(Theoretical background / Experimental setup / Null results)
In this section, Feynman discusses the theoretical background, experimental setup, and null results of the Michelson-Morley experiment.
1. Theoretical background:
“…the emerging beams D and F will be in phase and will reinforce each other, but if the two times differ slightly, the beams will be slightly out of phase and interference will result (Feynman et al., 1963, section 15–3 The Michelson-Morley experiment).”
The 1887 Michelson-Morley experiment was an attempt to detect ether by comparing the difference in time that a light beam travels parallel to the ether wind with another light beam that travels perpendicular to the ether wind. This is an interference experiment in which the interference fringes may be shifted if the light beams are slightly out of phase. To be precise, interference occurs whether the light beams are in phase or out of phase, but it may not be observable. (It is confusing for Feynman to say that the light beams will be out of phase such that interference will result.) In Michelson’s (1881) earlier experiment, the expected fringe shift was about 0.16 of the distance between the fringes, but the observed fringe shift was significantly less than the expected shift that it was deduced to be errors of measurement.
Theoretically speaking, if the two arms of the Michelson-Morley interferometer have exactly the same length, the null results of the Michelson–Morley experiment can be explained by length contraction alone. Therefore, Kennedy and Thorndike (1932) modified the Michelson–Morley interferometer by changing the length of an arm such that one side is shorter than the other. During the Kennedy–Thorndike experiment, the apparatus was held fixed in the laboratory and the interference fringes were observed over a period of months. The experiment requires extreme demands on the mechanical stability of the apparatus and it serves as a test to indirectly verify time dilation in addition to length contraction. The experimental results also help to support the claim that there are no phase shifts while the Earth is rotating around the Sun.
2. Experimental setup:
“This apparatus is essentially comprised of a light source A, a partially silvered glass plate B, and two mirrors C and E, all mounted on a rigid base (Feynman et al., 1963, section 15–3 The Michelson-Morley experiment).”
The Michelson-Morley experiment was performed using an apparatus similar to that as shown schematically in Fig. 15–2. The apparatus is essentially comprised of a light source A, a partially silvered glass plate B, and two mirrors C and E; the mirrors were placed at equal distances L from the glass plate. The function of the glass plate is to split an incoming beam of light into two outgoing beams that move in mutually perpendicular directions to the mirrors, whereby they are reflected back to the glass plate. Physics teachers may elaborate that the glass plate (or beam splitter) causes a phase shift, due to its refractive index, to the light beam that passes through it. Thus, a compensator plate of equal refractive index and thickness is used to compensate for the extra optical path length (through the glass plate) traveled by the light beam.
According to Feynman, it is difficult to make the length of the two arms exactly equal. (His discussion is misleading because it indicates that the purpose of the rotation of the apparatus is to solve the problem of unequal lengths.) Importantly, a maximum fringe shift was expected by revolving the apparatus through 90 degrees. Furthermore, the experimental results could be more convincing when the apparatus was rotated by many different angles instead of only 90 degrees. In the words of Michelson and Morley (1887), “[t]he apparatus was revolved very slowly (one turn in six minutes) and after a few minutes, the cross wire of the micrometer was set on the clearest of the interference fringes at the instant of passing one of the marks. The motion was so slow that this could be done readily and accurately.” Note that the apparatus was mounted on a basin filled with liquid mercury such that it can be slowly rotated.
Note: One may add that this is a difficult experiment because of the need to control for vibrations. In an earlier paper titled Michelson (1881) writes: “...owing to the extreme sensitiveness of the instrument to vibrations, the work could not be carried on during the day... Here, the fringes under ordinary circumstances were sufficiently quiet to measure, but so extraordinarily sensitive was the instrument that the stamping of the pavement, about 100 meters from the observatory, made the fringes disappear entirely!”
3. Null results:
“Although the contraction hypothesis successfully accounted for the negative result of the experiment, it was open to the objection that it was invented for the express purpose of explaining away the difficulty, and was too artificial (Feynman et al., 1963, section 15–3 The Michelson-Morley experiment).”
The Michelson-Morley experiment is the most famous failed experiment because of the null results. (Perhaps Feynman should avoid the term negative results because it suggests an opposite meaning to positive results that is different from null results.) Based on the null results, Lorentz formulates a contraction hypothesis. On the other hand, Poincaré proposes that it is impossible to discover an ether wind by any experiment and there is no way to determine an absolute velocity. However, Michelson and Morley (1887) disagree with Lorentz’s hypothesis and conclude that the ether is at rest with regard to the Earth’s surface. Interestingly, Michelson is the first American to receive the Nobel Prize for Physics (precisions in optical experiments).
The experimental results that significantly influenced Einstein and form the basis of his special theory of relativity were the observations of stellar aberration and Fizeau’s experiment instead of the Michelson and Morley experiment (Shankland, 1963). In a lecture series at the University of Buenos Aires, Einstein delivered his first lecture on 25 March 1925 by saying that Fizeau’s 1851 water tube experiment was “perhaps the most fundamental to the theory of special relativity… that demonstrates the impossibility of assuming that ether is completely dragged by matter (Einstein, 1925, p. 941).” In essence, Fizeau’s experimental results can be explained using the concept of relative velocity (instead of absolute velocity) of the running water with respect to the laboratory.
Questions for discussion:
1. What is the theoretical background behind the Michelson-Morley experiment?
2. What are the experimental considerations of the Michelson-Morley experiment?
3. What are the possible conclusions of the Michelson-Morley experiment?
The moral of the lesson: based on the null results of Michelson-Morley experiment, we can deduce that it is impossible to discover an ether wind by any experiment and there is no way to determine the absolute velocity of an object.
References:
1. Einstein, A. (1925). Professor Einstein Began His Lecture Series Yesterday. In D. K. Buchwald et al. (eds.) (2015). The Collected Papers of Albert Einstein, Volume 14 (English): The Berlin Years: Writings & Correspondence. Princeton: Princeton University Press.
2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.
3. Kennedy, R. J., & Thorndike, E. M. (1932). Experimental establishment of the relativity of time. Physical Review, 42(3), 400–418.
4. Michelson, A. A. (1881). American Journal of Science, 22(128), 120–129.
5. Michelson, A. A., & Morley, E. W. (1887). On the Relative Motion of the Earth and of the Luminiferous Ether. American Journal of Science. 34(203), 333–345.
6. Shankland, R. S. (1963). Conversations with Albert Einstein. American journal of physics, 31(1), 47–57.
No comments:
Post a Comment