Dataset: Michelson Speed-of-light Measurements

### Overview

These data were collected by Albert Michelson and his colleagues in the late 1800's.

### Observations

1. ↑ Michelson "Experimental Determination of the Speed of Light" (1880), link

* While the speed of light in air does vary with temperature, the variations we see in the dataset are far larger than a calculation based on air's index of refraction would imply.(Z. 1)

## Team Alpha

* Most of the data points with lowest distinctness were taken on the same day.

* Most of the data points were above the real value, even before the temperature correction.  Information on the accuracy of his timekeeping devices was not provided in this dataset.

* The mean velocity of the higher-distinctness measurements was higher. However, it does not look like higher-distinctness measurements were necessarily more accurate.

* temperature alone does not explain his range of values, there are likely other sources of error.

While Michelson's data correction attempted to take temperature into account, the refractive index of air, the medium he conducted his experiment in, also varies with humidity and barometric pressure- meteorologists now use Edlen's equation to account for this . The location he used to make his observations, what is now an open area in front of Michelson Hall at the US Naval Academy in Annapolis, MD   is between two rivers that feed into the Chesapeake Bay  and is highly subject to fluctuating atmospheric conditions. These, in combination with deficiencies in his equipment and apparatus, and possible human error, likely all contributed to the differences between his experimentally determined velocity and the true speed of light in a vacuum.

1. ↑ Scatterplot by date, with distinctness as color
2. ↑ Scatterplot of data before correction
3. ↑ Scatterplot of VelocityVacuum vs Distinctness
4. ↑ [1]]
5. ↑ https://emtoolbox.nist.gov/Wavelength/Edlen.asp
6. ↑ https://www.gutenberg.org/files/11753/11753-h/11753-h.htm
7. ↑ https://www.usna.edu/Library/sca/ve-collections/michelson/career.php-
8. ↑ https://upload.wikimedia.org/wikipedia/commons/9/9e/1924\_Map\_of\_US\_Naval\_Academy.png

## Team Beta

* There is clearly some source of systemic error in Michelson’s experiments. Whether this was from his modeling assumptions or his experimental setup is difficult to conclude based on the dataset alone.
* We find that Michelson’s notion of `Distinctness` doesn’t really account for a reduction in variance or bias (both of which I interpret to be sources of uncertainty).
* Epistemic status: shaky. We might conclude that there is a slight positive correlation between error and temperature.
* Overall, we could use more information or do more research to unpack what the sources of uncertainty were in Michelson’s experiment…
	+ …and Michelson could have been more conservative with his uncertainty estimates.

1. ↑ Beta 1 - Distribution of error in velocity (Mason) [2]
2. ↑ Beta 2 - Faceted (by distinctness) histograms [3]; Table in "Distinctness" section of report [4]
3. ↑ Beta 3 - Error vs. temperature with `geom\_smooth` overlay [5]

## Team Gamma

* It seems to be that while Michelson had a good idea of what uncertainty he introduced with his measurement techniques (+/- 51 km/sec), the exact speed of light in vacuum is still outside those bounds.
* It is possible that his setup or process was flawed (compensation for air?) to introduce a constant shift.
* Temperature seems to have an effect on the left and right extremes of the plot but is fairly constant from about 65 to 85 degrees. There are a few outliers (of high distinctness) that pull the data down and up respectively. This could be because he was only able to make measurements in the morning (lower temp measurements) and evening (higher temp measurements) when the atmospheric conditions sub-optimal.
* We would expect good distinctness (1) to be the tightest estimate of VelocityVacuum. However, 2 is actually the tightest grouping followed by 1 and then 3. Distinctness itself is therefore not a significant factor in the uncertainty bounds of the measurement.

Images from Elliott's Report

1. ↑ [6]
2. ↑ [7]
3. ↑ [8]
4. ↑ Elliott's Report

## Team Delta

* It's surprisingly accurate how close his results were to the true value of the speed of light.
	+ What else was the source of error that he would have missed?
* The distribution of distinctness was interesting because D3 wasn't as condensed around one point. This was surprising because there were more measurements at D3 and there were technically supposed to be more accurate. [1]

* + The less distinct seemed to be more Normal (but further away from the "True" value of light).
* Temp. vs. Date --> groups of temperature at specific dates. Seems pretty scattered. [2]

## Team Zeta

### Michelson's experiment was an incredible success for its time!

Michelson’s error, approximately 151.5 km/s (too high) was approximately 2.97 times his stated uncertainty (plus or minus 51 km/s). This seemed high until considering the relative error which was shockingly small - 0.05%!

### There's potential of a positive correlation between temperature and the speed of light.

The small sample makes generalization difficult from this dataset, but at the lowest temperatures (less than 60 degrees F), the estimated velocities of light in a vacuum were all 299,812 km/s or less, and at the highest temperatures (90 degrees F), the estimated velocities were all 299/952 km/s or higher.

### Increased distinctness does not lead to more accurate results.

There were significant questions around what the distinctions were around the “poor”, “fair”, “good” images that comprised the main quality axis in this data set. From the resulting velocities, sample size aside, it is not possible to correlate the data labeled as being higher quality as being more accurate. We were unable to find a clear definition of quantifiable metrics for this classification, leading us to believe that this is largely a subjective measure.
When looking at Velocity (with the Vacuum correction) divided into ‘Distinctness’ bins, the range of 1 values are the closest to the modern value for the speed of light.

### Michelson’s experiments were heavily limited by the methodology employed to gather the data - aka humans.

Michelson’s experiments were heavily limited by the methodology employed to gather the data. In addition to having a limited time window to collect the data, the data collection process required high dexterity and visual acuity. His process, as described in the linked reading, required waiting for sunset for ideal atmospheric conditions, and then employed highly manual tools for keeping track of time detecting the beam of light.

Key measurements were limited by the technologies of the time and dependent on humans:

1. Assessing distance and time between revolutions were by eye
2. Adjusting the micrometer screw was done by hand
3. Listening to the tuning fork was done by ear
4. Distinctness of the image was (sort of) subjective

At first glance, the +92 km/s to correct for atmospheric air vs. vacuum seemed to us poorly informed, as we could already see that his mean value was far above the true value.  Diving into his reasoning, however, it was quite precise. This +92 km/s comes from the +80 he allows for the difference in air vs. vacuum, controlling only for temperature and not pressure, with an additional +12 km/s from the maximal impact of temperature on the micrometer he was using to inform the angular measurement.

1. ↑  Measurements and Error Analysis
2. ↑  Report Q3 Observation
3. ↑  Air temperature vs. Observed Speed
4. ↑ Distribution of Data by Distinctness
5. ↑ Velocity vs Temp