Research
Most of Ehrenfest's scientific papers deal with fundamentals, and seek to clarify single points. His publications are renowned for clarity, by solving paradoxes or by providing clearer descriptions, or are inspiring by posing penetrating questions. His approach to science is best illustrated by what he wrote to Robert Oppenheimer in the summer of 1928, after Oppenheimer invited himself for an extended stay in Leiden: "If you intend to mount heavy mathematical artillery again during your coming year in Europe, I would ask you not only not to come to Leiden, but if possible not even to Holland, and just because I am really so fond of you and want to keep it that way. But if, on the contrary, you want to spend at least your first few months patiently, comfortably, and joyfully in discussions that keep coming back to the same few points, chatting about a few basic questions with me and our young people- and without thinking much about publishing (!!!)-why then I welcome you with open arms!! ". Characteristically, he did not like the abstraction of the new quantum theory of Heisenberg and Dirac.
Ehrenfest’s most important contribution from 1912 up to 1933 is the theory of adiabatic invariants. It is a concept derived from classical mechanics that on the one hand can serve to refine certain methods of Bohr's model of the atom (although initially Ehrenfest did not accept Bohr’s ideas) and on the other hand makes a link between atomic mechanics and statistical mechanics. He made major contributions to quantum physics, including the theory of phase transitions and the Ehrenfest theorem, which states that expectation values of a quantum system follow classical mechanics. His name is also given to the Ehrenfest paradox, an apparent paradox in relativity still discussed today, to the Ehrenfest model, and to Ehrenfest Time, the time characterizing the departure of quantum dynamics for observables from classical dynamics.
Ehrenfest was also interested in developing mathematical theories in economics. This interest was stimulated by his notion that there should be an analogy between thermodynamics and economic processes. While this did not result in publications, he did encourage his graduate student Tinbergen to follow up on this. Tinbergen's thesis was devoted to problems both from physics and economics, and he went on to become an economist and was awarded the first Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel in 1969.
Read more about this topic: Paul Ehrenfest
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