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The Schrödinger Equation describes astrophysical disks

Almost all of modern physics is based on two usually incompatible frameworks, that of relativity and of quantum field theory. These two frameworks describe the movements of objects on very different scales. General relativity describes the universe on a macro scale, while quantum mechanics does the same on a micro scale. It is not very often that the equations describing the sub atomic realm also describe large scale astronomical structures. In a surprising discovery, a researcher from The California Institute of Technology (Caltech) has found that the Schrödinger Equation accurately astrophysical disks around stars and supermassive black holes.

The disks can range in size from that of a solar system, to several light years across. The bigger disks may even have additional black holes and neutron stars in them, in orbit around the supermassive black hole in the centre. There are also stars, planets, moons, asteroids, comets, rocks, ice and other debris. In the bigger disks, all these are countless particles in orbit around a massive distortion in the very fabric of space itself. Accretion disks around supermassive black holes are among the most magnificent structures found in nature.

Over millions of years, the disks bend and warp as the objects interact with each other. Exactly how this looks has long remained a mystery. Computer simulations are too expensive to model the structures at the required complexity. One of the best attempts was in the movie Interstellar, based on the work of another Caltech researcher, Kip Thorne. The accuracy with which how the black hole was simulated by the visual effects department, actually advanced the science.

The approach used by Konstantin Batygin, a researcher at Caltech, to model the disks, involved an approach that broke up the problem into smaller, easier to solve parts. Instead of modelling each of the particles individually, the disk is approximated into a series of concentric wires. The interaction and the movement of these wires can then be used to get a picture of how the disk evolves over time.

Batygin started describing the disks by using an increasing number of thinner wires. When the number of wires approached infinity, the objects in the disk mathematically blurred together in a continuum. At this point, the Schrödinger Equation emerged from the calculations, and it transpired that the equation normally used to describe subatomic space was applicable on a macro scale as well. As all the properties of subatomic particles could not be measured accurately, the Schrödinger equation allowed for their study through the use of probabilities.

Batygin explains, “This discovery is surprising because the Schrödinger Equation is an unlikely formula to arise when looking at distances on the order of light-years. The equations that are relevant to subatomic physics are generally not relevant to massive, astronomical phenomena. Thus, I was fascinated to find a situation in which an equation that is typically used only for very small systems also works in describing very large systems.”

The paper with the findings is titled Schrödinger Evolution of Self-Gravitating Disks, and is appearing in the Monthly Notices of the Royal Astronomical Society.

Source: Caltech 

Aditya Madanapalle

Aditya Madanapalle

An avid reader of the magazine, who ended up working at Digit after studying journalism, game design and ancient runes. When not egging on arguments in the Digit forum, can be found playing with LEGO sets meant for 9 to 14-year-olds.