When using the term "the speed of light" it is sometimes necessary to make the distinction between its one-way speed and its two-way speed. 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 a mirror (or other method of reflection) and back again to the detector. 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 attempt to directly probe the one-way speed of light independent of synchronization have been proposed, but none have succeeded in doing so. Those experiments directly establish that synchronization with slow clock-transport is equivalent to Einstein synchronization, which is an important feature of special relativity. However, those experiments cannot directly establish the isotropy of the one-way speed of light since it has been shown that slow clock-transport, the laws of motion, and the way inertial reference frames are defined already involve the assumption of isotropic one-way speeds and thus, are equally conventional. In general, it was shown that these experiments are consistent with anisotropic one-way light speed as long as the two-way light speed is isotropic.
The "speed of light" in this article refers to the speed of all electromagnetic radiation 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.
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.17th General Conference on Weights and Measures (1983), Resolution 1, 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.Zhang (1997), p 24
Some authors such as Mansouri and Sexl (1977) as well as Will (1992) argued that this problem doesn't affect measurements of the isotropy of the one-way speed of light, for instance, due to direction-dependent changes relative to a "preferred" (aether) frame Σ. They based their analysis on a specific interpretation of the RMS test theory in relation to experiments in which light follows a unidirectional path and to slow clock-transport experiments. Will agreed that it is impossible to measure the one-way speed between two clocks using a time-of-flight method without a synchronization scheme, though he argued: "...a test of the isotropy of the speed between the same two clocks as the orientation of the propagation path varies relative to Σ should not depend on how they were synchronized...". He added that aether theories can only be made consistent with relativity by introducing ad hoc hypotheses. In more recent papers (2005, 2006) Will referred to those experiments as measuring the "isotropy of light speed using one-way propagation".
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.
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. If a signal sent from A at time is arriving at B at time and coming back to A at time , then the following convention applies: .
The details of this method and the conditions that assure its consistency are discussed in Einstein synchronization.
Slow clock-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. This effect is due to time dilation. This was measured in a variety of tests and is related to the twin paradox.
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 , with the anisotropy parameter κ between -1 and +1. This introduces a new linear term, (here ), 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:
ε can have values between 0 and 1. It was shown that this scheme can be used for observationally equivalent reformulations of the Lorentz transformation, see Generalizations of Lorentz transformations with anisotropic one-way speeds.
As required by the experimentally proven equivalence between Einstein synchronization and slow clock-transport synchronization, which requires knowledge of time dilation of moving clocks, the same non-standard synchronizations must also affect time dilation. It was indeed pointed out that time dilation of moving clocks depends on the convention for the one-way velocities used in its formula. That is, time dilation can be 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. The same conventionality also applies to the influence of time dilation on the Doppler effect. 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. Salmon described some variations of this argument using momentum conservation, from which it follows that two equal bodies at the same place which are equally accelerated in opposite directions, should move with the same one-way velocity. 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.