High School SMILE Meeting
1997-98 -- 05-06 Academic Years
Relativity and Cosmology

28 January 2003: Bill Colson [Morgan Park HS, mathematics} Is there intelligent life except on earth?
The key to the answer lies in Frank Drake's equation, which gives the number of intelligent civilizations as a product of various factors.  This equation is so famous and popular that it has been set to music, as indicated by this excerpt from the website http://www.setileague.org/songbook/equation.htm:

L is the lifespan of advanced societies.
fc is intelligence choosing to communicate.
fi, intelligence evolves.
fl is the fraction on which life emerges.
ne are the planets which could be life-sustaining.
fp is the fraction which develop planets,
R star is the rate of stellar formation.
Those who are musically challenged may consult the website http://www.setileague.org/general/drake.htm for additional details.  Alas, none of these probabilities is known with any precision, so that extra-terrestrial intelligence may or may not exist.

09 December 2003: Don Kanner (Lane Tech HS Physics Teacher)      General Relativity
Having just used Karlene Joseph's and Dan Caldwell's paper plate and marble centripetal force demonstration in his classroom, Don showed us how to illustrate a celestial object being pulled into a black hole (sparing no expense -- ha!) using a marble whirling around inside a the top of a 1 liter plastic pop bottle held vertically with its mouth pointed toward the floor. When one stops rotating the bottle, the marble continues to whirl around the inside until it falls out the mouth. In Einstein's General Theory of Relativity, gravity corresponds to a distortion (intrinsic curvature) of the space around a mass. We are thus led to following  the question: Assuming that the mouth of the bottle is analogous to a black hole, what portion of the area near the mouth of the bottle best fits Einstein's description of space-time distortion?

Now who says that you can't teach about black holes in high school? Don referred to the classic film Frames of Reference by Hume and Ivey. The following description is adapted from information on  the website of the Department of Physics and Astronomy of the University of Victoria (BC, Canada) [http://www.phys.uvic.ca]:

FRAMES OF REFERENCE (Educational Services, Inc., 1960) 25 min, snd, b.w.
Professors Patterson Hume and Donald Ivey of the University of Toronto demonstrate the behavior of a body under the force of gravity as viewed from different frames of reference and the behavior of a frictionless puck on a rotating table in the laboratory. Two excerpts from this film are also available which present the above material in a condensed form:
1. "Excerpt 1", 7 min. QA839 F7. Shows gravitational effects.
2. "Excerpt 2", 5 1/2 min. QA839 F72. Shows rotational effects.

PJ Comment:  The idea of "tunneling into the center of force" is very old.  Isaac Newton criticized the Descartes model of the solar system, pointing out that this would be precisely the outcome of that mode.  The Bohr Atomic Model was roundly criticized during the period 1915-1925, because electrons in atomic orbits would be expected to "wind down" into the center of the nucleus, in a time of about 10-9 seconds, because of the total power radiated by a free point charge q experiencing an acceleration of magnitude a. According to the Larmor formula

P = (2 k q2 a2 ) / (3 c3)
Note that the velocity of light c ~ 3 x 108 m/sec, and k ~ 9 x 109 Nt m2/Coul2 is the constant appearing in Coulomb's Law. In addition, it is a consequence of Quantum Mechanics that magnetic monopoles, if they happen to exist, will -- in effect -- gobble up both negatively and positively charged particles that come directly at them (zero angular momentum). This idea of orbiting into the center of attraction is a timeless, recurrent theme in physics!  For additional information see the History of Mathematics Website at St Andrews University [ http://www-groups.dcs.st-and.ac.uk/~history/] and especially the entry for Sir Isaac Newton, as well as Theories of Gravitation.

26 October 2004: Fred Schaal [Lane Tech HS  mathematics]           Hawking Hawking 
Fred has been reading the book The Theory of Everything by Stephen Hawking http://www.audiobooksonline.com/shopsite/1590072286.html. Fred indicated that when two black holes collapse together, one would expect the total entropy to be conserved, and that the entropy of a given black hole is proportional to its area.  However, this requirement of thermodynamic reversibility does not seem to be true.  How come?  For more details see these websites on Black Hole Thermodynamics:  http://nrumiano.free.fr/Estars/bh_thermo.html and http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BlackHoleThermo/BlackHoleThermo.pdf.

09 November 2004: Fred Schaal [Lane Tech HS  mathematics]           1 +1 = 1 
Fred remains puzzled as to how the Volume and surface Area depend upon the radius of a black hole.  Apparently, the standard formulas

V = 4 p R3/ 3
A = 4 p R2
do not apply.  Why? Porter Johnson explained that, in a curved space such as near or inside a black hole, distances are not merely equal to changes in coordinates, but one must take into account the curvature of space. For example, the surface of the earth is curved, and the standard formula for the area of a triangle (on a plane) is incorrect when the triangle is on the curved surface of the earth. For additional information see the paragraph The Size of a Black Hole on the website http://www.astro.uu.nl/~strous/AA/en/antwoorden/zwarte-gaten.html.  Bill Colson told us of the following statement by Stephen Hawking:
"God not only plays dice. He throws them where they can't be seen!"
Good question, Fred!

26 April 2005: Fred Schaal [Lane Tech HS, mathematics]              Follow-up Question on Book by Michio Kaku
As a follow-up of his comments about this book at the last SMILE meeting mp041205.html, Fred asked an important question concerning developments in twentieth century physics.  Here is the question, as well as an answers, given on-the-spot by Porter Johnson.

What is the Lorentz-Fitzgerald Contraction, and is it real?
Maxwell and his contemporaries developed the theory of electromagnetism in analogy to the theory of sound being developed by Lord Rayleigh and his contemporaries.  Sound clearly propagates in a material medium --- air, water, steel, etc.  Maxwell thought of electromagnetic waves as vibrations in a mysterious ether that permeated all of space.  It was a material medium that permeated all of space, but it was either difficult or impossible to detect its presence directly.  Because sound travels differently in the wind, light should travel differently in the "ether wind".  A few years after Maxwell's death (1876),  Michelson conducted a series of experiments to detect the motion of the earth through the ether  (1887) --- and failed!  Lorentz and Fitzgerald (1902) proposed an explanation of this (and other) unsuccessful experiments to detect ether wind, as a physical contraction of moving bodies in the direction of their motion. They developed the Lorentz transformation (actually discovered by Volk in 1881, who didn't recognize its importance) to explain this point. In 1905 Einstein proposed a a different explanation for non-detection of ether wind -- the theory of relativity.  In relativity, events that are simultaneous in one frame are not simultaneous in another inertial frame -- in effect there is no global time variable.  In the words of Einstein:
"There is no such thing as time -- only clocks"

Thanks, Fred!

10 May 2005: Fred Schaal [Lane Tech HS, mathematics]          There May Be Dark Matter in Your Living Room
Fred called attention to the fact that, according to current theories of cosmology, dark matter should exist.  This dark matter interacts very weakly with ordinary matter -- only through gravity, and not the electromagnetic field.  In other words, we can't see it, but it may permeate our  galaxy.  In particular, the flux of dark matter through the earth is estimated to be 106 particles per square-meter per second.  But  ... We don't feel a thing!

Wow! Thanks for the info, Fred. 

24 January 2006: Debbie Lojkutz (Joliet West HS, physics)             Einstein's Big Idea
Debbie brought an activity from the teachers manual of the Einsteins Big Idea program; it demonstrates potential and kinetic energy, specifically the conversion of potential to kinetic energy. Debbie had some ordinary flour placed into plastic cups into which she dropped marbles from various heights above the flour (that is, various potential energies). Each marble, when dropped, would go different depths into the flour; the depths could be measured by using drinking straws, which could be inserted into the flour until they touched the (submerged) marble. (But, shouldn't we measure the distance to the bottom of the marble?) This measurement can then be used to estimate the force stopping the marble in the flour. The depth into the flour should increase with height of the drop. Is it linear, or what?  Thanks for the ideas, Debbie!