One-way speed of light

. 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. Many tests of special relativity such as the Michelson–Morley experiment and the Kennedy–Thorndike experiment have shown within tight limits that in an inertial frame the two-way speed of light is isotropic and independent of the closed path considered. Isotropy experiments of the Michelson–Morley type do not use an external clock to directly measure the speed of light, but rather compare two internal frequencies or clocks. Therefore, such experiments are sometimes called "clock anisotropy experiments", since every arm of a Michelson interferometer can be seen as a light clock having a specific rate, whose relative orientation dependences can be tested. Since 1983 the metre 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 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 "the same time" is 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 is defined such that the one-way speed of light will be measured to be independent of the inertial frame chosen. Some authors such as Mansouri and Sexl (1977) However, others such as Zhang (1995, 1997) and Anderson et al. (1998) showed this interpretation to be incorrect. For instance, Anderson et al. pointed out that the conventionality of simultaneity must already be considered in the preferred frame, so all assumptions concerning the isotropy of the one-way speed of light and other velocities in this frame are conventional as well. Therefore, RMS remains a useful test theory to analyze tests of Lorentz invariance and the two-way speed of light, though not of the one-way speed of light. They concluded: "...one cannot hope even to test the isotropy of the speed of light without, in the course of the same experiment, deriving a one-way numerical value at least in principle, which then would contradict the conventionality of synchrony." Using generalizations of Lorentz transformations with anisotropic one-way speeds, Zhang and Anderson pointed out that all events and experimental results compatible with the Lorentz transformation and the isotropic one-way speed of light must also be compatible with transformations preserving two-way light speed constancy and isotropy, while allowing anisotropic one-way speeds. == Synchronization conventions ==

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. In isotropy experiments, simultaneity conventions are often not explicitly stated but are implicitly present in the way coordinates are defined or in the laws of physics employed. However, if one clock is moved away slowly in frame S 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. In the limit as the speed of transport tends to zero, this method is experimentally and theoretically equivalent to the Einstein convention. Though the effect of time dilation on those clocks cannot be neglected anymore when analyzed in another relatively moving frame S'. This explains why the clocks remain synchronized in S, whereas they are not synchronized anymore from the viewpoint of S', establishing relativity of simultaneity in agreement with Einstein synchronization. Therefore, testing the equivalence between these clock synchronization schemes is important for special relativity, and some experiments in which light follows a unidirectional path have proven this equivalence to high precision. Unfortunately, if the one-way speed of light is anisotropic, the correct time dilation factor becomes \mathcal{T}= \frac{1}{\gamma(1 - \kappa v/c)}, with the anisotropy parameter κ between -1 and +1. This introduces a new linear term, \lim_{\beta \to 0} \mathcal{T} = 1 + \kappa \beta + O(\beta^2) (here \beta=v/c), meaning time dilation can no longer be ignored at small velocities, and slow clock-transport will fail to detect this anisotropy. Thus it is equivalent to Einstein synchronization. Non-standard synchronizations As demonstrated by Hans Reichenbach and Adolf Grünbaum, Einstein synchronization is only a special case of a broader synchronization scheme, which leaves the two-way speed of light invariant, but allows for different one-way speeds. The formula for Einstein synchronization is modified by replacing with ε: Only when time dilation is measured on closed paths, it is not conventional 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 transformations preserving the constancy of the two-way speed of light. == Inertial frames and dynamics ==

It was argued against the conventionality of the one-way speed of light that this concept is closely related to dynamics, the laws of motion and inertial reference frames. Similarly, Ohanian argued that inertial reference frames are defined so that Newton's laws of motion hold in first approximation. Therefore, since the laws of motion predict isotropic one-way speeds of moving bodies with equal acceleration, and because of the experiments demonstrating the equivalence between Einstein synchronization and slow clock-transport synchronization, it appears to be required and directly measured that the one-way speed of light is isotropic in inertial frames. Otherwise, both the concept of inertial reference frames and the laws of motion must be replaced by much more complex ones involving anisotropic coordinates. However, it was shown by others that this is principally not in contradiction with the conventionality of the one-way speed of light. In addition, Iyer and Prabhu distinguished between "isotropic inertial frames" with standard synchrony and "anisotropic inertial frames" with non-standard synchrony. ==Experiments which appear to measure the one-way speed of light==

Experiments which claimed to use a one-way light signal The Greaves, Rodriguez, and Ruiz-Camacho experiment In the October 2009 issue of the American Journal of Physics, Greaves, Rodriguez, and Ruiz-Camacho proposed a new method of measurement of the one-way speed of light. In the June 2013 issue of the journal, Hankins, Rackson, and Kim repeated the Greaves et al. experiment intending to obtain with greater accuracy the one-way speed of light. This experiment assumed that the signal return path to the measuring device has a constant delay, independent of the end point of the light flight path, allowing measurement of the time of flight in a single direction. J. Finkelstein showed that the Greaves et al. experiment actually measures the round-trip (two-way) speed of light. Experiments in which light follows a unidirectional path Many experiments intended to measure the one-way speed of light, or its variation with direction, have been (and occasionally still are) performed in which light follows a unidirectional path. Claims have been made that those experiments have measured the one-way speed of light independently of any clock synchronization convention, but they have all been shown to actually measure the two-way speed, because they are consistent with generalized Lorentz transformations including synchronizations with different one-way speeds on the basis of isotropic two-way speed of light (see sections the one-way speed and generalized Lorentz transformations). In 1992, the experimental results were analyzed 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. 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 synchronization scheme but actually used the Jupiter system as a slowly-transported clock to measure the light transit times. The Australian physicist Karlov also showed that Rømer actually measured the speed of light by implicitly making the assumption of the equality of the speeds of light back and forth. Other experiments comparing Einstein synchronization with slow clock-transport synchronization ==Experiments that can be done on the one-way speed of light==

. Measurements on light from such objects were used to show that the one-way speed of light does not vary with frequency. 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 experiment (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, there is no vacuum dispersion of light. • {{cite web |date=19 November 2009 |title=Editor's Summary |website=Nature |url=http://www.nature.com/nature/journal/v462/n7271/edsumm/e091119-06.html == Experiments on two-way and one-way speeds using the Standard-Model Extension ==

While the experiments above were analyzed using generalized Lorentz transformations as in the Robertson–Mansouri–Sexl test theory, many modern tests are based on the Standard-Model Extension (SME). This test theory includes all possible Lorentz violations not only of special relativity, but of the Standard Model and general relativity as well. Regarding the isotropy of the speed of light, both two-way and one-way limits are described using coefficients (3×3 matrices): • \tilde{\kappa}_{o+} representing anisotropic differences in the one-way speed of counterpropagating beams along an axis, A series of experiments have been (and still are) performed since 2002 testing all of those coefficients using, for instance, symmetric and asymmetric optical resonators. No Lorentz violations have been observed as of 2013, providing current upper limits for Lorentz violations: \tilde{\kappa}_{e-} = (-0.31 \pm 0.73) \times 10^{-17}, \tilde{\kappa}_{o+} = (0.7 \pm 1) \times 10^{-14}, and \tilde{\kappa}_{tr} = (-0.4 \pm 0.9) \times 10^{-10}. For details and sources see ''''. However, the partially conventional character of those quantities was demonstrated by Kostelecky et al, pointing out that such variations in the speed of light can be removed by suitable coordinate transformations and field redefinitions. Though this doesn't remove the Lorentz violation per se, since such a redefinition only transfers the Lorentz violation from the photon sector to the matter sector of SME, thus those experiments remain valid tests of Lorentz invariance violation. There are one-way coefficients of the SME that cannot be redefined into other sectors, since different light rays from the same distance location are directly compared with each other; see the previous section. ==Theories in which the one-way speed of light is not equal to the two-way speed==

Theories equivalent to special relativity Lorentz ether theory In 1904 and 1905, Hendrik Lorentz and Henri Poincaré proposed a theory which explained the negative result of the Michelson-Morley experiment as being due to 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 principally only equal to the two-way speed in the aether frame, though not in other frames 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. Therefore, the Poincaré-Einstein convention is also employed in this model, making the one-way speed of light isotropic in all frames of reference. Even though this theory is experimentally indistinguishable from special relativity, Lorentz's theory is no longer used for reasons of philosophical preference and because of the development of general relativity. Generalizations of Lorentz transformations with anisotropic one-way speeds A synchronization scheme proposed by Reichenbach and Grünbaum, which they called ε-synchronization, was further developed by authors such as Edwards (1963), Anderson and Stedman (1977), who reformulated the Lorentz transformation without changing its physical predictions. All predictions derived from such a transformation are experimentally indistinguishable from those of the standard Lorentz transformation; the difference is only that the defined clock time varies from Einstein's according to the distance in a specific direction. Theories not equivalent to special relativity 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. One such "test theory" is the Standard-Model Extension (SME). It employs a broad variety of coefficients indicating Lorentz symmetry violations in special relativity, general relativity, and the Standard Model. Some of those parameters indicate anisotropies of the two-way and one-way speed of light. However, it was pointed out that such variations in the speed of light can be removed by suitable redefinitions of the coordinates and fields employed. Though this doesn't remove Lorentz violations per se, it only shifts their appearance from the photon sector into the matter sector of SME (see above ''''. ==References==