One-way speed of light

The one-way speed of light is the speed at which a light signal is sent from a transmitter to a receiver (and not back again). The constancy of the one-way speed of light in every inertial system is a basis of the special theory of relativity (SRT). All the experimentally verifiable predictions of the theory that directly affect this postulate can, however, be interpreted ambiguously according to the thesis of the conventionality of simultaneity . Accordingly, all synchronization methods are compatible with the SRT, which are based on a constant-isotropic two- way speed of light, i.e. the average speed from the transmitter to the receiver back to the transmitter, but which allow anisotropic one-way speeds of light. The two-way speed of light can be measured independently of the synchronization scheme, and all experiments carried out for this purpose are in accordance with their constancy and isotropy , cf. Tests of special relativity .

Test theories of the special relativity theory such as the Robertson-Mansouri-Sexl model (RMS) or the standard model extension (SME) were introduced to analyze two-way and one-way experiments, the latter going far beyond the SRT alone. These test theories allow the unambiguous determination of experimental confirmations or violations of the Lorentz invariance. The issue of conventionality plays only a role, if the result in terms of specific, compatible with the SRT synchronization methods interpreted to be what even has the presence of a possible violation of Lorentz no effect. In addition to the constancy and isotropy of the two-way speed of light, it could be determined experimentally that Einstein synchronization and synchronization by slow clock transport are equivalent, which in itself is a confirmation of the SRT. In contrast, the statements about the one-way speed of light derived from this equivalence depend on conventions that are implicitly used in concepts such as “ inertial system ” or “ dynamics of moving bodies”. Synchronization-independent information on the one-way speed of light can be provided if the propagation of different rays is compared directly with one another. This showed that the one-way speed of light of light in a vacuum is independent of its frequency and polarization and of the source speed.

Some authors reject the conventionality of the one-way speed of light or only partially use it in the evaluation of various experiments, which leads to different representations in modern publications. There is also an unfinished philosophical discussion about whether all synchronization methods are to be regarded equally as pure conventions, or whether Einstein synchronization is the only method that corresponds to all the principles of a relativistic theory of spacetime.

Two-way speed of light

The two-way speed of light is the mean speed from a point A, for example a light source, to a mirror B and back again. Since the light starts from A and comes back to A, only one clock is needed to measure the total time, consequently this speed can be determined experimentally regardless of the synchronization scheme. Any measurement in which light follows a closed path is considered a two-way speed measurement. The two-way speed of light is independent of the inertial system chosen. In fact, experiments like the Michelson-Morley experiment or the Kennedy-Thorndike experiment have shown that the two-way speed of light is isotropic and independent of the particular closed path.

One-way speed of light

Although mean speed can be measured along a two-way path, one-way speed of light in one direction or the other is undefined and cannot be found until “the same time” can be defined in two different locations. In order to measure the time it took for light to travel from one place to another, it is necessary to know the start and arrival times (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 from start to finish without a time delay - but no means are known to transmit or evaluate information without a time delay. Consequently, the measured value of the one-way speed depends on the method that was used to synchronize the start and finish clocks - and this is always based on a convention.

However, some authors such as Mansouri and Sexl (1977) or Will (1992) believe that this problem does not necessarily affect the isotropy of the one-way speed of light, for example in the case of deviations due to the influence of a “preferred” ( ether ) reference system Σ. Their analysis was based on a certain interpretation of the RMS test theory of special relativity in connection with one-way and watch transport experiments . While Will agreed that it is impossible to measure the speed of light between two clocks without a synchronization scheme, he felt that testing the isotropy of the speed between the two clocks when the direction of the propagation path changes relative to cannot should depend on the clock synchronization. He added that ether theories can then only be brought into agreement with the SRT with various ad hoc hypotheses . In more recent work (2005, 2006) Will described these experiments as measurements of the isotropy of the speed of light using one-way propagation.

However, this interpretation of RMS was supported by Zhang (1995, 1997) and Anderson et al . (1998) rejected. For example, Anderson et al. from the fact that the conventionality of simultaneity must already be taken into account in the preferred reference system, consequently all information on the one-way speed of light is already conventional in this system. They concluded that one could not hope to test the isotropy without deriving at least in principle a numerical value for the one-way speed of light in the same experiment, which then contradicts the conventionality of synchronization. RMS remains a useful test theory for analyzing tests of Lorentz invariance and two-way speed of light, but not one-way speed of light. Using generalized Lorentz transformations, Zhang and Anderson et al . Showed that all events and experimental results that are compatible with the Lorentz transformation are also compatible with transformations that contain the isotropy of the two-way speed of light, but also allow anisotropic one-way speeds of light (see Section Generalized Lorentz Transformation ).

Synchronization methods

Einstein synchronization

Henri Poincaré (1900) and Albert Einstein (1905) used a synchronization scheme (Poincaré- Einstein synchronization ) which defined the one-way equal to the two-way speed of light. This also defines the isotropy of the speed of light. According to this convention, clocks are synchronous if the following condition is met: A light signal is sent from clock 1 to clock 2 and is immediately sent back with the arrival time at 1 from . Clock 2 two must therefore be set according to the following convention. ${\ displaystyle t_ {1}}$ ${\ displaystyle t_ {3}}$

{\ displaystyle t_ {2} = t_ {1} + {\ tfrac {1} {2}} \ left (t_ {3} -t_ {1} \ right)}

.

whereby this convention represents a fundamental postulate of the special theory of relativity and the origin of the Lorentz transformation .

Non-standard synchronizations

As Hans Reichenbach and Adolf Grünbaum showed, very different conventions can be used for clock synchronization, in which the one-way speed of light is anisotropic, but the two-way speed of light is constant. The value ½ from the Einstein synchronization is replaced with the indefinite expression ε, the value of which can be between 0 and 1:

{\ displaystyle t_ {2} = t_ {1} + \ varepsilon \ left (t_ {3} -t_ {1} \ right)}

.

They concluded from this that it is in principle impossible to unambiguously determine the value of the one-way speed of light or its isotropy , regardless of a simultaneity convention. This was further developed by other authors by introducing generalized Lorentz transformations , in which the two-way speed of light is isotropic and constant, but the one-way speed of light can be anisotropic. These give the same experimental predictions as the Lorentz transformation in its standard form, but the latter is the simplest and most transparent, so that the alternatives need practically not be considered.

Slow watch transport

In addition to the light signal method, there is also the synchronization method of (infinitely) "slow clock transport": It is a direct consequence of time dilation that when two clocks are brought together and synchronized, and then one clock moves quickly and comes back, these clocks are no longer synchronized are (see twin paradox ). However, if a clock is slowly moved back and forth, then these clocks can be synchronized with any approximation by moving them slowly enough (in the limit area where the transport speed approaches zero) and thus minimizing the effect of time dilation within an inertial system. This makes this method equivalent to Einstein synchronization. On the other hand, from the point of view of another inertial system, the time dilation must be taken into account, and again analogous to the Einstein synchronization, the relativity of simultaneity results .

This method is also subject to the same conventions as the light signal synchronization. It must be taken into account that the time dilation of moving clocks also depends on the synchronization scheme. If a clock C moves from A to B, the measured value of the time dilation depends on the synchronization of A and B. It could be shown that this must also be taken into account in the relativistic Doppler effect.

Furthermore, the isotropy of inertial motion itself is based on a convention. If, for example, it is established that the inertial movement of the clocks is isotropic in all directions, this method is equivalent to Einstein synchronization and results in an isotropic one-way speed of light. If, however, the inertial movement of the clocks is determined to be anisotropic (for example by adopting the coordinates of another inertial system), it becomes equivalent to non-standard synchronizations and results in an anisotropic one-way speed of light.

Inertial Systems and Dynamics

Against the conventionality of the one-way speed of light, it was objected that the latter is closely linked to concepts such as dynamics , the laws of motion and inertial systems. A variation of this argument is that, according to the conservation of momentum, two identical bodies, which are accelerated from the same place by an explosion in opposite directions, must always have the same speed. Similarly, Ohanian (2004, 2005) argued that inertial systems must be defined in such a way that Newton's laws of motion remain valid as a first approximation. Since the laws of motion result in the same speeds in different directions with the same accelerations, and because experiments have shown the equivalence of Einstein synchronization and clock transport synchronization, the one-way speed of light must also be isotropic. Otherwise one would have to give up the laws of motion as well as the concept of the inertial system and introduce much more complicated constructs and apparent forces.

Others saw no objection in principle to conventionality in this. Salmon pointed out that momentum conservation in its standard form is defined from the outset to include isotropic one-way velocities. Since this is practically the same convention as the speed of light, objections of this type are based on a circular argument . Macdonald and Martinez (2004) argued to Ohanian that the laws of physics actually get much more complicated with nonstandard synchronization, but they remain consistent and valid. In addition, they argued that inertial systems do not necessarily have to be defined based on Newton's equations of motion. In addition, Iyer and Prabhu (2010) differentiated between “isotropic inertial systems” with standard synchronization and “anisotropic inertial systems” with non-standard synchronization.

Disposable tests of isotropy and constancy

In a series of precise one-way isotropy measurements with light of different frequencies, in accordance with the SRT, no anisotropies were detected. While some authors continue to view such experiments as direct measurements of the isotropy of the one-way speed of light, from a conventionalist point of view they are interpreted more as confirmations of the isotropy of the two-way speed of light (for different interpretations see sections One-way speed of light and Generalized Lorentz Transform ).

An important consequence of many of these experiments is also that they can be viewed as direct or indirect tests of the equivalence of Einstein and transport synchronization, which is also an important confirmation of the prediction of special relativity. In contrast, statements about the one-way speed of light derived therefrom depend on conventions in concepts such as the inertial system or dynamics of moving bodies "(for various interpretations in this context see the sections on slow clock transport and inertial systems and dynamics ).

Surname	year	description	${\ displaystyle \ Delta c / c}$
Rømers measurement of the speed of light	1676	The motion of Jupiter's moon Io is examined. The mean period of rotation of the moon could be determined from the entry and exit of Jupiter's shadow. With this value the time of the eclipse of the moon can be predicted and the speed of light could be determined from the measured delays. The role of the slow clock transport is played here by the movement of the Jupiter system.
Mössbauer rotor experiments	1960s	Here gamma radiation was sent from the edge of a disk to a detector in the middle. During the rotation, anisotropies in the speed of light would have led to a corresponding Doppler effect, but no shift was discovered.	${\ displaystyle <3 \ times 10 ^ {- 8}}$
Vessot et al.	1980	Comparison of the transit times of the uplink and downlink signals from Gravity Probe A.	${\ displaystyle \ sim 10 ^ {- 8} \!}$
Riis et al.	1988	Comparison of the frequency of the two-photon absorption in a fast particle beam, the direction of which has been changed relative to the fixed stars , with the frequency of an absorber at rest.	${\ displaystyle <3 \ times 10 ^ {- 9}}$
Krisher et al.	1990	In the Jet Propulsion Laboratory experiment , the phases between two resting hydrogen maser clocks at a distance of 21 km were compared using the Deep Space Network and an ultra-stable optical waveguide .	${\ displaystyle <2 \ times 10 ^ {- 8}}$
Nelson et al .	1992	Comparison of the frequencies of a moving hydrogen maser watch and laser light pulses. The distance was 26 km.	${\ displaystyle <1 {,} 5 \ times 10 ^ {- 6}}$
Wolf & Petit	1997	Direct test of the equivalence of Einstein synchronization and synchronization through slow clock transport with GPS .	${\ displaystyle <5 \ times 10 ^ {- 9}}$

In addition to isotropy measurements, special one-way methods for time-of-flight measurements have also been developed, but such measurements are more difficult due to the greater accuracy required in the synchronization. It should also be noted here that these measurements ultimately always relate to the underlying two-way speed of light. It was found that the speed of gamma radiation from a moving source corresponds to the speed of light (see Alväger ). Time-of-flight measurements with light and electrons showed that they move almost at the same speed (see Bertozzi, Brown, Guiragossián ). Also, measurements of neutrino speeds using of GPS -synchronisierten watches were no deviations.

Disposable tests independent of synchronization methods

If it is known that different rays were emitted from the same place and have propagated along the same route, then by direct comparison of these rays it is possible to determine certain properties of the one-way speed of light without a special clock synchronization being important. It could be shown that the one-way speed of light of different light rays does not depend on the different movement of the light source (see DeSitter, Brecher ). Other experiments investigating the arrival of light from distant astronomical events also showed that there is no dependence on light energy (vacuum dispersion) and on light polarization (vacuum birefringence) (see Modern Tests of Lorentz invariance ). Likewise, neutrinos of low energy arrived almost simultaneously with light from a distant supernova , which speaks for almost identical speeds (see measurements of the neutrino speed ).

Tests of one-way anisotropy in the standard model extension

While the above experiments were evaluated using generalized Lorentz transformations and the RMS test theory, many modern tests of Lorentz invariance are evaluated using the advanced standard model extension (SME). In addition to the SRT, this also contains the effects of possible Lorentz violations on the Standard Model and the general theory of relativity . Regarding the isotropy of the speed of light, SME contains coefficients (3x3 matrices) for both two-way and one-way (an) isotropies:

${\ displaystyle {\ tilde {\ kappa}} _ {e-}}$ can be interpreted as anisotropic shifts in the two-way speed of light,
${\ displaystyle {\ tilde {\ kappa}} _ {o +}}$ can be interpreted as anisotropic shifts in the one-way speed of light of oppositely propagating light rays,
${\ displaystyle {\ tilde {\ kappa}} _ {tr}}$ can be interpreted as isotropic (direction-independent) shifts in the one-way phase velocity of light.

A number of experiments have been (and are) carried out since 2002 to determine or exclude these and many other coefficients, using for example symmetrical and asymmetrical optical resonators . No Lorentz injuries were observed until 2013, with upper limits of:

{\ displaystyle {\ tilde {\ kappa}} _ {e -} = (- 0 {,} 31 \ pm 0 {,} 73) \ times 10 ^ {- 17}; {\ tilde {\ kappa}} _ {o +} = 0 {,} 7 \ ​​pm 1 \ times 10 ^ {- 14}; {\ tilde {\ kappa}} _ {tr} = - 0 {,} 4 \ pm 0 {,} 9 \ times 10 ^ {- 10}}

.

For details and sources see Modern Tests of Lorentz invariance # speed of light .

However, as Kostelecky et al emphasize, the sometimes conventional character of these variations in the speed of light must be pointed out. These can be made to disappear through suitable coordinate transformations and field redefinitions. However, this does not undo the existence of a Lorentz violation per se, but merely shifts it from the photon sector to the matter sector of SME, whereby the validity of SME for testing Lorentz violations remains unaffected. In addition, there are also photon coefficients that cannot be redefined in other areas, since they affect different rays that come from the same place and can therefore be compared directly with one another (see previous section on "vacuum birefringence").

Experimentally equivalent theories or reformulations of the STR

Lorentz's theory of ethers

One example is Lorentz's theory of ethers , which was developed by Hendrik Antoon Lorentz , Joseph Larmor , and Henri Poincaré between 1892 and 1905. It starts from a preferred reference system (the aether at rest), whereby the one-way speed of light is only constant relative to this system, and consequently not constant relative to all other systems. However, this was refuted by the Michelson-Morley experiment , so that the introduction of the Lorentz transformation (which, among other ad hoc hypotheses , includes a length contraction and time dilation of moving processes) became necessary. This also has the consequence that clocks directed according to the Poincaré-Einstein Convention and clocks directed with slow clock transport indicate the same time. The reason why this theory is experimentally equivalent to the special relativity theory is based on the fact that in the special relativity theory any inertial system can be selected from which all processes in stationary and moving bodies (with the exception of gravitation) can be described without contradiction . Moving bodies are subject to time dilation, Lorentz contraction, etc., the combination of which means that the "moving" observer can also consider themselves to be at rest and can assume the one-way and two-way speed of light to be constant. The Lorentzian ether theory is based on the fact that such an inertial system is called “absolute, substantial ether”, and all bodies resting in it can be viewed as “absolutely” resting and bodies moving relative to it as “actually” moving. Since the latter are subject to the same effects as "moving" bodies in the special theory of relativity, the moving observers can also imagine themselves at rest and describe the one-way and two-way speed of light as constant, although in "reality" they are not.

Although in principle consistent and in agreement with the predictions of the SRT, this model is not considered as a serious alternative by the great majority of physicists due to the cumbersome and unnatural introduction of ad hoc hypotheses.

Generalized Lorentz Transformation

Based on the Reichenbach-Grünbaum ε-synchronization, some authors such as Edwards (1963), Winnie (1970), Anderson and Stedman (1977) generalized the Lorentz transformations, with Einstein's postulate of the constancy of the one-way speed of light, measured in an inertial system, is replaced by the following postulate:

The two-way speed of light in a vacuum, measured in two (inertial) coordinate systems that move with constant relative speed, is the same, regardless of any assumptions about the one-way speed of light.

This enables, for example, the one-way speed of light in a certain direction to increase the value

{\ displaystyle c _ {\ pm} = {\ frac {c} {1 \ pm \ kappa}}}

.

assumes, whereby the sign is reversed in the opposite direction and κ can assume all possible values from −1 to 1. Only the average speed for the way there and back, i.e. H. the two-way speed of light remains as the only measurable speed. According to Anderson et al . the generalized Lorentz transformation results for arbitrary boosts with:

{\ displaystyle {\ begin {aligned} 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, \\ {\ tild e {\ gamma}} = & \ gamma \ left (1- \ kappa \ cdot \ mathbf {v} / c \ right), \\ {\ tilde {\ mathbf {v}}} = & {\ frac {\ mathbf {v}} {1- \ kappa \ cdot \ mathbf {v} / c}}, \ end {aligned}}}

where κ and κ 'are the synchronization vectors in S and S'. This transformation leaves the two-way speed of light unchanged, and allows different one-way speeds of light. κ = 0 results in Einstein synchronization and the usual Lorentz transformation. As Edwards, Winnie or Mansouri and Sexl showed, a kind of "absolute simultaneity" can even be created by a suitable choice of synchronization vectors. I.e. in a single reference system the one-way speed of light is isotropic, in all others the time displays of this preferred reference system are taken over by "external synchronization".

Experimentally not equivalent theories to the STR

Test theories of special relativity

These models were developed in order to allow the construction of models (in contrast to Lorentz's theory of ethers or Edwards reformulation) that do not agree experimentally with the special theory of relativity. This enables the assessment of experimental results if deviations from the Lorentz invariance are measured. A frequently used model is the Robertson-Mansouri-Sexl test theory (RMS), which allows the analysis of deviations from the two-way speed of light and the equivalence of Einstein synchronization and transport synchronization. On the other hand, for the long-term controversial statements of this model on the analysis of one-way measurements, see the section on one-way speed of light .

A model that goes even further is the Standard Model Extension (SME), which not only includes all effects of any Lorentz violations of the SRT, but also the Standard Model and the General Theory of Relativity. Here, too, coefficients relating to one-way and two-way light velocities are evaluated, but here the relationships are much more complicated, see section Tests of one-way anisotropy in the standard model extension .

Historical models

In the original theory of the aether at rest, not only the one-way but also the two-way speed of light is only constant for an observer who is at rest in the aether. In 1887 the Michelson-Morley experiment showed that the two-way speed of light does not depend on the speed of the ether.

The completely entrained aether, according to which the one-way speed of light is influenced by the movement of the aether within and in the vicinity of matter, was refuted by the phenomenon of aberration , the Sagnac effect etc.

In the emission theory , in which there is no ether, the one-way speed of light depends on the speed of the light source. But this theory has also been refuted many times (double star observations, pion experiments).

literature

Max Jammer : Concepts of Simultaneity: From Antiquity to Einstein and Beyond . Johns Hopkins University Press, 2008, ISBN 0-8018-8953-7 .

Allen Janis (2010): Conventionality of Simultaneity. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .

Guido Rizzi, Matteo Luca Ruggiero, Alessio Serafini: Synchronization Gauges and the Principles of Special Relativity . In: Foundations of Physics . 34, No. 12, 2004, pp. 1835-1887. arxiv : gr-qc / 0409105 . bibcode : 2004FoPh ... 34.1835R . doi : 10.1007 / s10701-004-1624-3 .

Sebastiano Sonego, Massimo Pin: Foundations of anisotropic relativistic mechanics . In: Journal of Mathematical Physics . 50, No. 4, 2008, pp. 042902-042902-28. arxiv : 0812.1294 . bibcode : 2009JMP .... 50d2902S . doi : 10.1063 / 1.3104065 .

Web links

Mathpages: Conventional Wisdom , Round Trips and One-Way Speeds , Teaching Special Relativity

Individual evidence

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↑ ^a ^b ^c ^d ^e ^f Anderson, R .; Vetharaniam, I .; Stedman, GE: Conventionality of synchronization, gauge dependence and test theories of relativity . In: Physics Reports . 295, No. 3-4, 1998, pp. 93-180. bibcode : 1998PhR ... 295 ... 93A . doi : 10.1016 / S0370-1573 (97) 00051-3 .
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[zhang-1] Yuan-Zhong Zhang: Special Relativity and Its Experimental Foundations . World Scientific , 1997, ISBN 978-981-02-2749-4 ( online ). online ( Memento of the original from May 19, 2012 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2

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