In 1905, Einstein published a paper in the German journal Annalen der Physik, the English title, “On the Electrodynamics of Moving Bodies,” appeared unassuming to the casual science readers of the era. However, this is the paper that is completely self-contained; without references to other scientific papers since it described a new idea as birth of a special theory of relativity. It created a revolution still un-abating to this day.
This theory frequently made use of operational definitions for physical observables and later known as physical operators. These can be separated into two distinct subdivisions: smooth and quantum, in other words, continuous and discrete. They are deeply connected to the more familiar mathematical operators and given examples in the many branches of mathematics. In arithmetic, there are 4 basic binary operators: +, -, x, and ¸ with unary operators of n-powers and n-roots. In set theory, there are the Ç and È binary operators. In calculus, there are the differential and the integral operators.
Physical operators are now extensively use in modern physics: quantum field theory (QFT), quantum mechanics (QM), and general relativity (GR). However, a truly smooth physical operator that can operate on all common elements of QFT, QM, and GR still does not exist.


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