In 2011, the OPERA experiment mistakenly observed neutrinos appearing to travel faster than light. Even before the mistake was discovered, the result was considered anomalous because speeds higher than that of light in a vacuum are generally thought to violate special relativity, a cornerstone of the modern understanding of physics for over a century. OPERA scientists announced the results of the experiment in with the stated intent of promoting further inquiry and debate. Later the team reported two flaws in their equipment set-up that had caused errors far outside their original confi...

In calculus, Leibniz's rule for differentiation under the integral sign, named after Gottfried Leibniz, tells us that if we have an integral of the form : \int_{y_0}^{y_1} f(x, y) \,\mathrm{d}y then for x in (x0, x1) the derivative of this integral is thus expressible : {\mathrm{d}\over \mathrm{d}x} \left ( \int_{y_0}^{y_1} f(x, y) \,\mathrm{d}y \right )= \int_{y_0}^{y_1} f_x(x,y)\,\mathrm{d}y provided that f and its partial derivative fx are both continuous over a region in the form [x0, x1] × [y0, y1]. Thus under certain conditions, one may interchange the integral and partial di...