Tests of special relativity
Tests of special relativity are carried out to this day. They were vital to the development and acceptance of the theory; modern experiments continue to agree with the theory. Contrary to popular beliefs, the special theory of relativity is not just the result of thought experiments and was developed not only to explain a single test result, the famous Michelson-Morley experiment . Rather, the strength of the theory lies in the fact that it is the only one that can explain several fundamentally different experiments without contradiction. In addition to the classic experiments, there are also tests of theory today. B. in the experimentally difficult to access area of the Planck scale or in neutrino physics. So far, their results also confirm the predictions of the theory. Compilations of various tests were given by Jakob Laub , Zhang, Mattingly, Clifford Will , and Roberts / Schleif.
The range of validity of the special theory of relativity is restricted to all phenomena in “flat space-time ”, i.e. H. all uniform and accelerated movements in the absence of gravity. The latter deals with the general theory of relativity ; for the corresponding experimental tests see tests of general relativity .
Experiments that paved the way for SRT
The prevailing theory in the 19th century was that of the dormant ether , a medium in which light spreads, just as sound spreads in air . From this it follows that light in this ether spreads constantly and independently of the speed of the light source. An observer who moves relative to this aether should consequently be able to measure a kind of “ether wind”, just as an observer who moves relative to the air must notice a head wind .
First order experiments
Now a series of optical experiments were carried out, which, despite their relative inaccuracy, should actually have produced a positive result if the ether were completely at rest. However, Augustin Jean Fresnel (1818) was able to solve this problem by introducing an auxiliary hypothesis. He introduced the so-called Fresnel entrainment coefficient, which says that a fraction of the ether is entrained depending on the refractive index of the matter. The necessity of this entrainment coefficient in the ether theory was proven directly by the Fizeau experiment (1851). Later it could be shown that all optical ether drift experiments of the first order have to produce a negative result for this reason. Electrostatic experiments were also carried out. Its negative result could not be explained with Fresnel's theory, and so Hendrik Antoon Lorentz (1892, 1895) had to introduce a series of auxiliary variables for moving observers. This includes a location variable according to which the electrostatic fields contract in the direction of movement, and a time variable according to which the time coordinates depend on the respective location, the so-called "local time". This ensured that all first-order optical and electrostatic experiments had to yield a negative result.
Second order experiments
However, the Fresnel-Lorentz theory of the ether at rest had to produce positive results if the experiments were precise enough to be able to measure quantities of the second order in v / c . The first experiment of this kind was the Michelson-Morley experiment (1881, 1887), with which the change in the distance or the relative speed of light in the ether wind is measured by means of an interferometer , with the help of which two rays were mirrored perpendicular to each other and brought together again should. However, the result was negative. The only way to make this result compatible with a dormant ether was the contraction hypothesis put forward by George Francis FitzGerald (1889) and Lorentz (1892) . This means that (as was already known) not only electrostatic fields contract, but also the binding forces in the matter are affected, and thus the matter itself is subject to this contraction. This was made plausible by the assumption that the binding forces themselves are electrical in nature. However, since no compelling theoretical reason could be given for this assumption, the length contraction was viewed as an ad hoc hypothesis .
In addition to the optical Michelson-Morley experiment, its electrodynamic equivalent was also carried out in 1903 - the Trouton-Noble experiment . Here it should be shown that a capacitor moving in the ether shows a torque. But here too the result was negative. The length contraction was also subjected to a direct test in the experiments of Rayleigh and Brace (1902, 1904), because it was assumed that this leads to birefringence - again the result was negative. (The Trouton-Rankine experiment (1908) carried out later , which was supposed to prove whether the length contraction has an influence on the resistance of a coil, also had a negative result.)
In order to explain all the experiments carried out before 1904, Lorentz had to expand his theory again, and therefore introduced the complete Lorentz transformation within the framework of Lorentz's ether theory , and Henri Poincaré declared (1905) that the non-existence of an absolute movement ( principle of relativity ) is evident is a law of nature.
Refutations of the moving ether
The idea that the aether is carried along completely within or in the vicinity of the earth, whereby the negative aether drift experiments could be explained, was refuted by
- the Fizeau experiment ,
- the experiments of Oliver Lodge (1893), who wanted to use rotating disks to find out whether the ether was carried along,
- the Hammar experiment (1935), in which one interferometer arm was wrapped in lead and the other was exposed,
- the Sagnac effect and
- by the existence of the aberration of light .
The assumption that the entrainment is proportional to the mass and therefore only applies to the earth as a whole was refuted by the Michelson-Gale experiment (measurement of the Sagnac effect due to the earth's rotation).
Special theory of relativity
initial situation
Albert Einstein showed in 1905 that the following models and experiments
- Maxwell-Lorentz electrodynamics (independence of the speed of light from the source speed)
- the electromagnetic induction is only dependent on the relative movement
- the negative ether drift experiments (no preferred reference system)
- the aberration of light and the Fizeau experiment (no complete ether entrainment)
A logically coherent whole will only result if the constancy of the speed of light in all inertial systems and the principle of relativity is assumed. The result is the special theory of relativity, in which the concepts of space and time are subjected to a fundamental revision and the Galileo transformation is replaced by the Lorentz transformation . The Lorentz transformation is no longer a collection of auxiliary variables (as was the case with Lorentz), but concerns the nature of space and time and reflects a fundamental (Lorentz) symmetry, whereby it is also the basis for successful theories such as the standard model . From now on there was no more space for the material ether as a preferred reference system equipped with a state of motion. A number of experimentally verifiable predictions are associated with this Lorentz symmetry or invariance:
| Relativity Principle | Constancy of the speed of light | Time dilation |
|---|---|---|
| Every uniformly moving person in motion (who is at rest in an inertial system) is not able to measure his “absolute” state of motion with the help of an experimental arrangement that is moved along with it. | In all inertial systems, the measured speed of light is the same in all directions ( isotropy ), regardless of the speed of the light source, and it cannot be exceeded by bodies with mass either. | A clock C (i.e. every periodic process), which is moved back and forth between two synchronized clocks A and B, which are at rest in an inertial system, slows down compared to clocks A and B. |
| In addition, there are other relativistic effects such as length contraction , Doppler effect , aberration, etc. The experimental predictions of relativistic theories such as the Standard Model are also connected with this. | ||
Basic experiments
All statements of the SRT can be derived phenomenologically from the following three experiments:
- Michelson-Morley experiment , with which the directional dependence of the speed of light is tested with respect to a preferred reference system. This determines the relationship between longitudinal and transversal lengths of moving bodies.
- Kennedy-Thorndike experiment , with which the dependence of the speed of light on the relative speed of the measuring device is tested with respect to a preferred reference system. This determines the relationship between the longitudinal length and the duration of the time sequences of moving bodies.
- Ives-Stilwell experiment , with which the relativistic Doppler effect and thus the time dilation is demonstrated.
From these experiments and assuming the Poincaré- Einstein synchronization , the complete Lorentz transformation follows, where the Lorentz factor is:
- .
The combination of these experiments is not only important for the phenomenological derivation of the Lorentz transformation, but also because, taken alone, most of the experiments can be interpreted ambiguously. For example, isotropy experiments like the Michelson-Morley experiment can also be viewed as a simple consequence of the relativity principle, according to which every observer can see himself as at rest. Thus these experiments are also compatible with Galileo-invariant theories like the emission theory or the complete ether entrainment , in which the speed of light is not constant. Only through the addition of other experiments that exclude the competing Galileo invariant theories (such as the Ives-Stilwell experiment or the refutations of the ether entrainment or the emission theory) only the Lorentz invariance and thus the SRT remain as the only theory that can explain all experiments.
Constancy of the speed of light
Interferometry, resonators
To measure the isotropy of the speed of light, variants of the Michelson-Morley experiment and the Kennedy-Thorndike experiment are carried out. In contrast to Michelson-Morley, arms of different lengths are used in Kennedy-Thorndike experiments, with the evaluation being carried out over months. This would allow any effects of changes in the speed of the apparatus as it rotates around the sun to be determined. In modern resonator experiments , a possible anisotropy of the speed of light was reduced to ∼10 −17 using optical resonators . Not only terrestrial tests are carried out, but also when using Lunar Laser Ranging , i. H. for optical measurements between the earth and the moon, a variant of the Kennedy-Thorndike experiment could be carried out.
In the 1960s, various types of Mössbauer rotor experiments were carried out, where the transmitter and receiver were mounted on a rotating disk. By utilizing the Mössbauer effect , anisotropy of the speed of light could be excluded with great accuracy on the basis of the measured Doppler shift. (Similar experiments were used to measure time dilation, see below.)
Dependence on source speed and energy
With an emission theory , which says that the speed of light depends on the speed of the light source, the negative outcome of the ether drift experiments could also be explained. However, a number of tests have shown that the speed of light is independent of the source speed: for example meson observations , where the photons did not take over the speed of the decaying mesons, the Sagnac effect and the observation of binary stars , whose orbits are distorted when the light propagates at different speeds should appear.
By observing light rays of different energies (up to 31 GeV) from distant astronomical sources, it could also be shown that the speed of light does not depend on the frequency and energy of the light.
Disposable measurements
In addition, a series of precise one-way measurements with light were carried out, all of which confirmed the predictions of the special theory of relativity and the isotropy of the speed of light. It should be noted here, however, that only the two-way speed of light, i.e. H. from A to B back to A, can be measured directly , because the one-way speed of light (from A to B) depends on the definition of simultaneity and thus on the selected synchronization scheme. The Poincaré- Einstein synchronization makes the one-way equal to the two-way speed of light. Now other synchronizations and theories are also conceivable that result in an anisotropic one-way speed of light and are nevertheless experimentally equivalent to the special theory of relativity, since here, too, phenomena such as time dilation of moving clocks occur and the two-way speed of light is constant. However, within this class of theories, only the special theory of relativity can be seriously considered, since it clearly expresses the Lorentz symmetry, while all other theories (such as the Lorentz theory of ethers ) only through a series of auxiliary hypotheses and extreme assumptions about clock synchronization can achieve the same results.
Isotropy of space, mass and energy
Measurements of a possible anisotropy of space, mass, energy and a related violation of the Lorentz invariance were also made by the Hughes-Drever experiment and various types of it. In contrast to the resonator experiments on photons, the properties of protons , neutrons and electrons are investigated here. If, for example, the speed of light does not match the limit speed of matter or the atomic interactions, then this should lead to deviations in the energy levels of atomic nuclei . The accuracy achieved, with which anisotropy can be excluded, is currently around ∼10 −24 eV , which makes these experiments one of the most accurate tests of the SRT at all. These experiments can also be understood as "clock anisotropy experiments", since the compared frequencies and periodic processes function as clocks.
Time dilation and length contraction
The time dilation and the related transversal relativistic Doppler effect could first be demonstrated directly by the Ives-Stilwell experiment (1938), where the shift of the center of gravity between overlapping light waves was evaluated. Modern Ives-Stillwell measurements are carried out in heavy ion storage rings with saturation spectroscopy , whereby a maximum deviation from the time dilation of ∼10 −8 has been achieved. Another variant are the Mössbauer rotor experiments , where light is sent on a disk from a source in the middle to a receiver at the edge. The Doppler effect is carried out using the Mössbauer effect .
The time dilation of moving particles could also be confirmed with great accuracy by comparing measurements in the atmosphere with particle accelerator experiments. The Hafele-Keating experiment , on the other hand, directly examines the so-called twin paradox . In this experiment, however, the gravitational time dilation of general relativity plays an essential role.
While the confirmation of the time dilation is already routine in particle accelerators, it is practically hardly possible to observe the Lorentz contraction directly, since the dimensions of the particles to be observed are too small. However, there are indirect confirmations, such as the behavior during collisions of heavy ions , which can only be explained if the increased density due to the Lorentz contraction is taken into account. The contraction also leads to a strengthening of the Coulomb field perpendicular to the direction of movement, the effects of which have also already been observed. All of this means that relativistic effects such as time dilation and length contraction have to be taken into account when designing particle accelerators.
Relativistic energy and momentum
Since 1901, a series of measurements have been carried out to check whether the mass of the particles in cathode rays depends on their speed. The results actually showed such a dependency, but the accuracy, and thus the usefulness in distinguishing between different competition theories, was long disputed. Finally, in further experiments it could be clearly established that the results agree with the predictions of the special theory of relativity.
Today, these predictions regarding the increase in relativistic energy are routinely confirmed in particle accelerators such as the Large Electron-Positron Collider (electron-positron collisions) or the Relativistic Heavy Ion Collider ( hadron collisions). The relativistic formulas are not only confirmed very precisely, but are also necessary for the construction of cyclotrons and synchrotrons , through which the particles are accelerated to almost the speed of light.
Sagnac and Fizeau
Another experimental prediction of the SRT is that two rays traveling in opposite directions along a closed path, with the transmitter / receiver moving relative to that path, will take different lengths of time to return to the receiver (a consequence of the independence of the speed of light from the source , see above). This effect could actually be demonstrated with the help of a Sagnac interferometer and today, for example, must also be taken into account for the function of the GPS navigation system .
If such experiments take place within dense and moving media, the Fresnel entrainment coefficient proven by the Fizeau experiment must also be taken into account. This was described above as a confirmation of an almost resting aether, but in the SRT it results as a simple consequence of the relativistic speed addition theorem for low speeds.
More modern tests
Technological advances in recent years have enabled a number of high-precision measurements to test modern theories of quantum gravity , which may allow minimal violations of the Lorentz invariance. This also includes deviations from the weak equivalence principle , since, according to the general theory of relativity, a “local Lorentz invariance” (LLI) applies in free-falling reference systems.
- In addition to the modern variations by Michelson-Morley and Kennedy-Thorndike already mentioned above, clock anisotropy experiments in the sense of the Hughes-Drever experiment , which cover the proton and neutron sector, are also carried out. Spin-polarized torsion balances are examined for possible deviations from the Lorentz invariance in the electron sector .
- The time dilation is demonstrated in modern experiments by observing the Doppler effect of lithium , these experiments being valid for the electron, proton and photon sector.
- Other experiments use Penning traps , where deviations from the cyclotron movement in the magnetic field and the Larmor precession can be observed in electrostatic and magnetic fields .
- Deviations from the CPT symmetry , the break of which would in most cases imply a violation of the Lorentz invariance, are determined by experiments on neutral mesons , Penning traps and muons . No CPT injuries have been identified to date.
- Other test options are threshold energy effects in light, electrons and other particles. A Lorentz violation could mean that the resulting reactions no longer correspond to the standard values.
- Research is being carried out into spatial anisotropies in the neutrino oscillations . Similarly, measurements of neutrino speed performed.
- Astronomical tests are carried out in connection with the time of flight of photons, where possible influences of dispersion and birefringence leading to Lorentz violation can be measured. This could lead to photons of different energies , frequencies or polarizations spreading at different speeds. Synchrotron beams in particular are further candidates for investigations . Similarly, diffraction rings examined for possible deviations from the Lorentz whose photons can thereby get out of phase.
- In addition, observations are made in the Higgs sector.
Test theories
Due to the manifold possibilities of a violation of the Lorentz invariance due to quantum phenomena in modern experiments, various test theories have been developed, which deviate from the special theory of relativity in their experimental consequences by adding various parameters and thus give the possibility to predict possible deviations or to interpret them theoretically. These include the older test theory by Robertson-Mansouri-Sexl (1977), and the standard model extension, which is becoming more and more important, with an even greater number of parameters, which includes other test theories.
status
The special theory of relativity has been confirmed by many experiments. Despite great efforts, it has not yet been possible to experimentally determine violations of the Lorentz invariance. If these are found in the future, they can only be located in the area of the Planck scale that has so far hardly been experimentally accessible .
See also
Individual evidence
- ↑ a b Jakob Laub : About the experimental basis of the principle of relativity. In: Yearbook of radioactivity and electronics. Vol. 7, 1910, ZDB -ID 533845-1 , pp. 405-463.
- ↑ Yuan Zhong Zhang: Special Relativity and Its Experimental Foundations (= Advanced Series on Theoretical Physical Science. Vol. 4). World Scientific, Singapore et al. a. 1997, ISBN 981-02-2749-3 .
- ^ A b c David Mattingly: Modern Tests of Lorentz Invariance. In: Living Reviews in Relativity. Vol. 8, No. 5, 2005, doi: 10.12942 / lrr-2005-5 .
- ^ A b Clifford M. Will : Special Relativity: A Centenary Perspective. In: Thibault Damour , Olivier Darrigol , Bertrand Duplantier, Vincent Rivasseau (eds.): Einstein, 1905–2005. Poincaré Seminar 2005 (= Progress in Mathematical Physics. Vol. 47). Birkhäuser, Basel a. a. 2006, ISBN 3-7643-7435-7 , pp. 33-58, arxiv : gr-qc / 0504085 .
- ↑ a b Tom Roberts, Siegmar Schleif: What is the experimental basis of Special Relativity? . In: Usenet Physics FAQ . University of California, Riverside . 2007. Accessed December 10, 2014.
- ^ Claus Lämmerzahl: Special Relativity and Lorentz Invariance. In: Annals of Physics . Vol. 14, No. 1/3 = Special Issue Albert Einstein , 2005, pp. 71-102, doi: 10.1002 / andp.200410127 .
- ↑ a b Howard P. Robertson : Postulates versus Observation in the Special Theory of Relativity. In: Reviews of Modern Physics. Vol. 21, No. 3, 1949, pp. 378-382, doi: 10.1103 / RevModPhys.21.378 .
- ↑ Aous A. Abdo et al. a .: A limit on the variation of the speed of light arising from quantum gravity effects. In: Nature . Vol. 462, No. 7271, 2009, pp. 331-334, doi: 10.1038 / nature08574 , arxiv : 0908.1832 , PMID 19865083 .