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The Mysterious Connection Between Cyclic Imaginary Time and Temperature
An Apparent Accident May Contain a Great Mystery in Physics
There is a special kind of beauty that occurs when entirely different concepts, theories of branches of human knowledge reveal themselves to be, in fact, intimately connected. In a letter to his friend, the mathematician Marcel Grossman, Albert Einstein wrote:
“It is a glorious feeling to discover the unity of a set of phenomena that seem at first to be completely separate.”
— Albert Einstein
In this article, I will describe some incredibly elegant connections between two fundamental branches of theoretical physics, namely, quantum mechanics (QM), which represents the Universe at the levels of atoms and subatomic particles, and statistical mechanics (SM), which applies statistical methods to describe the behavior of collections of particles.
Mathematically these connections are a consequence of a simple arithmetical substitution which makes cyclic imaginary time equivalent to temperature. Putting it in another way, periodicity in imaginary time is equivalent to (the inverse of) temperature.
“A hidden connection is stronger…
