Alternative explanation for the Michelson-Morley experiment Daquan Gao 3929 Stonyrun Drive,Louisville KY 40220 USA daquangao@hotmail.com Abstract: The famous Michelson-Morley experiment has been reanalyzed by us. We show that the transverse beam of light follows a diagonal path because of addition of light and the movement of the source. If one adheres the principle that the speed of light is constant as generally believed, light in that experiment should have kept the original direction when it is emitted. Résumé: La célèbre expérience de Michelson - Morley a été réanalysés par nous. Nous montrons que la poutre transversale de la lumière suit un parcours en diagonale en raison de l'addition de la lumière et du mouvement de la source. Si l'on adhère au principe que la vitesse de la lumière est constante comme on le croit généralement, la lumière dans cette expérience aurait dû garder la direction d'origine quand il est émis Key words: Frame of reference, speed and direction of light, Galilean transformation.
The Michelson-Morley (MM) experiment 1 has been analyzed by many physicists 2. This paper tries to analyze the result of the MM experiment further and suggest a simple and more reasonable explanation for the experiment. Although it seems to be contradictory to the established theory, we still want to share it because the topic's importance deserves closer reexamination. To facilitate further discussion, we present a schematic diagram of the MM interferometer. Mirror Transverse V Splitter S Longitudinal Mirror Fig.1 Schematic diagram of the apparatus used in Michelson-Morley experiment. As shown in figure 1, light from source S is split into two beams. The longitudinal beam and the transverse beam go to the mirrors in the end of the arms and get reflected from the mirrors back into the splitter region. The longitudinal direction is the direction in which the earth rotates around the sun in speed of v (30km/s). Both arms are equal in length (L). Results show light beams take the same time to travel their round trips in both arms.
It should be noted that the interferometer is free to rotate around a base. The rotation allows the two arms to adopt any orientation. We choose this particular orientation because it is supposed to show the maximum difference between the times spent by the light on the beams. The experiment is meant to detect the relative motion of the earth in the then supposedly existent ether. The ether would be fixed in space. For that purpose, the revolution of the earth around the sun is chosen because the sun would be a good approximation to represent the non-moving ether in space. Here we will not discuss about the ether since it is already shown that the concept is not necessary. We still, however, want to keep time (time span) and length in the traditional (or classical as in Newtonian mechanics) sense. We will examine the light path on each of the two arms and see what the paths will behave when they are seen in both the sun s coordinate system and the earth s coordinate system. We present the following figure (Fig. 2) to depict the light path of the transverse beam. With these two figures, we analyze the results for this experiment. 1. In the sun s coordinate system In the figure, the mirror at the end of the transverse arm in Fig.2 travels from B to D in the velocity of v (30 km/s, the speed of revolution of the earth around the sun), light travels from A to D as the arrowed line indicates. The speed of the light beam is now the vector sum, v3=v+v2, where v2 is equal to c (speed of light) in numerical value. With this arrangement, time spent for the light beam traveling from A to the point D is equal to L/c. The time for the round trip of the vertical beam is thus 2L/c. We get this by the equation,
(ct) 2 +(vt) 2 =L 2 +(vt) 2 (1). The derivation of Eq.1 is as follows. AB is the length with value L, BD is the length vt, AD has length (c 2 +v 2 ) 1/2 t. Since AD 2 =AB 2 +BD 2, we get Eq.1. The vectors in Fig.2 v, v2 and v3 does not represent the length of the triangle ABD, they only have the same direction with the sides. Therefore t=l/c for the forward journey. The time for the back journey can be obtained likewise. Here we used vector addition for the speed of light in the sun s coordinate system. We added the speed of the source to the speed of light, c. We here define c as the speed value where the source is at rest in the coordinate system. B D E V V2 V3 A F Fig.2 Light paths for the transverse beam. We can do the same for the light in the longitudinal direction. Because the initial speed vector of light and the vector of the earth revolution are in the same direction, we can simply use addition or subtraction of the numerical values as the resultant speed of light. In the forward direction
light travels at speed c+v for a distance of L+vT; in the reverse direction, light travels at c-v for a distance of L-vT. This yields a round trip time of 2T=2L/c. Here we present our reasoning for such a seemingly very simple Galilean transformation. If the light beam on the transverse arm changes its initial direction as shown in the figure for sun s coordinate system, the speed of light in the longitudinal direction has to be treated likewise, adding or subtracting the speed of the source. If the speeds of light and source are treated as vectors, the resultant speed is always the addition of speed of light and the speed of the source vectorially. 2. In the earth s coordinate system If the above situation is really what happened, the light in the transverse direction as seen in the earth s coordinate system would appear to travel the path of ABA as in Fig.2. The time it spends will certainly be 2L/c. For the longitudinal arm, the light will take 2L/c because the longitudinal arm will appear to be at rest. 3. For constant speed of light If speed of light is a constant, then the light beam of the transverse direction for Michelson- Morley experiment has to keep traveling in the initial direction, from A to B, in the sun s coordinate system. This is a natural consequence if light is considered as a wave and there is no medium present in space. Transverse light will keep traveling in the AB direction regardless of the speed of the earth revolution around the sun. In this situation, the time light spent on the transverse arm would be 2L/c. The time light spent on the longitudinal arm, using the same treatment of Michelson and Morley, would be
tt = LL cc vv + LL cc + vv = 2LL 1 vv2 cc2 cc (2) Following Lorentz, the longitudinal length would need to be contracted by multiplying (1-v 2 /c 2 ). The Lorentz contraction was originally (1-v 2 /c 2 ) 1/2. We have a different result if we apply the principle of constant speed of light to Lorentz s way of length contraction. In the earth s coordinate, the light beam would appear lagging behind the transverse arm. We need to expand this here, because it may not be intuitive. The constancy of speed of light requires the speed of light unchanged, including its direction when light departs from the source. When light departs from the source, the splitter of the interferometer, or point A in Fig.2, it actually goes towards the space between the earth and the sun. Although it seems that the light beam is always travelling around the interferometer, it points to the space. We need to have the sun s coordinate system in our mind when we consider the light s actual path or its direction in the earth coordinate system. This situation could be understood easier if we place the MM interferometer on a moving train. The transverse light beam would travel the same way as if the train were at rest in the moment of emission if speed of light is constant. In other words, when the vector of a transverse light traveling has a component of the source, light can keep its perpendicular (or transverse) relation with the source motion. In the MM experiment, L is 11m in length. AD in Fig.2 is only 1.1mm. The mirror should have been wider than that. Therefore no one is sure whether light goes the direction of AB or AD as in the sun s coordinate system. There may be ways to verify this question experimentally such as using a much longer armed interferometer.
4. Concluding remarks In section 1 and 2, we used Galilean transformation for the two coordinate systems, sun and earth. This is because we believed that light can be considered as a ray of particles and the speed of the source can be added to the transverse light to cause the direction change from AB to AD viewing in the sun s coordinate system. In section 3, we described the situation where Galilean transformation cannot be applied because the wave nature of light is applied, where travelling of light (speed and direction) would not be affected by the relative motion of the source. Therefore we want to raise this not so trivial question, does light travel from A to B or from A to D in the transverse direction in the sun s coordinate system? The first situation where Galilean transformation is used seems to be more reasonable. Therefore we want everyone s attention and suggest a direction of experimental investigation.
Fig.1 Schematic diagram of the apparatus used in Michelson-Morley experiment. Fig.2 Light paths for the transverse beam 1 Michelson, A. A.; Morley, E. W., American Journal of Science 34: 333 (1887). 2 Lorentz, Hendrik Antoon, Zittingsverlag Akad. V. Wet. 1: 74 (1892)