An unpredictable universe: a deep dive into chaos theory

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It would be really nice to know the weather forecast not just a week in advance, but a month or even a year in the future. But predicting the weather presents a number of tricky issues that we can never fully resolve. The reason it’s not just the complexity – scientists regularly tackle complex problems with ease – it’s something much more fundamental. This is something that was discovered in the middle of the 20th century: the truth that we live in a chaotic universe which in many ways is completely unpredictable. But deep within this chaos lurk surprising patterns, patterns that, if we ever come to fully understand them, could lead to deeper revelations.

Understanding the chaos

One of the beautiful things about physics is that it is deterministic. If you know all the properties of a system (where “system” can mean anything from a simple particle in a box to weather conditions on Earth or even the evolution of the universe itself) and that you know the laws of physics, then you can perfectly predict the future. You know how the system will evolve from state to state as time goes on. It is determinism. This is what allows physicists to make predictions about how particles, weather, and the entire universe will evolve over time.

It turns out, however, that nature can be both deterministic and unpredictable. We got clues this way in the 1800s when the King of Sweden offered a prize to anyone who could solve the so-called three-body problem. This problem deals with the prediction of motion according to the laws of Isaac Newton. If two objects in the solar system interact only by gravity, Newton’s laws tell you exactly how those two objects will behave in the future. But if you add a third body and let it play the gravitational game, then there is no solution and you will not be able to predict the future of this system.

Related: After the Big Bang came a moment of sheer chaos, study reveals

French mathematician Henri Poincaré (arguably a super genius) won the prize without actually solving the problem. Instead of solving it, he wrote about the problem, describing all the reasons why it could not be fixed. One of the most important reasons he pointed out was that small differences at the start of the system would lead to big differences at the end.

This idea was largely abandoned and physicists continued on, assuming the universe to be deterministic. That is, they did so until the middle of the 20th century, when mathematician Edward Lorenz was studying a simple model of Earth’s weather on a first computer. When he stopped and restarted his simulation, he ended up with very different results, which shouldn’t be a problem. He was putting in the exact same entries, and he was solving the problem on a computer, and computers are really good at doing the exact same thing over and over again.

What he found was a surprising sensitivity to initial conditions. A small rounding error, no more than 1 part in a million, would lead to completely different behavior of the weather in its model.

What Lorenz essentially discovered was chaos.

Stumbling in the dark

It is the signature sign of a chaotic system, as identified for the first time by Poincaré. Normally, when you start a system with very small changes in the initial conditions, you only get very small changes in the output. But this is not the case with the weather. A very small change (for example, a butterfly flapping its wings in South America) can cause a huge time difference (like the formation of a new hurricane in the Atlantic).

Chaotic systems are everywhere and, in fact, dominate the universe. Glue a pendulum to the end of another pendulum, and you have a very simple but very chaotic system. The three-body problem intrigued by Poincaré is a chaotic system. The population of species over time is a chaotic system. Chaos is everywhere.

This sensitivity to initial conditions means that with chaotic systems, it is impossible to make firm predictions, because we can never know exactly, precisely, to the infinite point, the state of the system. And if you ever get away from it all, after enough time you will have no idea what the system is doing.

This is why it is impossible to predict the weather perfectly.

Related: Twisted physics: 7 mind-boggling discoveries

Secrets of Fractals

There are a number of surprising characteristics buried in this unpredictability and chaos. They mainly appear in what is called phase space, a map that describes the state of a system at different times. If you know the properties of a system at a specific “snapshot”, you can describe a point in phase space.

As a system evolves and changes its state and properties, you can take another snapshot and describe a new point in phase space, creating a collection of points over time. With enough such points, you can see how the system has performed over time.

Some systems exhibit a pattern called attractors. This means that no matter where you start the system, it eventually evolves into a particular state that it particularly likes. For example, no matter where you drop a bullet in a valley, it will end up at the bottom of the valley. This fund is the attractor of this system.

When Lorenz examined the phase space of his simple weather model, he found an attractor. But this attractor was unlike anything seen before. Its weather system had regular patterns, but the same condition was never repeated twice. There are never two points in the space of overlapping phases. Already.

Contradiction

There are a number of surprising characteristics buried in this unpredictability and chaos. They mainly appear in what is called phase space, a map that describes the state of a system at different times. If you know the properties of a system at a specific “snapshot”, you can describe a point in phase space.

As a system evolves and changes its state and properties, you can take another snapshot and describe a new point in phase space, creating a collection of points over time. With enough such points, you can see how the system has performed over time.

Some systems exhibit a pattern called attractors. This means that no matter where you start the system, it eventually evolves into a particular state that it particularly likes. For example, no matter where you drop a bullet in a valley, it will end up at the bottom of the valley. This fund is the attractor of this system.

When Lorenz examined the phase space of his simple weather model, he found an attractor. But this attractor was unlike anything seen before. Its weather system had regular patterns, but the same condition was never repeated twice. There are never two points in the space of overlapping phases. Already.

It seemed like an obvious contradiction. There was an attractor; that is, the system had a preferred set of states. But the same state has never been repeated. The only way to describe this structure is like a fractal.

If you look at the phase space of Lorenz’s simple weather system and zoom in on a small piece of it, you will see a tiny version of the same phase space. And if you take a smaller part of it and zoom in again, you’ll see a smaller version of the same attractor. And so on until infinity. Things that look the same as you take a closer look at them are fractals.

So the weather system has an attractor, but it’s strange. This is why they are literally called strange attractors. And they arise not only in weather conditions, but in all kinds of chaotic systems.

We do not fully understand the nature of strange attractors, their meaning, or how to use them to work with chaotic and unpredictable systems. This is a relatively new area of ​​math and science, and we’re still trying to figure it out. It is possible that these chaotic systems are, in some sense, deterministic and predictable. But that’s yet to be determined, so for now we’ll just have to make do with our weather forecast for the weekend.

Paul M. Sutter is an astrophysicist at Ohio State University, host of “Ask an astronaut and “Space radio, “and author of”Your place in the universe. “

Learn more by listening to the episode “Is the universe really predictable? “ on the “Ask a Spaceman” podcast, available on iTunes and on the web at http://www.askaspaceman.com.

Thanks to Carlos T., Akanksha B., @TSFoundtainworks and Joyce S. for the questions that led to this article! Ask your own question on Twitter using #AskASpaceman or by following Paul @PaulMattSutter and facebook.com/PaulMattSutter.



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