Einstein's Ph.D. Thesis: A Remarkable Journey in Science
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Chapter 1: The Genesis of a Scientific Legend
In 1905, Albert Einstein completed his Ph.D. thesis under the guidance of Professor Alfred Kleiner, an experimental physicist at the University of Zürich. The dissertation, titled "A New Determination of Molecular Dimensions," marked a significant milestone in his academic journey, although it was presented at ETH, which at that time was not authorized to confer Ph.D. degrees. Instead, students were allowed to submit their work to the University of Zürich until 1909.
This year, known as Einstein's annus mirabilis or "miraculous year," was pivotal, as he published four transformative papers that altered the landscape of physics. One of these papers addressed the photoelectric effect, which earned him the Nobel Prize in Physics in 1921. The other groundbreaking topics included Brownian motion, special relativity, and the seminal equation linking mass and energy, E=mc². While his early papers garnered widespread acclaim, his doctoral thesis initially received less recognition.
Einstein's thesis was printed in Bern on April 30, 1905. Notably, it consisted of only 24 pages, a brevity that would be considered unusual by today's academic standards. In this work, he sought to develop a novel theoretical approach for calculating molecular sizes. He presented Avogadro's number based on viscosity data from sugar solutions in water, although his initial estimates were off by a factor of nearly three. With further refinements, he approached the currently accepted value.
This video titled "Einstein's PhD thesis" dives into the history and significance of Einstein's groundbreaking dissertation, exploring its impact on modern science.
Section 1.1: The Dedication
Einstein dedicated his thesis to Marcel Grossmann, a close friend and skilled mathematician who provided invaluable support during his studies. Grossmann's assistance included sharing course notes and recommending Einstein for a position at the patent office, demonstrating the importance of friendship and collaboration in academia.
Subsection 1.1.1: The Thesis' Core Concepts
The main focus of Einstein's thesis was hydrodynamics and the relationship between viscosity coefficients. He analyzed the stationary flow of a homogeneous and incompressible fluid while disregarding acceleration effects. Utilizing the Navier-Stokes equations, he modeled the fluid's motion.
Einstein then introduced identical spherical particles suspended in the liquid, ensuring their total volume was smaller than that of the fluid. He made several assumptions: the absence of external forces, independence from other particles' movements, and boundary conditions where flow velocity was zero at the particle surfaces. This led to a revised viscosity factor known as 'effective viscosity' (η*).
Section 1.2: Advancements in Molecular Understanding
Einstein's work culminated in a remarkable formula for the diffusion constant of suspended particles, applying Van't Hoff's law and Stokes' law. He successfully estimated Avogadro's number and the radii of sugar molecules, a significant accomplishment in molecular physics.
In 1909, French physicist Jean Perrin independently calculated a different value for Avogadro's number, prompting Einstein to share his hydrodynamic methods with him. After some correspondence, discrepancies in Einstein's viscosity calculations were identified, leading to a revision of his thesis work. This correction was published in 1911, alongside new calculations that estimated Avogadro's number to be N = 4.15 x 10²³.
In the video "The Shortest PhD Thesis, EVER. Unbelievably short! Einstein, Rector and more...", viewers can gain insight into the brevity and impact of Einstein's thesis, showcasing its remarkable journey through academia.
Chapter 2: The Legacy of Einstein's Dissertation
Despite initial inaccuracies, Einstein's continued efforts led to an improved value of N = 6.56 x 10²³, which aligned more closely with modern values. Today, Avogadro's number is known to be N = 6.022 x 10²³, a testament to the enduring relevance of Einstein's work.
Throughout his career, Einstein emphasized the importance of precise molecular size determination. His dissertation earned positive reviews from his advisors, who recognized the complexity and significance of his calculations. Dr. Kleiner, in particular, commended Einstein's aptitude for tackling challenging scientific problems.
Interestingly, as recounted in Carl Seelig's biography, Einstein humorously noted that his dissertation was initially returned for being too brief. After adding a single sentence, it was accepted without further comment.
In conclusion, Einstein's Ph.D. thesis, "A New Determination of Molecular Dimensions," not only laid the groundwork for his future accomplishments but also became one of his most cited works, demonstrating its profound impact on scientific inquiry. This narrative serves as a reminder that even foundational contributions may not be perfect and encourages graduate students facing the pressures of dissertation writing to persevere.
Thank you for engaging with this exploration of Einstein's academic journey. Your thoughts, feedback, and comments are welcomed!