Institute of Experimental Physics,
University of Vienna
1. New Didactic Tools | 4. Entropy: Bridging the Gap |
2. Exploring Phase Space | 5. The Sophomore Phase Transition |
3. Adventures in -space | 6. There is Nothing New ... |
* This paper was read at the Gordon Research Conference on "Physics in Research and Education",
How to explain physics using little math?
Help comes from Hardware and Theory:
Use Live Simulation and Intuitive Geometry (of phase space) as didactic tools. |
To give an example:
Applet Sinai |
Most have hyperspherical phase space volumes (except LJ and spin lattice) |
Phase space:
Explore the simple but surprising properties of n-spheres |
(2) |
Applet Harddisks Note the density of the velocity component vx |
Projecting constant densities on hyperspherical surfaces down onto one axis we find, depending on dimension, (see Fig. 2)
p2(x) | = | ||
p3(x) | = | ||
p4(x) | = | ||
p5(x) | = | ||
p12(x) | = | ||
Thus the Maxwell-Boltzmann distribution
may be derived solely from the geometry of highdimensional spheres.
Applet Harddisks Watch the density of the velocity component vx as N is increased. |
Applet Hspheres
|
(3) |
Applet Boltzmann
|
Applet Entropy1
|
[`moron'=nitwit, `sophos' = the wise one]
In addition to the above, some further truths are attainable in the course of the third term:
In the 18th century, higher education, including
mathematics, was reserved to men.
The Italian art critic and `popular science writer' Francesco
Algarotti found it unbearable that one half of humanity should
not be able to grasp the impact of Newton's revolution.
So he sat down and wrote a bestselling book in which he sketched
Newton's ideas using plain language only. Instead of formulae he
invoked similes and intuitive-geometrical arguments.
Newtonianism for the Ladies: How to explain physics using absolutely no math | |
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Francesco Algarotti, the ''Swan of Padua'' |