Brownian motion hydrodynamics: A study on logic, fact, and similitude

The article analyzes some new results that are emerging from highly resolved experimental analysis of Brownian trajectories, addressing their deep connection with the hydrodynamic modeling in light of resolving the paradoxes of the infinite speed of propagation of hydrodynamic fields, which is intrinsic to the assumption of incompressibility in liquids and to the parabolic nature of the hydrodynamic equations. The key quantity is the added mass and its emergence as a consequence of the physically consistent extension of the regularity properties to hydrodynamic-thermal fluctuations (logic). This extension is compared and contrasted with the experimental observations of the added mass effect (fact), the signature of which is the deviation of the squared variance of Brownian velocity fluctuations at equilibrium from the Maxwellian prediction, developing a careful statistical analysis of their statistical validity. Finally, the analogy (similitude) of the added mass effect with other field-theoretical mechanisms of mass gain (e.g., electron's self-energy in quantum field theory) is addressed.