- What did Robert Brown originally observe about pollen grains suspended in water, and why did it rule out a biological cause?
- How did Einstein's equations connect a particle's random drift to molecular collisions, temperature, and viscosity?
Statistical Mechanics
Explaining bulk thermodynamic behavior from particle statistics.
- How did Einstein apply Planck's quantum hypothesis to explain the heat capacity of solids?
- Why does a solid's heat capacity fall toward zero as temperature approaches absolute zero, according to Einstein's model?
- Why was this the first successful application of quantum ideas to matter rather than light?
- Why does the ideal gas law fail to describe a gas as it is compressed toward liquefaction?
- What longstanding scientific debate did Zsigmondy's observations of Brownian motion help settle?
- How did watching pollen-like particles jitter in liquid let Perrin count atoms he could never see directly?
- Why did Einstein's 1905 mathematics of Brownian motion need Perrin's painstaking measurements to become proof?
- What is the two-dimensional Ising model and why do physicists still use Onsager's exact solution to it as a benchmark?
- What does it mean for fluctuations to occur 'at every scale of length simultaneously,' and why did that break the standard tools of physics?
- How did Einstein's Brownian motion paper provide evidence that atoms actually exist?
- What is a Boltzmann machine, and how did it extend Hopfield's physical intuition about neural networks?