# Geertruida de Haas-Lorentz

Geertruida Luberta "Berta" de Haas-Lorentz (20 November 1885 – 1973) was a Dutch physicist and a professor at the Technical University of Delft. She was the first to theoretically study thermal fluctuations in electric circuits, treating electrons as Brownian particles. Consequently she is considered one of the pioneers of electrical noise theory. She was the daughter and doctoral student of Hendrik Lorentz. She went by the name Berta, or Ber.

## Life

Berta Lorentz was born in Leiden, Netherlands, the eldest daughter of the physicist and 1902 Nobel Prize in Physics winner Hendrik Lorentz and Aletta Catharina Kaiser. Berta was the eldest of four children. Her siblings were Johanna Wilhelmina (born 1889), Gerrit (born 1893, died 1894), and Rudolf (born 1895). At that time of her birth, her father was Professor of Theoretical Physics at the University of Leiden. Her mother, Aletta Kaiser, took care of the children and household, did charity work, and was heavily involved with the local women's suffrage movement.
On 22 December 1910, Berta Lorentz married Wander Johannes de Haas, who would become professor of experimental physics in Leiden, and they went on to have two sons and two daughters. Some of their children changed their last name to "Lorentz de Haas."
She studied physics at the University of Leiden with her father as dissertation advisor and earned her doctor's degree in 1912 on a thesis entitled "On the theory of Brownian motion and related phenomena" (Dutch: Over de theorie van de Brown'schen beweging en daarmede verwante verschijnselen).
After defending her doctoral dissertation in Leiden, De Haas-Lorentz taught physics at the Technical University of Delft and translated some of her father's works into German. She also wrote a biography of her father.
Berta de Haas-Lorentz died in 1973 in Leiden.

## Research

De Haas-Lorentz was one the first to apply Albert Einstein's theory of Brownian motion to other domains. During her thesis work, she was the first to carry out a theoretical analysis of thermal fluctuation of electrons in electrical circuits, predating the experimental discovery of the Johnson–Nyquist noise. She considered that a circuit with resistance R and inductance L should store an energy E = LI$^2$/2, where I is the current. If there was a fluctuating thermal current, by the equipartition theorem the energy would be related to the thermal energy kT where k is the Boltzmann constant and T is the temperature. De Haas-Lorentz obtained,
    ${\sqrt {\langle I^{2}\rangle }}={\sqrt {\frac {2kT}{L}}}$,
where the angle brackets denote the thermal average.
She was also the first to propose thermal fluctuations limit the detection of electromagnetic radiation.
In collaboration with her husband, the De Haas couple showed that experiments carried by James Clerk Maxwell failed to prove the hypothesis of André-Marie Ampère, that magnetism in matter is caused by microscopic current loops.
She also predicted the London penetration depth for superconductivity in 1925, before the development of the London equations in 1935.

## Selected works

* De Haas-Lorentz, Geertruida (1912). Over de theorie van de Brown'sche beweging en daarmede verwante verschijnselen [On the theory of Brownian motion and related phenomena] (PDF) (Doctoral dissertation thesis) (in Dutch). University of Leiden.
* De Haas-Lorentz, Geertruida (1913). Die Brownsche Bewegung und einige verwandte erscheinungen [Brownian motion and some related phenomena] (in German). Braunschweig: F. Vieweg. OCLC 5160522.
* De Haas-Lorentz, Geertruida; Lorentz, H. A. (1919). Theorie der quanta [Theory of quanta]. OCLC 81861598.
* Lessen over theoretische natuurkunde : aan de Rijks-Universiteit te Leiden [Lessons on theoretical physics at Leiden State University]. Vol. 1–5. 1919–1926. OCLC 805502380. – contributing author
* Lorentz, H. A.; Bruins, Eva Dina; Reudler, Johanna; De Haas-Lorentz, Geertruida Luberta (1928). Kinetische Probleme [Kinetic Problems] (in German). Leipzig: Akademische Verlagsgesellschaft. OCLC 28005510.
* De Haas-Lorentz, Geertruida Luberta (1946). De beide hoofdwetten der thermodynamica en hare voornaamste toepassingen [The two main laws of thermodynamics and their main applications] (in Dutch). 's-Gravenhage: M. Nijhoff. OCLC 361410098.
* De Haas-Lorentz, Geertruida Luberta, ed. (1957). H. A. Lorentz: impression of his life and work. Amsterdam: North-Holland Pub. Co. OCLC 317334917.