Physics307L:People/Barron/Final rough

Speed of Light from a Cardboard Tube

Alexander T. J. Barron

Experiment conducted with Justin Muehlmeyer

Junior Lab, Department of Physics & Astronomy, University of New Mexico

Abstract

I measure the speed of light in air utilizing a time-to-amplitude converter (TAC), a photo-multiplier tube (PMT), and an LED pulse-generator in a light-tight environment. By positioning the pulse-generator at varying distances from the PMT/TAC apparatus, one can obtain various data sets corresponding to the change in distance between the two components. For each change in distance, I record a new amplitude from the TAC, corresponding to change in time readings. Plotting change in distance vs. change in time yields the perfect environment for taking a least-squares linear fit of the data, of which the slope is the speed of light in air. In the process of finding c_air, I use different data-taking strategies as well as investigate a phenomenon known as "time walk," which without correction nullifies any useful data taking from this equipment set.

Introduction

Even after the Michelson-Morley experiment in 1887 gave reasonable doubt as the existence of the aether, certain scientists argued into the early 20th century against case for (what we now call) relativity, based on statistical uncertainty [1, 2]. Least-squares analysis specifically was targeted as covering up true values in its effort to smooth out errors, thereby burying results leading to aether-positive results. Through Einstein's theory of special relativity, and corroborating evidence, we now know almost irrevocably that the aether is not a factor in measurements of the speed of light, so good experiments involving least-squares analysis can be pursued with impunity.

All experiments measuring the speed of light involve taking measurements of time taken for light to traverse a given path[3]. The most common method up to 1944 was to partition light "packets" with periods of zero luminosity, thereby creating specific boundary times with which to measure between[3]. We follow this approach with more modern tools.

Methods and Materials

In order to measure the time-of-flight (TOF) of light packets, we position a moveable LED-pulse generator inside a several meter-long cardboard tube. The generator fills the entire cross-sectional area of the tube, ensuring light-tight conditions. On the opposite end of the tube, we position a fixed PMT. On the inner side of each device is a polarizer, used to maintain near-constant intensity of light received by the PMT. I address the reason for the polarizers in appendix A. The generator and PMT are both connected to the TAC, which measures the difference in time between the generation of the pulse and the receipt of the pulse by the PMT. The PMT is also connected to a digital oscilloscope through a second anode connection. We read the voltage output of the TAC via the oscilloscope along with the reading from the PMT.

References

1. Heyl, Paul R. "The Application of the Method of Least Squares." Science, New Series, Vol. 33, No. 859 (Jun. 16, 1911), pp. 932-933. American Association for the Advancement of Science. JSTOR

   Heyl argues that the method of least-squares to average out error may be flawed, specifically in the context of extended Michelson-Morley-like experiments. He proposes a "mathematical theorem," providing a rule of thumb regarding acceptable least-squares error analysis.

2. Freedman, Hugh D.;, Roger A.; Ford, and A. Lewis Young. Sears and Zemansky's University Physics: With Modern Physics. San Francisco: Benjamin-Cummings Pub Co, 2004.

3. Dorsey, N. Ernest. "The Velocity of Light." Transactions of the American Philosophical Society, New Series, Vol. 34, No. 1 (Oct., 1944), pp. 1-110. American Philosophical Society. JSTOR

   Dorsey covers tomes of material in this paper, including a nicely-put summary of error analysis and the least-squares approach. He analyzes a number of historical experiments measuring the speed of light and reviews their accuracy based on procedure, equipment, and effectiveness of error documentation. There doesn't seem to be any mention of confidence intervals in a standardized way, but rather each uncertainty is reported based on logical arguments and various extremum.

4. Mulholland, J. Derral. The Speed of Light." Science, New Series, Vol. 180, No. 4093 (Jun. 29, 1973), pp. 1321-1322. American Association for the Advancement of Science. JSTOR

   Mulholland argues for the light-second as the more fundamental and useful unit regarding the speed of light.