Test theories of special relativity
Encyclopedia
Test theories of special relativity give a mathematical framework for analyzing results of experiments to verify special relativity
.
An experiment to test the theory of relativity cannot assume the theory is true, and therefore needs some other framework of assumptions that are wider than those of relativity. For example a test theory may have a different postulate about light concerning one-way speed of light
vs. two-way speed of light, it may have a preferred frame
of reference, and may violate Lorentz invariance in many different ways. Test theories predicting different experimental results from Einstein's special relativity, are Robertson's test theory (1949), and the Mansouri-Sexl theory (1977) which is equivalent to Robertson's theory.
Another, more extensive model is the Standard-Model Extension
, which also includes the Standard Model
and General relativity
.
(1949)
extended the Lorentz transformation
by adding additional parameters.
He assumed a preferred frame
of reference, in which the one-way speed of light
is isotropic, and since he applied Poincaré-Einstein synchronization in all relatively moving frames, the one-way speed of light is by definition also isotropic in all other frames. However, the two-way speed of light in those moving frames is anisotropic, because this speed not only depends on the one-way speed, but also on the additional parameters added by Robertson. On the other hand, in special relativity
both the one- and two-way speed of light is isotropic, and because only the two-way speed is accessible to experimental tests, Robertson's theory gives different experimental predictions as special relativity. Thus by evaluating the additional parameters, this theory serves as a framework for assessing possible violations of Lorentz invariance.
They chose the coefficients a, b, d, e of the following transformation between reference frames:
where T, X, Y, Z are the Cartesian coordinates measured in a postulated (preferred) ether
frame (in which the speed of light c is isotropic), and t, x, y, z are the coordinates measured in a frame moving in the +X direction (with the same origin and parallel axes) at speed v relative to the preferred frame. And therefore
is the factor by which the interval between ticks of a clock increases when it moves (time dilation
) and
is factor by which the length of a measuring rod is shortened when it moves (length contraction
). If
and 
and 
then the Lorentz transformation follows. The purpose of the test theory is to allow a(v) and b(v) to be measured by experiment, and to see how close the experimental values come to the values predicted by special relativity. (Notice that Newtonian physics, which has been conclusively excluded by experiment, results from 
)
The value of e(v) depends only on the choice of clock synchronisation and cannot be determined by experiment. Contrary to Robertson, Mansouri-Sexl discussed different synchronization schemes.
That is, in Robertson's theory the one-way speed of light is isotropic in all reference frames due to Poincaré-Einstein synchronization, while the two-way speed of light is anisotropic. In the Mansouri-Sexl theory, both the one- and two-way speed of light are anisotropic if external synchronization is used. Since only the two-way speed is accessible to experimental tests, both test theories are experimentally equivalent.
However, it is possible to make such an ether/test-theory (independent of the chosen synchronization) experimentally equivalent to special relativity, by giving the effects of time dilation and length contraction the exact relativistic value. So Mansouri and Sexl spoke about the "remarkable result that a theory maintaining absolute simultaneity is equivalent to special relativity." They also noticed the similarity between this test theory and Lorentz ether theory
of Hendrik Lorentz
, Joseph Larmor
and Henri Poincaré
. Though Mansouri, Sexl, and the overwhelming majority of physicists, prefer special relativity over such an ether theory, because the latter "destroys the internal symmetry of a physical theory".
, time dilation
, length in the direction of motion
, length perpendicular to the direction of motion
Deviations from the two-way (round-trip) speed of light are given by:
where
is the speed of light in the preferred frame, and 
is the speed of light measured in the moving frame at an angle 
from the direction in which the frame is moving. To verify that special relativity is correct, the expected values of the parameters are 
, and thus 
.
Some fundamental experiments to test those parameters, still repeated with increased accuracy, are:
and others.
Contrary to the Roberson-Mansouri-Sexl (RMS) framework, which is kinematic in nature and restricted to special relativity, SME not only accounts for special relativity, but for dynamical effects of the standard model
and general relativity
as well. It investigates possible spontaneous breaking of both Lorentz invariance and CPT symmetry
. RMS is fully included in SME, though the latter has a much larger group of parameters that can indicate any Lorentz or CPT violation.
A couple of SME parameters was tested in a 2007 study sensitive to 10-16. It employed two simultaneous interferometers over a year's observation: Optical in Berlin
at 52°31'N 13°20'E and microwave in Perth
at 31°53'S 115°53E. A preferred background (leading to Lorentz Violation) could never be at rest relative to both of them. For a large number of other experiments, carried out in recent years, see Mattingly. A list of derived and already measured SME-values was given by Kostelecký and Russell.
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...
.
An experiment to test the theory of relativity cannot assume the theory is true, and therefore needs some other framework of assumptions that are wider than those of relativity. For example a test theory may have a different postulate about light concerning one-way speed of light
One-way speed of light
The "one-way" speed of light from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed from the source to the detector and back again...
vs. two-way speed of light, it may have a preferred frame
Preferred frame
In theoretical physics, a preferred or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different from those in other frames....
of reference, and may violate Lorentz invariance in many different ways. Test theories predicting different experimental results from Einstein's special relativity, are Robertson's test theory (1949), and the Mansouri-Sexl theory (1977) which is equivalent to Robertson's theory.
Another, more extensive model is the Standard-Model Extension
Standard-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...
, which also includes 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...
.
Robertson
Howard Percy RobertsonHoward Percy Robertson
Howard Percy Robertson was an American mathematician and physicist known for contributions related to physical cosmology and the uncertainty principle...
(1949)
extended the 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...
by adding additional parameters.
He assumed a preferred frame
Preferred frame
In theoretical physics, a preferred or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different from those in other frames....
of reference, in which the one-way speed of light
One-way speed of light
The "one-way" speed of light from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed from the source to the detector and back again...
is isotropic, and since he applied Poincaré-Einstein synchronization in all relatively moving frames, the one-way speed of light is by definition also isotropic in all other frames. However, the two-way speed of light in those moving frames is anisotropic, because this speed not only depends on the one-way speed, but also on the additional parameters added by Robertson. On the other hand, in 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...
both the one- and two-way speed of light is isotropic, and because only the two-way speed is accessible to experimental tests, Robertson's theory gives different experimental predictions as special relativity. Thus by evaluating the additional parameters, this theory serves as a framework for assessing possible violations of Lorentz invariance.
Mansouri-Sexl
Another test-theory is that of Mansouri-Sexl (1977).They chose the coefficients a, b, d, e of the following transformation between reference frames:
where T, X, Y, Z are the Cartesian coordinates measured in a postulated (preferred) ether
Luminiferous 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....
frame (in which the speed of light c is isotropic), and t, x, y, z are the coordinates measured in a frame moving in the +X direction (with the same origin and parallel axes) at speed v relative to the preferred frame. And therefore
is the factor by which the interval between ticks of a clock increases when it moves (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...
) and
is factor by which the length of a measuring rod is shortened when it moves (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...
). If
and and then the Lorentz transformation follows. The purpose of the test theory is to allow a(v) and b(v) to be measured by experiment, and to see how close the experimental values come to the values predicted by special relativity. (Notice that Newtonian physics, which has been conclusively excluded by experiment, results from )The value of e(v) depends only on the choice of clock synchronisation and cannot be determined by experiment. Contrary to Robertson, Mansouri-Sexl discussed different synchronization schemes.
- Internal clock synchronization like the Poincaré-Einstein synchronization by using light signals, or synchronization by slow clock transport. Those synchronization schemes are in general not equivalent, except the case when a(v) and b(v) have their exact relativistic value.
- External clock synchronization by choosing a "preferred" reference frame (like the CMBCosmic microwave background radiationIn cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....
) and using the clocks of this frame to synchronize the clocks in all other frames ("absolute" synchronization).
That is, in Robertson's theory the one-way speed of light is isotropic in all reference frames due to Poincaré-Einstein synchronization, while the two-way speed of light is anisotropic. In the Mansouri-Sexl theory, both the one- and two-way speed of light are anisotropic if external synchronization is used. Since only the two-way speed is accessible to experimental tests, both test theories are experimentally equivalent.
However, it is possible to make such an ether/test-theory (independent of the chosen synchronization) experimentally equivalent to special relativity, by giving the effects of time dilation and length contraction the exact relativistic value. So Mansouri and Sexl spoke about the "remarkable result that a theory maintaining absolute simultaneity is equivalent to special relativity." They also noticed the similarity between this test theory and Lorentz ether theory
Lorentz 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....
of 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...
, Joseph Larmor
Joseph Larmor
Sir Joseph Larmor , a physicist and mathematician who made innovations in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter...
and Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
. Though Mansouri, Sexl, and the overwhelming majority of physicists, prefer special relativity over such an ether theory, because the latter "destroys the internal symmetry of a physical theory".
Experimental tests with RMS
Test theories of special relativity are currently used in the evaluation process of many modern tests of Lorentz invariance. To second order, the parameters of the RMS-framework have the following form:, time dilation, length in the direction of motion, length perpendicular to the direction of motionDeviations from the two-way (round-trip) speed of light are given by:
where
is the speed of light in the preferred frame, and is the speed of light measured in the moving frame at an angle from the direction in which the frame is moving. To verify that special relativity is correct, the expected values of the parameters are , and thus .Some fundamental experiments to test those parameters, still repeated with increased accuracy, are:
- Michelson-Morley experimentMichelson-Morley experimentThe Michelson–Morley experiment was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University in Cleveland, Ohio. Its results are generally considered to be the first strong evidence against the theory of a luminiferous ether and in favor of special...
, testing the direction dependence of the speed of light with respect to a preferred frame. Current precision:
- Kennedy-Thorndike experimentKennedy-Thorndike experimentThe Kennedy–Thorndike experiment first conducted in 1932, is a modified form of the Michelson–Morley experimental procedure, and tests special relativity....
, testing the velocity dependence of the speed of light with respect to a preferred frame. Current precision:
- Ives-Stilwell experimentIves-Stilwell experimentThe Ives–Stilwell experiment exploits the transverse Doppler effect . This was the first direct, quantitative confirmation of the time dilation factor. Together with the Michelson–Morley and Kennedy–Thorndike experiments, it forms one of the fundamental tests of special relativity theory...
, testing the relativistic Doppler effectRelativistic Doppler effectThe relativistic Doppler effect is the change in frequency of light, caused by the relative motion of the source and the observer , when taking into account effects described by the special theory of relativity.The relativistic Doppler effect is different from the non-relativistic Doppler effect...
, and thus the relativistic 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...
. Current precision:
Standard Model Extension
Another, more extensive, model is the Standard Model Extension (SME) by Alan KosteleckýAlan Kostelecký
Alan Kostelecký is a theoretical physicist who is currently a distinguished professor of physics at Indiana University, Bloomington. He is noted for his work on Lorentz symmetry breaking in particle physics...
and others.
Contrary to the Roberson-Mansouri-Sexl (RMS) framework, which is kinematic in nature and restricted to special relativity, SME not only accounts for special relativity, but for dynamical effects of 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. It investigates possible spontaneous breaking of both Lorentz invariance and CPT symmetry
CPT symmetry
CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...
. RMS is fully included in SME, though the latter has a much larger group of parameters that can indicate any Lorentz or CPT violation.
A couple of SME parameters was tested in a 2007 study sensitive to 10-16. It employed two simultaneous interferometers over a year's observation: Optical in Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
at 52°31'N 13°20'E and microwave in Perth
Perth, Western Australia
Perth is the capital and largest city of the Australian state of Western Australia and the fourth most populous city in Australia. The Perth metropolitan area has an estimated population of almost 1,700,000....
at 31°53'S 115°53E. A preferred background (leading to Lorentz Violation) could never be at rest relative to both of them. For a large number of other experiments, carried out in recent years, see Mattingly. A list of derived and already measured SME-values was given by Kostelecký and Russell.
External links
- Roberts, Schleif (2006); Relativity FAQ: What is the experimental basis of special relativity?
- Kostelecký: Background information on Lorentz and CPT violation