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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.
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. Similarly, differences in the one-way propagation between left- and right-handed photons, leading to vacuum birefringence, were excluded by observation of the simultaneous arrival of distant star light. For current limits on both effects, often analyzed with the Standard-Model Extension, see Vacuum dispersion and Vacuum birefringence.
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 (3x3 matrices):
\tilde{\kappa}_{e-} representing anisotropic shifts in the two-way speed of light,
\tilde{\kappa}_{o+} representing anisotropic differences in the one-way speed of counterpropagating beams along an axis,
\tilde{\kappa}_{tr} representing isotropic (orientation independent) shifts in the one-way phase velocity of light.
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-}=\scriptstyle(-0.31\pm0.73)\times10^{-17}, \tilde{\kappa}_{o+}=\scriptstyle 0.7\pm1\times10^{-14}, and \tilde{\kappa}_{tr}=\scriptstyle -0.4\pm0.9\times10^{-10}. For details and sources see Modern searches for Lorentz violation#Speed of light.
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 form 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.
In 1904 and 1905, Hendrik Lorentz 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 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.
A sychronisation scheme proposed by Reichenbach and Grünbaum, which they called ε-synchronization, was further developed by authors such as Edwards (1963), Winnie (1970), Anderson and Stedman (1977), who reformulated the Lorentz transformation without changing its physical predictions. For instance, Edwards replaced Einstein's postulate that the one-way speed of light is constant when measured in an inertial frame with the postulate:
So the average speed for the round trip remains the experimentally verifiable two-way speed, whereas the one-way speed of light is allowed to take the form in opposite directions:
c_{\pm}=\frac{c}{1\pm\kappa}.
κ can have values between 0 and 1. In the extreme as κ approaches 1, light might propagate in one direction instantaneously, provided it takes the entire round-trip time to travel in the opposite direction. Following Edwards and Winnie, Anderson et al. formulated generalized Lorentz transformations for arbitrary boosts of the form:
\begin{align}
d\tilde{t}'= & \tilde{\gamma}\left[1+\kappa\cdot\tilde{\mathbf{v}/c-\kappa'\cdot\tilde{\mathbf{v}'/c\right]d\tilde{t}-\left(\kappa'+\tilde{\gamma}\tilde{\mathbf{v}'\right)\cdot d\tilde{\mathbf{x}/c\\
& -\left[\tilde{\gamma}\left(1+\kappa\cdot\tilde{\mathbf{v}/c\right)-1\right]\frac{\kappa'\cdot\tilde{\mathbf{v}}{\tilde{\mathbf{v}^{2}c}\tilde{\mathbf{v}\cdot d\tilde{\mathbf{x}+\tilde{\gamma}\kappa\cdot\tilde{\mathbf{v}\left(\kappa\cdot d\tilde{\mathbf{x}\right)/c,\\
d\tilde{\mathbf{x}'= & -\tilde{\gamma}\tilde{\mathbf{v}d\tilde{t}+d\tilde{\mathbf{x}+\left[\tilde{\gamma}\left(1+\kappa\cdot\tilde{\mathbf{v}/c\right)-1\right]\frac{\tilde{\mathbf{v}\cdot d\mathbf{x}{\tilde{\mathbf{v}^{2}\tilde{\mathbf{v}-\tilde{\gamma}\tilde{\mathbf{v}\left(\kappa\cdot d\tilde{\mathbf{x}\right)/c,\\
\tilde{\gamma}= & \gamma\left(1-\kappa\cdot \mathbf{v}/c\right),\\
\tilde{\mathbf{v}= & \frac{\mathbf{v}{1-\kappa\cdot \mathbf{v}/c},
\end{align}
(with κ and κ' being the synchrony vectors in frames S and S', respectively). This transformation indicates the one-way speed of light is conventional in all frames, leaving the two-way speed invariant. κ=0 means Einstein synchronization which results in the standard Lorentz transformation. As shown by Edwards, Winnie and Mansouri-Sexl, by suitable rearrangement of the synchrony parameters even some sort of "absolute simultaneity" can be achieved, in order to simulate the basic assumption of Lorentz ether theory. That is, in one frame the one-way speed of light is chosen to be isotropic, while all other frames take over the values of this "preferred" frame by "external synchronization".
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.
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 (RMS) theories. To date, all experimental results agree with special relativity within the experimental uncertainty.
Another 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 Experiments on two-way and one-way speeds using the Standard-Model Extension.
Before 1887 it was generally believed that light travelled as a wave 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. At the time, the obvious explanation for this effect was that objects in motion through the aether experience the combined effects of time dilation and length contraction in the direction of motion.
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 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.
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