Cartesian vortex theory, cosmic vortices, and the route to cosmogony

The foundation of René Descartes’s mechanics was torn asunder during early-18th-century debates in the Paris Academy of Sciences. The Cartesians constructed intuitive mechanical descriptions of the universe based on the three elements of primitive matter as devised by Descartes. One was the “subtle minute matter” constituting the Sun and the stars. Capable of moving at great speed, that form of matter permeated all space not occupied by the two other, denser elements. The second and principal form of celestial matter, spherical ether particles, moved in large vortical structures and transmitted force as an instantaneous impulse. The coarsest and most lethargic element composed planetary bodies, including Earth.

In the Cartesian view, the mechanics of the solar system was controlled by the action of the ether particles, through their impulsive coupling to planetary bodies. In Descartes’s cosmogony, the guiding hands of vortices set in motion by the creator continually returned bodies to their proper orbits. The idea persisted because the Cartesians convincingly argued that the action of the ether particles mimicked that of the central force of gravity described by Isaac Newton and Gottfried Leibniz. Eventually, the Cartesian vortices vanished in their own ether, as they failed to describe the world as powerfully as did Newtonian mechanics.

A few centuries after the debates in the Paris Academy, Carl Friedrich von Weizsäcker developed a cosmogony that embraced vortices—but his mid-20th-century vortices emerged during the evolution of an accretion disk around a central star. Weizsäcker laid down the foundations of what we now understand is a multistage process that plays out over millions of years: Gas collapses, the accretion disk comes into being, mass accretes, primary planetesimals form, and a UV flux from the central star removes the lightest elements from the outer regions of the disk. The vortices arise in Weizsäcker’s system because, on the one hand, viscous stresses act to enforce uniform rotation, but on the other, the Keplerian velocity—the speed determined by equating centripetal and gravitational force—falls with distance from the central star. Thus, the viscous forces decelerate the inner regions of a disk and accelerate the outer regions; the result is a state of quasi-stable vortex structures as shown in panel a of the figure. Weizsäcker surmised that such vortices act to focus primordial matter for gravitational collapse into protoplanets.

Scientists are working to formulate the precise mechanisms for agglomeration on scales too small for gravitational collapse and to explain how those mechanisms lead to gravitationally controlled growth. And in the decades since Weizsäcker’s work, we have learned that accretion disks are rather less peaceful than in his model. Turbulence abounds and vortices arise from shear, magnetorotational, and so-called streaming instabilities and other sources; panel b of the figure shows a simulation. Nonetheless, in the current understanding, vortices play the same qualitative role as in Weizsäcker’s vision: They are the future homes of consolidated matter. Vortices may be intrinsically transient, but they seem to persist in theories of cosmogony.

View the original article for this supplement, “The universe in a cup of coffee” PHYSICS TODAY, May 2011, page 66 .