How Much Energy in an Ounce?

Albert Bartlett's letter in the June APS News corrects an estimate of the "energy in an ounce" from "85 million tons" to "607 thousand tons" of TNT. However, the energy released from even one ton of trinitrotoluene is quite a bit greater when it is burned slowly in air vs allowed to detonate. In any event, the energy in an ounce would be exactly equal to the energy of an ounce, not the energy of xxx tons! You know what I mean?

John Michael Williams
Redwood City, California

Whose Famous Constant?

A common misunderstanding of the history of "Newton's" universal gravitational constant is repeated in the July issue of APS News. Newton did not use a constant in expressing the universal law of gravitation; he expressed it verbally in terms of direct and inverse proportionalities. In an interesting review of the history of "Big G" titled, "The Cavendish experiment as Cavendish knew it" (Am. J. Phys. v. 55, p. 210 [1987]), B. E. Clotfelter points out that this constant is introduced for the first time only near the end of the Nineteenth Century. Cavendish referred to his own work as "Experiments to Determine the Density of the Earth." Clotfelter points out that there was no unit for force until the dyne was proposed in 1873, and that "...the idea of measuring such a constant (as G) is less likely to occur to an experimenter when no unit for force is available."

David Gavenda
University of Texas at Austin

Advice Given to Budding Chemical Engineer

The July issue of APS News included a question from a parent whose son has taken the AP Physics exam and is interested in a career in chemical engineering. As an APS member with a degree in physics who now works in a chemical engineering department, I can only suggest to Mr. Levitt that chemical engineering is an excellent discipline for a scientifically curious young person to consider. The best chemical engineers regularly use their fundamental understanding of the physical world based on physics, chemistry, and mathematics to solve complex and fascinating problems. One useful source of information for young people interested in chemical engineering is a website hosted by the American Institute of Chemical Engineers ( Many other disciplines also offer intellectually challenging career options, but I can think of no reason why Mr. Levitt should discourage his son from exploring a career in chemical engineering.

David Sholl
Carnegie Mellon University, Pittsburgh, Pennsylvania


I suppose I am in a unique position to offer advice in that I started as an Engineering major (Electrical) but switched to Physics after my first college Physics course. And I worked with many Chemical Engineers during my career as a Polymer Physicist with DuPont. However, the most important advice I can give would be general advice I would give any parent with a child at this stage of life.

To Mr. Levitt:

  • Don't sweat the decision. No matter what the choice now, it is likely to change.
  • Encourage your son to get advice from a broad cross section of people (but my experience with high school guidance counselors has not been good).
  • Most importantly, remember that it is your son's career and the decision must ultimately be his.
To the son:
  • Pick something and begin to focus on that. A good place to start is with one of the career exploration programs that let you "shadow" professionals in several occupations. It will give you a small taste of some of the possibilities.
  • Until you learn more, keep an open mind. College opens new vistas for most students. Chances are that you will change no matter what you choose.
  • Take a broad range of courses in college.
  • Above all, if you have an abiding passion about some subject, find a way to pursue it.
  • But remember, even with passion, life gets grim unless you can make a comfortable living.
  • Keep an eye out for interesting opportunities. No one can predict what doors will be open to them in the future.
  • One other point, there are very few jobs with no satisfaction and none without some sort of drudgery.

Specifically addressing Chemical Engineering:

  • We will continue to need products made with chemical processes. I would expect demand to remain strong for Chemical Engineers and the salary is usually quite good.
  • A wide variety of jobs are open including "hands on" design of plants and equipment, design and operation of systems to control the manufacturing process & basic research in a wide range of industries.
  • It also offers an excellent entry into management.
On the other hand, I was able to solve a number of long term problems at DuPont because my Physics training gave me a different perspective and different tools to work with.

Farren H. Smith
Camden, South Carolina

Whose Famous Formula?

In APS News, August/September 2000, the "This Month in Physics History" column was entitled "September 1905: Einstein's Most Famous Formula," and it stated: "But it was later that year (1905), in a paper received by the Annalen der Physik on September 27, applying his equations to study the motion of a body, that Einstein showed that mass and energy were equivalent, a startling new insight he expressed in a simple formula that became synonymous with his name: E=mc2. However, full confirmation of his theory was slow in coming. It was not until 1933, in Paris, when Irene and Frederic Joliot-Curie took a photograph showing the conversion of energy into mass."

In contrast, the "100 YEARS AGO" item in the 6 April 2000 issue of Nature (Vol. 404, p 553) is taken from the 5 April 1900 issue of Nature (note the dates), and it states: "The calculations of M. Henri Becquerel show that this energy is of the order of one ten-millionth of a watt per second. Hence a loss of weight of about a milligram in a thousand million years would suffice to account for the observed effects, assuming the energy of the radiation to be derived from the actual loss of material."

The assumption that accounts for the stated figures in the April 1900 issue of Nature is E=mc2. But according to APS News, this is "Einstein's most famous formula" which in September 1905 was "a startling new insight." I think that there is a problem that ought to be resolved.

Caroline H. Thompson
Aberaeron, United Kingdom

APS News replies:
The author is quite correct that specific instances of the relation between mass and energy predated Einstein's work in 1905. To put this in proper perspective, we offer a quote from the book "Inward Bound" by the late physicist and historian of physics Abraham Pais: "...the strength of (Einstein's equations relating mass, energy and velocity) lies in their generality, their independence of dynamical details, in particular their independence of the origin and nature of the mass m. For specific forms of energy the relation

E-->mc2 as v-->0

had been known well before 1905. Already in 1881, J.J. Thomson (see this month's This Month in Physics History-ed.) had noted the energy-mass equivalence for the case of an electrically charged body. Shortly thereafter, the first theoretical E-m-v relations appeared, based on a specific model of a charged particle: its shape shall be a rigid little sphere, whatever its velocity. This was the model studied in great detail by Max Abraham, theorist in Goettingen."

Copernicus and the Scientific Impulse
Owen Gingerich is not the first historian of astronomy to downplay the role of observational evidence in the inception of the heliocentric model and instead elevate the role of what he calls 'the Aesthetic Impulse' ("Copernicus and the Aesthetic Impulse," APS News, July 2000, THE BACK PAGE). There are similar sentiments expressed in Thomas S. Kuhn's The Copernican Revolution: Planetary Astronomy in the Development of Western Thought (Harvard Univ Pr, 1957), and also in Arthur Koestler's The Sleepwalkers: A History of Man's Changing Vision of the Universe (Hutchison, 1959). I have always felt uneasy with this attitude, for these reasons:

It is indeed legitimate to argue, as Owen Gingerich does, that "Copernicus relied on aesthetic principles, ideas pleasing to the mind." However, it is also justifiable to argue that Copernicus also relied on observational evidence, and further, on the epistemological inferences derived from them.

In his life work De Revolutionibus (1543), Copernicus made the following relevant points: "The Earth is impregnated by the Sun and generates offspring every year;" and more pertinently, the (brilliant and resplendent) Sun is "named by some the lantern of the universe," and by others the "visible god," "king of the sky," "pilot of the world," "overseer of everything," etc. (Now what is this, if not (almost literally blinding) observational evidence?) It is from these (quite enlightening) remarks that Copernicus went on to deduce that "the center of the universe is the natural point where to place the Sun so as to best illuminate the cosmos."

Copernicus also cites several ancient authors who assigned one or more motions to the Earth. Moreover, there is a passage in the extant manuscript of De Revolutionibus which mentions Aristarchus of Samos (third century BC). Although this passage was not printed in the first published version of De Revolutionibus in 1543, it is reproduced in some of the modern editions of the great book. Although Aristarchus's work on the heliocentric model has been lost, it is unambiguously mentioned in several other surviving books from antiquity, notably one by Aristarchus's contemporary Archimedes of Syracuse.

What is more interesting is that the only surviving book by Aristarchus is entitled (very significantly) On the Sizes and Distances (from the Earth) of the Sun and Moon. In this book, Aristarchus describes certain measurements that he carried out himself (one of which is inaccurate). Aristarchus then went on to do the correct mathematical analysis and computations from which he derived values for the four quantities mentioned in the title. Whereas Aristarchus's two values for the Moon are impressively accurate, his two values for the Sun are out by a factor of about 20 - owing to the inaccuracy of one measured quantity. This resulted in a solar system about 20 times smaller than true. These became the accepted values until the 17th century, as confirmed by Owen Gingerich when he remarked that "unknown to Tycho Brahe, the solar system was 20 times larger than he or anyone else imagined."

Nevertheless, Aristarchus's work still resulted in a Sun that was nearly seven times larger than the Earth in terms of radius, and about 300 times larger than the Earth in terms of volume. There is a suggestive anecdote about Rutherford's model of the atom. When asked why he placed the nucleus stationary at the center and the electrons orbiting the nucleus and not the other way around, Rutherford is said to have replied: For the same reason why we consider the elephant to be stationary and the fleas jumping up and down on him - and not the other way around.

In The Copernican Revolution, Thomas S. Kuhn stated: "the Greeks produced (no) evidence for the earth's motion." (p. 43) I submit that the known work of Aristarchus (discussed by Kuhn at some length) IS evidence, albeit indirect and inconclusive, for the earth's motion.

My reading of Copernicus's writings suggests to me that he wanted to replace the basically (as he obviously believed) untrue geocentric model with the essentially true heliocentric model. Copernicus hinted that a soundly composed heliocentric model would make more accurate predictions and a better calendar than those derived from the existing geocentric model. It was these justifiable beliefs and expectations that motivated Copernicus to go into all the trouble to construct a detailed new model of the universe. It took much more time and work by others, but Copernicus's beliefs and expectations were fulfilled in the end.

In conclusion, I would say that Copernicus was more of a modern scientist than Thomas S. Kuhn, Arthur Koestler, and Owen Gingerich have portrayed him. Moreover, what seems to have motivated Copernicus (and also Aristarchus, Galileo, Kepler, etc.) was the 'Scientific Impulse.'

Theo Theocharis
London, England

APS encourages the redistribution of the materials included in this newspaper provided that attribution to the source is noted and the materials are not truncated or changed.

Editor: Alan Chodos
Associate Editor: Jennifer Ouellette

October 2000 (Volume 9, Number 9)

Table of Contents

APS News Archives

Contact APS News Editor

Articles in this Issue
Site Visits To Identify Strong Candidates for New Education Program
NMD Decision Follows APS Action
Neutrinos, CP Violation Highlight DPF 2000
Scientific Visits Encouraged to Palestinian Universities
Powers of Ten: Astronomy's Greatest Hits
Nikitin Slams Russian Nuclear Waste
U.S. Team Makes Strong Showing at 2000 International Physics Olympiad
APS Co-Sponsors Summer Industrial Internship with IBM/Almaden
OPA Summer Intern Gains Valuable Hill Experience
In Brief
Editorial Cartoon
Zero Gravity: The Lighter Side of Science
This Month in Physics History
Physics and Technology Forefronts
The Back Page