Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen.¶
Einstein, A. (1905). Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik, 322(8), 549-560.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Diffusion
- At the microscopic scale, Einstein's
This sourceResolves Brownian motion via statistical mechanics; derives the Stokes-Einstein relation D = kT/(6πηa) connecting diffusion coefficient to temperature, viscosity, and particle radius; predicts mean-square displacement <x²> = 2Dt.
- At the microscopic scale, Einstein's
- Inertia
- . Relativistic inertia: Einstein's 1905 special relativity
This sourceResolves Brownian motion via statistical mechanics; derives Stokes-Einstein relation D = kT/(6πηa) connecting diffusion coefficient to temperature, viscosity, and particle radius; predicts mean-square displacement <x²> = 2Dt. Einstein Brownian motion, Stokes-Einstein relation, molecular-scale foundation, temperature dependence, mean-square displacement.
- . Relativistic inertia: Einstein's 1905 special relativity
- Random Walk
- In physics, it is the drunkard's walk and the foundation of Brownian motion: a pollen grain buffeted by independent molecular collisions executes a random walk whose √t spreading Einstein used to confirm the atomic hypothesis and measure Avogadro's number, and the same structure underlies thermal diffusion, polymer chain conformations, and the random-walk model of electrical resistance in disordered media.
This sourceIdentifies Brownian motion as a random walk with √t displacement, confirming the atomic hypothesis and enabling measurement of Avogadro's number.
- In physics, it is the drunkard's walk and the foundation of Brownian motion: a pollen grain buffeted by independent molecular collisions executes a random walk whose √t spreading Einstein used to confirm the atomic hypothesis and measure Avogadro's number, and the same structure underlies thermal diffusion, polymer chain conformations, and the random-walk model of electrical resistance in disordered media.
- Time
- Space allows objects to exist in different places simultaneously; time permits only one moment at each location, enforcing strict succession, a distinction Einstein (1905) made operationally precise by showing that the simultaneity of distant events is observer-dependent while the temporal ordering of causally connected events is invariant.
This sourceResolves Brownian motion via statistical mechanics; derives Stokes-Einstein relation D = kT/(6πηa) connecting diffusion coefficient to temperature, viscosity, and particle radius; predicts mean-square displacement <x²> = 2Dt. Einstein Brownian motion, Stokes-Einstein relation, molecular-scale foundation, temperature dependence, mean-square displacement.
- Space allows objects to exist in different places simultaneously; time permits only one moment at each location, enforcing strict succession, a distinction Einstein (1905) made operationally precise by showing that the simultaneity of distant events is observer-dependent while the temporal ordering of causally connected events is invariant.
Mechanisms¶
- Random-Walk Simulation
- The spread it predicts follows the classic square-root-of-time diffusion scaling, which is why doubling the horizon only widens the expected envelope by about 40%.
This sourceDerives root-mean-square displacement as proportional to the square root of elapsed time, so doubling time increases spread by about 41%.
- The spread it predicts follows the classic square-root-of-time diffusion scaling, which is why doubling the horizon only widens the expected envelope by about 40%.
Verification¶
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Does it back the claim? Not recorded. Neither this nor any other of the 5 citations of this work carries a recorded support check.
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Registry ID ref:548a60e8bd3f · see in the full table