Posted on 01/04/2022 12:20:44 PM PST by Red Badger
A physics problem that has plagued science since the days of Isaac Newton is closer to being solved, say a pair of Israeli researchers. The duo used "the drunkard's walk" to calculate the outcome of a cosmic dance between three massive objects, or the so-called three-body problem.
For physicists, predicting the motion of two massive objects, like a pair of stars, is a piece of cake. But when a third object enters the picture, the problem becomes unsolvable. That's because when two massive objects get close to each other, their gravitational attraction influences the paths they take in a way that can be described by a simple mathematical formula. But adding a third object isn't so simple: Suddenly, the interactions between the three objects become chaotic. Instead of following a predictable path defined by a mathematical formula, the behavior of the three objects becomes sensitive to what scientists call "initial conditions" — that is, whatever speed and position they were in previously. Any slight difference in those initial conditions changes their future behavior drastically, and because there's always some uncertainty in what we know about those conditions, their behavior is impossible to calculate far out into the future. In one scenario, two of the objects might orbit each other closely while the third is flung into a wide orbit; in another, the third object might be ejected from the other two, never to return, and so on.
CLOSE In a paper published in the journal Physical Review X, scientists used the frustrating unpredictability of the three-body problem to their advantage.
"[The three-body problem] depends very, very sensitively on initial conditions, so essentially it means that the outcome is basically random," said Yonadav Barry Ginat, a doctoral student at Technion-Israel Institute of Technology who co-authored the paper
(Excerpt) Read more at livescience.com ...
only works in 2D.
in 3D, prob. of ‘drunken walk’ approaches zed.
“two of the objects might orbit each other closely while the third is flung into a wide orbit”
I got flung once as described here. ...out of a mosh pit.
The third object generally lands on it’s ass and slides a short distance before it’s friends hand it it’s drink and tells it to get back in the pit which the third object is more than happy to oblige.
Here, hold my beer.
At this point they seem satisfied with probability rather than certainty. Seems inadequate, still.
Calculus is the mathematics of approximations. At some point the approximations are ‘close enough’.................
Euler?
Lagrange?
The Hillary Klintoon walk?
As a retired physicist, sure glad I retired in 1985...
That’s why designers, engineers and architects put tolerances on drawings/models.
And thus the phrase “Close enough for Government Work.” was born...................
I just came upon a drawing of Newton with the following verbiage overlaid:
“Think you’re bored? Sir Isaac Newton invented calculus during the plague. Do you have any idea of how bored you must be to invent calculus?”
Wish I had seen this years ago when I was teaching some grad math. ‘Twould have added some humor to “Calculus on Manifolds”.
My very first computer program was for a school assignment to encode numerical solutions the restricted three-body problem. Earth, Moon and spaceship, for example. You can get a good handle on that.
As for this project, I’m not sure that assigning probabilities to different outcomes is the same as “cracking” the problem. As usual, the headline writer promises much more than the researchers do themselves.
“That’s why designers, engineers and architects put tolerances on drawings/models.”
Those are manufacturing tolerances.
There are no tolerances in the above, only probabilities of a given outcome.
Heisenberg says that is impossible to know................
There should be a ministry!!
Translated: We cannot characterize the intial conditions properly, so we cannot solve the problem.
“Calculus is the mathematics of approximations. “
Differential Calculus is the mathematics of approximations.
Heisenberg didn’t know if his cat was alive or dead... LOL
But he knew where it was!...................
Picky-picky....................
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