One-way speed of light

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.^{[1][2][3][4][5][6][7][8]}

Experiments that attempted to probe the one-way speed of light have been proposed, but none has succeeded in doing so.^[9] It was later shown that these experiments are in fact measuring the two-way speed.^[1][10]

The 'speed of light' in this article refers to the speed of all electromagnetic radiation in vacuum.

One-way vs. two-way speed of light

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 has been defined as the distance traveled by light in vacuum in ¹⁄_299,792,458 second.^[11] 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 is defined such that the one-way speed of light will be measured to be independent of the inertial frame chosen.^[12]

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

See also: Einstein synchronization

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

See also: Twins paradox

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.^[13][14]

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.^[15]

J. Finkelstein showed that this experiment actually measures the round trip (two-way) speed of light.^[16]

The JPL experiment

This experiment, carried out in 1990 by the NASA Jet Propulsion Laboratory, measured the time of flight of light signals through a fibre optic link between two hydrogen maser clocks.^[17] In 1992 the experimental results were analysed by Clifford Will who concluded that the experiment did actually measure the one-way speed of light.^[18]

In 1997 the experiment was re-analysed by Zhang who showed that, in fact, only the two-way speed had been measured.^[19] 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.^[20]

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 experiment (1913), conclusively repeated in the x-ray spectrum by K. Brecher in 1977;^[21] or the terrestrial experiment by Alväger, et al. (1963);^[22] 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.^[23]

Other simultaneity issues

According to Debs and Redhead,^[24] the same reasoning can also be applied to time dilation. 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).^[25] Thus the so-called twin paradox occurs in all theories, in which the two-way speed of light is constant.

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

See also: Lorentz ether theory

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 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.

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.^[5]

This allows the one-way speed of light to take the form c/(1+q) in a given direction, with the sign of q reversed in the opposite direction. In the extreme as q 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.^[26]

Theories not equivalent to special relativity

Test theories

See also: Test theory and Test theories of special relativity

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^[27] theories. To date, all experimental results agree with special relativity within the experimental uncertainty.

Aether theories

See also: Luminiferous aether

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 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.

References

1. ^ ^{a b} Yuan-Zhong Zhang (1997). Special Relativity and Its Experimental Foundations. World Scientific. ISBN 9789810227494. http://www.worldscibooks.com/physics/3180.html. 
2. ^ Anderson, R.; Vetharaniam, I.; Stedman, G. E. (1998), "Conventionality of synchronisation, gauge dependence and test theories of relativity", Physics Reports 295 (3-4): 93–180, Bibcode 1998PhR...295...93A, doi:10.1016/S0370-1573(97)00051-3 
3. ^ Conventionality of Simultaneity entry by Allen Janis in the Stanford Encyclopedia of Philosophy, 2010
4. ^ Mathpages: Conventional Wisdom and Round Trips and One-Way Speeds
5. ^ ^{a b} Edwards, W. F. (1963). "Special Relativity in Anisotropic Space". American Journal of Physics 31 (7): 482–489. Bibcode 1963AmJPh..31..482E. doi:10.1119/1.1969607. 
6. ^ Winnie, J. A. A. (1970). "Special Relativity without One Way Velocity Assumptions". Philosophy of Science 37: 81–99, 223–38. JSTOR 186029. 
7. ^ Rizzi, Guido; Ruggiero, Matteo Luca; Serafini, Alessio (2004). "Synchronization Gauges and the Principles of Special Relativity". Foundations of Physics 34 (12): 1835–1887. arXiv:gr-qc/0409105. Bibcode 2004FoPh...34.1835R. doi:10.1007/s10701-004-1624-3. 
8. ^ Sonego, Sebastiano; Pin, Massimo (2008). "Foundations of anisotropic relativistic mechanics". Journal of Mathematical Physics 50 (4): 042902-042902-28. arXiv:0812.1294. Bibcode 2009JMP....50d2902S. doi:10.1063/1.3104065. 
9. ^ Michael Tooley (2000). Time, tense, and causation. Oxford University Press. p. 350. ISBN 9780198250746. http://books.google.co.uk/books?id=xNHU8Kpy-PsC. 
10. ^ Jong-Ping Hsu, Yuan-Zhong Zhang (2001). Lorentz and Poincaré Invariance: 100 Years of Relativity. World Scientific. ISBN 9789810247218. http://books.google.co.uk/books?id=jryk42J8oQIC. 
11. ^ 17th General Conference on Weights and Measures (1983), Resolution 1,
12. ^ Zhang (1997), p 24
13. ^ Hafele, J.; Keating, R. (July 14, 1972). "Around the world atomic clocks:predicted relativistic time gains". Science 177 (4044): 166–168. Bibcode 1972Sci...177..166H. doi:10.1126/science.177.4044.166. PMID 17779917. http://www.sciencemag.org/cgi/content/abstract/177/4044/166. Retrieved 2006-09-18. 
14. ^ C.O. Alley, in NASA Goddard Space Flight Center, Proc. of the 13th Ann. Precise Time and Time Interval (PTTI) Appl. and Planning Meeting, p. 687-724, 1981, available online at http://www.pttimeeting.org/archivemeetings/index9.html
15. ^ Greaves, E. D.; Rodríguez, An Michel; Ruiz-Camacho, J. (2009), "A one-way speed of light experiment", American Journal of Physics 77 (10): 894–896, Bibcode 2009AmJPh..77..894G, doi:10.1119/1.3160665 
16. ^ Finkelstein, J. (2009), "One-way speed of light?", American Journal of Physics 78 (8): 877, arXiv:0911.3616, Bibcode 2009arXiv0911.3616F, doi:10.1119/1.3364868 
17. ^ T P Krishner et al. Phys Rev D 42 (1990) 731
18. ^ C N Will Phys. Rev. D 45 (1992) 403
19. ^ Zhang (1997), pp. 148–150
20. ^ Zhang (1997), pp. 91-94
21. ^ Brecher, K. (1977), "Is the speed of light independent of the velocity of the source", Physical Review Letters 39: 1051–1054, Bibcode 1977PhRvL..39.1051B, doi:10.1103/PhysRevLett.39.1051. 
22. ^ Alväger, T.; Nilsson, A.; Kjellman, J. (1963), "A Direct Terrestrial Test of the Second Postulate of Special Relativity", Nature 197 (4873): 1191, Bibcode 1963Natur.197.1191A, doi:10.1038/1971191a0 
23. ^ Amelino-Camelia, G (2009). "Astrophysics: Burst of support for relativity". Nature 462 (7271): 291–292. Bibcode 2009Natur.462..291A. doi:10.1038/462291a. PMID 19924200. Lay summary – Nature (19 November 2009). 
24. ^ Debs, Talal A.; Redhead, Michael L. G. (1996). "The twin "paradox" and the conventionality of simultaneity". American Journal of Physics 64 (4): 384–392. Bibcode 1996AmJPh..64..384D. doi:10.1119/1.18252. 
25. ^ Bailey, H.; Borer, K.; Combley F.; Drumm H.; Krienen F.; Lange F.; Picasso E.; Ruden W. von; Farley F. J. M. ; Field J. H.; Flegel W. & Hattersley P. M. (1977). "Measurements of relativistic time dilatation for positive and negative muons in a circular orbit". Nature 268 (5618): 301–305. Bibcode 1977Natur.268..301B. doi:10.1038/268301a0. 
26. ^ Zhang (1997), pp. 75–101
27. ^ Mansouri R., Sexl R.U. (1977), "A test theory of special relativity. I: Simultaneity and clock synchronization", General. Relat. Gravit. 8 (7): 497–513, Bibcode 1977GReGr...8..497M, doi:10.1007/BF00762634