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The second paper explained Brownian motion, which established the Einstein relation = and compelled physicists to accept the existence of atoms. The third paper introduced Einstein's special theory of relativity , which proclaims the constancy of the speed of light c {\displaystyle c} and derives the Lorentz transformations .
This observation is useful in defining Brownian motion on an m-dimensional Riemannian manifold (M, g): a Brownian motion on M is defined to be a diffusion on M whose characteristic operator in local coordinates x i, 1 ≤ i ≤ m, is given by 1 / 2 Δ LB, where Δ LB is the Laplace–Beltrami operator given in local coordinates by ...
Within months, Einstein's description of Brownian motion was experimentally verified by Henry Siedentopf. [8]: 103–106 In 1905, Einstein developed his special theory of relativity, which reconciled the Galilean relativity of motion with the observed constancy of the speed of light (a paradox of 19th-century physics). [14]
In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected [clarification needed] connection revealed independently by William Sutherland in 1904, [1] [2] [3] Albert Einstein in 1905, [4] and by Marian Smoluchowski in 1906 [5] in their works on Brownian motion.
Wilhelm Ostwald, one of the leaders of the anti-atom school of energeticism, later told Arnold Sommerfeld that he had been converted to a belief in atoms by Einstein's complete explanation of Brownian motion. [4] The paper also provided the best way up to that time of estimating the Avogadro constant—the corrected value from Einstein's paper ...
For example, Albert Einstein noted in his 1905 paper on Brownian motion that the same random forces that cause the erratic motion of a particle in Brownian motion would also cause drag if the particle were pulled through the fluid. In other words, the fluctuation of the particle at rest has the same origin as the dissipative frictional force ...
The equation for Brownian motion above is a special case. An essential step in the derivation is the division of the degrees of freedom into the categories slow and fast. For example, local thermodynamic equilibrium in a liquid is reached within a few collision times, but it takes much longer for densities of conserved quantities like mass and ...
On September 26, 1905 (received June 30), Albert Einstein published his annus mirabilis paper on what is now called special relativity. Einstein's paper includes a fundamental description of the kinematics of the rigid body, and it did not require an absolutely stationary space, such as the aether.