# Analysis of the experiments “One-way measurement of the speed of light”

Abstract

This page analyses the experiments “One-way measurement of the speed of light”, which use the latest technological advances today. The results of all experiments show that the measured velocity of light in “East-to-West” direction is higher, and in the direction “West-to-East” is lower than the speed of the light in vacuum. The difference is equal to the linear velocity of the Earth’s surface at the latitude where the experiment is carried out. The so-named by modern physics “anisotropy of the speed of light”, in fact undoubtedly demonstrates that the speed of light in vacuum (in the reference system related to the stationary space) differs from the measured speed of light in the frame of reference related to the moving Earth’s surface. It means that the measured speed of light is not the same for all inertial systems, which is the basis of the special theory of relativity.

The Global Positioning System (GPS), is a satellite-based radionavigation system that provides high accuracy geolocation and time information anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites.

Based on the GPS, Marmet makes measurements and reports in “GPS and the Constant Velocity of Light” that an electromagnetic signal takes about 28 nanoseconds longer when traveling eastward from San Francisco to New York than when traveling westward from New York to San Francisco (Marmet, 2000). Using GPS, Kelly also determined that an electromagnetic signal takes 414.8 nanoseconds more time to circumnavigate the Earth eastward near the equator than when travelling westward around the same path (Kelly, 2005). Both researchers concluded that the observed travel-time differences in different directions arise, because the electromagnetic radiation (the light) travels relative to the surface of the Earth at a speed (c-V) eastward, and at a speed (c+V) westward, where V is the linear speed of the Earth’s surface at the respective latitude, and c is the speed of light in vacuum.

Now we will analyze in the two aforementioned reference systems, both of the cases – the case “Eastward Transmission” and the case “Westward Transmission”. In both cases, the transmitter and the receiver are fixed on the Earth’s surface and are stationary in the reference system related to the Earth’s surface.

What the observers will see (located in the two aforementioned frames of reference)?

For the observer, situated in the frame of reference related to the Earth’s surface, the transmitting and receiving stations, fixed on the Earth’s surface, are stationary.

However, the observer situated in the approximately stationary in relation to the space ECI coordinate system, will observe how the Earth is rotating and that every point of the Earth’s surface is moving. They will see that the transmitting and receiving stations, positioned steadily on the ground surface, move eastward (along with the ground surface), at the linear speed V for the respective latitude.

4.1. The case “Eastward Transmission”. Analysis of the results of the measurement of the velocity of the electromagnetic signal by observers located in the two considered frames of reference.

The case “Eastward Transmission”. Station B is located precisely east of station A. Let the fixed position of station A and the fixed position of station B on the Earth’s surface at moment t are XA(t) and XB(t), respectively. The ground distance between the station A and the station B is equal to D.

Station A transmits an electromagnetic signal (light beam) eastward at time tI to station B, which receives it at time tF. The time interval of the light beam travel is (tF – tI). During this time interval, each point of the Earth’s surface has moved in the stationary space at a distance Δ=V(tF – tI), where V is the linear velocity of the Earth’s surface in the stationary space for the respective latitude.

#### Analysis of the results of the measurement of the speed of the electromagnetic signal (or of a light beam) by observers located in the two aforementioned frames of reference.

•  In the stationary in relation to the spaceEarth-centered inertial coordinate system” (the ECI frame of reference).

The observer-1, located in the stationary in relation to the space frame of reference, will see how the fixed on the ground transmission and reception stations are moving eastward in the stationary space with the linear velocity V of the Earth’s surface in the stationary space for the respective latitude.

The observer-1 will found that the electromagnetic signal passes in the stationary “empty space” a definite distance – from the position XA(tI) of station A at the moment of transmission tI, to the position XB(tF) of station B at the moment of receiving tF (see Fig. 4.1). They will measure that the distance travelled by the electromagnetic signal is equal to the distance between the two stations D on the ground, plus the distance Δ=V(tF – tI), which the station B passes during the travel-time of the electromagnetic signal (tF – tI) with the speed V (the linear velocity of the Earth’s surface in the stationary space at the respective latitude).

Therefore, the observer-1 (located in the stationary in relation to the space frame of reference), will measure the speed of the electromagnetic signal (can be a light beam) and will confirm that it is equal to c(the speed of light in vacuum):

In the frame of reference, related to the Earth’s surface.

The observer-2, positioned on the Earth’s surface will see that the electromagnetic signal passes for the same interval of time (tF – tI) exactly the distance D (the distance between the fixed on the ground transmission and reception stations). Therefore, the observer-2 (located in the frame of reference, related to the Earth’s surface), will measure the speed of the electromagnetic signal (or of the light beam) and will get:

Obviously, the measured speed by observer-2 is lower than the measured by the observer-1 (equation (3)), and the difference is equal to the linear velocity of the Earth’s surface at the respective latitude:

This theoretical result corresponds exactly to the results of the above-mentioned experiments made by Marmet and Kelly, using GPS:

the measured velocity the electromagnetic signals in the reference system related to the Earth’s surface in the direction “from West to East” is equal to c2 = (cvacuum – V), where cvacuum is the speed of light in vacuum, and V is the linear speed of the Earth’s surface in the stationary space at the respective latitude.

4.2. The case “Westward Transmission”. Analysis of the results of the measurement of the velocity of an electromagnetic signal by observers located in the two considered frames of reference

The case “Westward Transmission”. The scenario is the same:

Station A transmits an electromagnetic signal (light beam) at time tI, but now westward to station B, which receives it at time tF. During this time interval, each point of the Earth’s surface again has moved in the stationary space at a distance Δ=V(tF – tI), where V is the linear velocity for the respective latitude. The time interval of the signal travel is (tF – tI), but it is smaller than the travel time interval (tF – tI) of the electromagnetic signal in the case “ Eastward Transmission”. This is because, in this case, the receiving station approaches the transmitting station, rather than moves away from it.

#### Analysis of the results of the measurement of the speed of the electromagnetic signal (or of a light beam) by observers located in the two aforementioned frames of reference.

•  In the stationary in relation to the space “Earth-centered inertial coordinate system” (the ECI frame of reference).

The observer-1, situated in the stationary in relation to the space frame of reference, will see again that the fixed on the ground transmission and reception stations are moving eastward in the stationary space with the velocity V of the surface of the Earth for the respective latitude. However, in this case, they will find that the distance, traveled by the electromagnetic signal, will be equal to the distance D between the two stations on the ground, minus the distance Δ=V(tF – tI). Here, Δ is the distance that the station B passes during the travel-time of the electromagnetic signal (tF – tI) with a velocity V (the linear velocity of the Earth’s surface in the stationary space at the respective latitude).

Therefore, the observer-1, situated in the stationary (in relation to the surrounding space) frame of reference, will measure the speed of the electromagnetic signal (the light beam) and will confirm again that it is equal to cvacuum (the speed of light in vacuum):

•  In the frame of reference, related to the Earth’s surface:

Obviously, the measured speed by the observer-2 is higher than the measured by the observer-1 (equation (6)), and the difference is equal to the linear velocity of the Earth’s surface in the stationary space at the respective latitude:

This theoretical result again accurately corresponds to the results of the above-mentioned experiments made by Marmet and Kelly using GPS that:

the measured velocity the electromagnetic signals in the reference system related to the Earth’s surface in the direction “from East to West” is equal to c2 = (cvacuum + V) ,

, where cvacuum is the speed of light in vacuum, and V is the linear velocity of the Earth’s surface in the stationary space at the respective latitude.

4.3. Conclusion

The experiments “One-way measurement of the speed of light” demonstrate that the measured speed of light is not the same in different directions in the reference system related to the Earth’s surface.

These experiments are actually irrefutable proof that the measured speed of light in a local time-spatial region with a uniform intensity of the gravitational field is not the same for all inertial frames of reference.

Many scientists have given evidence that the “Light Speed Invariance is a Remarkable Illusion” (Gift, 2010). However, this is avoided to be formally discussed by the physical society.

Nowadays, the value of the speed of light in vacuum is recommended by the CGPM (Conférence Générale des Poids et Mesures), in the following way:

“[CGPM] recommends the use of the resulting value for the speed of propagation of electromagnetic waves in vacuum c = 299 792 458 metres per second.” (15th meeting of the CGPM, Resolution 2, 1975).

An important NOTE can be made to BIPM (Bureau international des poids et mesures):

It is clear that if we are located on the Earth’s surface (in the frame of reference related to the Earth’s surface) and we have to measure the “speed of light in vacuum”: it must take the arithmetic mean of the measured speed of light in two opposite directions (from East to West) and (from West to East).

This note also relates to the currently accepted definition of the base unit of length “meter” through the speed of light:

“The metre is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.” (17th meeting of the CGPM, Resolution 1, 1983).

CONSEQUENCE. The definition of the base unit of length “meter” through the unregulated measurement of the speed of light in vacuum, carries the problem over the whole area of applied physics and technology!

=> to the parent webpage

If you haven’t read the analysis of the “Sagnac’s experiment” yet, it is worth to read it here!

If you haven’t read the analyses of the “Michelson-Gale-Pearson” experiment yet, it is worth to read it here!

The revealing the fact that the inappropriate conceptual design, embedded in the construction of the Michelson’s interferometer, however indisputably shows that the claim “the speed of light is the same in all inertial frames of reference” is a great delusion and the “Michelson-Morley experiment” is actually the primary root cause for the biggest blunder in physics of the 20th century – the special theory of relativity.

Furthermore, the analysis of the article “On the Electrodynamics of Moving Bodies”, where Einstein has published the special theory of relativity shows exactly where and how the claim “the speed of light is the same in all inertial frames of reference” was applied …