# Special relativity theory

special relativity theory is a physical theory over space and time, which have consequences, whose speed cannot be neglected in relation to the speed of light in particular for the kinetics and dynamics of objects.

Special relativity theory dissolved contradictions,between Maxwell electrodynamics and the result of the Michelson Morley experiment had arisen. After pre-working Henri Poincaré and Hendrik Antoon Lorentz it 1905 by the publication „for the electrodynamics of moved bodies “(facsimile) by Albert Einstein one justified.

InContrast to the landläufigen opinion is the statement of relativity theory not „everything is relative “. Some is relative, which was regarded before as absolute, however is based it in the core on a postulate „of the Nichtrelativität “in it: The formulation of the laws of nature depends not on the reference system, is therefore not relative, but absolute and/or. invariantly. The question, which is treated in relativity theory, is called: It gives size in physics, which is regarded in classical physics as absolute, however inReality relative, i.e. on the viewer are dependent (for example „simultaneousness “). In addition, this question is only one part „of relativity theory “. Indeed Einstein with the designation was never lucky „relativity theory “for its theory.

Note: This text does withoutconsciously as far as possible on formulas. The article offers a further formula-free entrance over Minkowski diagrams. Who is interested in the appropriate effects in formulas, can follow the existing left to the appropriate single topics. The einführende represents article relativity theory, in whichstands for internal connection special relativity theory with general relativity theory likewise justified by Einstein.

## Why a new theory of space and time?

The laws of the classical mechanics have the special characteristic that they apply in each inertial system, thus in each unaccelerated moved system, equally (relativity principle). This fact is it, itone e.g. permits, also in the ICE during full travel. to drink, without having to worry about it that one is straight with 300 km/h on the way, and her it permits a coffee also to live on earth without itself lastingto care for the fact that the same circles with high speed around the sun. The transformations (conversion formulas), with which in the classical mechanics by an inertial system into the other one are converted, are called Galileitransformationen, and the characteristic that the laws not of the inertial systemdepends, thus with a Galileitransformation does not change, calls one according to Galilei invariance. The formulas for a Galileitransformation follow directly from the classical conception of a Euclidean space and a time independent of it.

End 19. Century it was however recognized thatthe electrodynamics, which very successfully describes the electrical, magnetic and optical phenomena, is not Galilei invariant. If one assumes now the fact that the classical conceptions of space and time are valid means this that it for electrodynamics a preferential reference systemto give must. In particular electrodynamics forecasts that for electromagnetic waves (thus in particular for light) the propagation speed in the vacuum (speed of light) has always a fixed, constant value. If it now a preferential reference system (called ether system, because one itselfat that time presented, the light waves were waves of a medium, which was called ethers) gives, in which electrodynamics applies, then should only in this the light with speed of light on the way be. Thus it should be possible by measurement of the speed of light, thoseown speed in relation to the ether system to determine (to the comparison: If we drive apart from a course, from which we know that he - relative to the earth - is with 200 km/h on the way, it itself however relative to us only with 150km/h moves, then we that we move with 50 km/h relative to the earth in the same direction) know.

On the basis of this consideration there were some experiments, which tried, to measure the speed of the earth in relation to the ether system. The most famousof it the Michelson Morley attempt, into by interference the times, is which need rays of light in different directions, with one another to be compared. All these attempts could prove however no movement.

Einstein's solution of the problem was now the postulate that alsoelectrodynamics (and at all each law of nature) in each reference system invariably applies, and the reason, why mathematically obviously did not function, because of a wrong conception of space and time was. Special relativity theory supplies an alternative understanding of space and time,with also electrodynamics no more of the reference system does not depend. Their forecasts were experimentally successfully examined.

Mathematically the changed conceptions are expressed over space and time in changed formulas, in order to convert from an inertial system into the other one. Instead of thatGalilei-Transformation takes over this task now the Lorentztransformation, and accordingly the independence of the physical laws from the inertial system means now truck time invariance. Electrodynamics is as standard equipment lorentzinvariant.

## Relativistic effects

if electrodynamics in each reference system equally invariably applies, thenin particular also their forecast for a constant vacuum speed of light in each reference system applies. The light is thus in each reference system equivalent fast.

From this fact some effects can be derived, which contradict the classical conception of space and time.

### Relativity thatSimultaneousness

the statement of the special relativity theory, which probably contradicts the used conceptions most strongly, is the relativity of the simultaneousness: The simultaneousness, or more generally the temporal sequence of two events depends on the observer.

This fact leaves itself direct with the following Thought experiment understand:

In the center of a platform a lamp stands. For an observer, who stands on the platform, is directly clear: If the lamp is switched on, then the light reaches both ends of the platform at the same time: It has into bothTo put back directions the same way.

We regard now the situation from the view of a passenger of a course driving past with constant speed: The light possesses also in relation to the course in both directions the speed of C. At the time of sending are both platform endsequivalent far from the lamp removes. The platform moves however with constant speed of v to the rear. Thus the front platform end comes to meet the ray of light, so that the light running forward puts a shorter distance back, to it this platform endreached. Turned around the rear platform end moves toward the hastening after light, so that the light must put a somewhat longer way back here, until it reached this end. Therefore the light will thus achieve the front platform end in former times asthe rear, and both ends of the platform are thus reached not at the same time.

The observer at the platform and the observer in the course are thus not itself united over the question whether „the light reaches the two events the front end of thePlatform “and „the light achieves the rear end of the platform “is simultaneous. The observer in the course takes events farther back (thus in the direction, in which for it the platform moves) relative to the observer at the platform „late “truely, andall the more strongly, the further in the back the event takes place. Turned around events find further in front (thus in the direction, from which the platform comes) „premature “instead of.

With the relativity principle this is compatible. The direction, from for the observer inCourse the platform comes, is the direction, into which from view of the observer at the platform the course drives. Events are corresponding in this direction in relation to the description of the observer in the course are late for it.

The simultaneousness of events, their placeonly perpendicularly to the direction of motion changes, is alike in both reference systems: If the lamp on half height of the course hangs, then the light becomes simultaneous both for the observer at the platform and for the observer in the course the underand top side of the course reach.

More to the topic see under relativity of the simultaneousness.

### Zeitdilatation

taking we now on, at the platform stands also a station clock, whose second hand - from view of the observer at the station - moves on each second a line.We have thus a set of events: „The second hand jumps on 1 “, „the second hand jumps on 2 “, etc. The observer in the course sees now also the station clock. However each time, if the pointer moves on, the station clock has itself alreadyPiece with the station to the rear moves. Since now events, which take place farther back, from its view take place relative to the view of the observer at the platform late, all the more, the further in the back it takes place, it follows from the fact that thoseClock for it ever more strongly follows - in other words: it goes too slowly. The same applies naturally also to all other procedures on the platform. One calls this effect Zeitdilatation.

The Zeitdilatation applies - according to the relativity principle - alsoturned around: If the observer in the course leads a clock with itself, then this clock goes - like also all other procedures in the course for the observer at the platform more slowly. The fact that both observers see the other one slowed down, likesappear at first sight paradoxical. However one must hold oneself before eyes that the times are based in each case on different places. If e.g. at the platform a whole set of clocks are set up, and the traveler in the course its clockalways with the straight clock driving past at him compares (thus therefore always another), then it agreeing with the observer at the platform will state that this proceeds ever more strongly opposite its clock. However it becomes anotherReason call: While the observer at the platform attributes this to the Zeitdilatation of the observer in the course, the observer in the course will state that the clocks at the platform run all more slowly than its clock, but the clocks all the more stronglyproceed, the further they stand in front. Thus it always compares its clock with a new clock, which continues to proceed still.

To note it is here that the Zeitdilatation does not refer to directly by the observer seen the hand movement. For the latters must to be also still considered that the light from the clock needs a time of different lengths to the observer depending upon distance, which leads for a moved clock to an additional change of the directly observed speed. This Doppler effect leads those for clocks,to come on the observer, to an apparent acceleration of the clock. In order to derive the Zeitdilatation from the directly observed data, the light running time must be out-counted only.

For the proof of the Zeitdilatation therefore the transversal Doppler effect is particularly suitable. Here becomes perpendicularly to the direction of motion measured, so that the distance of the source (clock), which can be measured, changes momentarily not substantially. Nonrelativistically one might determine no Doppler effect in this case at all. Experiments show however a slowing down, which is to due direct to the Zeitdilatation.

### Dependence of the time on the way, proper time

a direct consequence of the Zeitdilatation is that the applied time depends on the way. Assumed, someone rises into the course and drives up to the next station. There it rises into a course over, that againto the starting point goes back. Another observer waited there in the meantime at the platform. After the return they compare their clocks. From view of the observer left now the traveler has both with the Hinfahrt and with the return trip oneZeitdilatation experience. Thus its clock follows now. This is apparently contradictory (paradoxically), since also from view of the traveler the staying experiences a Zeitdilatation and leaves itself thereby to explain that the traveler transferred, thus its reference system changed.Details see under twin paradox.

One calls the time, which reads off each observer on its own clock, proper time. It concerns thereby the only time, which can be defined clearly.

### Lorentzkontraktion

turns we us again the observer upthe platform too. When course drives through, determines it that in the same moment, to which at the beginning of the course passes the front end of the platform also the rear end of the course the rear end of the platform it happens. It closes,that course and platform are equivalent long.

For the observer in the course the situation presents itself however completely differently: Since „the rear “event (the course end passes the rear platform end) for it happens later than „the front “(the course beginning happenedthe front platform end), he that the course is longer than the platform, closes because finally the course end at the platform had not still at all arrived, when the course beginning left him already again.

Thus that is for the observer in the coursePlatform more briefly and/or the course longer than for the observer on the platform. The relativity principle demands that both is the case: If from view of the course driver (moved) the platform is shortened, then platform observer must also from view (moved)Course shortened its.

One calls this Verkürzung of moved articles Lorentzkontraktion.

The Lorentzkontraktion applies only in direction of motion, since to the direction of motion the simultaneousness of the events in both reference systems agrees perpendicular. Both observers thus e.g. are itself. over the height of theContact wire unite.

### Relativistic speed addition

taking we now on, in the course runs a person, e.g. the Schaffner, with constant speed forward. How quickly is it now seen from the platform on the way? In the Newton's mechanics the situation is simple: ThatCourse puts a certain distance back in a given time, in addition comes the distance, which went to the Schaffner in the course. Thus the speed of the Schaffner in the course adds itself simply for the speed of the course. If thus the course also100 km/h on the way is and the Schaffner in the course with 1 km/h runs, then it has 101 km/h relative to the platform.

In relativity theory the thing looks however differently. From the platform the time, those is regarded the Schaffnere.g. from a car to the next needs, because of the Zeitdilatation longer than for the course traveler. Besides the car is truck-time-shortened seen from the platform. In addition still that the Schaffner runs forward, thus the event comes „reaching the nextCar “in the course takes place further in front: Due to the relativity of the simultaneousness this that the event for the observer at the platform takes place later, means as for the course traveler. Altogether thus all result in these effects that the speed difference of the Schaffner to the coursefor the observer at the platform is smaller than for the observer in the course. In other words: The Schaffner is seen from the platform more slowly on the way, than it the addition of the speed of the course and the speed of the Schaffner of the courseout seen one resulted in. The formula, with which one computes this speed, is called relativistic addition theorem for speeds.

The extreme case arises, if one regards a ray of light running forward. In this case the slowing down effect is so strong that thatRay of light also from the platform again speed of light has. The Konstanz of the speed of light is the basis of relativity theory.

Now the Schaffner can run however in the course, but also not only forward to the rear. In this case is the event„the Schaffner reaches the next railroad car “further in the back in the course, and thus for the platform observer relative to the course traveler „comes prematurely “, while the other effects work still „slowing down “. The effects waive themselves straight if the Schaffner with the same speedin the course to the rear runs, as the course drives: In this case also relativity theory comes to the result that the Schaffner rests relative to the platform. For higher speeds to the rear the observer at the platform sees now a higher speed,as it after the classical mechanics would expect. This goes again up to the extreme case of the ray of light directed to the rear, which is seen from the platform accurate again also with speed of light on the way.

### Momentum conservation and relativistic mass

in the station give it alsoa play salon with Billiardti. On one occur, when the course drives past, the straight following, from view of the observer at the platform described: Two Billiardkugeln, which in each case the same absolute speed as the course has to move however perpendicularly to the track one on the other,it collides completely flexibly (however not central), in such a way that the connecting straight line of their centers with its direction of motion forms the angle 45°. By the collision they change now its direction straight parallel to the track, so that them - stillequivalent fast - now toward the course and in opposite direction further-roll.

The following picture points this impact again to the elucidation:

In the classical mechanics the impulse of an object is defined as the product of mass and speed of theObject. The total impulse, which arises as a result of simply adding of the single pulses, is a preservation size. Indeed in such a way defined impulse from platform view is received with the above impact: There the balls itself both before and after the impact alsoagainst-same speed move, is in such a way defined impulse forwards as after the impact zero.

We regard now however the Billiardspiel from the course. Before the impact the balls roll diagonally one on the other: Parallel to the track both have the speed of thePlatform (they with the platform along-move there), and perpendicularly to the track they have each other opposite speeds (this component is based on the movement of the balls relatively perpendicularly to the platform to the course). Their impulse perpendicularly to the track is thus zero,parallel to the track the total impulse is 2 times ball mass times platform speed.

After the impact now the one ball has the speed - and concomitantly the impulse - zero (we remember: from platform view it is with course speed in course directionon the way been), thus now the other ball must carry the entire impulse. In order to determine the speed of the other ball, we must use however now the relativistic speed addition regarded in the previous section, and as stated above, this ball has nowa smaller speed than the double of the platform speed (= course speed). If now thus the impulse is to be received, then, so that the product is again alike, their mass must more largely its than the masses of the balls before the impact. Now actsit itself however straight around one of the two mentioned of the balls, which is only, which changed, their speed, which is higher than the speed before the impact. Therefore must, if one defines the impulse further as mass times speed, the mass with the speed wants to increase.

Indeed one can save the momentum conservation by use of a speed-dependent mass in the formula for the impulse. One calls this mass term relativistic mass. It is to be noted that this mass not in the inertia law F = m·A to be used can do, details sees in the article mass.

One calls the relativistic mass of a body for speed of zero also its proper mass. With increasing amount of the speed also the relativistic mass takes of theBody too. If the speed goes against the speed of light, then the mass - and concomitantly the impulse - goes approximately infinitely.

### Equivalence of mass and energy

a further consequence of relativity theory is the equivalence of mass and energy. Thisit means that the energy is proportional E to the mass m, whereby the proportionality constant (C 2) is a universal, not from the object, its speed or other things dependent constant. Thus it concerns an equivalence of both sizes:The indication of one of the two sizes is equivalent to the indication of the others. This equivalence can be deduced from the definition of the relativistic impulse, however there is no simple thought experiment, from which one could understand her without explicit calculation.

ThoseFormula for the mass suppl. IE equivalence belongs to the most famous formulas of physics:

[itex] E = mc^2< /math>

The formula turned around in particular meaning, because it links not only the kinetic energy , but each form of energy with a mass, and. For example the nucleons have the atomic nucleus as free particles a higher mass than the core built up from them, because (negative) the binding energy contributes also to the mass (mass defect). Turned around each mass can be converted into other forms of energy (e.g. becomes with the Annihilation of Subject and antimatter the entire mass in radiation energy converted).

## From space and time to space-time

in view of the relativistic effects described above the question arises naturally, how these effects are to be interpreted. Regards one the movement of an observer in the space-time diagram(Minkowski diagram), then one recognizes that the change reference system (both classical-mechanically and relativistically) with one „dumps “of the time axis accompanies. This describes „the relativity of the Gleichortigkeit “: While the observer in the course states that e.g. its suit-case over itin the baggage net the whole time at the same place remains, is not therefore thus straight for the observer at the platform that the same suit-case with the course along-moves, not at the same place remains clear. Which the relativity theory of Newton's space and time, is the fact differentiates the fact that for to each other moved reference systems also the simultaneousness is relative as described above. This leads to the fact that with the time axis also the local axle is tilted at the same time.

Now is a movement, in which two axes of coordinates are changed,well-known: the turn in the area. It is logical to understand also the reference system change as a kind turn in space and time how the following picture clarifies:

However there, as in the picture is to be likewise recognized, is a substantial differencebetween turns in the area and reference system changes: While during turns in the area both axles are turned into the same direction, with reference system change local axle and time axis are turned into the opposite direction. This leads to the fact that itself the diagonals (dashed in the picture)do not change. The diagonals describe however the straight way of the light, their unchangeableness with reference system change meant thus straight that the speed of light is constant.

If now however the reference system change is a kind turn in space and time, then must, thus sosomewhat, space and time are at all meaningful a unit form, as length, width and height a unit form, i.e. the area. From space and time one calls this unit space-time (see in addition also Lorentz-Transformation and Minkowski area). It is any longer possible to indicate a completely determined direction independently of the observer than the time direction exactly the same as it in the area no clear (observer-independent) in front does not give. Thus e.g. run. both the black time axis and the yellow „turned “time axis in time direction.However it - in contrast to the normal area - is not possible for past and future in space-time to turn the time direction up to the direction in space to turn or in the time to thus exchange.

During more exact view thatOne sees turn (left picture) that each coordinate square is transferred again into a square equal in size (the turned square right above of the origin is hatched in the picture). Besides is the intersection of the turned y axis (yellow line) with the intersection of the turnedjust as far removes for first parallels of the x axis (light brown line) from the origin as the ungedrehte intersection. The y-value of this intersection is however smaller than for the ungedrehten intersection. This leads to the phenomenon of the perspective Verkürzung, if the line from x-directionone looks at.

If one regards now similar to the right picture, then one sees that the coordinate square is transferred also here into a surface equal in size. Only in this case the effect has that the intersection „of the turned “time axis (yellow) with thatmore highly, thus later is appropriate for next parallels of the turned space axis ( light brown), than in the ungedrehten case. If we accept now, the space axes with everyone let us tick a clock „set “, then one sees immediately that the clock in „the turned “coordinate system, thus thoserelative to the observer moved clock, apparent more slowly goes (between two Ticks passes more time of the observer). Also it becomes clear from the analogy to the turn that it concerns also here only one „perspective “effect. Thus explains itself also completelyinformally the apparent contradiction that both observers see the clock running in each case different more slowly: Also the perspective Verkürzung is mutually noticed, without that would lead to contradictions, as the following picture illustrates:

(Picture: Illustration of the mutual perspective Verkürzung- to still draw)

a substantial difference of the reference system change to the turn is however that for times instead of a Verkürzung an extension (slowing down: Time dilatation is noticed). One can recognize this by above confrontation well: During the turn in the areathe intersection moves after the yellow and light brown the line down (perspective Verkürzung), with the reference system change however after above.

The twin paradox emerges in this view as space-time analogue for triangle inequation, as the following confrontation shows:

The fact that withArises to reference system changes instead of a perspective Verkürzung an extension (Dilatation) here, is it shown in the reverse sign of the inequation: While in the area the straight way is the shortest, it is in space-time with the longest proper time.

## Relativity theory at low speeds

Normally is accepted, relativity theory becomes relevant only at very high speeds. The following example shows that in certain cases already at low speeds visible differences result. (Reference: This section needs an electron to understand basic knowledge within the range of electromagnetism

. )(an electrically negatively charged particle) move parallel to a resting, charge-neutral wire, in which an electric current flows, whereby the electrons move within the wire with the same speed in the same direction, like the individual electron outside.

Due to of theRiver has the wire a magnetic field, and there the electron perpendicularly induced to the magnetic field, drags on it by the Lorentzkraft to the wire, as the following picture shows.

(Picture: Electron beside the wire; still to draw)

regarding we the systemin the reference system of the electron, then the leader has still a magnetic field (because to rest, but but the positively charged remainder moves its electrons out atomic trunks), but since the electron naturally rests relative to itself, it experiencesalso no Lorentzkraft. We have thus apparently a problem.

If one considers however the statements of relativity theory, then one determines:

• The electrons are moved in the quiescent system of the wire, therefore lorentzkontrahiert. That is, in „the wire reference system “more is in a given volumeElectrons as in „the electron reference system “.
• With atomic trunks it turned around straight: In „the electron reference system “are to be found in a given volume more atomic trunks, than in „the wire reference system “, since atomic trunks in the latter rest.

In the electron reference system we have thus per volume less electricallynegative electrons and more electrically positive of atomic trunks than in the wire reference system. Since in the wire reference system however from both present equal (the wire was uncharged after a condition altogether), outweighs in the electron reference system the positive charge was much, i.e. the wire is positively charged.Since positive and negative charges dress mutually, it is clear that the electron is drawn to the wire.

This view applies already to small speeds.

## Special relativity theory and quantum theory

contrary to general relativity theory, with that stillis unclear, how it with the quantum theory into a theory of the quantum gravitation be merged can, belong special relativistic quantum theories to the standard devices of modern physics. Many experimental results cannot actual at all be understood, without both the principles of the quantum theory andto consider the space-time understanding of special relativity theory.

Already in the halfclassical bore Sommerfeld' atom model succeeds only with inclusion of special relativity theory explaining the fine structure from atomic energy levels to.

Paul Dirac developed a wave equation, the Dirac-Gleichung, those the behavior of Electrons with consideration of special relativity theory in quantum mechanics describes. This equation leads to the description of the spin and the forecast of the positron as antiparticle of the electron. Also the fine structure can as in the halfclassical models by nonrelativistic quantum mechanicsnot to be explained.

However: The straight existence of antiparticles shows that during the combination of special relativity theory and quantum theory simply a relativistic version of usual quantum mechanics cannot come out. Instead is a theory necessary, in which the particle number is variable- Particles can be destroyed and produced (simplest example: the generation of pairs of particles and antiparticles). Carry this out (relativistic) the Quantenfeldtheorien, for instance quantum electrodynamics as particularly relativistic theory of the electromagnetic reciprocal effect and quantum chromodynamics as description of the strong Kraft,which holds the components together of atomic nuclei.

In shape of the standard model of elementary particle physics relativistic Quantenfeldtheorien form the backbone of the today's physics of the smallest particles. The forecasts of the standard model can be tested at particle accelerators with high precision, and the combination of specialRelativity theory and quantum theory belong thereby to the most strictly examined theories of modern physics.

## literature

• Einstein, Albert: Over special and general relativity theory, Springer 2001, ISBN 3540424520
• Bondi, Hermann: EinsteinMultiplication table - introduction to relativity theory Fischer 1974, ISBN 3-436-01827 (easily understandable introduction for laymen, unfortunately only second-hand available)
• max fount: The relativity theory of Einstein, Springer, ISBN 3-540-04540-6
• friend, Jürgen: Special relativity theory for first-year university student, vdf Hochschulverlag 2005, ISBN 3-7281-2993-3(some chapters are to read in www.relativitaet.info)
• Giulini, Domenico: Special relativity theory, Fischer 2004, ISBN of 3-596-15556-8
• sponsors, stroke ore: Special relativity theory and the classical field theory, Elsevier - spectrum academic publishing house 2004, ISBN 3-8274-1434-2
• Fayngold, Moses: Special Relativity and of MON ion Fasterthan Light, WILEY VCH, ISBN 3527403442 (nice collection of apparent contradictions of the blanks and their dissolution)

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