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Implementation of the Fizeau Aether Drag Experiment for an Undergraduate Physics Laboratory by Bahrudin Trbalic Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 c Massachusetts Institute of Technology 2020. All rights reserved. ○ Author................................................................ Department of Physics May 8, 2020 Certified by. Sean P. Robinson Lecturer of Physics Thesis Supervisor Certified by. Joseph A. Formaggio Professor of Physics Thesis Supervisor Accepted by . Nergis Mavalvala Associate Department Head, Department of Physics 2 Implementation of the Fizeau Aether Drag Experiment for an Undergraduate Physics Laboratory by Bahrudin Trbalic Submitted to the Department of Physics on May 8, 2020, in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics Abstract This work presents the description and implementation of the historically significant Fizeau aether drag experiment in an undergraduate physics laboratory setting. The implementation is optimized to be inexpensive and reproducible in laboratories that aim to educate students in experimental physics. A detailed list of materials, experi- mental setup, and procedures is given. Additionally, a laboratory manual, preparatory materials, and solutions are included. Thesis Supervisor: Sean P. Robinson Title: Lecturer of Physics Thesis Supervisor: Joseph A. Formaggio Title: Professor of Physics 3 4 Acknowledgments I gratefully acknowledge the instrumental help of Prof. Joseph Formaggio and Dr. Sean P. Robinson for the guidance in this thesis work and in my academic life. The Experimental Physics Lab (J-Lab) has been the pinnacle of my MIT experience and I’m thankful for the time spent there. Thanks to Dana and Kaylee for the assistance in making this experiment a reality. I wish to thank Abdurrahman, Harith, Al Barra, Bilal, Amro and all my friends including my roommates at KBL for a wonderful and memorable time at MIT. Thanks to Selver, Nuzdeim, Sladan and Amer for teaching me physics in my early days. I wish to thank my research supervisor and an amazing professor Cardinal Warde. Thanks to Mohammad Ghassemi, who has been an wonderful mentor throughout my MIT time. Lastly, I want to thank everyone in the MIT community for making it such an amazing place to study and live in. 5 6 Contents 1 Introduction 15 1.1 Historical relevance of the Fizeau experiment . 15 1.2 Ease of replication of the setup . 16 2 History of the Fizeau experiment 17 2.1 Original aether drag experiment . 17 2.2 The Experimental Setup and Methods used by Fizeau . 18 2.3 Results and their interpretation by Fizeau . 20 2.4 Replications of Fizeau’s experiment . 21 2.5 The significance of Fizeau’s experiment to the theory of special relativity 22 3 Theoretical background 23 3.1 Special relativity . 23 3.1.1 The velocity addition formula . 24 3.1.2 Comparison of the nonrelativistic and relativistic velocity ad- dition formulae . 25 3.2 Interferometry . 26 3.2.1 Fringe patterns . 26 3.2.2 Phase difference due to moving water . 28 3.3 Hydrodynamics . 29 3.3.1 Flow of a viscous fluid . 29 3.3.2 Michelson and Morley’s water flow velocity measurement . 31 7 4 Experimental setup 33 4.1 Physical considerations . 33 4.1.1 Cost . 34 4.1.2 Space . 34 4.1.3 Maintenance . 34 4.2 Integral parts of the experiment . 34 4.2.1 Optical system . 35 4.2.2 Pipe and pump system . 37 4.2.3 Peripheral devices . 40 5 Experimental procedures and results 41 5.1 Experimental Setup and Procedures . 41 5.1.1 Measurements of the geometric properties of the experimental setup . 42 5.1.2 Index of refraction of water . 43 5.1.3 Water Velocity Meter Calibration . 44 5.1.4 Alignment of the laser beams . 45 5.1.5 Interference pattern image capturing . 46 5.2 Data analysis and results . 47 5.2.1 Data acquisition . 47 5.2.2 Data analysis . 47 5.2.3 Results . 49 5.3 Error analysis . 51 6 Further improvements 53 6.1 Ultrasonic velocity measurement . 53 6.2 Colour Infusion . 55 7 Conclusion 57 A Video Analysis Code 59 8 B Student Manual 61 9 10 List of Figures 2-1 The simplified setup of the Fizeau experiment. In this case the wateris flowing counterclockwise, as indicated by the arrows. The light source on the right emits light that goes through a beam splitter m0. The two light beams traverse the pipes, reflect at the mirror m, and come back to the beam splitter via the pipes. 19 2-2 The simplified setup of the replica of the Fizeau experiment doneby Michelson and Morley. As with the original experiment, there are two parallel glass pipes through which water can flow. The main difference between the two experimental setups is the positioning of the beam splitter and the light source. 21 3-1 The interference pattern produced by two plane waves converging onto a screen. 27 3-2 The pressure difference measurement technique implemented by Michel- son and Morley. The L-shaped probe is facing the water stream. It measures the static and dynamic pressure in the fluid. The other I- shaped probe measures only the static pressure. The difference between the two measurements is the dynamic pressure which depends on the velocity of the water at the R w distance from the center of the pipe. − Varying w we can measure the velocity profile. 31 11 4-1 Shown are a) the Michelson interferometer and b) the modified Michel- son interferometer used for the Fizeau experiment. Note that the colours are used for illustrative purposes to make it easier to follow individual beams. 35 4-2 The Modified Michelson interferometer with extended distances be- tween the M2-M3 and S-M1 components. Illustrated is the placement of pipes that carry water. 36 4-3 The pipe and laser system. 38 4-4 The mounted windows using a union straight connector. They can be easily connected to the ends of the pipes. (Modified from McMaster- Carr [1]). 39 4-5 The custom made stand for the pipes. It keeps the separation and elevation of the pipes constant. 39 5-1 Water is driven through two long pipes using a pump. An interfer- ometry setup measures the phase difference caused by the asymmetry of the direction of the water flow and the laser beam propagation. A camera attached to a Raspberry Pi will be used to measure the phase difference. 42 5-2 The intensities along the fringes were added to produce a single num- ber. In the case of the image here, that was done by summing the columns of the image matrix. The result was an intensity distribu- tion as a function of the horizontal pixel value. This procedure was repeated for every velocity level. 48 5-3 The position of two interference pattern peaks as a function of phase along the horizontal axis and velocity along the vertical axis. A solid vertical line is drawn as a reference for the maximal shift of the left intensity peak position. 49 12 5-4 Phase shift data as a function of the velocity of the water flow. The error bars represent the uncertainty in the readings of the central peak of the intensity distribution and the uncertainty in the water velocity flow measurement. 50 5-5 Same as above. The data is more noisy because the camera was not focused well enough on the fringe pattern. The clustering of data points at near 4 m/s is due to the length of the video of the fringe pattern at that velocity. 50 6-1 A method for measuring the water velocity between points A and B. We send a sharp ultrasonic pulse at point A and measure the time it takes to detect it at point B. 54 6-2 A method for measuring the water velocity in the pipe. Left image is the pipe before the colour arrives while the right one is the pipe when the colour has arrived. We infuse red food colour in the pipe inlet and then we compare the delay between the colour arrival between the left and right side. A meter stick is used to measure the distance between the two observation points. 55 6-3 A method for measuring the water velocity in the pipe. Left image is the pipe before the colour arrives while the right one is the pipe when the colour has arrived. We infuse red food colour in the pipe inlet and then we compare the delay between the colour arrival between the left and right side. A meter stick is used to measure the distance between the two observation points. 56 13 14 Chapter 1 Introduction It is widely accepted that experimental physics education is indispensable form school curricula. Experiments are especially important in undergraduate physics education. They enable students to apply their theoretical knowledge, test hypotheses, and ob- serve the natural world with all of its vastness and limitations. Experiments have been the backbone of the development of physics and the only way to challenge hy- potheses. However, there exists a great inequality between theoretical and practical teaching when it comes to allocation of time and resources. Practical education is being neglected despite its pedagogical effectiveness. Most of it is due the impractica- bility of developing, maintaining and supervising hands-on education. Nevertheless, there is a vast number of affordable and implementable experiments that could be used to educate and motivate students. One of them is the adaptation of the Fizeau aether drag experiment described in this thesis work.
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