Hermann Ludwig von Helmholtz
By: Chris Steward
Abstract
Hermann Ludwig von Helmholtz was born in 1821, the oldest
of 6 children. Throughout his life, he was very interested
in science and medicine. After studying, Helmholtz was able to
do things that no else could, such as measure the speed of nerve
signals. Eventually, Helmholtz would solve the wave equation, leading to
the spatial solution that describes the way plane waves propagate.
Biography
Hermann Ludwig Ferdinand von Helmholtz, also known as Hermann von Helmholtz,
was a German physicist born August 31, 1821 in Potsdam. He was the oldest of
6 children. His father, August Helmholtz, was a teacher of philosophy and
classics. Throughout his early life, Helmholtz took an avid interest in science
and medicine; at the age of 17, he attended the Friedrich Wilhelm
Institute as a scholarship student studying medicine.[1][2]
At the institute, he studied under Johannes Müller, who believed in
carrying all of his experiments to the limit of physical and chemical
explanation. Doing this created a need for Helmholtz to learn very advanced
math. He went on to teach himself the works of mathematicians such as
Euler, Lagrange, Bernoulli, and D'Alembert. In 1842, he completed his
doctorate with a dissertation on the connections between nerve fibers and nerve
cells. After graduating, Helmholtz was required to serve 8 years in the army to
“re-pay” his scholarship.[3]
In 1842, Helmholtz’s first post was at Charité Hospital in Berlin as a
house surgeon. In 1843, he was transferred to Potsdam to be assistant surgeon to
the Royal Hussars. In the five years he was at Potsdam, Helmholtz used his spare
time to continue with his scientific studies. During this time, he “published a
demonstration of the strictly chemical nature of fermentation and noted that a
vitalistic account would be equivalent to assuming a perpetual-motion process. His
papers on metabolism during muscular activity (1845) and on physiological and animal
heat (1846, 1847) clearly indicated the great goal toward which his creative mind
inevitably tended” [2]. In 1847, Helmholtz then
published his first draft of “The conservation of Force.” While not the first
person to study conservation of energy, he gave the principal a generalized mathematical
form which led to expressions for kinetic and potential energy in mechanics,
thermodynamics, electricity, and magnetism. Helmholtz’s early life led to great
breakthroughs in science.[2]
Importance to Optics
Perhaps best known for his research on the eye, nervous system and the law of
conservation of energy, Helmholtz also dabbled in the world of physical optics. Many
of Helmholtz’s experiments were taken up by other researchers and these formed new
notions about optics. For example, Helmholtz theorized there were electromagnetic
waves far into the invisible spectrum, but never followed up on this. Later, one of
Helmholtz’s students, Heinrich Rudolph Hertz, resumed his research and became the
iscoverer of radio waves. Helmholtz also came up with a solution to the wave
equation that, for the first time, described the propagation of electromagnetic waves.
Looking at the wave equation
with wave speed c, Helmholtz
derived the equation
this came to be known as the Helmholtz
equation. Solutions to Helmholtz’s equation are physically described as
“plane waves,” having the mathematical form 
or including time and using the vector notation,
where 
is the wave vector. Recall that 
, and the solution to Helmholtz’s equation becomes 
. Imaginary
numbers do not describe any physical quantity, so, ignoring the imaginary part of
the solution to Helmholtz’s equation, we find that the quantity 
satisfies the spatial solution to Helmholtz’s equation. Helmholtz’s was the first
to solve the wave equation and obtain a physically meaningful result.[4][5]
The world of optics was changed from this moment. Now, opticians had a way
to meaningfully describe the motion of electromagnetic waves, or light. Given the
wave equation, one could now obtain the result. Looking
at the one-dimensional case and with t=0,1,2 and 3, and x from 0 to 4pi, one
can visualize a light wave propagating in the following manner:
As shown in the picture, it can be seen that the waves described by
Helmholtz traveled sinusoidally while propagating in one direction. When dealing with all
three dimensions, waves travel as expanding circles.
[5]
The waves have highs and low,
with wave fronts described by Helmholtz’s solution to the wave equation.
References
1. "Biography Resource Center" 2003. http://www.galenet.com.ezproxy.library.arizona.edu/servlet/BioRC(U of A students/faculty only) (25 Sep 2003)
2. "Hermann Ludwig Ferdinand von Helmholtz." Encyclopedia of World Biography, 2nd ed. 17 Vols. Gale Research, 1998
3. "Hermann von Helmholtz." World of Scientific Discovery, 2nd ed. Gale Group, 1999
4. "PlanetMath: Helmholtz Equation." November 13, 2003, http://planetmath.org/encyclopedia/HelmholtzDifferentialEquation.html (September 2003)
5. "The Helmholtz Equation." October 2, 2001 http://www.maths.soton.ac.uk/staff/Andersson/MA361/node50.html (October 15, 2003)
First posted 11-23-2003. Modified 12-9-2003. Cosine graphs created with Matlab