Return to:    List of Papers on Web Sites

            1 - Introduction.
            Many experiments, like the Michelson-Morley and Sagnac experiments and others, are testing the fundamental nature of light. It is conflicting to observe that the velocity of photons is measured as a constant, when the observer moves away from that light source. Photons, just as any other particle, possess an independent existence and are not created by a physicist's thought, as claimed in quantum mechanics. Since all other particles are measured with additive velocities (V-v) or (V+v) with respect to a moving frame, why can photons not obey that same rule? Since Newton's mechanics has shown that all relative velocities produce a Doppler frequency shift, we must expect logically that some special phenomena prevent us from detecting the real change of relative velocity. It is quite incorrect to believe that this phenomenon cannot be explained using physical reality and Newton physics.  As required by the principle of mass-energy conservation ^[1], the atoms (nucleus and electrons) forming the local standard reference meter and the moving clock have acquired some extra mass due to the materialization of kinetic energy. Quantum mechanics shows ^[1] that this increase of energy changes the de Broglie electron wavelength and consequently, the Bohr radius and the clock rate. It is surprising to find new hypotheses like space-time distortion, and even more, the suggestion of "new logic" to explain these observations, while it is not taken into account that the rate of the moving clock is naturally modified due to the increase of mass (following the absorption of kinetic energy). The simple application of the principle of mass-energy conservation explains naturally all these experiments.
            We must add that there is only one Real Logic. An assumed Superior Logic, applicable to modern physics is not compatible with Real Logic. We must recall that an empirical equation used to predict the outcome of a physical system is not an explanation. When there is no physics underneath these mathematical equations, they give empirical predictions of what will happen to the system. Mathematical equations generally deal with symbols, but they never explain "why". A real explanation must answer the question of causality, which is asked by why? An equation is never the "cause" of a phenomenon.

            2 - Switching between Frames of Reference.
            Let us consider the frame of reference of a small stars cluster, with stars having all the same velocity, as illustrated on figure 1. One of those stars is our Sun, which is surrounded by the Earth moving around it. In this star frame, an observer measures that the photons are emitted at velocity c with respect to the star system. That light (hn, on figure 1) travels toward the Earth, but the Earth moves away at velocity v_E with respect to the star system as illustrated on figure 1.

Figure 2

1

            However, since we deal with observers measuring lengths and recording clock displays using their proper units, we need to determine the number of local units in other frames. Of course, when the standard meter used to make measurements is moved to another frame, its physical length is also changed. Therefore when the moving observer determines the length of a moving body, he is now doing it with respect to the local standard meter (which is different). The number "" represents the number of times the designated standard units of length have been counted when measuring L. The number of times a (moving) particular length is longer than the standard length located on the station [s], is represented by_v[s]. 

            The definition of these indexes is the following. The sub indexes "s" or "v" (in _s,_v) specify the frame where the body is located when it is measured. The quantity inside the square parenthesis, indicates in which frame [s] or [v], the standard reference unit used for the measurement, is located. We see that the same rod, at different locations, can be designated by four numbers_s[s],_s[v],_v[s] or _v[v].

            We take the example when the observer on the train uses his local meter to measure the length of the moving train. He finds that this number _v[v] is identical to the number of units on the station _s[s] before the train started to move, even if it is not the same physical length (L_v>L_s ). However, when the same physical rod, in the same frame (constant L_v) is measured using different standard units [v] or [s], the numbers measured with respect to each standard lengths units [v] or [s] follows

2

            Since the moving observer uses his local moving standard units, he might believe that the length does not increase when his own velocity increases. He does not realize that his train is physically longer, but this is not measurable, because his local standard meter has increased in the same proportion.  In doing local mathematical calculations, he will normally use the number _v[v] to calculate the length, which is identical to the number _s[s]. In fact equation 2 also implies that the real physical length L_v is equal to g times L_s. In order to apply physics correctly, the moving observer must compensate for the fact that he does not possess the same standard unit of length as when he is located on the station frame. Therefore he must apply a correction due to the change of length of his measuring local standard meter as given in equation 2.

3

4

            3 - Einstein's Clock Synchronization Technique.
            On the station frame, an observer calculates the velocity of light, using his proper units [s] and the standard method used by Einstein. A pulse of light is emitted from location A toward B (see figure 2). The station observer measures the velocity of light, calculating the quotient of the length L_v, divided by the difference of local time between light emitted from A and received at B (see figure 2). Since the train is in motion, for the station observer, the distance L_v between A and B is represented by _v[s] and not _s[s], because the train is really longer when in motion. Measuring the "time interval" means only, that the station observer records the displays shown respectively on both clocks, at the instant light is at location A (CD_A) and later B (CD_B). This experiment gives c.

5

            We notice that clocks A, B, a and ß have not been synchronized yet. Let us apply the Einstein's synchronization method to the moving frame. A pulse of light is emitted from location A on the station (see figure 2). Later, at the moment some photons pass through location a, the Clock Display (CD_a[v]) on clock a is recorded. Also, when light reaches location ß, the Clock Display on ß (CD_ß[v]) is recorded. As seen by the train observer, the velocity of light on the moving train is given by the following quotient. --- The distance _v[v] (between a and ß) divided by: " the Difference of Clock Display between clock ß, (when light arrives)" minus "the display on clock a (when light passed in a)".

            In the case of clocks A and B on the station, this synchronization method is identical as above, using clocks A and B and the station length _v[s]. Finally, the synchronization must be done between clocks A and a. The most reliable way is to synchronize them at the same value (same display), when clock a passes just besides clock A (see left hand side of figure 2).

         4 - Synchronization of Moving Clocks a and ß, with a Third Clock µ.
            We have seen above, that there are two perfectly equivalent methods to synchronize clocks. Method #1 uses a two-way reflected beam of light on a mirror, while method #2 is carrying a third clock µ on the moving frame between a and ß. Of course, due to their kinetic energies, both clocks a and ß on the train, run at a slower rate. As a consequence of that slower clock rate, we show that when all three clocks A and B and a are all synchronized at zero, at the same instant, the fourth clock ß cannot show a Clock Display equal to zero, due to the Einstein's synchronization technique described above. This phenomenon does not seem to have been noticed directly previously. However, we will see that it is the "cause" of the Sagnac effect. This deficient synchronization of clock ß with respect to the others has been demonstrated in a previous paper ^[1].  We use here method #2, which is mathematically equivalent.  The result is identical.
            We consider that clock µ starts moving from clock a to clock ß, at the moment clock a passes besides clock A (see left hand side of figure 2). Since clock µ moves at the additional velocity e[s] (with respect to v[s]), the Difference of Clock Displays (DCD[s]) is recorded on clock A, while clock µ travels across the distance _v[s] with respect to the moving frame:  This gives:

6

            The difference of Clock Display (in units [s]) corresponds to an apparent time interval called Dt[s]. In equation 6, DCD[s] is the apparent time interval during which clock µ moves across the distance _v[s]. We have already seen

7

8

9

10

11

12

13

that equation 9.37 which gives the difference between "the difference of clock display on clock ß" minus "the difference of clock display µ" (which has been synchronized with a), is equal to minus 

            5 - Table of Clock Synchronization.
            We have shown above that the synchronization of clocks on a moving frame is such that clocks a and ß must necessarily be synchronized with a different display "at the same instant". This is required even if both clocks a and ß are located on the same frame. However, both clocks (A and B) at each extremity of the station frame show the same display at the same instant. An observer on the station frame could observe that clocks a and ß do not show an identical display at the same instant. However, the observer on the train could not detect any difference when synchronizing his local clocks, because both methods of synchronization using light, or carrying clock µ, agree with the above Einstein's discordant synchronization, between a and ß. Since this phenomenon has not been discussed previously (except in ^[1]), and in order to give a non-ambiguous description, we present a table of Clock Displays appearing simultaneously on the four clocks A, B, a and ß as a function of the apparent time on clock A, for each successive second [s] as given in equation 13.
 

Clock A  Seconds [s]	Clock B  Seconds [s]	Clock a Seconds [v]	Clock b Seconds [v]
0	0	0	-v/c2
1	1	1/g	(1/g)-(v/c2)
2	2	2/g	(2/g)-(v/c2)
3	3	3/g	(3/g)-(v/c2)
-----	-----	-----	-----

            6- Velocity of Light in a Moving Frame.
            Let us calculate the distance "L₂" (see figure 2) traveled by the beam of light emitted at the velocity c, from location A, at rest on the station, during the time light passes from a to ß located in the moving frame.  Using Galilean coordinates, we calculate the velocity of the photons moving at velocity (c-v) with respect to the moving train.  The photons must travel across the moving distance L_v[s] when we consider the relative velocity (c-v) before passing from a to ß.  Consequently, the time T_L2[s] (or DCD_v[s]) taken to pass from a to ß, at the relative velocity (c-v), is equal to:

14

            We have _v[s] is the number of rest meters in length L_v[s].  From equation 14 the time for light to travel across L

15

16

17

            We have seen above (line after equation 14) that in equation 17 the length _v is given using rest frame units.  However, the moving observer uses the moving units which is a number g times smaller because the moving standard meter is longer.  Substituting equation 2 in 17, we get:

18

19

            Equations 18 and 19 show that the time interval for light to travel from a to ß is the sum of two quantities.  The first term (_v/c) corresponds to a time interval expected assuming the velocity of light.  The second term must be explained by another phenomenon.

20

21

          The error is due to Einstein's clock synchronization method which gives a wrong synchronization.  It is very important to notice that this error in clock synchronization is enormously more important than the usual relativistic correction.  For example, in a frame moving at the velocity of rotation of the Earth, (with (v/c)»0.000001), this correcting term (_v v/c

            7 - Experimental Confirmation of the Discordant Einstein's Synchronization Method with the GPS.
             There are direct measurements proving that the velocity of light in one direction is c±v with respect to the moving observer. This discordant synchronization given in equation 13 has been measured in the world system of clock synchronization with the Global Positioning System. It is then observed experimentally that the Einstein's method of synchronization using the "half time interval" taken by a reflected beam of light is inadequate to determine the correct time. A correction (which is the Sagnac effect) has to be added.
            As an example, let us assume that clock a (from figure 2) is in New York (N.Y.), and clock ß is in San Francisco (S.F.) as illustrated on figure 3. The velocity v is the velocity of rotation of the Earth around the pole axis, at the location where the experiment is done. The distance  is the distance between New York and San Francisco (dotted line on figure 3).

22

            where w is the angular velocity of rotation of the Earth, A_E is the projected area on the Earth equator plane of the path used by light (or by a slowly moving clock) between the two stations. We define  as the distance between the two stations, both moving at velocity v. The circumference of the Earth is called "circ". Therefore the area A_E is

23

24

            8 - Synchronizing Clocks with the GPS.
            Other experiments can be realized to test the difference of synchronization (time) between clocks. Experiments, with north-south displacements of clocks, have also been verified experimentally. Instead of exchanging directly the radio signals or moving clocks between New York (N.Y.) and San Francisco (S.F.) as illustrated on figure 3, let us assume that a radio signal is sent from New York to a station at the North Pole (N.P.) of the Earth before being reflected (or re-emitted) toward San Francisco. This can be done using a satellite located above the North Pole. In this case, in agreement with the GPS, we observe that the simultaneous exchange of radio synchronization between a and ß, does not show the difference of 14 ns, since light never travels across meridians, as illustrated on figure 3. Then, light never has to move directly against the Earth velocity of rotation. The projection of the light path on the area A, defined above (equation 23) is zero, because light travels along the meridians, via the North Pole. Of course, there is a higher order correction related to the transverse velocity of light with v that can be considered elsewhere, but this is clearly not observable experimentally.
            A similar result is obtained when we carry an atomic clock µ, at constant geodesic altitude in the north-south direction from New York to the North Pole (N.P.). Of course, in that case, clock µ might increase its rate because of the decrease of tangential velocity of Earth rotation at higher latitudes. However, it has been demonstrated that the flatness of the Earth is such that the gravitational potential at the pole compensates exactly for the loss of rotational velocity v. Since no meridians are crossed, the GPS correctly calculates a zero correction on clock µ, at its arrival at the North Pole. For the same reason, a null correction is also calculated on clock µ by the GPS when it is moved from the North Pole (N.P.) to San Francisco (S.F.).
           Either using simultaneous light transmission or carrying a clock µ, it is remarkable that both methods of synchronization of clocks between New York and San Francisco, across the North Pole, give an identical zero correction. However, when the radio signal or the moving clock, crosses the meridians, the correction of 14 ns, as calculated by equation 13, appears in both methods.

            9 - Observation of the One-Way Velocity of Light as c±v.
          Knowing that the Sagnac effect, the GPS, all the related experiments described above and also using Newton physics lead to identical results, we can rely on the GPS data. Consequently, the GPS is a reliable tool to measure directly the one-way velocity of light.
            Let us start our experiment with an atomic clock at the North Pole of the Earth. At this location, there is evidently no problem with the velocity of Earth rotation (which is non-existent). From the North Pole (N. P.), let us initiate an independent synchronization with the two clocks a and ß located respectively in New York and in San Francisco. Since both methods, (transmission of simultaneous radio signals or carrying an atomic clock), lead to the same result, we can use the synchronization method that we prefer. From the North Pole, and moving along the meridians, the projection of the path on the Earth equator A_E is zero. Consequently in that case, synchronizations of the clocks in N.Y. and S.F. with the one at the North Pole, do not need any correction (A_E =0 in equation 22).
            Therefore, two clocks in San Francisco and in New York are now in perfect synchronization. Using this synchronization, let us measure the velocity of light between N.Y to S.F. and also between S.F. and N.Y. Let the observer in New York send a radio signal (across the meridians) to San Francisco at the same time another radio signal travels in the opposite direction. This simultaneous exchange of radio signals can be done using the refraction of the ionosphere or via a satellite at a low altitude above the same meridian. Since the two clocks have been previously accurately synchronized in the paragraph above, the absolute time of emission and reception can be measured directly on each local clocks (a and ß). If the path length of the radio signal is not much longer than the shortest path (passing across the meridians), the average time interval measured simultaneously in both directions is about 15 000 microseconds.
            In that case, an accurate measurement of the time interval given by the synchronization above with the North Pole, (in agreement with the GPS) shows that light takes an extra 0.014 microsecond to travel eastward (from S.F. to N.Y.). Also light arrives at the western station (from N.Y. to S.F.) 0.014 microsecond before the average 15000 microseconds interval needed to travel a distance of about 4500 km. Since there is a difference of 0.014 microsecond between each direction, this shows that light moves at a different velocity eastward than westward. We calculate that the velocity "v" of rotation of the Earth at the latitude of those cities is about one millionth of the velocity of light. From the above data, the time interval for light from New York toward the approaching San Francisco is also about one millionth shorter. Also the time interval for light to move from San Francisco to New York (which has moved away) is about one millionth longer. Clearly, the velocity of light with respect to an observer resting on the Earth surface is c+v between N.Y. and S.F. and c-v between S.F. and N.Y.   One must conclude that the velocity of light is c with respect to a frame at rest.
        -
        Some people have a restricted interpretation when the say that the velocity of light is c with respect to the non-rotating (zero velocity) frame.   Since the observations above had to be made using the velocity component of the rotating Earth, some people have claimed that the observed change of velocity is directly due to the rotating Earth and consequently, the velocity of light is c "only" with respect to a non-rotating frame.  This naïve conclusion is misleading, because it implies incorrectly that the velocity of light (measured in a moving frame) cannot be different from c when the frame moves in straight line.  We can see that the velocity c±v, measured from a rotating frame, is a special case of velocity c±v due to a linear motion.
       -
        We can show that logically, the velocity of light is also c±v for an observer moving in straight line (without any rotation).
        Let us show first that a statement claiming that light moves at velocity c, “only” with respect to a non-rotating frame is not a physical explanation.  This statement implies that the real velocity of light cannot be c±v, if the frame is not rotating (but just translating).  The word “only” implies that the velocity is c±v in a rotating frame but it would not be c±v in a translating frame (even if the velocity is the same).  There exists no direct physical mechanism capable of explaining that light can move at velocity c±v with respect to a rotating frame and c with respect to a translating frame.  Claiming that the velocity of light is c in a frame translating at velocity v, and simultaneously claiming that the velocity is c±v in a rotating frame, which is the same phenomenon, is incoherent.
        In physics, an explanation requires that an observation is coherent with respect to a well-described physical mechanism.  When we claim that the velocity of light is c±v, this is the direct logical consequence of the application of the well-known Galilean coordinates.  With the Galilean coordinates, we understand logically that when a traveler moves in the universe at velocity v with respect to particles moving at velocity c, the velocity of the particles with respect to the moving frame is c-v.  Here the particles are photons.  This last description is a direct physical explanation compatible with conventional logic (without magic).  Therefore the simple statement that, the velocity of light is c, "only" with respect to a non-rotating frame is non-coherent.
        -
         Let us show now that the velocity of light is c±v with respect to an observer, moving in straight line at velocity v.  Let us consider two flashes of light emitted from our Earth moving in a direction parallel to its motion, during its orbit around the Sun.  The two light beams are emitted simultaneously in opposite directions along the Earth’s orbit.  Around the Sun, there are some stationary stations reflecting light, which are distributed so that light emitted from Earth can circle the Sun simultaneously in both directions.  For example, we can assume eight stationary mirrors reflecting light and forming an octagon around the sun.  For the beam moving in the same direction as the Earth, the moving observer will measure a longer time interval (than in opposite direction) before light completes the rotation around the Sun and reaches Earth again, because the Earth has moved a small distance, during that travel time interval of light.  The velocity of light calculated is then c-v (for the Earth observer).  Also, for the observer on the moving Earth, the velocity will be calculated as c+v for the beam of light moving in the opposite direction.
        Between each of the eight pairs of mirrors, in the forward direction, when the observer uses his proper units in his frame and Einstein’s synchronization, the moving observer will “believe” that the velocity of light is c.  This is due to the erroneous clock synchronization explained above.  Also, we could install a GPS around the Sun (as the one on Earth) and we would find, just as on Earth, those clocks are slowing down and standard meters dilated due to the kinetic energy of the observer.  The distance between a pair of mirrors corresponds to the distance between New York and San Francisco on Earth, as in the example above.  Again, the velocity of light moving along a straight line moves at velocity c-v with respect to the observer on Earth, if he uses a correct synchronization method (i.e. from the Sun's pole).
        -
        The most remarkable thought experiment is when the Sun is completely removed from the center of the system above.  We mean, an experiment done very far in empty outer space.  Then again, the observer moves at velocity v, in straight line, along one side of the octagon.  Due to the observer’s velocity, light will take more time to complete the complete octagonal path when he moves in the same direction as light, than if light and the observer are moving in the opposite direction.  In fact, any mass, either the Earth or the Sun is irrelevant.  Again, this is the classical Sagnac effect.
        One must conclude that using traveler’s local units, we always find the same number of local units for the velocity of light, due to the error in Einstein’s clock synchronization demonstrated previously (and also in this paper).  The real velocity of light is really a constant c with respect to an absolute frame at rest.  Consequently, it is (c±v) (and not c) with respect to a moving frame, as measured on a real absolute clock (which takes the variation of units into account), which would not be modified due to its kinetic energy.  The simplest way to make sure that we always use the same time rate, is actually always looking at the "very same clock" (with a telescope if necessary) and correct for the delay of transmission calculated by the observer at rest.
        We must conclude that the hypothesis of a constant velocity of light with respect to a moving frame of reference is an illusion and therefore an error.

            10 - Absolute Frame of Reference.
            One must conclude that the GPS and all the related experiments give a striking proof that the velocity of light is not constant with respect to an observer, contrary to Einstein's hypotheses. The measured velocity of light is c-v in one direction and c+v in the other. The velocity of light is equal to c with respect to an absolute frame in space. This is now an experimental fact. Finally, we have seen how it is apparently constant in all frames using proper values and a correct clock synchronization.
            We can consider the velocity of light with respect to a group of stars around the Sun. However, there is nothing that says that that star cluster is at an absolute rest. It probably moves around our galaxy which itself moves around the local cluster of galaxies. From what we have seen here, we see that the star cluster mentioned above is just another moving frame, in which again, we have an "apparent" velocity of light equal to c in all directions, because we do not know yet, how to get an absolute synchronization of clocks from the absolute frame.
            A simple way does not seem to exist, which would enable us to use light to determine the absolute velocity with respect to the fundamental frame in the universe. We have mentioned in a previous paper ^[9] that there seems to be an absolute frame of reference related to the 3K-radiation dipole in space. It exists, however, another solution than the 3K radiation.  Light seems to be inadequate, to verify our absolute velocity with respect to an absolute frame. It exists however another solution to locate that absolute frame, but this is beyond the scope of this paper.
            Most physicists believe that the velocity of light is constant with respect to all frames. As explained above, this is wrong.  Let us go back to the question: The velocity of light is "c" with respect to what? The principle of mass-energy conservation requires that light moves at a constant velocity with respect to an absolute frame. Furthermore in all other frames, the velocity of light is always measured to be constant (equal to c) with respect to that moving frame, but it is an "illusion" due to Einstein's discordant clock synchronization.
           Some scientists suggest the existence of an "aether" to carry light. A naive "aether" hypothesis leads to a prediction of the velocity of light that could be measured "directly" as c±v with respect to the observer. This is not that simple.  One extremely important point is that there exists no observational justification^{[10, 11]} to assume that an aether can possess its own energy that can be borrowed when needed. On the contrary, all the physical phenomena are explained naturally without having to borrow any energy or momentum from an assumed medium.  For the moment, the sole property of that assumed aether is to establish an absolute origin to the velocity-frame of light and physical matter, because this frame of reference is absolutely needed to comply with the principle of energy and momentum conservation.  That absolute frame might be simply determined by the average velocity of all matter in the universe.
            One must conclude that there exists no space-time distortion of any kind. It is no longer necessary to fascinate people with the magic of relativity. Unless we accept the absurd solution that the distance between N.Y. to S.F. is smaller than the distance between S.F. and N.Y., we have to accept that in a moving frame, the velocity of light is different in each direction. As mentioned above, this difference is even programmed in the GPS computer in order to get the correct Global Positioning. This proves that the experimental velocity of light with respect to a moving observer is c±v.

         11 - References.
[1] P. Marmet, Einstein's Theory of Relativity versus Classical Mechanics, Newton Physics Books (1997), 2401 Ogilvie, Gloucester, On. Canada K1J 7N4.  Book on the Web.
[2] P. Marmet, Classical Description of the Advance of the Perihelion of Mercury, Physics Essays Vol. 12. No: 4, 1999. Web Site
[3] Sadeh et al. Science 162, 897-8 (1968)
[4] Straumann N. General Relativity and Relativistic Astrophysics, Springer-Verlag, Berlin, Second printing 1991, pp. 459,
[5] CCIR Internat. Telecom, Union Annex to Vol 7, No: 439-5. Geneva 150-4 (1990).
[6] CCDS Bur. Int. Poids et Mes. 9^th Sess., 14-17, 1980.
[7] Saburi et al. IEEE Trans. IM25, 473-7, 1976.
[8] A. G. Kelly, "The Sagnac Effect and the GPS Synchronization of Clock-Stations" Ph. D. HDS Energy Ltd., Celbridge, Co. Kildare, Ireland. Also, A. G. Kelly, Inst. Engrs. Ireland 1995 and 1996, Monographs 1 & 2.
[9] P. Marmet, The Origin of the 3K Radiation, Apeiron Vol, 2 Nr, 1. January 1995 Web Site
[10] P. Marmet, Classical Description of the Advance of the Perihelion of Mercury, Physics Essays, Vol. 12, No: 3, 1999.
[11] P. Marmet, C. Couture, Relativistic Deflectionof Light Near the Sun Using Radio Signals and Visible Light,
        Physics Essays, Vol. 12, No: 1 (1999) Web Site
---
Return to:    List of Papers on Web Sites

Contact E-Mail Address:

Revised - Nov. 2000