Status of special relativity
Encyclopedia
Special relativity
is a physical theory that plays a fundamental role in the description of all physical phenomena, as long as no considerable influence of gravitation
occurs. Many experiments played (and still play) an important role in its development and justification and the strength of the theory lies in the fact that it is the only one that can correctly predict to high precision the outcome of all known (and very different) experiments. Many of those experiments are still conducted with increased precision and the only area where deviations of the predictions of special relativity are not completely ruled out by experiment is at the Planck scale
and below. Collections of various tests on special relativity were given by Jakob Laub
, Zhang, Mattingly, Clifford Will, and Roberts/Schleif.
Special relativity is restricted to flat spacetime
, i.e., to all phenomena without significant influence of gravitation
. The latter lies in the domain of general relativity
and the corresponding Tests of general relativity
must be considered.
, a stationary medium in which light is propagating like sound
is propagating in air. From that it follows that the speed of light
is constant in all directions in the aether and is independent of the velocity of the source. Thus an observer moving relative to the aether must consequently measure some sort of "aether wind" as an observer moving relative to air measures an apparent wind
.
and thus demonstrating the relative motion of the aether. Yet the results were negative. This problem was solved by Augustin Fresnel (1818) by the introduction of an auxiliary hypothesis, the so called "dragging coefficient", that is, matter is dragging the aether to a small extent. This coefficient was directly demonstrated by the Fizeau experiment
(1851) and it was later shown that all optical experiments must give a negative result due to this coefficient.
Also, some electrodynamic experiments were conducted whose negative result cannot be explained by Fresnel's theory. Thus Hendrik Lorentz
(1892, 1895) was forced to introduce several new auxiliary variables for moving observers. For example, a location-variable by which electrostatic fields contract in the line of motion and another variable ("local time") by which the time coordinates for moving observers depend on their current location.
.svg.png)
The stationary aether theory, however, would give positive results when the experiments are precise enough to measure magnitudes of second order in 
. The first experiment of this kind was the Michelson–Morley experiment (1881, 1887) where two rays of light, traveling for some time in different directions were brought to interfere so that different orientations relative to the aether should lead to a displacement of the interference fringes. But the result was negative again. The only way out of this dilemma was to assume that matter is contracted in the line of motion with respect to the aether (length contraction
, by George Francis FitzGerald (1889) and Lorentz (1892)). That is, the older hypothesis of a contraction of electrostatic fields was extended to intermolecular forces. However, since there was no theoretical reason for that, the contraction hypothesis was considered ad hoc
.
Besides the optical Michelson–Morley experiment, its electrodynamic equivalent was also conducted, the Trouton–Noble experiment. By that it should be demonstrated that a moving condenser must be subjected to a torque
. Again, the result was negative. Then it an attempt was also made to measure some consequences of length contraction in the laboratory frame, since it was assumed that it would lead to birefringence
– again the results were negative. (The Trouton–Rankine experiment conducted in 1908 also gave a negative result when measuring the influence of length contraction on a coil
.)
To explain all experiments conducted before 1904, Lorentz was forced to again expand his theory by introducing the complete Lorentz transformation
. Henri Poincaré
declared in 1905 that the impossibility of demonstrating absolute motion (principle of relativity
) is apparently a law of nature.
which showed that the velocity of two light rays is unaffected by the rotation of the platform; and the existence of the aberration of light
. Also, the assumption that aether drag is proportional to mass and thus only occurs with respect to Earth as a whole was refuted by the Michelson–Gale–Pearson experiment, which demonstrated the Sagnac effect through Earth's motion.
(1905) drew the conclusion from established theories and facts such as the following only form a logical coherent system when the concepts of space and time are subjected to a fundamental revision.
The result is special relativity
theory, which is based on the constancy of the speed of light in all inertial frames of reference
and the principle of relativity
. Here, the Lorentz transformation is not a mere collection of auxiliary hypotheses any more but reflects a fundamental Lorentz symmetry and forms the basis of successful theories such as Quantum electrodynamics
. Special relativity offers a large number of testable predictions, such as:
The effects of special relativity can phenomenologically be derived from the following three types of experiments (besides these experiments, a large number of other types of experiments were, and still are, conducted):
The combination of these effects is important since most of them can be interpreted in different ways when viewed individually. For example, isotropy experiments such as Michelson-Morley can be seen as a simple consequence of the relativity principle, according to which any inertially moving observer can consider himself as at rest. Therefore, it is also compatible to Galilean-invariant theories like emission theories or complete aether drag, which also contain some sort of relativity principle. Only by the addition of other experiments that exclude the Galilean-invariant theories (such as the Ives–Stillwell experiment or refutations of emission theories and complete aether drag) Lorentz-invariance and thus special relativity remains as the only theory that can explain all those experiments.
To measure the isotropy
of the speed of light variations of the Michelson-Morley and Kennedy-Thorndike experiment
s are still under way. Contrary to Michelson-Morley-, the Kennedy-Thorndike-experiments employ different arm lengths and the evaluations last several months. In that way, the influence of different velocities during Earth's orbit around the sun can be observed. In modern variants of Michelson-Morley and Kennedy-Thorndike, laser
, maser
and optical resonators are used reducing the possibility of any anisotropy of the speed of light to
for Michelson-Morley and 
for Kennedy-Thorndike. Not only terrestrial tests are being conducted but also Lunar Laser Ranging Experiment
s as a variation of the Kennedy-Thorndike-experiment.
In addition, extremely precise clock-comparison experiments (because periodic processes and frequencies can be considered as clocks) such as the Hughes–Drever experiment
s are also still conducted. They are not restricted to the photon sector as Michelson-Morley but directly determine any anisotropy of mass by measuring the ground state of nuclei
. In other words, they determine the anisotropy of space providing an upper limit of such anisotropies of
GeV
. Thus they belong to the most precise measurements at all.
Another type of isotropy experiments are the Moessbauer rotor experiments in the 1960s, by which the anisotropy of the Doppler effect on a rotating disc can be observed by using the Moessbauer effect (those experiments can also utilized to measure time dilation, see below).
in which the light rays are moving independently of the velocity of the rotating apparatus; the de Sitter double star experiment
showing that the orbits of the stars don't appear scrambled due to different propagation times of light.
Other observations also demonstrated that the speed of light is independent of the frequency and energy of the light rays.
) are based on extreme and implausible assumptions concerning some dynamical effects, which are aimed at hiding the "preferred frame" from observation.
, was directly observed in the Ives–Stilwell experiment (1938) for the first time, where the displacement of the center of gravity of the overlapping light waves was evaluated. In modern Ives-Stilwell experiments in heavy ion storage ring
s using saturated spectroscopy
the maximum deviation from time dilation was limited to
. Another variant is the Moessbauer rotor experiment in which gamma ray
s were sent from the middle of a rotating disc to a receiver at the edge of the disc so that the transverse Doppler effect can be evaluated by means of the Moessbauer effect. By measuring the lifetime of muon
s in the atmosphere and in particle accelerators the time dilation of moving particles was also verified. On the other hand, the Hafele–Keating experiment confirmed the twin paradox
, i.e. that a clock moving from A to B back to A is retarded with respect to the initial clock. However, in this experiment the effects of general relativity
also play an essential role.
Direct confirmation of length contraction
is hard to achieve in practice since the dimensions of the observed particles are vanishingly small. However, there are indirect confirmations; for example, the behavior of colliding heavy ion
s can only be explained if their increased density due to Lorentz contraction is considered. Contraction also leads to an increase of the intensity of the Coulomb field
perpendicular to the direction of motion whose effects already have been observed. Consequently, both time dilation and length contraction must be considered when conducting experiments in particle accelerators.
Today, special relativities predictions are routinely confirmed in particle accelerator
s such as the Relativistic Heavy Ion Collider
. For example, the increase of relativistic momentum
and energy is not only precisely measured but also necessary to understand the behavior of cyclotron
s and synchrotron
s etc., by which particles are accelerated near to the speed of light.
. Today the consideration of this effect is necessary for many experimental setups and for the correct functioning of GPS
.
If such experiments are being conducted in moving media it is also necessary to consider Fresnel's dragging coefficient as demonstrated by the Fizeau experiment
. Although this effect was initially understood as giving evidence of a nearly stationary aether or a partial aether drag it can easily be explained with special relativity by using the velocity composition law.
(SME). RMS has three testable parameters with respect to length contraction and time dilation. From that, any anisotropy of the speed of light can be assessed. On the other hand, SME includes many Lorentz violation parameters, not only for special relativity, but for the Standard model
and General relativity
as well, thus it has a much larger number of testable parameters.
in recent years deviations of Lorentz invariance (possibly following from those models) are again the target of experimentalists. Because "local Lorentz invariance" (LLI) also holds in freely falling frames experiments concerning the weak Equivalence principle
belong to this class of tests as well. The outcomes are analyzed by test theories (as mentioned above) like RMS or, more importantly, by SME.
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
is a physical theory that plays a fundamental role in the description of all physical phenomena, as long as no considerable influence of gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
occurs. Many experiments played (and still play) an important role in its development and justification and the strength of the theory lies in the fact that it is the only one that can correctly predict to high precision the outcome of all known (and very different) experiments. Many of those experiments are still conducted with increased precision and the only area where deviations of the predictions of special relativity are not completely ruled out by experiment is at the Planck scale
Planck scale
In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1019 GeV at which quantum effects of gravity become strong...
and below. Collections of various tests on special relativity were given by Jakob Laub
Jakob Laub
Jakob Johann Laub was a physicist from Austria-Hungary, who is most well known for his work with Albert Einstein in the early period of special relativity.-Life:...
, Zhang, Mattingly, Clifford Will, and Roberts/Schleif.
Special relativity is restricted to flat spacetime
Minkowski space
In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...
, i.e., to all phenomena without significant influence of gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
. The latter lies in the domain of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
and the corresponding Tests of general relativity
Tests of general relativity
At its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's...
must be considered.
Refutations of the aether
The predominant theory of light in the 19th century was that of the luminiferous aetherLuminiferous aether
In the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....
, a stationary medium in which light is propagating like sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
is propagating in air. From that it follows that the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
is constant in all directions in the aether and is independent of the velocity of the source. Thus an observer moving relative to the aether must consequently measure some sort of "aether wind" as an observer moving relative to air measures an apparent wind
Apparent wind
Apparent wind is the wind experienced by a moving object.-Definition of apparent wind:The Apparent wind is the wind experienced by an observer in motion and is the relative velocity of the wind in relation to the observer....
.
First-order experiments
A series of optical experiments were conducted, which should have given a positive result for magnitudes to first order in and thus demonstrating the relative motion of the aether. Yet the results were negative. This problem was solved by Augustin Fresnel (1818) by the introduction of an auxiliary hypothesis, the so called "dragging coefficient", that is, matter is dragging the aether to a small extent. This coefficient was directly demonstrated by the Fizeau experimentFizeau experiment
The Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative speeds of light in moving water. Albert Einstein later pointed out the importance of the experiment for special relativity...
(1851) and it was later shown that all optical experiments must give a negative result due to this coefficient.
Also, some electrodynamic experiments were conducted whose negative result cannot be explained by Fresnel's theory. Thus Hendrik Lorentz
Hendrik Lorentz
Hendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
(1892, 1895) was forced to introduce several new auxiliary variables for moving observers. For example, a location-variable by which electrostatic fields contract in the line of motion and another variable ("local time") by which the time coordinates for moving observers depend on their current location.
Second-order experiments
. The first experiment of this kind was the Michelson–Morley experiment (1881, 1887) where two rays of light, traveling for some time in different directions were brought to interfere so that different orientations relative to the aether should lead to a displacement of the interference fringes. But the result was negative again. The only way out of this dilemma was to assume that matter is contracted in the line of motion with respect to the aether (length contractionLength contraction
In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer...
, by George Francis FitzGerald (1889) and Lorentz (1892)). That is, the older hypothesis of a contraction of electrostatic fields was extended to intermolecular forces. However, since there was no theoretical reason for that, the contraction hypothesis was considered ad hoc
Ad hoc
Ad hoc is a Latin phrase meaning "for this". It generally signifies a solution designed for a specific problem or task, non-generalizable, and not intended to be able to be adapted to other purposes. Compare A priori....
.
Besides the optical Michelson–Morley experiment, its electrodynamic equivalent was also conducted, the Trouton–Noble experiment. By that it should be demonstrated that a moving condenser must be subjected to a torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
. Again, the result was negative. Then it an attempt was also made to measure some consequences of length contraction in the laboratory frame, since it was assumed that it would lead to birefringence
Birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
– again the results were negative. (The Trouton–Rankine experiment conducted in 1908 also gave a negative result when measuring the influence of length contraction on a coil
Coil
A coil is a series of loops. A coiled coil is a structure in which the coil itself is in turn also looping.-Electromagnetic coils:An electromagnetic coil is formed when a conductor is wound around a core or form to create an inductor or electromagnet...
.)
To explain all experiments conducted before 1904, Lorentz was forced to again expand his theory by introducing the complete Lorentz transformation
Lorentz transformation
In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik...
. Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
declared in 1905 that the impossibility of demonstrating absolute motion (principle of relativity
Principle of relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....
) is apparently a law of nature.
Refutations of complete aether drag
The idea that the aether is completely dragged within or in the vicinity of earth, by which the negative aether drift experiments could be explained, was refuted by the experiments of Oliver Lodge (1893) by means of rotating disks; by Hammar (1935) by means of an interferometer with one arm enclosed by mercury while the other one was free; the Sagnac effectSagnac effect
The Sagnac effect , named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in...
which showed that the velocity of two light rays is unaffected by the rotation of the platform; and the existence of the aberration of light
Aberration of light
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...
. Also, the assumption that aether drag is proportional to mass and thus only occurs with respect to Earth as a whole was refuted by the Michelson–Gale–Pearson experiment, which demonstrated the Sagnac effect through Earth's motion.
Basic experiments
Eventually, Albert EinsteinAlbert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
(1905) drew the conclusion from established theories and facts such as the following only form a logical coherent system when the concepts of space and time are subjected to a fundamental revision.
- Maxwell-Lorentz's electrodynamics (independence of the speed of light from the speed of the source)
- the negative aether drift experiments (no preferred reference frame)
- Moving magnet and conductor problemMoving magnet and conductor problemThe moving magnet and conductor problem is a famous thought experiment, originating in the 19th century, concerning the intersection of classical electromagnetism and special relativity. In it, the current in a conductor moving with constant velocity, v, with respect to a magnet is calculated in...
(only relative motion is relevant) - the Fizeau experimentFizeau experimentThe Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative speeds of light in moving water. Albert Einstein later pointed out the importance of the experiment for special relativity...
and the aberration of lightAberration of lightThe aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...
(no complete aether drag)
The result is special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
theory, which is based on the constancy of the speed of light in all inertial frames of reference
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...
and the principle of relativity
Principle of relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....
. Here, the Lorentz transformation is not a mere collection of auxiliary hypotheses any more but reflects a fundamental Lorentz symmetry and forms the basis of successful theories such as Quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...
. Special relativity offers a large number of testable predictions, such as:
| Principle of relativity | Constancy of the speed of light | Time dilation Time dilation In the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at... |
|---|---|---|
| Any uniformly moving observer in an inertial frame cannot determine his "absolute" state of motion by a co-moving experimental arrangement. | In all inertial frames the measured speed of light is equal in all directions (isotropy Isotropy Isotropy is uniformity in all orientations; it is derived from the Greek iso and tropos . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary... ), independent of the speed of the source, and cannot be exceeded by moving bodies. |
The rate of a clock C (= any periodic process) traveling between two synchronized clocks A and B at rest in an inertial frame is retarded with respect to the two clocks. |
| Also other relativistic effects such as length contraction Length contraction In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer... , Doppler effect Doppler effect The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from... , aberration Aberration An aberration is something that deviates from the normal way.Aberration may refer to:In optics and physics:*Optical aberration, an imperfection in image formation by an optical system... and the experimental predictions of relativistic theories such as the Standard Model Standard Model The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon... can be measured. |
||
The effects of special relativity can phenomenologically be derived from the following three types of experiments (besides these experiments, a large number of other types of experiments were, and still are, conducted):
- Michelson–Morley experiment, by which the dependence of the speed of light on the direction of the measuring device can be tested.
- Kennedy–Thorndike experiment, by which the dependence of the speed of light on the velocity of the measuring device can be tested.
- Ives–Stilwell experiment, by which time dilationTime dilationIn the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...
can be tested.
The combination of these effects is important since most of them can be interpreted in different ways when viewed individually. For example, isotropy experiments such as Michelson-Morley can be seen as a simple consequence of the relativity principle, according to which any inertially moving observer can consider himself as at rest. Therefore, it is also compatible to Galilean-invariant theories like emission theories or complete aether drag, which also contain some sort of relativity principle. Only by the addition of other experiments that exclude the Galilean-invariant theories (such as the Ives–Stillwell experiment or refutations of emission theories and complete aether drag) Lorentz-invariance and thus special relativity remains as the only theory that can explain all those experiments.
Interferometers, resonators, clock-comparison
Isotropy
Isotropy is uniformity in all orientations; it is derived from the Greek iso and tropos . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary...
of the speed of light variations of the Michelson-Morley and Kennedy-Thorndike experiment
Kennedy-Thorndike experiment
The Kennedy–Thorndike experiment first conducted in 1932, is a modified form of the Michelson–Morley experimental procedure, and tests special relativity....
s are still under way. Contrary to Michelson-Morley-, the Kennedy-Thorndike-experiments employ different arm lengths and the evaluations last several months. In that way, the influence of different velocities during Earth's orbit around the sun can be observed. In modern variants of Michelson-Morley and Kennedy-Thorndike, laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
, maser
Maser
A maser is a device that produces coherent electromagnetic waves through amplification by stimulated emission. Historically, “maser” derives from the original, upper-case acronym MASER, which stands for "Microwave Amplification by Stimulated Emission of Radiation"...
and optical resonators are used reducing the possibility of any anisotropy of the speed of light to
for Michelson-Morley and for Kennedy-Thorndike. Not only terrestrial tests are being conducted but also Lunar Laser Ranging ExperimentLunar laser ranging experiment
The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. Lasers on Earth are aimed at retroreflectors planted on the moon during the Apollo program, and the time for the reflected light to return is determined...
s as a variation of the Kennedy-Thorndike-experiment.
In addition, extremely precise clock-comparison experiments (because periodic processes and frequencies can be considered as clocks) such as the Hughes–Drever experiment
Hughes–Drever experiment
Hughes–Drever experiments are testing the isotropy of mass and space. As in Michelson–Morley experiments, the existence of a preferred frame of reference, or deviations from Lorentz invariance can be tested, which also affects the validity of the equivalence principle...
s are also still conducted. They are not restricted to the photon sector as Michelson-Morley but directly determine any anisotropy of mass by measuring the ground state of nuclei
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
. In other words, they determine the anisotropy of space providing an upper limit of such anisotropies of
GeVGEV
GEV or GeV may stand for:*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*GEV or Grid Enabled Vehicle that is fully or partially powered by the electric grid, see plug-in electric vehicle...
. Thus they belong to the most precise measurements at all.
Another type of isotropy experiments are the Moessbauer rotor experiments in the 1960s, by which the anisotropy of the Doppler effect on a rotating disc can be observed by using the Moessbauer effect (those experiments can also utilized to measure time dilation, see below).
Dependency on source velocity, and energy
Emission theories, according to which the speed of light depends on the velocity of the source, can explain the negative outcome of the aether drift experiments as well. However, a series of experiments definitely ruled out these models. For example, the Alväger–Experiment where the photons don't acquire the speed of the decaying mesons; the Sagnac experimentSagnac effect
The Sagnac effect , named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in...
in which the light rays are moving independently of the velocity of the rotating apparatus; the de Sitter double star experiment
De Sitter double star experiment
The de Sitter effect was described by de Sitter in 1913 and used to support the special theory of relativity against a competing 1908 emission theory by Walter Ritz that postulated a variable speed of light...
showing that the orbits of the stars don't appear scrambled due to different propagation times of light.
Other observations also demonstrated that the speed of light is independent of the frequency and energy of the light rays.
One-way speed of light
A series of one-way measurements were undertaken, all of them confirming the isotropy of the speed of light. However, it is to be noticed that only the two-way speed of light (from A to B back to A) can directly be measured since the one-way speed depends on the definition of simultaneity and therefore on the method of synchronization. The Poincaré-Einstein synchronization makes the one-way speed equal to the two-way speed, yet one can think of other synchronizations, which also give a isotropic two-way speed but an anisotropic one-way speed. It was also shown that synchronization by slow clock transport is equivalent with Einstein synchronization and also non-standard synchronization as long as the moving clocks are subjected to time dilation. Now, because the one-way speed is depending on the definition of simultaneity, only the two-way speed is directly accessible by experiment so there are many models with anisotropic one-way speed of light that are experimentally equivalent to special relativity. However, from all of these only special relativity is acceptable for the overwhelming majority of physicists since all other synchronizations are much more complicated than Einstein's one, and because the other models (like Lorentz ether theoryLorentz ether theory
What is now often called Lorentz Ether theory has its roots in Hendrik Lorentz's "Theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century....
) are based on extreme and implausible assumptions concerning some dynamical effects, which are aimed at hiding the "preferred frame" from observation.
Time dilation and Length contraction
The transverse Doppler effect, and thus time dilationTime dilation
In the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...
, was directly observed in the Ives–Stilwell experiment (1938) for the first time, where the displacement of the center of gravity of the overlapping light waves was evaluated. In modern Ives-Stilwell experiments in heavy ion storage ring
Storage ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating for a long period of time, up to many hours. Storage of a particular particle depends upon the mass, energy and usually charge of the particle being stored...
s using saturated spectroscopy
Saturated spectroscopy
Saturated spectroscopy is the method by which the exact energy of the hyperfine transitions within an atom can be found. When a monochromatic light is shone through an atom, the Absorption cross section is broadened due to Doppler broadening...
the maximum deviation from time dilation was limited to
. Another variant is the Moessbauer rotor experiment in which gamma rayGamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...
s were sent from the middle of a rotating disc to a receiver at the edge of the disc so that the transverse Doppler effect can be evaluated by means of the Moessbauer effect. By measuring the lifetime of muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
s in the atmosphere and in particle accelerators the time dilation of moving particles was also verified. On the other hand, the Hafele–Keating experiment confirmed the twin paradox
Twin paradox
In physics, the twin paradox is a thought experiment in special relativity, in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth...
, i.e. that a clock moving from A to B back to A is retarded with respect to the initial clock. However, in this experiment the effects of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
also play an essential role.
Direct confirmation of length contraction
Length contraction
In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer...
is hard to achieve in practice since the dimensions of the observed particles are vanishingly small. However, there are indirect confirmations; for example, the behavior of colliding heavy ion
Heavy ion
Heavy ion refers to an ionized atom which is usually heavier than helium. Heavy-ion physics is devoted to the study of extremely hot nuclear matter and the collective effects appearing in such systems, differing from particle physics, which studies the interactions between elementary particles...
s can only be explained if their increased density due to Lorentz contraction is considered. Contraction also leads to an increase of the intensity of the Coulomb field
Coulomb's law
Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...
perpendicular to the direction of motion whose effects already have been observed. Consequently, both time dilation and length contraction must be considered when conducting experiments in particle accelerators.
Relativistic mass and energy
Starting with 1901, a series of measurements was conducted aimed at demonstrating the velocity dependence of the mass of cathode rays. The results actually showed such a dependency but the precision necessary to distinguish between competing theories was disputed for a long time. Eventually, it was possible to unambiguously rule out all competing models except special relativity.Today, special relativities predictions are routinely confirmed in particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...
s such as the Relativistic Heavy Ion Collider
Relativistic Heavy Ion Collider
The Relativistic Heavy Ion Collider is one of two existing heavy-ion colliders, and the only spin-polarized proton collider in the world. It is located at Brookhaven National Laboratory in Upton, New York and operated by an international team of researchers...
. For example, the increase of relativistic momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
and energy is not only precisely measured but also necessary to understand the behavior of cyclotron
Cyclotron
In technology, a cyclotron is a type of particle accelerator. In physics, the cyclotron frequency or gyrofrequency is the frequency of a charged particle moving perpendicularly to the direction of a uniform magnetic field, i.e. a magnetic field of constant magnitude and direction...
s and synchrotron
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...
s etc., by which particles are accelerated near to the speed of light.
Sagnac and Fizeau
Special relativity also predicts that two light rays traveling in opposite directions around a loop or closed path require different flight times to come back to the moving emitter/receiver (this is a consequence of the independence of the speed of light from the velocity of the source, see above). This effect was actually observed and is called the Sagnac effectSagnac effect
The Sagnac effect , named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in...
. Today the consideration of this effect is necessary for many experimental setups and for the correct functioning of GPS
Global Positioning System
The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...
.
If such experiments are being conducted in moving media it is also necessary to consider Fresnel's dragging coefficient as demonstrated by the Fizeau experiment
Fizeau experiment
The Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative speeds of light in moving water. Albert Einstein later pointed out the importance of the experiment for special relativity...
. Although this effect was initially understood as giving evidence of a nearly stationary aether or a partial aether drag it can easily be explained with special relativity by using the velocity composition law.
Test theories
Several test theories have been developed to assess a possible positive outcome in Lorentz violation experiments by adding certain parameters to the standard equations. These include the Robertson-Mansouri-Sexl framework (RMS) and the Standard-Model ExtensionStandard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
(SME). RMS has three testable parameters with respect to length contraction and time dilation. From that, any anisotropy of the speed of light can be assessed. On the other hand, SME includes many Lorentz violation parameters, not only for special relativity, but for the Standard model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
and General relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
as well, thus it has a much larger number of testable parameters.
Other modern tests
Due to the developments concerning various models of Quantum gravityQuantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
in recent years deviations of Lorentz invariance (possibly following from those models) are again the target of experimentalists. Because "local Lorentz invariance" (LLI) also holds in freely falling frames experiments concerning the weak Equivalence principle
Equivalence principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...
belong to this class of tests as well. The outcomes are analyzed by test theories (as mentioned above) like RMS or, more importantly, by SME.
- Besides the mentioned variations of Michelson–Morley and Kennedy–Thorndike experiments, Hughes–Drever experimentHughes–Drever experimentHughes–Drever experiments are testing the isotropy of mass and space. As in Michelson–Morley experiments, the existence of a preferred frame of reference, or deviations from Lorentz invariance can be tested, which also affects the validity of the equivalence principle...
s are also continued for isotropy tests in the protonProtonThe proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
and neutronNeutronThe neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
sector.
- To detect possible deviations in the electronElectronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
sector, spin-polarizedSpin polarizationSpin polarization is the degree to which the spin, i.e., the intrinsic angular momentum of elementary particles, is aligned with a given direction. This property may pertain to the spin, hence to the magnetic moment, of conduction electrons in ferromagnetic metals, such as iron, giving rise to...
Torsion balances are used.
- Time dilation is confirmed by observation of the Doppler effect of LithiumLithiumLithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...
and those experiments are valid in the electron, proton, and photon sector.
- Other experiments use Penning trapPenning trapPenning traps are devices for the storage of charged particles using a homogeneous static magnetic field and a spatially inhomogeneous static electric field. This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particles which have...
s to observe deviations of cyclotron motion and Larmor precessionLarmor precessionIn physics, Larmor precession is the precession of the magnetic moments of electrons, atomic nuclei, and atoms about an external magnetic field...
in electrostatic and magnetic fields.
- Possible deviations from CPT symmetryCPT symmetryCPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...
(whose violation represents a violation of Lorentz invariance as well) can be determined in experiments with neutral mesonMesonIn particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s, Penning trapPenning trapPenning traps are devices for the storage of charged particles using a homogeneous static magnetic field and a spatially inhomogeneous static electric field. This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particles which have...
s and muonMuonThe muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
s.
- Also observations in the HiggsHiggs bosonThe Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
sector are under way.
- Astronomical tests are conducted in connection with the flight time of photons, where Lorentz violating factors could cause anomalous dispersion and birefringenceBirefringenceBirefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
leading to a dependency of photons on energyEnergyIn physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
, frequencyFrequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
or polarizationPolarizationPolarization is a property of certain types of waves that describes the orientation of their oscillations. Electromagnetic waves, such as light, and gravitational waves exhibit polarization; acoustic waves in a gas or liquid do not have polarization because the direction of vibration and...
.
- With respect to Threshold energyThreshold energyIn particle physics, the threshold energy for production of a particle is the minimum kinetic energy a pair of traveling particles must have when they collide. The threshold energy is always greater than or equal to the rest energy of the desired particle...
of distant astronomical objects, Lorentz violations could lead to alterations in the standard values for the processes following from that energy.
- Other candidates for astronomical observations are synchrotron radiationSynchrotron radiationThe electromagnetic radiation emitted when charged particles are accelerated radially is called synchrotron radiation. It is produced in synchrotrons using bending magnets, undulators and/or wigglers...
and Neutrino oscillations. Also, Airy disks are investigated to find possible deviations of Lorentz invariance that could drive the photons out of phase.
See also
- Tests of general relativityTests of general relativityAt its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's...
- History of special relativityHistory of special relativityThe history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others...