Showing posts with label physics education. Show all posts
Showing posts with label physics education. Show all posts

Tuesday, March 25, 2025

Check the Math

I took Sociology 304 Research Methods in the spring of 2007. The professor was Young S. Kim. We were assigned to review two research papers each week. In the first class meeting, Dr. Kim said that these were not to be summaries but must be criticisms. After class, I approached his desk and asked if undergraduates could competently criticize a peer-reviewed publication. He replied, “Check the math.”

 

I do not know that I found any mathematical errors because I only archived three of my assignments from that class and none of those identified any such problems. However, a few months ago, researching an article for the American Astronomical Society, I found this from 1948: 

  • “Evolution of the Universe” by Ralph A. Alpher and Robert Herman, Nature, No. 4124 ,Vol. 162, November 13, 1948 identified errors in 
  • “The Evolution of the Universe” by George Gamow, Nature, No. 4122, Vol. 162, October 30, 1948. 

(At that time, Alpher and Herman were doctoral candidates and Gamow was their advisor. Earlier that year, Physical Review published "The Origin of Chemical Elements" by Ralph Alpher, Hans Bethe, and George Gamow. Although he checked their math on a computer at the National Bureau of Standards, Robert Herman declined to belisted as "Delter." (Wikipedia citing Gamow here:  https://en.wikipedia.org/wiki/Alpher%E2%80%93Bethe%E2%80%93Gamow_paper )


 “The condensation-mass obtained from this corrected density comes out not much different from Gamow's original estimate. However, the intersectionpoint rmat. = rrad. occurs at t=8·6 x 1017 sec.  3 x 1010 years (that is, about ten times the present age of the universe). This indicates that, in findingthe intersection, one should not neglect the curvature term in the general equation of the expanding universe. In other words, the formation ofcondensations must have taken place when the expansion was becoming linear with time.”  

 


Interesting as that was to read, I was more impressed with the discovery that cosmologists in 1948 accepted an estimated age of the Universe at 3 billion (3*109) years. The simple truth is that estimates of the size and age of the universe have been expanding. 

It is also interesting that their work required the radius of the known universe to be proportional to  [the square root of (minus one)] light years. Imagine that!

 

For more on Young S. Kim see:

Kim, Y. S., Barak, G., & Shelton, D. E. (2009). Examining the “CSI-effect” in the cases of circumstantial evidence and eyewitness testimony: Multivariate and path analyses. Journal of Criminal Justice, 37(5), 452–460. https://doi.org/10.1016/j.jcrimjus.2009.07.005

https://psycnet.apa.org/record/2009-15801-001

  

Previously on NecessaryFacts

 

Imaginary Numbers are Real; Pegasus is Not 

Two Books on Fermat’s Last Theorem 

Pi in the Sky over Austin

Elisha Loomis and the Pythagorean Proposition

 

Saturday, October 12, 2019

Physics for Astronomers: The Works of Steven Weinberg

The telescope is a wonderful instrument, but if you do not know what you are looking at, you have not gained much. The stars are pretty at any magnification. 

[This article originally appeared in the October 2019 issue of Sidereal Times of the Austin Astronomical Society.] 

Understanding the views requires learning astrophysics; and that is hard work. Think of it like basketball. One of my physics professors was answering homework questions at the blackboard. “I don’t understand number 3. …. How do you do number 5?... What equation do you use for number 1?...” He was going along and then he stopped. “You people would go out in the backyard and shoot hoops for 45 minutes and not make a single shot and still say you had a good time. How long did you spend on number 4? How many ways did you try to solve it?” It was a valid argument. On the other hand, you could have Michael Jordan or LeBron James come to your backyard and be your coach, but the honest fact is that you will not ever be good enough to play in the NBA. Still, you can improve your skills and your appreciation of the masters and their game. And so, too, with astrophysics, if you want to “show good game” (whether or not you turn professional), let the greats be your coaches. 

This past July, our guest speaker was Nobel laureate Steven Weinberg. His topic was “Gravitational Wave Astronomy.” Dr. Weinberg delivered a layman’s overview of the development of the field and its current state. Having done my homework before the lecture, I was impressed by his clear, concise, and cogent explanations. So, I went to the UT libraries and checked out four of his books.

They had nine copies of Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley & Sons, Inc. 1972). Two are missing. One is in the Life Sciences Library Hall of Noble Words. One is at Perry-CastaƱeda Library. The rest are in the Kuehne Physics Mathematics Astronomy Library. The great body of mathematical discussions are beyond my skill level – like having to play guard against LeBron James: the moves are easy to explain, but doing them is a workout. However, Weinberg’s narratives are understandable and compelling. He takes the reader where no one has gone before. He has his own framework for presentation, different from the traditional teachings.

Weinberg maintains that Einstein’s preference for Riemann geometry and our respect for Einstein have limited the ways that we choose to approach these problems. Instead, Weinberg begins with the equivalence of gravity and inertia. That, he says, allows us to understand quantum events in ways that the geometric approach cannot.  

Over the course of 633 pages, Gravitation and Cosmology ties the historical development with the modern discoveries. The histories of the theory of gravity, non-Euclidean geometry, and the principle of relativity open the book. Part One closes with a detailed examination of the special theory of relativity from Lorentz transformations through the discovery of antiparticles. 

Part Two covers the General Theory of Relativity with a treatment of the equivalence principle that is so important to Weinberg’s framework. He also provides mere outlines of mathematics including tensor analysis, covariant differentiation, and div-grad-curl. These are only to make the text complete. Other books are better at explaining the subjects. And, just to note, Einstein went back to the books to learn tensors; and it is recorded elsewhere that Einstein’s wife at least checked his math if she did not actually do his homework for him. 

Part Three explains General Relativity, including Post-Newtonian Mechanics and Post-Newtonian Hydrodynamics. (The physics of moving water allows us to approach the problems involving huge bodies of discrete particles.) Part Three Section 10 Chapter 8 addresses the Quantum Theory of Gravitation which was the topic of Dr. Weinberg’s lecture to us on July 12. In the book, it is marked with asterisk meaning that you can skip it. Back then, it was just theory. Gravitation waves were predicted by relativity and quantum mechanics, but would not be detected for another thirty years.
Weinberg by David Levine for NYRB.
This drawing appeared in
"Nature’s Biggest Secret,"
October 21, 1993.
Framed prints are for sale from
The New York Review of Books.

The last third of the book, Part Five, is dedicated to Cosmology. The greater mass of that consists of the so-called “Standard Model” what we in the backyard call the Big Bang Theory. Weinberg takes you from “the first three minutes” to the synthesis of helium and to the formation of galaxies. The book closes with considerations of other models. 

Dr. Steven Weinberg is tireless in taking physics to the public. He summarized the Standard Model in The First Three Minutes: A Modern View of the Origin of the Universe (Basic Books, 1977). If you go to the website of The New York Review of Books and put his name in the search box you will find that he is quite popular. (Use quotes and the full name “Steven Weinberg” to narrow the results.) He wrote seven major essays for them, six on physics, one on politics.

Weinberg is quite outspoken on social issues, especially as they impact science. Among his other books is Facing Up: Science and Its Cultural Adversaries (Harvard University Press, 2001). He does defend against religion and creationism, but most of the book is a defense of science against post-modernism. To Weinberg, the philosophy of science is worth studying, and defending it matters. 

Weinberg’s The Discovery of Subatomic Particles (Scientific American Library, 1983) creates a bridge between a physics textbook and a popularization. His narrative history from the Greeks through the electron of the 19th century and up to the hadron of our day is easy to read. In the text, he presents the standard equations as verbal statements. “Electric force on a body = Electric charge of the body on which the force acts X Electric field.” However, the Appendix delivers all of the equations in their standard forms. In the Appendix, Weinberg starts with Newton’s Second Law and ends with particle collisions. 

You can find pithy sayings by Dr. Weinberg in Wikiquote. Most of them are about subatomic physics. Interesting as they are to ponder, they will not make good bumperstickers. 

Five hundred years before Galileo the Persian astronomer Abd al-Rahman al-Sufi (known in the Latin West as Azophi) catalogued the Andromeda Galaxy. He knew that it was a cloud among the fixed stars but did not know what it was. By the time Edwin Hubble settled the question in 1925, astronomers had been informed by Newtonian mechanics, Maxwell’s Equations, Planck’s quanta, and Einstein’s General Relativity. Physics is hard work. The pay-off is understanding what you are looking at—and why the looking is important. Dr. Steven Weinberg explains it all. 

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Saturday, July 13, 2019

STEVEN WEINBERG ON GRAVITY WAVES

On Friday night, July 12, Nobel laureate Steven Weinberg was the guest speaker at the monthly Austin Astronomy Club meeting. His topic was gravitational waves. 

(The grammar can be important. A “gravity wave” is actually a weather event here on Earth. Waves on the ocean are gravity waves. But we call gravitation waves “gravity waves” just as we sometimes are careless with “speed” and “velocity”.)

Dr. Steven Weinberg
(UT Austin)
Dr. Weinberg said that the LIGO (Laser Interferometer Gravitational-Wave Observatory) apparatus was an advance in the technology of perception as significant as Galileo’s use of the telescope. According to the LIGO website, gravitation waves are as different from electro-magnetic radiation (“light waves “) as light is from sound. 

Dr. Weinberg credited A. A. Michelson with the development of the kind of interferometer used for these investigations. (The Michelson-Morely Experiment of 1887 failed to find the "ether" in which light travels.) Reading websites before the lecture, it was apparent to me that these arrangements are extensions of the Michelson-Morley experiment. Long paths of light set at right angles and placed far apart (Hanford, Washington; Livingston, Louisiana; and Pisa, Tuscany), are superimposed so that the smallest variation is revealed by an interference pattern. 

Entropy is real. The Moon will collide with the Earth – eventually. When neutron stars and black holes orbit each other, the losses of energy are (what else?) astronomically immense, and collisions and collapses are recorded as “chirps” of about a half a second. 
 
https://www.ligo.caltech.edu/page/ligo-gw-interferometer
It is also true that as they rotate on their individual axes, massive bodies produce gravitation waves.* Any acceleration does, even when you turn the corner on your bike or in your car. But gravity is extremely weak. At shoulder height, place a golf ball next to a bowling ball and let go of the golf ball. They don’t stick. Now, try it with magnets. I was once told that machine shop gauge blocks are finished so fine that if they touch they cannot be separated because the molecular forces are insuperable: the two blocks become one. Gravity is not like that. 

So, even though gravitation waves were argued by Newton, Leibniz, Kant, and Berkeley, it was 300 years before they were first detected on 14 September 2015. Dr. Weinberg also praised the intellectual honesty of the previous attempts by Joseph Weber and others which meticulously ruled out false positives until nothing was left.

*The gravitation waves produced by a massive superdense rotating body are caused by minor variations within or on the surface of the body. A vibrating perfect sphere produces no gravitation waves.

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Tuesday, January 1, 2019

Neutron Irradiated Dimes

Today you can get rocks, fossils, gems, meteorites, astronaut ice cream, gyroscopes, and magnets at any museum store. Irradiated dimes were sold at Oak Ridge National Laboratory from 1949 to 1967. They speak from the heart of the atomic age. On the one hand, Oak Ridge was a secret town that officially did not exist. On the other hand, the actual use of the atomic bomb proved impossible to miss. 

What we call “Oak Ridge” today (ZIP Codes 37830 and 37831) was built by the federal government as part of the Manhattan Project. The under-developed area of eastern Tennessee had small farming towns—Edgemoor, Elza, and Robertsville, among others—but was largely uninhabited. The purpose of the new city, which grew to 75,000, was to separate fissionable uranium (U 235) from the other isotopes, mostly U 238. It also produced plutonium. In addition, the site manufactured other isotopes that have industrial and medical uses such as antimony (Sb 124). 
 
Case legends on irradiated dimes.
AMERICAN MUSEUM OF ATOMIC ENERGY NEUTRON IRRADIATED 
(in black)
ORNL – UCNC – OAK RIDGE NEUTRON IRRADIATED
AMERICAN MUSEUM OF ATOMIC ENERGY NEUTRON IRRADIATED 
(in blue)
Not shown: 
OAK RIDGE NATIONAL LABORATORY – NEUTRON IRRADIATED – 
(May be the earliest variety.)
The town was finally opened on March 19, 1949. The American Museum of Atomic Energy began the same year. It was re-dedicated as the American Museum of Science and Energy in 1978.  
UCNC is the Union Carbide Nuclear Company. 
The Union Carbide Corporation Nuclear Division operated 
the Y-12 separation plant at ORNL.  
The division apparently used the two names at different times. 
UCNC also operated a uranium mine in Emery County, Utah. 
See Western Mining History here.
This quote is most likely from a 1954 ORNL press release:
"One of the most popular exhibits in the American Museum of Atomic Energy is a “dime irradiator.” To date, more than 250,000 dimes have been irradiated, encased in plastic and returned to their owners as souvenirs. The irradiator works as follows: A mixture of radioactive antimony and beryllium is enclosed in a lead container. Gamma rays from the antimony are absorbed by the beryllium atoms and a neutron is expelled by the beryllium atom in the process.            
“These neutrons, having no electrical charge, penetrate silver atoms in the dime. Instead of remaining normal silver-109, they become radioactive silver-110. After irradiation, the dime is dropped out through a slot in the lead container and rests momentarily before a Geiger tube so that its radioactivity may be demonstrated. It is then encased in the souvenir container. Radioactive silver, with a half-life of 22 seconds, decays rapidly to cadmium-110 (In 22 seconds, half of the radioactivity in each dime is gone, in another 22 seconds half the remainder goes, and so on until all the silver-110 has become cadmium).  Only an exceedingly minute fraction of the silver atoms have been made radioactive." From “Irradiated Dimes - American Museum of Atomic Energy and New York World's Fair (1950s, 1960s)” At Oak Ridge Associated Universities website here. (ORAU operates the AMSE.)
Some typical eBay prices of the moment.
 The press release cites a figure of 250,000 dimes given out. By the time the program ended, the figure was close to 1,000,000. This summary from 9 November 2013 by CoinTalk user mrweaseluv was based on an article that I wrote for Coin World. (I visited ORNL twice in September 1999 to interview people and tour the museum and the city.). 
“A beryllium case was placed over small lump of [radioactive] antimony [Sb 124]. The antimony gave off gamma rays that excited the beryllium which emitted neutrons that struck the dimes. The half-life was 24.6 seconds. Some of the Ag-109 atoms became Ag-110. Giving off an electron, the Ag-110 became Cadmium (Cd-110), which is stable. Another 51.82% of the silver atoms became Ag-107, the remaining 41.18 of the silver remained Ag-109. Of the remaining 5% was comprised of other isotopes, the most stable of which is Ag-108 which remains radioactive for five years, though the amount in a dime is statistically unimportant at the human level. Dimes are also made of copper. Cu-63 and Cu-65 represent almost 69.17% and almost 30.83% of the mass and are stable. When they absorb a neutron, they become zinc. The remaining fraction of a percent is Cu-67 which is radioactive for two-and-half days. Only silver dimes could be used. When the government switched to cupro-nickel, it was only a matter of time before silver dimes became scarce. The program was discontinued in 1967. Ni-63 remains radioactive for 92 years, decaying much quicker than Ni-59 which has a half-life of 80,000 years.”  (Cited from CoinTalk dot com here. )
See also: 
MORE ON IRRADIATED DIMES
By Pascal Brock, Harold Levi, Bruce Perdue, Ken Berger, 
The following is taken from the TAMS Journal, Vol.14, No. 1, February 1974.
“The Neutron Irradiated Dime, Atomic Energy Commission, New York World's Fair, 1964-1965” by Stephen P. Alpert, TAMS # 2134.
The E-Sylum: Volume 14, Number 52, December 18, 2011, Article 10

“Antimony-124 is used together with beryllium in neutron sources; the gamma rays emitted by antimony-124 initiate the photodisintegration of beryllium. The emitted neutrons have an average energy of 24 keV. Natural antimony is used in startup neutron sources.”

“Gamma rays are ionizing radiation and are thus biologically hazardous. Due to their high penetration power, they can damage bone marrow and internal organs. Unlike alpha and beta rays, they pass easily through the body and thus pose a formidable radiation protection challenge, requiring shielding made from dense materials such as lead or concrete.”

“The decay scheme is rather complex, as it includes more than 25 β− transitions and about 70 γ transitions with energies spread between 148 keV and 2807 keV. However, only about a tenth of them have probabilities greater than 1 %.”
124Sb – Activity measurement and determination of photon emission intensities Part A – COMMISSARIAT A L'ENERGIE ATOMIQUE ISSN 0429 3460

Title: A Study of the Nuclear Radiations from Antimony and Arsenic
Authors: Mitchell, Allan C.; Langer, Lawrence M.; McDaniel, Paul W.
Publication: Physical Review, vol. 57, Issue 12, pp. 1107-1117
Publication Date: 06/1940

 I find that date revealing. We have a poor sense of history or at least I do. Obviously, research into the physics and chemistry of radiation had been continuing for almost 50 years. But we too easily see Hiroshima and Nagasaki as the dawn of the Atomic Age. In fact, Wilhelm Rƶntgen announced x-rays in 1895, and by 1906 they found medical applications. Admittedly, the first decade was a period of uneven and sometimes tragic results. 

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Friday, December 28, 2018

Problems with Pop Sci from Sky & Telescope (Part 2)

Similar to my critique of Steven Hawking’s A Brief History of Time, the source of the many problems may be that the editors at Sky & Telescope are trying to condense complicated truths into a few lines of common English.

February 22: “Small meteorites aren’t hot when they hit the ground. Earth’s atmosphere heats and removes a very thing surface layer, but the rest of the meteorite is still ice-cold from its time in space.”
and
August 13: “Occasionally, meteor-watchers hear a hiss or crackle accompany particularly bright fireballs. Astronomers still debate the source of the sound.”
Those two resulted in an interesting search: “are meteorites hot or cold when they hit earth?” Apparently the answer may be “yes.” The consensus is that they are cold. They quickly lose their outer layers by ablation, the same phenomenon used to protect spacecraft: the outer layers burn away carrying the heat. That said, accounts of meteorites being at least warm are not totally discounted. At the same time, also accepted are reports of newly-fallen objects being covered with frost. That meteorites are hot when they fall was commonly accepted until recently even by educated people. An article in Popular Astronomy for February 1934 took the Smithsonian to task for perpetuating the error. (See Astrophysics Data Site archive of Harvard online here.) 

December 27: “In 50 million years or so, Phobos will spiral into Mars, crashing on its surface or breaking up in pieces. In the meantime, though, the little moon has quite a view: Mars fills much of its sky because of the close orbit.”  The spiral is not a possible orbit. That was a teaching point from a Heinlein juvenile novel. Living in a spacefaring culture, our young hero takes an aptitude test to be trained as a pilot. “What would you do if you suddenly found that you were spiraling in to a planet?” It is a trick question because the spiral is not a possible orbit. Considering the problem again, the easiest general statement is that successive elliptical orbits decay by atmospheric drag. 
Logarithmic Spiral
Wolfram Mathworld
Archimedean spiral
Wikipedia
Seashell Spirals 
Mathematical Association of America
Re-entry of Orbital Debris
NASA JSC
Video Tutorials on Mechanics and Orbital Motion
Physics Department at the University of New South Wales
Brief Discussion
Animations

As for what will happen to Phobos, the Wikipedia article rests in part on a NASA Web Archive. As stated above: it could break up or hit the surface. We will just have to wait and see.

October 31: “As it sails beyond the solar system, Voyager I hears the lonely radio whistles of plasma waves passing through interstellar space. Listen here: https://is.gd/voyagerwhistlesThis was interesting, but it is a transduction. Note that the video (YouTube here: https://www.youtube.com/watch?v=LIAZWb9_si4) also presents color blobs representing those waves. We can make them sounds in any octave, lines or shapes in any color, depending on our choices of coordinates.  And, as we all know, you really cannot hear radio waves traveling through interstellar space.

December 5: “You can cry in space, but your tears won’t fall—due to water tension (and a lack of gravity) they form a floating, liquid sphere.” “There is no gravity in space” is one of those many easy sayings spoken by people who watch television shows about science, but who never take a formal class in astronomy or physics. If you lived in a spacefaring culture you might be told that if you were trapped in a gravity well, your tears would be pulled away from your face as the tremendous inertial acceleration overpowers the molecular adhesion that holds them to your face. If you were “in space” as a passenger of an accelerating vehicle, you would experience an inertial force indistinguishable from “gravity.”  
Einstein's Imaginary Elevator
From The Boy Scientist by John Llewellen, Simon and Schuster, 1955.
(Some tests could reveal the larger context of your condition. You might be on a rocket accelerating; you might be in a spinning torus like the classic space station; you might be on a large body such as a moon or planet in space. But within the reach of a human—a fathom—it would be difficult to find any differences. The differences were explained to me by a friend of mine from high school who went to MIT. I am not smart: I learn well.)

March 28: “Thanks to its solar wind, the Sun is losing roughly an Earth’s worth of mass every 150 million years.”
And
March 29: “Because the Sun is (slowly) losing mass, Earth’s orbit gets about an inch bigger every other year.”
And
April 15: “The Moon is drifting away from Earth at a rate of 1.5 inches per year.”
And
July 7: The expansion of space means that the solar system is expanding, too, but only at an infinitesimal amount: one part in septillion over its lifespan. 
1.     A so-called “solar wind” is an essential characteristic of every star. The phrase is just a way that we conveniently think of the energy of the star. The loss of mass is integral to the nature of the star and we know how stars age. 
2.    What is interesting is that Earth is losing mass, also. That must mean that all of the planets and, in fact, all other material bodies do so as well. Net loss to Earth is 50,000 tonnes per year (BBC News Magazine online here). That is the difference between the meteoric dust which falls in and the hydrogen and helium gasses which escape into space. Other effects come from the core’s heat being lost, volcanoes and other relatively minor events. (See this homework problem from Weber State University.)
3.    Finally, as for the expansion of “space” (or space-time, or the stuff “in” it or “in” which space-time exists), while not quite lying with statistics, casually tossing out large numbers obfuscates the question. If the universe is 13.8 billion years old and expanding one part in a septillion over 10 billion years, the numbers just do not explain the facts we believe from observation and measurement – unless the expansion rate is highly variable, greatly slowing down or expected to greatly increase. Deceleration seems to be the accepted theory of the day. But it is more complicated than can be explained in five lines of a calendar page.
·              Universe's Expansion Rate Is Different Depending on Where You Look By Elizabeth Howell, Space.com Contributor July 13, 2018 04:03 pm ET
·              The Expanding Universe: From Slowdown to Speed Up; Distant supernovae are revealing the crucial time when the expansion of the universe changed from decelerating to accelerating By Adam G. Riess, Michael S. Turner on September 23, 2008
4.    Just to note about the actual age of our planet and its sisters: “The inner edge of the Sun’s habitable zone is moving outwards at a rate of about 1 metre per year. The latest model predicts a total habitable zone lifetime for Earth of 6.3 billion–7.8 billion years, suggesting that life on the planet is already about 70% of the way through its run. Other planets — especially those that form near the outer boundary of a star’s habitable zone or orbit long-lived, low-mass stars — may have habitable-zone lifetimes of 42 billion years or longer.” (Daily news blurb from Nature online here.) 

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