contradiction is resolved by the finding that for an observer on the Earth's surface is not the proper time Δτ, but the observer time t = Δτ / (1 ​​- ( v / c ) 2) 1/2 is relevant to what the because of the very small denominator measured values ​​results. One can instead take advantage of the muons seen by the shorter path (length contraction) as the reason.

Relation to other theories

Classical Mechanics

The special theory of relativity takes the place of the dynamic laws of classical mechanics. However, the laws of classical mechanics for centuries have been repeatedly confirmed very precisely. However, always speeds were considered, which were much smaller than the speed of light. For such small speeds, the special theory of relativity should so the same results as classical mechanics. This means that the Lorentz transformations for very small velocities must give the Galilean transformations. It follows immediately that the momentum, kinetic energy and all other sizes for small velocities take the well-known classical values ​​.

When the train in the above thought experiments much slower drives than the speed of light, the difference between the concepts of simultaneity observer is very small. The result is that the other relativistic effects are so small that they can hardly observe. So if the time dilation is so small that it goes unnoticed, only the spatial coordinates are apparently transformed by the Lorentz transformation. If the length contraction remains unnoticed, the Galilean transformations remain exactly left.

This illustrates that the special theory of relativity for very small velocities yields the same results as classical mechanics. The fact that an old, proven theory must be contained in a new theory is called the correspondence principle. Thus, the special theory of relativity satisfies the correspondence principle with respect to the classical mechanics. For non - mechanical, electromagnetic processes, which is not always the case, as illustrated by the statement of the Lorentz force.

General Theory of Relativity

In consideration of gravitational effects, the general theory of relativity takes the place of the special theory of relativity. In this respect also a correspondence principle must be satisfied, since the predictions of special relativity are confirmed experimentally very precisely.

In contrast to the special theory of relativity space-time is curved in the general theory of relativity and the theory must therefore be formulated strictly local. For large distances, therefore deviations from the statements of special relativity may result. The treatment of gravitation is valid only for small distances, especially in the vicinity of large masses, or more generally in the vicinity of large energies, the theory of special relativity.

A particularly illustrative effect, showing the limit of the validity of the special theory of relativity, is the Shapiro delay: For light that is near, sent over to a body of great mass such as the sun, measures an observer, the further from the solid body is removed, a smaller speed than the expected vacuum speed of light. An observer directly at the light beam on the other hand measures the "right" speed of light. Apparently, the laws of special relativity, such as the constancy of the speed of light apply only in small areas. In the general theory of relativity, thereby, the clear that the spacetime is called a Lorentzian manifold or a Riemann space, at each space-time point locally by a Minkowski space, however - can be described - this is the flat spacetime of special relativity.

Quantum theory

In contrast to the general theory of relativity, in which is still unclear how they can be merged with quantum physics to a theory of quantum gravity, are specifically relativistic quantum theories to the standard tools of modern physics. In fact, many experimental results can not be understood if one does not take into account both the principles of quantum theory and the space-time understanding of the special theory of relativity.

Already in the semi-classical Bohr - Sommerfeld model of the atom, it is possible only with the inclusion of special relativity to explain the fine structure of atomic energy levels.

Paul Dirac developed a wave equation, the Dirac equation, which describes the behavior of electrons taking into account the special theory of relativity in quantum mechanics. This equation leads to a description of the spin, a property of the electron that is only determined by the non-relativistic quantum mechanics, but can not be explained, and for the prediction of the positron as the antiparticle of the electron. Also, the fine structure can not be explained as in the semi-classical models by nonrelativistic quantum mechanics.

However: Just the existence of antiparticles shows that the association of special theory of relativity and quantum theory simply can not get out a relativistic version of the usual quantum mechanics. Instead, a theory is needed, in which the particle number is variable - particles can be produced and destroyed ( the simplest example: the pairing of particles and antiparticles ). This is performed by the ( relativistic ) quantum field theories such as quantum electrodynamics as a special- relativistic theory of the electromagnetic interaction and quantum chromodynamics as a description of the strong force, which holds together the building blocks of atomic nuclei.

In the form of the Standard Model of elementary particle physics relativistic quantum field theories form the backbone of today's physics of elementary particles. The predictions of the Standard Model of particle accelerators can be tested with high precision, and the unification of special relativity and quantum theory is among the most rigorously examined theories of modern physics.

Aether theories

The special theory of relativity is often interpreted in the literature as a counter- theory to the ether. The most ether theories of special relativity are incompatible and are refuted by the experimental confirmation of the predictions of special relativity.

An exception is the Lorentz ether theory which had been simultaneously developed by Hendrik Antoon Lorentz and Henri Poincaré before and with the special theory of relativity. This theory is identical to the special theory of relativity in their predictions, however, assumes that there is an absolutely resting reference system but can be distinguished by any observation of any other frame of reference. This theory is now considered obsolete, because the postulate of unobservable rest system violates the principle of economy. In addition, it is still unclear whether the Lorentz ether theory of general relativity is compatible.

Other concrete applications

Other direct applications are already therefore not obvious because they would usually occur only when approaching the speed of light. There are so more numerous indirect applications, of which - not exhaustive - some are mentioned here:

• Throughout the chemistry of the electron spin is essential that presupposes the relativistic quantum mechanics ducks ( Dirac equation).
• In particle physics, a relativistic treatment is usually required.
• Among the more indirect applications include many irradiation and diagnostic methods of medicine which is based on X-ray or nuclear spin effects, for example.
• Among the so-called " ultra-relativistic effects " include those based on the propagation of light or other electromagnetic waves method of radio, television and telephony technologies.
• Furthermore, the equivalence of mass and energy is one of them, ie the whole on the equation E = mc2 based nuclear technology.