Friday, December 18, 2009

Where's Albert?

Albert Einstein is considered one of the greatest physicists of the 20th century, and perhaps of all time. He certainly is one of the best-known physicists, being selected by TIME Magazine as their Person of the Century in 1999. Yet, Einstein is curiously absent in the 4th edition of Intermediate Physics for Medicine and Biology. If you look in the index under Einstein, you find only one entry: on page 393, where Russ Hobbie and I introduce the unit of an einstein (a mole of photons) in a homework problem.

Does Einstein’s work appear anywhere else in Intermediate Physics for Medicine and Biology? Certainly his masterpiece, the general theory of relativity, has little or no direct impact on biology or medicine. I don’t believe we even refer indirectly to this monumental description of gravity. However, Einstein’s earlier theory, special relativity, does appear occasionally in our book. In Chapter 8 on Biomagnetism, we write “the appearance of the magnetic force is a consequence of special relativity,” a topic we explore further in Homework Problems 5 and 23. Yet, the relationship between electrodynamics and relativity is mentioned as an aside, and is not a central feature of our analysis of magnetism. We could have left out mention of relativity from Chapter 8 altogether, and the rest of the chapter would be unaffected.

Special relativity enters in a more profound way in Chapter 15, on the Interaction of Photons and Charged Particles with Matter. There, we analyze Compton Scattering, and need the relationship between photon energy E and momentum p, given by special relativity as E = pc, where c is the speed of light. Moreover, the concept of rest mass m is introduced in this chapter, and we use Einstein’s most famous equation E = mc2, relating energy and mass. Rest mass appears again in the discussion of pair production, where enough photon energy must be present to produce an electron-positron pair. The equation appears one more time in Chapter 17 on Nuclear Physics and Nuclear Medicine, where mass can be converted into energy in nuclear reactions.

Besides relativity, Einstein also played a leading role in the development of quantum mechanics, especially as related to the quantization of light and the idea of photons. This idea is first presented in Chapter 9, in a section on the Possible Effects of Weak External Electric and Magnetic Fields, where we compare the photon energy (equal to Planck’s constant times the frequency of the radiation) to the thermal energy. The idea is developed in more detail in Chapter 14, in a section about The Nature of Light: Waves versus Photons. The idea of photons is central to Chapter 15, and particularly Sec. 15.2 on Photon Interactions. There, we discuss the photoelectric effect—one mechanism by which x rays interact with tissue—which is the research that won Einstein the Nobel Prize.

One final place where Einstein’s research impacts Intermediate Physics for Medicine and Biology is in the study of diffusion (Chapter 4). Einstein did fundamental work on diffusion in his doctoral thesis, and derived a relationship between the diffusion constant and the viscosity that we give as Eq. 4.23.

Subtle is the Lord: The Science and Life of Albert Einstein, by Abraham Pais, superimposed on Intermeidate Physics for Medicine and Biology.
Subtle is the Lord,
by Abraham Pais.
In summary, we rarely mention Einstein by name in our book, but his influence is present throughout, and most fundamentally when we discuss the idea of a photon. For readers interested in Einstein’s life and work, I recommend the brilliant biography Subtle is the Lord by Abraham Pais. I have heard good things about Isaacson’s more recent biography, Einstein: His Life and Universe, although I haven’t read it. You might also enjoy the American Institute of Physics website about Einstein prepared by the AIP Center for the History of Physics. Einstein published most of the ideas I have discussed in one miraculous year, 1905. John Rigden describes these publications and their impact in his book Einstein 1905: The Standard for Greatness (I have not read this book either, but I understand it is good). Finally, the equation E = mc2 has received a lot of press recently, including a NOVA special and Bodanis’s book E=mc2: A Biography of the World’s Most Famous Equation.

1 comment:

  1. General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations. I am a college sophomore with a dual major in Physics and Mathematics @ University of California, Santa Barbara. By the way, i came across these excellent physics flash cards. Its also a great initiative by the FunnelBrain team. Amazing!!!