Massive astrophysical objects governed by subatomic equation

March 5, 2018, California Institute of Technology
An artist's impression of research presented in Batygin (2018), MNRAS 475, 4. Propagation of waves through an astrophysical disk can be understood using Schrödinger's equation -- a cornerstone of quantum mechanics. Credit: James Tuttle Keane, California Institute of Technology

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.

The work, done by Konstantin Batygin, a Caltech assistant professor of planetary science and Van Nuys Page Scholar, is described in a paper appearing in the March 5 issue of Monthly Notices of the Royal Astronomical Society.

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.

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.

Using this approximation to model disk evolution, however, had unexpected results.

"When we do this with all the material in a disk, we can get more and more meticulous, representing the disk as an ever-larger number of ever-thinner wires," Batygin says. "Eventually, you can approximate the number of wires in the disk to be infinite, which allows you to mathematically blur them together into a continuum. When I did this, astonishingly, the Schrödinger Equation emerged in my calculations."

The Schrödinger Equation is the foundation of : It describes the non-intuitive behavior of systems at atomic and subatomic scales. One of these non-intuitive behaviors is that subatomic particles actually behave more like waves than like discrete particles—a phenomenon called wave-particle duality. Batygin's work suggests that large-scale warps in astrophysical disks behave similarly to , 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.

The Schrödinger Equation is well studied, and finding that such a quintessential equation is able to describe the long-term evolution of astrophysical disks should be useful for scientists who model such large-scale phenomena. Additionally, adds Batygin, it is intriguing that two seemingly unrelated branches of physics—those that represent the largest and the smallest of scales in nature—can be governed by similar mathematics.

"This discovery is surprising because the Schrödinger Equation is an unlikely formula to arise when looking at distances on the order of light-years," says Batygin. "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 that is typically used only for very small systems also works in describing very large systems."

"Fundamentally, the Schrödinger Equation governs the evolution of wave-like disturbances." says Batygin. "In a sense, the waves that represent the warps and lopsidedness of astrophysical disks are not too different from the waves on a vibrating string, which are themselves not too different from the motion of a quantum particle in a box. In retrospect, it seems like an obvious connection, but it's exciting to begin to uncover the mathematical backbone behind this reciprocity."

Explore further: Curious tilt of the sun traced to undiscovered planet

More information: Konstantin Batygin, Schrödinger evolution of self-gravitating discs, Monthly Notices of the Royal Astronomical Society (2018). DOI: 10.1093/mnras/sty162

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3 / 5 (2) Mar 05, 2018
This is the type of connection between the quantum world and the cosmos that I have been trying to point out for some time. Many of the systems that we see being played out in huge, grandly slow time and immense space is actually the same sort of thing that happens on the sub-atomic scale on an instantaneous timeframe.
3 / 5 (2) Mar 05, 2018
I love the comparison of quantum mechanics and astrophysics! In simpler terms, since we cannot see small things at the micro-scale which move very fast and cannot be observed ( Heisenberg principle ), we try to predict their behavior by using a statistical inferences. Then we try to make sense of our universe with this understanding which we see almost uniformly but frozen/displaced in time. I think these two will always have issues from a physics perspective and coming up with a unified theory will be a long ways ahead.

Just imagine trying to predict a planets location by hitting it with a large object such as a moon from across the universe and trying to use that information to predict an electrons behavior?
5 / 5 (3) Mar 05, 2018
I wouldn't say it's that surprising.. the model involves replacing planets (point-like objects) with a continuum. By doing so, one is basically delocalising the planets, allowing them to interact like waves. Which is exactly the kind of system one would expect to find quantum effects in.
5 / 5 (1) Mar 05, 2018
I wonder how many of the people commenting could even write down Schrodingers Equation or have ever solved it for a hydrogen atom?
Whydening Gyre
not rated yet Mar 05, 2018
Just imagine trying to predict a planets location by hitting it with a large object such as a moon from across the universe and trying to use that information to predict an electrons behavior?

Interestingly enuff - I find that analogy plausible...
not rated yet Mar 05, 2018
In a Chemistry class (a long time ago) we once had a visiting prof. who said that whenever he got stuck on a problem he would take long walks in public gardens and woods. He said that sometimes, though not always, he found that Nature had already solved the problem albeit in a different circumstance.
I am not suggesting the this as being the same as in the article but it isn't surprising that the macro might of insights to the micro. Didn't something similar happen with the Gamma/Beta functions that ushered in Super String theory?
5 / 5 (1) Mar 06, 2018
I wonder how many of the people commenting could even write down Schrodingers Equation or have ever solved it for a hydrogen atom?

Tried many times to solve it and failed.

From observations the overwhelming preponderance have no comprehension of a DE.

Some time ago I heard this postulated with regards to the orbits of stars and black holes around a supermassive blackhole.

If one visualizes elliptical orbits and considers the velocities relative to distance from the supermassive blackhole it would seem reasonable to see the distribution look like a hydrogen electron.
not rated yet Mar 07, 2018
How about the correspondence between Schrodingers and the wave equation used in hydrodynamics, and with the Mathieu equation? The distinction is still in the complex solutions, which have special meaning in a quantum context which doesn't imply in a macroscopic setting.
5 / 5 (1) Mar 13, 2018
Space/time must interact with mass/energy in the form of a wave. The Schrodinger equation describes this phenomenon, which is the "secret" of wave-particle duality.

In the double-slit experiment, space/time itself creates the complex interference pattern that is the hallmark of the experiment. Individually released photons/ electrons/ molecules are guided by constructive interference onto the wave crests, much like a duck is naturally drawn up onto wave crests of water. When one attempts to measure what is passing through one of the slits, the cohesive nature of the wave of space/time passing through that slit is disrupted, and the complex interference pattern disappears.

Following that logic, waves of space/time wave must also interact with mass/energy at the largest of cosmological scales, such as in this Caltech research-- and even larger scales. This is an indication that the range of space/time wavelengths in the universe may be infinite.
not rated yet Mar 27, 2018
Consider that IF (BIG If) galaxies represent Electrons, on a Mega-Cosmic scale, then as we see them we have a UMHB at the center, and energy/mass swirling around it. It is able to gain energy, as clouds of gas or globular clusters, and when the central black hole has gained enough mass in it's torus (think total energy in electron orbital) it spits out a pair of 'Jets' in opposite directions, just like expelling photons from an electron in changing energetic levels within it's 'Orbital'.

But at one spin per billion years, we see our own 'Electron-Galaxy' as a semi-frozen entity, where energy takes the form of matter so as to be further condensed, and the deepest density is at the BH levels.

How many seconds away from the Big Bang is the Greater Cosmos, since IT's timescale is so different, it should be super close to The BB. Are we part of the Quark-Gluon Liquid Plasma at the Microsecond level, with BH's tossing photon pairs that get stopped since Universe has not re-ionized?

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