One-way speed of light
Encyclopedia
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 (or "two-way" speed of light) from the source to the detector and back again. Albert Einstein
chose a synchronization convention (see Einstein synchronization) that made the one-way speed equal to the two-way speed. The constancy of the one-way speed in any given inertial frame, is the basis of his special theory of relativity
although all experimentally verifiable predictions of this theory do not depend on that convention.
Experiments that attempted to probe the one-way speed of light have been proposed, but none has succeeded in doing so. It was later shown that these experiments are in fact measuring the two-way speed.
The 'speed of light' in this article refers to the speed of all electromagnetic radiation
in vacuum.
Experiments have shown within tight limits that in an inertial frame the two-way speed of light is independent of the closed path considered.
Since 1983 the meter
has been defined as the distance traveled by light in vacuum in second
. This means that the speed of light can no longer be experimentally measured in SI units, but the length of a meter can be compared experimentally against some other standard of length.
The Lorentz transformation
is defined such that the one-way speed of light will be measured to be independent of the inertial frame chosen.
If however one clock is moved away slowly and returned the two clocks will be very nearly synchronized when they are back together again. The clocks can remain synchronized to an arbitrary accuracy by moving them sufficiently slowly. If it is taken that, if moved slowly, the clocks remain synchronized at all times, even when separated, this method can be used to synchronize two spatially separated clocks.
It has been shown that (in the limit as the speed of transport tends to zero) this method is experimentally and theoretically equivalent to the Einstein convention.
J. Finkelstein showed that this experiment actually measures the round trip (two-way) speed of light.
Jet Propulsion Laboratory
, measured the time of flight of light signals through a fibre optic link between two hydrogen maser clocks. In 1992 the experimental results were analysed by Clifford Will who concluded that the experiment did actually measure the one-way speed of light.
In 1997 the experiment was re-analysed by Zhang who showed that, in fact, only the two-way speed had been measured.
Will later confirmed that this conclusion was indeed correct.
(1913), conclusively repeated in the x-ray spectrum by K. Brecher in 1977;
or the terrestrial experiment by Alväger, et al. (1963); they show that, when measured in an inertial frame, the one-way speed of light is independent of the motion of the source within the limits of experimental accuracy. In such experiments the clocks may be synchronized in any convenient way, since it is only a change of speed that is being measured.
Observations of the arrival of radiation from distant astronomical events have shown that the one-way speed of light does not vary with frequency.
. That is, time dilation is measured by synchronizing two stationary clocks A and B, and then the readings of a moving clock C are compared with them. Changing the convention of synchronization for A and B makes the value for time dilation (like the one-way speed of light) directional dependent. However, when time dilation is measured on closed paths, it is not conventional any more and can unequivocally be measured like the two-way speed of light. Time dilation on closed paths was measured in the Hafele–Keating experiment and in experiments on the Time dilation of moving particles such as Bailey et al. (1977).
Thus the so-called twin paradox
occurs in all theories, in which the two-way speed of light is constant.
and Henri Poincaré
proposed a theory which explained this result as being due the effect of motion through the aether on the lengths of physical objects and the speed at which clocks ran. Due to motion through the aether objects would shrink along the direction of motion and clocks would slow down. Thus, in this theory, slowly transported clocks do not, in general, remain synchronized although this effect cannot be observed. The equations describing this theory are known as the Lorentz transformations. In 1905 these transformations became the basic equations of Einstein's special theory of relativity which proposed the same results without reference to an aether.
In the theory, the one-way speed of light is not, in general, equal to the two-way speed, due to the motion of the observer through the aether. However, the difference between the one-way and two-way speeds of light can never be observed due to the action of the aether on the clocks and lengths. This theory is thus experimentally indistinguishable from special relativity. For reasons of philosophical preference and because of the development of general relativity
Lorentz' theory is no longer used.
The two way speed of light in a vacuum as measured in two (inertial) coordinate systems moving with constant relative velocity is the same regardless of any assumptions regarding the one-way speed.
This allows the one-way speed of light to take the form in a given direction, with the sign of reversed in the opposite direction. In the extreme as approaches 1, light might propagate in one direction instantaneously, provided it takes the entire round-trip time to travel in the opposite direction. The average speed for the round trip remains the experimentally verifiable two-way speed.
All predictions of Edwards' theory are experimentally indistinguishable from those of special relativity; the difference is only that the defined clock time varies from Einstein's according to the distance in a specific direction. For this reason, Edwards' theory is not a test theory of special relativity, but an experimentally equivalent though more complex theory.
In Einstein's special theory of relativity, all inertial frames of reference are equivalent and there is no preferred frame. There are theories, such as Lorentz ether theory
that are experimentally and mathematically equivalent to special relativity but have a preferred reference frame. In order for these theories to be compatible with experimental results the preferred frame must be undetectable. In other words it is a preferred frame in principle only, in practice all inertial frames must be equivalent, as in special relativity.
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...
from a source to a detector, cannot be measured
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...
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 (or "two-way" speed of light) from the source to the detector and back again. Albert Einstein
Albert 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...
chose a synchronization convention (see Einstein synchronization) that made the one-way speed equal to the two-way speed. The constancy of the one-way speed in any given inertial frame, is the basis of his special theory of 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...
although all experimentally verifiable predictions of this theory do not depend on that convention.
Experiments that attempted to probe the one-way speed of light have been proposed, but none has succeeded in doing so. It was later shown that these experiments are in fact measuring the two-way speed.
The 'speed of light' in this article refers to the speed of all electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
in vacuum.
The two-way speed
The two-way speed of light is the average speed of light from one point, such as a source, to a mirror and back again. Because the light starts and finishes in the same place only one clock is needed to measure the total time, thus this speed can be experimentally determined independently of any clock synchronization scheme. Any measurement in which the light follows a closed path is considered a two-way speed measurement.Experiments have shown within tight limits that in an inertial frame the two-way speed of light is independent of the closed path considered.
Since 1983 the meter
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
has been defined as the distance traveled by light in vacuum in second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
. This means that the speed of light can no longer be experimentally measured in SI units, but the length of a meter can be compared experimentally against some other standard of length.
The one-way speed
Although the average speed over a two-way path can be measured, the one-way speed in one direction or the other is undefined (and not simply unknown), unless one can define what is "the same time" in two different locations. To measure the time that the light has taken to travel from one place to another it is necessary to know the start and finish times as measured on the same time scale. This requires either two synchronized clocks, one at the start and one at the finish, or some means of sending a signal instantaneously from the start to the finish. No instantaneous means of transmitting information is known. Thus the measured value of the average one-way speed is dependent on the method used to synchronize the start and finish clocks. This is a matter of convention.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...
is defined such that the one-way speed of light will be measured to be independent of the inertial frame chosen.
Clock synchronization schemes
The way in which distant clocks are synchronized can have an effect on all time-related measurements over distance, such as speed or acceleration measurements.Einstein convention
This method synchronizes distant clocks in such a way that the one-way speed of light becomes equal to the two-way speed of light. The details of this method, and the conditions that assure its consistency are discussed in Einstein synchronization.Slow transport
It is easily demonstrated that if two clocks are brought together and synchronized, then one clock is moved rapidly away and back again, the two clocks will no longer be synchronized.If however one clock is moved away slowly and returned the two clocks will be very nearly synchronized when they are back together again. The clocks can remain synchronized to an arbitrary accuracy by moving them sufficiently slowly. If it is taken that, if moved slowly, the clocks remain synchronized at all times, even when separated, this method can be used to synchronize two spatially separated clocks.
It has been shown that (in the limit as the speed of transport tends to zero) this method is experimentally and theoretically equivalent to the Einstein convention.
Experiments which appear to measure the one-way speed of light
There are still occasional experiments that appear to measure the one-way speed of light independently of clock synchronization but they have so far all been shown to actually measure the two-way speed.The Greaves, Rodriguez and Ruiz-Camacho experiment
In the October 2009 issue of the American Journal of Physics Greaves, Rodriguez and Ruiz-Camacho reported a measurement of the one-way speed of light.J. Finkelstein showed that this experiment actually measures the round trip (two-way) speed of light.
The JPL experiment
This experiment, carried out in 1990 by the NASANASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
Jet Propulsion Laboratory
Jet Propulsion Laboratory
Jet Propulsion Laboratory is a federally funded research and development center and NASA field center located in the San Gabriel Valley area of Los Angeles County, California, United States. The facility is headquartered in the city of Pasadena on the border of La Cañada Flintridge and Pasadena...
, measured the time of flight of light signals through a fibre optic link between two hydrogen maser clocks. In 1992 the experimental results were analysed by Clifford Will who concluded that the experiment did actually measure the one-way speed of light.
In 1997 the experiment was re-analysed by Zhang who showed that, in fact, only the two-way speed had been measured.
Will later confirmed that this conclusion was indeed correct.
Rømer's measurement
The first experimental determination of the speed of light was made by Ole Christensen Rømer. It may seem that this experiment measures the time for light to traverse part of the Earth's orbit and thus determines its one-way speed, however, this experiment was carefully re-analysed by Zhang, who showed that the measurement does not measure the speed independently of a clock sychronization scheme but actually used the Jupiter system as a slowly transported clock to measure the light transit times.Experiments that can be done on the one-way speed of light
Although experiments cannot be done in which the one-way speed of light is measured independently of any clock synchronization scheme, it is possible to carry out experiments that measure a change in the one-way speed of light due, for example, to the motion of the source. Such experiments are the De Sitter double star experimentDe 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...
(1913), conclusively repeated in the x-ray spectrum by K. Brecher in 1977;
or the terrestrial experiment by Alväger, et al. (1963); they show that, when measured in an inertial frame, the one-way speed of light is independent of the motion of the source within the limits of experimental accuracy. In such experiments the clocks may be synchronized in any convenient way, since it is only a change of speed that is being measured.
Observations of the arrival of radiation from distant astronomical events have shown that the one-way speed of light does not vary with frequency.
Other simultaneity issues
According to Debs and Redhead, the same reasoning can also be applied to 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...
. That is, time dilation is measured by synchronizing two stationary clocks A and B, and then the readings of a moving clock C are compared with them. Changing the convention of synchronization for A and B makes the value for time dilation (like the one-way speed of light) directional dependent. However, when time dilation is measured on closed paths, it is not conventional any more and can unequivocally be measured like the two-way speed of light. Time dilation on closed paths was measured in the Hafele–Keating experiment and in experiments on the Time dilation of moving particles such as Bailey et al. (1977).
Thus the so-called 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...
occurs in all theories, in which the two-way speed of light is constant.
Lorentz ether theory
In 1904 and 1905, Hendrik LorentzHendrik 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...
and Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
proposed a theory which explained this result as being due the effect of motion through the aether on the lengths of physical objects and the speed at which clocks ran. Due to motion through the aether objects would shrink along the direction of motion and clocks would slow down. Thus, in this theory, slowly transported clocks do not, in general, remain synchronized although this effect cannot be observed. The equations describing this theory are known as the Lorentz transformations. In 1905 these transformations became the basic equations of Einstein's special theory of relativity which proposed the same results without reference to an aether.
In the theory, the one-way speed of light is not, in general, equal to the two-way speed, due to the motion of the observer through the aether. However, the difference between the one-way and two-way speeds of light can never be observed due to the action of the aether on the clocks and lengths. This theory is thus experimentally indistinguishable from special relativity. For reasons of philosophical preference and because of the development 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...
Lorentz' theory is no longer used.
Edwards' theory
Edwards' theory allows for a more general method of clock synchronization than Einstein's theory, without changing its physical predictions. It replaces Einstein's postulate that the one-way speed of light is constant when measured in an inertial frame with the postulate:The two way speed of light in a vacuum as measured in two (inertial) coordinate systems moving with constant relative velocity is the same regardless of any assumptions regarding the one-way speed.
This allows the one-way speed of light to take the form in a given direction, with the sign of reversed in the opposite direction. In the extreme as approaches 1, light might propagate in one direction instantaneously, provided it takes the entire round-trip time to travel in the opposite direction. The average speed for the round trip remains the experimentally verifiable two-way speed.
All predictions of Edwards' theory are experimentally indistinguishable from those of special relativity; the difference is only that the defined clock time varies from Einstein's according to the distance in a specific direction. For this reason, Edwards' theory is not a test theory of special relativity, but an experimentally equivalent though more complex theory.
Test theories
A number of theories have been developed to allow assessment of the degree to which experimental results differ from the predictions of relativity. These are known as test theories and include the Robertson and Mansouri-Sexl theories. To date, all experimental results agree with special relativity within the experimental uncertainty.Aether theories
Before 1887 it was generally believed that light travelled at a constant speed relative to the hypothesised medium of the aether. For an observer in motion with respect to the aether, this would result in slightly different two-way speeds of light in different directions. In 1887, the Michelson–Morley experiment showed that the two-way speed of light was constant regardless of direction or motion through the aether.Preferred reference frame
A preferred reference frame is a reference frame in which the laws of physics take on a special form. The ability to make measurements which show the one-way speed of light to be different from its two-way speed would, in principle, enable a preferred reference frame to be determined. This would be the reference frame in which the two-way speed of light was equal to the one-way speed.In Einstein's special theory of relativity, all inertial frames of reference are equivalent and there is no preferred frame. There are theories, such as 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....
that are experimentally and mathematically equivalent to special relativity but have a preferred reference frame. In order for these theories to be compatible with experimental results the preferred frame must be undetectable. In other words it is a preferred frame in principle only, in practice all inertial frames must be equivalent, as in special relativity.