Quang の phiến đạo tốc độ

Quang tốcの ngữ を sử う thời, phiến đạo tốc độ と vãng phục tốc độ を khu biệt する tất yếu がある tràng hợp がある. ある quang nguyên から kiểm xuất khí までのPhiến đạo tốc độは, quang nguyên とKiểm xuất khíそれぞれの địa điểm での thời khắc をどのように đồng kỳ させるかについての quy ước ( thời kế の đồng kỳ phương pháp に quan する tứ ý đích な quyết định ) と độc lập にTrắc địnhすることができず, thật tế に thật nghiệm đích に trắc định されているのは quang nguyên から kiểm xuất khí までのVãng phục tốc độである.アインシュタインは quang の phiến đạo tốc độ が vãng phục tốc độ と đẳng しくなるような thời kế の đồng kỳ pháp を tuyển んだ (en:アインシュタインの đồng kỳ pháp). Nhậm ý の quán tính hệ において quang の phiến đạo tốc độ が nhất định であることが bỉ のĐặc thù tương đối tính lý luậnの cơ sở となってはいるが, その lý luận の dư ngôn のうち thật nghiệm đích に kiểm chứng khả năng であったものは toàn て, この đồng kỳ pháp の tuyển び phương には y tồn していない. ( つまり đặc thù tương đối tính lý luận は chứng minh されているが, その thời kế の đồng kỳ pháp については nhậm ý tính が tàn っている )

Đồng kỳ pháp に y tồn せず, trực tiếp に quang の phiến đạo tốc độ を trắc định しようと thí みた thật nghiệm がいくつかあるが, どれも thành công には chí っていない. それらの thật nghiệm は trực tiếp đích にはTrì い thời kế thâu tống による đồng kỳ pháp( slow clock-transport ) がアインシュタインの đồng kỳ pháp と đẳng 価であることを xác lập しており, これは đặc thù tương đối tính lý luận の trọng yếu な đặc trưng となっている. これらの thật nghiệm は trì い thời kế thâu tống と đẳng 価であることが kỳ されているため, quang の phiến đạo tốc độ の đẳng phương tính を trực tiếp đích に xác lập できていないが,ニュートン lực họcや quán tính hệ の định nghĩa の sĩ phương tự thể についても phiến đạo tốc độ が đẳng phương đích であることを仮 định しているため, tứ ý tính に quan してはどれも đồng じ vấn đề を bão えている. Nhất bàn に, これらの thật nghiệm は, quang の vãng phục tốc độ が đẳng phương đích であり, かつ phiến đạo tốc độ が phi đẳng phương đích である tràng hợp と chỉnh hợp khả năng であることが kỳ されている.

この ký sự における “Quang tốc” とは toàn てのĐiện từ baのChân khôngTrung の tốc độ のことをいう.

Vãng phục tốc độ

マイケルソン càn hồ kếにおける quang の vãng phục lộ

Quang の vãng phục tốc độ とは, ある điểm ( quang nguyên ) から kính まで hành って quy ってきた quang の, bình quân tốc độ である. Quang は đồng nhất địa điểm から phát し, また đạt するため, hợp kế thời gian の trắc định には nhất つの thời kế しか tất yếu としない. それゆえ, この tốc độ は, いかなる thời kế の đồng kỳ phương pháp からも độc lập に, thật nghiệm đích に trắc định することができる. Trực tuyến を vãng phục する tràng hợp だけでなく, quang が bế lộ ( closed path ) をつくるいかなる trắc định も, vãng phục tốc độ の trắc định をしていることになる.

マイケルソン・モーリーの thật nghiệmやKennedy–Thorndikeの thật nghiệmといった đa くのĐặc thù tương đối tính lý luận の kiểm chứng thật nghiệmは, ある quán tính hệ における quang の vãng phục tốc độ は, đẳng phương đích であり, bế lộ の thủ り phương と độc lập である, ということを cực めて cao い tinh độ で kỳ してきた. マイケルソン・モーリー hình の đẳng phương tính に quan する thật nghiệm は, マイケルソン càn hồ kế の toàn て oản が đặc định の chu kỳ を trì っており, toàn thể で tương đối đích な phương giác の y tồn tính を kiểm chứng することができるQuang thời kếとみなせることから, “Thời kế đồng kỳ thật nghiệm” とも hô ばれることがある.

1983 niên dĩ lai, quang が chân không trung で1Miểuあたりに tiến む cự ly の1⁄299,792,458として1メートルが định nghĩa されてきた.これはつまり, quang tốc はもはやQuốc tế 単 vị hệでは thật nghiệm đích に trắc định できず, メートルの trường さを tha の trường さの cơ chuẩn に đối して bỉ giác することが tất yếu であることを ý vị する.

Phiến đạo tốc độ

Quang hành soaを khảo える tế の phiến đạo の quang lộ

Vãng phục lộ にわたる bình quân tốc độ は trắc định khả năng であるが, ある phương hướng への phiến đạo tốc độ については, nhị つの biệt 々の địa điểm での “Đồng thời” とは hà であるかを định nghĩa しない hạn り, vị định nghĩa のままである. Quang がある tràng sở から biệt の tràng sở へと tiến むのにかかった thời gian を trắc định するには, xuất phát thời khắc と đáo trứ thời khắc を đồng じ thời gian xích độ で trắc định する tất yếu がある. これを thật hiện するためには, nhị つの đồng kỳ した thời kế を xuất phát địa điểm と đáo trứ địa điểm それぞれに trí くか, xuất phát địa điểm から đáo trứ địa điểm まで thuấn thời に hà らかの thủ đoạn で xuất phát thời khắc に quan する tín hào を tống るかのどちらかが tất yếu となる. ある tình báo を, thuấn gian đích に di tống する thủ đoạn は tri られていない ( quang tốc を siêu える tình báo vân bàn の thủ đoạn tự thể, nhất bàn đích には tồn tại しないと khảo えられている ). それゆえ, phiến đạo の bình quân tốc độ の trắc định trị はいつも xuất phát địa điểm と đáo trứ địa điểm の thời kế の đồng kỳ に dụng いられた phương pháp に y tồn しており, nhân gian の trắc で tứ ý đích に định nghĩa を quyết める thoại となっているのである.ローレンツ変 hoánは, quang の phiến đạo tốc độ が quán tính hệ の tuyển び phương と độc lập に trắc định されるように định nghĩa されている.

MansouriやSexl (1977)またClifford Will(1992)は, ある đặc định の (エーテル) tọa tiêu hệ Σに đối する tương đối đích な phương hướng y tồn tính の変 hóa を khảo えるなどすれば, この vấn đề は quang の phiến đạo tốc độ の đẳng phương tính の trắc định に ảnh hưởng しないと chủ trương した. Bỉ らの phân tích はRMS kiểm chứng lý luậnの,Quang の phiến đạo lộ を trắc る thật nghiệmやTrì い thời kế thâu tốngの thật nghiệm との quan hệ における đặc định の giải 釈に cơ づいている. Willは đồng kỳ pháp なしに quang の quang hành thời gian を dụng いて nhị つの thời kế の gian の phiến đạo tốc độ を trắc định することは bất khả năng であるとしているが,“... Vân bàn lộ の phương hướng がΣ hệ に đối して変 hóa するときの, đồng じ nhị つの thời kế の gian の tốc độ の đẳng phương tính の kiểm chứng は, それらがどのように đồng kỳ されたかによらないはずである”と chủ trương している. Bỉ はアドホックな仮 thuyếtを thiệu giới することによって, エーテル lý luận だけが tương đối tính と chỉnh hợp をとることができると gia えている.また tối cận の luận văn (2005, 2006)でWillはそれらの thật nghiệm を “Phiến đạo vân bàn を dụng いた quang tốc の đẳng phương tính”を trắc định するものと hô んでいる.

しかし tha の, Zhang (1995, 1997)やAndersonet al.(1998)などは, この giải 釈が ngộ りであると kỳ している. Lệ えば, Andersonet al.は, ある đặc định の tọa tiêu hệ を tuyển ぶ thời điểm で kí に đồng thời tính についての tứ ý đích quyết định がなされており, その tọa tiêu hệ における quang の phiến đạo tốc độ や tha の tốc độ の đẳng phương tính に quan する toàn ての仮 định もまた tứ ý đích quyết định であることを chỉ trích している. それゆえ, RMS lý luận はローレンツ bất 変 tính と quang の vãng phục tốc độ について phân tích するのに hữu dụng な kiểm chứng lý luận に lưu まっており, quang の phiến đạo tốc độ についてはそうではない. Bỉ らは “... Quang の phiến đạo tốc độ の đẳng phương tính については, đồng nhất の thật nghiệm nội で, nguyên lý đích には thiếu なくとも phiến đạo tốc độ の sổ trị を đạo xuất しなくては kiểm chứng する vọng みがないが, それは đồng kỳ pháp に quan する tứ ý tính と mâu thuẫn することになる”と kết luận phó けている.ローレンツ変 hoán の, phiến đạo tốc độ に quan する phi đẳng phương tính を khảo lự した nhất bàn hóaを dụng いて, ZhangとAndersonはローレンツ変 hoán と quang の phiến đạo tốc độ の đẳng phương tính に chỉnh hợp する toàn ての sự tượng と thật nghiệm kết quả が, quang の vãng phục tốc độ の nhất định tính と đẳng phương tính を bảo ったまま, phiến đạo tốc độ の phi đẳng phương tính を hứa すものとも chỉnh hợp することを chỉ trích した.

Đồng kỳ pháp の quy ước

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

“Einstein synchronization”も tham chiếu

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$t_{1}$is arriving at B at time$t_{2}$and coming back to A at time$t_{3}$,then the following convention applies:

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

The details of this method, and the conditions that assure its consistency are discussed inEinstein 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 due totime dilation.This was measured in a variety of tests and is related to thetwin 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', establishingrelativity of simultaneityin agreement with Einstein synchronization.Therefore, testing the equivalence between these clock synchronization schemes is important for special relativity, and someexperiments in which light follows a unidirectional pathhave proven this equivalence to high precision.

Non-standard synchronizations

As demonstrated byHans ReichenbachandAdolf Grünbaum,Einstein synchronization is only a special case of a more 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 ½ with ε:

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

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, seeGeneralizations 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 oftime dilationof moving clocks, the same non-standard synchronisations 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 theDoppler 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 theHafele–Keating experimentand in experiments on theTime dilation of moving particlessuch as Baileyet al.(1977). Thus the so-calledtwin paradoxoccurs 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 todynamics,thelaws of motionandinertial reference frames.Salmon described some variations of this argument usingmomentumconservation, 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 complicated 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.Salmon argued that momentum conservation in its standard form assumes isotropic one-way speed of moving bodies from the outset. So it involves practically the same convention as in the case of isotropic one-way speed of light, thus using this as an argument against light speed conventionality would be circular.And in response to Ohanian, both Macdonald and Martinez argued that even though the laws of physics become more complicated with non-standard synchrony, they still are a consistent way to describe the phenomena. They also argued that it's not necessary to define inertial frames in terms of Newton's laws of motion, because other methods are possible as well.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 reported a new method of measurement of the one-way speed of light.In the June 2013 issue of the American Journal of Physics Hankins, Rackson and Kim repeated the Greaves et al. experiment obtaining with greater accuracy the one way speed of light.This experiment proves with greater accuracy 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 claimed that the Greaves et al. experiment actually measures the round trip (two-way) speed of light.

In the November issue of the Indian Journal of Physics, Ahmed et al. published a comprehensive review of One-Way and Two-Way Experiments to test the isotropy of the speed of light.

Experiments in which light follows a unidirectional path

List of eclipses of the Jupiter moon Io that formed the basis of Ole Rømer's discovery of the finite speed of light.

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 synchronisation 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 sectionsthe one-way speedandgeneralized Lorentz transformations).

These experiments also confirm agreement between clock synchronization by slow transport and Einstein synchronization.Even though some authors argued that this is sufficient to demonstrate the isotropy of the one-way speed of light,it has been shown that such experiments cannot, in any meaningful way, measure the (an)isotropy of the one way speed of light unless inertial frames and coordinates are defined from the outset so that space and time coordinates as well as slow clock-transport are described isotropically(see sectionsinertial frames and dynamicsandthe one-way speed). Regardless of those different interpretations, the observed agreement between those synchronization schemes is an important prediction of special relativity, because this requires that transported clocks undergotime dilation(which itself is synchronization dependent) when viewed from another frame (see sectionsSlow clock-transportandNon-standard synchronizations).

The JPL experiment

This experiment, carried out in 1990 by theNASAJet Propulsion Laboratory,measured the time of flight of light signals through a fibre optic link between two hydrogen maser clocks.In 1992 the experimental results were analysed byClifford Willwho 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 byOle 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	Year		$\Delta c/c$
Moessbauer rotor experiments	1960s	Gamma radiation was sent from the rear of a rotating disc into its center. It was expected that anisotropy of the speed of light would lead to Doppler shifts.	$<3\times 10^{-8}$
Vessotet al.	1980	Comparing the times-of-flight of the uplink- and downlink signal ofGravity Probe A.	$\sim 10^{-8}\!$
Riiset al.	1988	Comparing the frequency of two-photon absorption in a fast particle beam, whose direction was changed relative to the fixed stars, with the frequency of a resting absorber.	$<3\times 10^{-9}$
Nelsonet al.	1992	Comparing the frequencies of a hydrogen maser clock and laser light pulses. The path length was 26 km.	$<1.5\times 10^{-6}$
Wolf & Petit	1997	Clock comparisons between hydrogen maser clocks on the ground and cesium and rubidium clocks on board 25GPSsatellites.	$<5\times 10^{-9}$

Experiments that can be done on the one-way speed of light

Artist's illustration of a brightGamma-ray burst.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 theDe 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 vacuumdispersionof light.Similarly, differences in the one-way propagation between left- and right-handed photons, leading to vacuumbirefringence,were excluded by observation of the simultaneous arrival of distant star light.For current limits on both effects, often analyzed with theStandard-Model Extension,seeVacuum dispersionandVacuum birefringence.

Experiments on two-way and one-way speeds using the Standard-Model Extension

Tường tế は “Modern searches for Lorentz violation”を tham chiếu

While the experiments above were analyzed usinggeneralized Lorentz transformationsas in theRobertson–Mansouri–Sexl test theory,many modern tests are based on theStandard-Model Extension(SME). This test theory includes all possible Lorentz violations not only of special relativity, but of theStandard ModelandGeneral relativityas 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-wayphase velocityof light.

A series of experiments have been (and still are) performed since 2002 testing all of those coefficients using, for instance, symmetric and asymmetricoptical resonators.No Lorentz violations have been observed as of 2013, providing current upper limits for Lorentz violations:${\tilde {\kappa }}_{e-}=\scriptstyle (-0.31\pm 0.73)\times 10^{-17}$,${\tilde {\kappa }}_{o+}=\scriptstyle 0.7\pm 1\times 10^{-14}$,and${\tilde {\kappa }}_{tr}=\scriptstyle -0.4\pm 0.9\times 10^{-10}$.For details and sources seeModern searches for Lorentz violation#Speed of light.

However, the partially conventional character of those quantities was demonstrated byKosteleckyet 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 violationper 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.

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

“Lorentz ether theory”も tham chiếu

Hendrik Antoon Lorentz

In 1904 and 1905,Hendrik LorentzandHenri Poincaréproposed 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 theLorentz 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 isexperimentally indistinguishablefrom special relativity, Lorentz's theory is no longer used for reasons of philosophical preference and because of the development ofgeneral relativity.

Generalizations of Lorentz transformations with anisotropic one-way speeds

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:

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.

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, Andersonet al.formulated generalized Lorentz transformations for arbitrary boosts of the form:

${\begin{aligned}d{\tilde {t}}'=&{\tilde {\gamma }}\left[1+\kappa \cdot {\tilde {\mathbf {v} }}/c-\kappa '\cdot {\tilde {\mathbf {v} }}'/c\right]d{\tilde {t}}-\left(\kappa '+{\tilde {\gamma }}{\tilde {\mathbf {v} }}'\right)\cdot d{\tilde {\mathbf {x} }}/c\\&-\left[{\tilde {\gamma }}\left(1+\kappa \cdot {\tilde {\mathbf {v} }}/c\right)-1\right]{\frac {\kappa '\cdot {\tilde {\mathbf {v} }}}{{\tilde {\mathbf {v} }}^{2}c}}{\tilde {\mathbf {v} }}\cdot d{\tilde {\mathbf {x} }}+{\tilde {\gamma }}\kappa \cdot {\tilde {\mathbf {v} }}\left(\kappa \cdot d{\tilde {\mathbf {x} }}\right)/c,\\d{\tilde {\mathbf {x} }}'=&-{\tilde {\gamma }}{\tilde {\mathbf {v} }}d{\tilde {t}}+d{\tilde {\mathbf {x} }}+\left[{\tilde {\gamma }}\left(1+\kappa \cdot {\tilde {\mathbf {v} }}/c\right)-1\right]{\frac {{\tilde {\mathbf {v} }}\cdot d\mathbf {x} }{{\tilde {\mathbf {v} }}^{2}}}{\tilde {\mathbf {v} }}-{\tilde {\gamma }}{\tilde {\mathbf {v} }}\left(\kappa \cdot d{\tilde {\mathbf {x} }}\right)/c,\\{\tilde {\gamma }}=&\gamma \left(1-\kappa \cdot \mathbf {v} /c\right),\\{\tilde {\mathbf {v} }}=&{\frac {\mathbf {v} }{1-\kappa \cdot \mathbf {v} /c}},\end{aligned}}$

(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.

Theories not equivalent to special relativity

Test theories

“Test theory”および “Test theories of special relativity”も tham chiếu

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 theStandard-Model Extension(SME). It employs a broad variety of coefficients indicating Lorentz symmetry violations in special relativity,general relativity,and theStandard 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 violationsper se,it only shifts their appearance from the photon sector into the matter sector of SME (see aboveExperiments on two-way and one-way speeds using the Standard-Model Extension.

Aether theories

“Luminiferous aether”も tham chiếu

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, theMichelson–Morley experimentshowed 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.

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 asLorentz ether theorythat 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.

Further reading

• Janis, Allen (2010)."Conventionality of Simultaneity".InZalta, Edward N.(ed.).Stanford Encyclopedia of Philosophy( anh ngữ ).
• Mathpages:Conventional Wisdom,Round Trips and One-Way Speeds,Teaching Special Relativity
• Rizzi, Guido; Ruggiero, Matteo Luca; Serafini, Alessio (2004). “Synchronization Gauges and the Principles of Special Relativity”.Foundations of Physics34(12): 1835–1887.arXiv:gr-qc/0409105.Bibcode:2004FoPh...34.1835R.doi:10.1007/s10701-004-1624-3.
• Sonego, Sebastiano; Pin, Massimo (2008). “Foundations of anisotropic relativistic mechanics”.Journal of Mathematical Physics50(4): 042902-1–042902-28.arXiv:0812.1294.Bibcode:2009JMP....50d2902S.doi:10.1063/1.3104065.