# Physics307L F09:People/Mahony/Rough

SJK 13:53, 2 December 2009 (EST)
13:53, 2 December 2009 (EST)
I think this is a very good rough draft. There is a lot of work needed (see all comments below), but I think you've written a really good foundation to make that very do-able. My guess is that the most substantial work will be required in expanding the results and conclusions section. I gave you some ideas for that, and also you'll naturally be able to expand it due to your "extra data" next week. OK, Good luck!

# The Speed of Light

SJK 11:19, 30 November 2009 (EST)
11:19, 30 November 2009 (EST)
Author & Contact info is missing. Also, a more descriptive title is needed. As it is now, a reader may assume your article is a vast review of all topics related to the speed of light, whereas a more descriptive title could indicate that you're measuring speed of light in a specific way, etc.

## Abstract

SJK 11:31, 30 November 2009 (EST)
11:31, 30 November 2009 (EST)
You are homing in on a short and to-the-point abstract, compared with an abstract that gives more motivation and conclusion. That's OK, if done precisely, which you can probably do. In terms of getting a bit more practice, though, I'd probably prefer that you: (1) expanded the first sentence a bit, if you can add a bit of "why" it's important. (2) Add a second sentence saying that there's a variety of extremely precise methods for measuring the speed of light. (3) then in your next sentence, preface it by saying you're using the time of flight method. (4) your sentence "by positioning the LED..." can be broken up into two sentences -- first that you created fixed distances and measured the change in time delays for each; next that you used linear regression to produce ___ m/s. (5) Finally, add a conclusion sentence--is it consistent w/ accepted value and any other comments.

The speed of light is an important fundamental constant in physics. In this experiment we use a Time-Amplitude Converter to measure the delay between an LED and a photomultiplier tube. By positioning the LED at different distances from the PMT, and using the conversion ratio of voltage to time, we were able to fit our data to a line, with the slope corresponding to our measured speed of light of 2.941(15)*10^8 m/s.

SJK 11:25, 30 November 2009 (EST)
11:25, 30 November 2009 (EST)
LED is not defined and probably should be. PMT is almost defined, you just need to put (PMT) after the "photomultiplier tube." It's good to define almost all acronyms, although you can use your judgement on some of them, such as DNA, e.g.

## Introduction

SJK 11:49, 30 November 2009 (EST)
11:49, 30 November 2009 (EST)
This is an excellent foundation for the introduction, but it's too succinct, I think. It's so concise that it could almost serve as half an abstract! In some cases, such as when page limits are very short, this could be OK. In this case, though, I'd like you to expand each of your ideas. I think you can do this relatively easily based on what you have. Just build sentences around what you already have. For example, what was the community focusing on after 1887? Since you mention it, how was it that special relativity gained wide acceptance? References to key experiments? More important are the "many experiments done to more accurately measure the speed." What were the nature of these experiments? What are the different methods? Can you link to a few specific research papers that reported a value for the speed? Finally, your last sentence is the only sentence about what you're reporting here. You can expand this to say that you're using time of flight, and that you will compare your result with the accepted value, or you could say that the result you produce does compare favorably. And / or that this experiment is a satisfying way to explore methods for measuring the speed of light.

With the refutation of the aether theory by the Michelson-Morley experiment in 1887, light became a subject of focus in the scientific community.[1] Equally controversial was Einstein's theory of special relativity, published in 1905, which proposed that the speed at which light propagated was a fundamental constant, invariant of the speed of the reference frame in which it was observed.[2] This theory became widely accepted, and throughout the rest of the 20th century, many experiments were done to more accurately measure this speed.[3] In 1983 the meter was redefined by the CGPM as the distance traveled by light in 1/299,792,458 seconds, giving the speed of light the exact value of 299,792,458 meters/second.[4] In our experiment, we set out to measure this speed to see if our experimental data matched the accepted value.

## Methods

SJK 12:01, 30 November 2009 (EST)
12:01, 30 November 2009 (EST)
Your style for the methods section is great. And the information you have included is very good with some minor additions needed (as noted). Some details are missing: did you average the signals? How much averaging? How did you define "intensity" on the oscilloscope? Also, in your results section, you talk about "in the 1st trial," but the methods does not mention trials, or differences between them (as far as I can see).

More important is that data analysis methods are completely missing. You may talk about this sufficiently below (I haven't looked closely yet), but in any case, it belongs in the methods section. Just like you do for the equipment, you'll want to cite the software that you use, and you'll want to spell out any algorithms you developed. It's up to you whether you want to include specific formulas or link to them in an appendix or elsewhere.
Figure 1: Time Walk Effect- Different amplitudes of a signal cause a time shift in a trigger signal.
SJK 11:50, 30 November 2009 (EST)
11:50, 30 November 2009 (EST)
Is there a model number for LED or PMT? If not, can you describe them somehow? (pulse rate, color, etc.)
We positioned a photomultiplier tube (PMT) powered by a Bertran 313B Power Supply on one end of a carboard tube. We placed a LED in the other end, powered by a Harrison Laboratories 6207A PSU. We measured the time difference between the LED's pulse and the photomultiplier's response with a Ortec 567 TAC/SCA Module plugged into a Harshaw NQ-75 NIM Bin. We placed a Canberra 2058 Delay Module between the PMT and the TAC to guarantee the response pulse would be received by the TAC after the triggering pulse from the LED. SJK 11:56, 30 November 2009 (EST)
11:56, 30 November 2009 (EST)
All figures used in a report will be referred to in the text. You can do that here by saying something like "See Figure 2 for experimental setup." Or work it into a sentence as you did for the time walk figure. Probably you'll need to renumber those so that the first one you refer to is Figure 1. Also, figure captions need a bit more detail: For time walk figure: tell reader what the x and y axes represent, and what the typical scales would be (nanoseconds/ volts). For Figure 2, I'm not sure how to expand it, but probably should, even if just saying "with key equipment labeled" instead of "labels." I do love the panorama, BTW.

We measured the TAC's voltage using a Tektronix TDS 1002 Oscilloscope. This voltage corresponded to the time between the LED trigger pulse and the PMT response pulse with the LED at different positions, all 10 cm apart. As the LED got closer to the PMT, the intensity would increase, and this would cause error due to "time walk." The oscilloscope displays a signal by triggering when the signal reaches some threshold. The "time walk" effect is the change in time of this trigger signal due to a change in amplitude of the input signal. In this experiment, a change in intensity of the LED signal causes the oscilloscope and the TAC to trigger at a different time, and the TAC will produce a different voltage. To minimize the error due to time walk (see Figure 1) we used a set of polarizers placed on the PMT and the LED to keep the intensity of the LED pulses constant. We measured the intensity of the LED when it was at its maximum distance from the PMT, and then we rotated the PMT with the polarizer attached so that the intensity of the LED signal remained constant for every measurement with the LED in a closer position.

Figure 2: Panorama of the setup with labels

## Results and Discussion

SJK 13:40, 2 December 2009 (EST)
13:40, 2 December 2009 (EST)
I really like your plot: it clearly conveys a lot of information very clearly. It's definitely a good way of presenting your net result. I think, though, some other figures should be included to make the results section more substantial. To do this, ask yourself what the reader may want to see after looking at the figure you have. In my mind, this would be individual linear regression fits for some or all of the data sets. If you did that as a preceding figure, I think you'd have enough to talk about. As it is now, there is very little text in your results and discussion section, which is not standard. So, I think it'd be good by starting out, even the way you have, "In the first trial..." and then saying, "Trial one and the linear regression fit is displayed in Figure X.A. Subsequent trials (Figure X.B-E) included 11 positions, separated by __ cm. As seen in Figure X, no noticeable trend was seen in terms of uncertainty of individual measurements, or on residuals (you could even plot all the residuals on another graph, which could be interesting"

In the first trial, we measured the voltage of the TAC with the LED in 10 different positions. For every subsequent trial, we measured the voltage with the LED at 11 positions. After the first trial, we used the averaging function on the oscilloscope. This function took a time average of a signal, which reduced the noise, so we could better measure its voltage. The TAC was set to produce a 10V signal for a 100 ns delay. We used this ratio of 1V/10ns to convert our measured voltages into times.

I used the chi-square minimization technique to fit the data with a line. The slope of the line and standard error were used in a weighted average to compute the measured speed of light. This value was:

$2.941(15)\cdot 10^{8} m/s$

The exact speed of light is approximately:

$2.998\cdot 10^{8} m/s$

The calculated speed of light was 4 sigma away. Assuming only normally distributed random error, the probability of measuring the same value we did is 0.006%.SJK 13:35, 2 December 2009 (EST)
13:35, 2 December 2009 (EST)
A couple comments about this. First, this is definitely on the right track for how to compare your measurement to a precise accepted value. As you've written it, though, your wording should be, "the probability of measuring 4 sigma or more away from the mean (in either direction) is 0.006%." That is, you're reporting 1 minus the error integral from -4sigma to + 4sigma. Furthermore, you should add a comment, "Thus, it is almost certain that substantial systematic error remained in our measurements." (You can make a goal of eliminating or identifying this systematic error next week.)

I would be pretty much OK with this kind of comparison. But it's worth noting that when you're out on those tails of the distribution, the estimate of the standard deviation of the mean is pretty important. In reality, we usually don't care so much about whether it's 0.006% or 0.3% : in either case we'd be pretty certain there's substantial systematic error. But if you are reporting those kinds of numbers and asserting confidence, then I think what you need to do is use "Student's t-test," which would account for how many degrees of freedom were used in estimating the standard error. It's worth reading, just to find out that the guy who invented it was using the pseudonum "Student" because his employer, Guinness, didn't want him revealing the trade secret that the brewery was using statistics to improve its processes: http://en.wikipedia.org/wiki/T_test#History
Figure 3: Trials 1-6, the accepted speed of light, and the calculated value from the measurements, along with their corresponding uncertainties, are shown.
SJK 13:42, 2 December 2009 (EST)
13:42, 2 December 2009 (EST)
Usually, the figure legend is not included (probably due to space limitations?). However, it works well for you, so I'd leave it. Nevertheless, I think more description in the figure legend is needed to explain what the various symbols and error bars refer to. E.g. green triangle represents the mean of all 6 trials and the error bars represent one standard error of the mean.
The supplementary data and analysis can be seen here.SJK 13:44, 2 December 2009 (EST)
13:44, 2 December 2009 (EST)
Hyperlinks are usually not included in the text, but rather you'd have a numbered "reference" (endnote) here and in the reference would include the link. For example, "Raw data and source code are freely available[7]."

## Conclusions

SJK 13:46, 2 December 2009 (EST)
13:46, 2 December 2009 (EST)
Aside from the revised language regarding probability as I mentioned above, I think this is a pretty good conclusion. I think investigating the systematic error next week would be good, including trying out the DAQ card if you'd like.

The probability of measuring the same value we did is 0.006%. Assuming only normally distributed random error, the likelihood of this happening again is quite low. I conclude that the experimental data deviated from the accepted value due to systematic error. I believe the cause of this error was inadequate minimization of the time walk effect caused by the reliance on human judgment in determining when the intensity of the LED pulse signal matched the original signal. This error might be reduced by the use of a computer to measure the LED signal, rather than using the screen of an oscilloscope. This method is far more quantitative, and I believe it would yield more accurate results.

## Acknowledgements

SJK 13:48, 2 December 2009 (EST)
13:48, 2 December 2009 (EST)
You can revise this to make it more typical. "I thank Ryan Long for help with electronic lab notebook, instrumentation setup, data acquisition, and data analysis...I thank A. Barron for his open access lab report which provided guidance on bib tex references and manuscript style (this is not something you'd read in a peer-reviewed report, but I really like that you give him props, so I think you should leave it in and just try to make it sound "formal."

Thanks my lab partner Ryan for his help with running the lab, taking data, and finishing up the lab notebook with me. I'd also like to thank Dr. Koch for his helpful explanations of various parts of the setup.

Thanks to A. Barron, who I referred to for help in formatting citations as well as getting a general idea of what I needed to write.[5]

## References

SJK 11:43, 30 November 2009 (EST)
11:43, 30 November 2009 (EST)
These first two are the kind of original peer-reviewed research I'm looking for--good!
1. Michelson, Albert Abraham & Morley, Edward Williams (1887), "On the Relative Motion of the Earth and the Luminiferous Ether", American Journal of Science 34: 333–345 [Michelson]
2. Albert Einstein (1905) "Zur Elektrodynamik bewegter Körper", Annalen der Physik 17: 89 SJK ~~~~~
~~~~~

[SR]

3. Measurement of the speed of light. T. G. Blaney C. C. Bradley G. J. Edwards B. W. Jolliffe D. J. E. Knight W. R. C. Rowley K. C. Shotton & P. T. Woods Nature 251, 46 (1974) | doi:10.1038/251046a0. http://www.nature.com/nature/journal/v251/n5470/pdf/251046a0.pdf

[Blaney]

4. Base unit definitions: Meter. Nov 15 2009. http://physics.nist.gov/cuu/Units/meter.html

[NIST]

5. A. Barron's Final Report

[Barron]