Physics Classics

The Back of the Envelope was a monthly column during 1983-84 by E.M. Purcell in the American Journal of Physics.  Every month Purcell (who did much of the seminal work on Nuclear Magnetic Resonance in solutions, along with Pound, Bloch, and others) would propose a series of  3 questions to the reader and provide answers to the previous month’s questions.  The questions were mostly meant to be simple order of magnitude estimation problems which could literally be done on the back of an envelope. These types of problems are also often called Fermi problems after another famous connoisseur, Enrico Fermi. Examples:

1. At room temperature in air how long could a pencil remain balanced on its point? At absolute zero?
2. How fast can a 10 mg water droplet spin without falling apart? (ignoring aerodynamic forces)
3. If the library of congress were printed in tungsten on a postcard would it be readable with a standard electron microscope?

To get another taste of this style of doing physics -  read the lecture “Life at Low Reynolds Number” – given in 1973 – a time when biophysics was nowhere near as mainstream as it is today. (with some exceptions like Helmholtz).  Many observations made in this famous lecture foreshadowed future developments of the field.  Purcell discusses the special difficulties that E. Coli experience in propelling themselves in an environment with no inertia where viscocity dominates their motion. (It was widely believed that the bacteria vibrated their flagella instead of rotating them because no one could conceive of how a bacteria could contain a rotary joint with a bearing much less a rotary motor)  Now of course, there are many known examples of single molecule motors which exist – Actin/Myosin, Kinesin etc. Interesting fact: for the fluid flow around a swimming human to have the same reynolds number as a bacteria in water – the human would have to swim through molasses and restrict her stroke so that her limbs move no faster than 1cm / s!

Another fine example of his work is found in the MIT radiation lab series – a thick >10 volume set which contained nearly everything that was then known on the subject of microwave engineering.  Along with many other authors, he gives a series of brilliant arguments for how the engineering concepts of impedance and reactance can be extended to high frequency circuits where the free space wavelength is of the same length scale as the circuit elements.

See also Relativistic Electromagnetism

Also highly recommended is the series of columns in AJP by Victor Weisskopf – “The Search for Simplicity“