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Towers of Physics

August 12, 2011

Would Pisa, Italy, be known to anyone outside its region if it were not for its famous leaning tower? And would this tower be known that well except for the famous experiment on falling bodies by Galileo that's usually depicted in one cartoon or another? In actuality, the tower experiment may have been just a thought experiment of Galileo's, but it was written as if it had actually occurred by one of his disciples, Vincenzo Viviani.

Galileo, himself, wrote no record of such an experiment, perhaps because the result, that lighter objects fall just as fast as heavier ones, was contrary to what Aristotle had written. Aristotle was considered by the Church as the authority on all scientific matters that didn't contradict the Bible. Aristotle's philosophy was the official philosophy of the Church in Galileo's time, and if your science wasn't found in Aristotle, too bad for you, observational evidence notwithstanding.[1]

Enrico van Lint (1808-1884) - The Leaning Tower in Pisa, Italy. Dated on back Jan 24 1866.The Leaning Tower in Pisa, Italy.

This is the right image from a stereography, dated January 24, 1866. The tower did not lean as much in Galileo's day.

Photograph by Enrico van Lint (1808-1884), via Wikimedia Commons.

Galileo's experiment wasn't the only significant physics experiment that involved dropping objects from towers. One other, published in 1903, involved a more direct demonstration of the Coriolis effect than seen in the Foucault pendulum, although that wasn't the primary purpose of the experiment. I wrote about the Foucault pendulum in a previous article (A Foucault Gyroscope, February 14, 2011).

The Coriolis force is the apparent force seen on a falling body that results from Earth's rotation beneath the object. The net result is that objects land slightly eastwards from where they would be expected to land based on a plumb line trajectory. The 1903 experiment, by Edwin H. Hall of the eponymous Hall effect, was designed to test a possible small deflection towards the south.[2-3] Quoting from Hall's 1903 paper,
"The question whether a sphere falling from rest through a few hundred feet of still air swerves perceptibly towards the south, from the vertical path indicated by the plumb line, is not, perhaps, one of the largest or more urgent problems of physics; but it has the dignity of venerable ages and the charm of mystery. It was familiar to Newton; it has been answered in the negative, on theoretical grounds, by Gauss and Laplace, and in the positive, on experimental grounds, by nearly every one of the investigators who have from time to time through more than two centuries made the actual trial."[2]

In his experiment, Hall dropped 948 one-inch metal balls through a distance of about twenty meters inside the left tower of Harvard University's Jefferson Laboratory, pictured below. He found a 0.149 cm eastward deviation, which was slightly less than theoretical calculations, but assumed to be correct within the experimental error. The southwards deviation that his experiment was designed to find was 0.0050 cm, or just about his experimental error. Hall's paper states no conclusion on the matter of southwards motion.[3]

Harvard University Jefferson Laboratory left tower.The left tower of the Jefferson Laboratory, Harvard University, as it appears today.

Hall's ball drop experiment and the Pound-Rebka experiment were conducted here.

Photo by Lubos Motl, via Wikimedia Commons.

Another famous physics experiment was performed in that same Harvard tower by Robert Vivian Pound and his graduate student, Glen Rebka. The Pound–Rebka experiment examined the gravitational redshift of the Mössbauer spectrum of 57Fe. It was a straightforward confirmation of general relativity.[4-6]

Details of the experiment can be found in the references,[6-7] or as a summary on Wikipedia. They reveal the various tricks used to coax a signal out of noise. Just as for Hall's experiment, the measured effect was extremely small, being about a tenth percent of the 57Fe resonance linewidth.[5] Both the Hall experiment and the Pound–Rebka experiment show that attention to detail is the hallmark of the able experimentalist.

As I summarized in a previous article (Eratosthenes, March 17, 2011), there's one experiment that was performed much earlier than Galileo in which a tall tower was essential. That was the measurement of the size of the Earth by Eratosthenes, a Greek mathematician and friend of Archimedes, who lived from about 276 BC - 195 BC.

Eratosthenes' method relied on two observations. The Sun was directly above a particularly deep well in Siena, Egypt, on June 22 of each year, since the Sun could be seen from the bottom of the well. A 120 meter tower in Alexandria cast a shadow on that same date at 7.2 degrees. Simple trigonometry, combined with the known 787.5 km distance between the tower and the well, gave the Earth's radius as 6,266.7259 km, within two percent of the established value.

EratosthenesEratosthenes

(Via Wikimedia Commons).

References:

  1. Aristotle (384-322 B.C.E.)
  2. Edwin Hall, "Do Falling Bodies Move South - Part I," Physical Review vol. 17, no. 3 (1903), pp. 179 - 190. (Search Google Books for a free version of this volume. The ads in this 1903 volume of Physical Review are entertaining, also.)
  3. Edwin Hall, "Do Falling Bodies Move South - Part II," Physical Review vol. 17, no. 4 (1903), pp. 245 - 254. (Search Google Books for a free version of this volume. The ads in this 1903 volume of Physical Review are entertaining, also.)
  4. Anders O. Persson, "The Coriolis Effect: Four centuries of conflict between common sense and mathematics, Part I: A history to 1885," History of Meteorology, vol. 2 (2005), p. 1ff.
  5. Paul Horowitz, "Obituary-Robert Vivian Pound," Physics Today, vol. 69, no. 9 (September, 2010), pp. 65f.
  6. R. V. Pound and G. A. Rebka, Jr. , "Apparent Weight of Photons," Phys. Rev. Lett., vol. 4, no. 7 (1960), pp. 337–341
  7. Physical Review Focus, "The Weight of Light," July 12, 2005.