Massive astrophysical objects governed by subatomic equation

[Jim__]

From phys.org:

Quantum mechanics is the branch of physics governing the sometimes-strange behavior of the tiny particles that make up our universe. Equations describing the quantum world are generally confined to the subatomic realm—the mathematics relevant at very small scales is not relevant at larger scales, and vice versa. However, a surprising new discovery from a Caltech researcher suggests that the Schrödinger Equation—the fundamental equation of quantum mechanics—is remarkably useful in describing the long-term evolution of certain astronomical structures.

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Massive astronomical objects are frequently encircled by groups of smaller objects that revolve around them, like the planets around the sun. For example, supermassive black holes are orbited by swarms of stars, which are themselves orbited by enormous amounts of rock, ice, and other space debris. Due to gravitational forces, these huge volumes of material form into flat, round disks. These disks, made up of countless individual particles orbiting en masse, can range from the size of the solar system to many light-years across.

Astrophysical disks of material generally do not retain simple circular shapes throughout their lifetimes. Instead, over millions of years, these disks slowly evolve to exhibit large-scale distortions, bending and warping like ripples on a pond. Exactly how these warps emerge and propagate has long puzzled astronomers, and even computer simulations have not offered a definitive answer, as the process is both complex and prohibitively expensive to model directly.

While teaching a Caltech course on planetary physics, Batygin (the theorist behind the proposed existence of Planet Nine) turned to an approximation scheme called perturbation theory to formulate a simple mathematical representation of disk evolution. This approximation, often used by astronomers, is based upon equations developed by the 18th-century mathematicians Joseph-Louis Lagrange and Pierre-Simon Laplace. Within the framework of these equations, the individual particles and pebbles on each particular orbital trajectory are mathematically smeared together. In this way, a disk can be modeled as a series of concentric wires that slowly exchange orbital angular momentum among one another.

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[Loki Liesmith]

1. You can model lots of physical situations via Schrdinger eqn

[DetlefK]

2. Um, actually... a way better comparison would be Fick's laws of diffusion.

These guys want an equation to explain what happens to a perturbation in a dust-disc?

Here's an idea: If you combine Fick's laws of diffusion, you get an equation how a perturbation of concentration spreads out over time.

dc/dt = D * d²c/dx²

[Jim__]

3. Why do you think that would lead to a better approximation?

My understanding is that their major concern is the orbital evolution of gravitationally interacting objects. From the article:

As an analogy, in our own solar system one can imagine breaking each planet into pieces and spreading those pieces around the orbit the planet takes around the sun, such that the sun is encircled by a collection of massive rings that interact gravitationally. The vibrations of these rings mirror the actual planetary orbital evolution that unfolds over millions of years, making the approximation quite accurate.

[DetlefK]

4. Because the Schrdinger-equation stems from radically different origins.

The Schrödinger-equation is a Hamiltonian equation where the momentum-variable has been modified to account for particle-wave-duality. And the solutions of this modified Hamiltonian equation are certain Eigenvalues and Eigenfunctions that tell you how your system behaves.



On second thought:
Batygin's work suggests that large-scale warps in astrophysical disks behave similarly to particles, and the propagation of warps within the disk material can be described by the same mathematics used to describe the behavior of a single quantum particle if it were bouncing back and forth between the inner and outer edges of the disk.

This reminds me of pseudo-particles in a solid-state body.