In common usage, the word “chaos” means disorder, but is this the same for physics? Actually not. The concept of chaos in physics means “unpredictable” and is used for physical systems whose state changes over time.
A physical system can simply be thought of as a slice of the universe that we prefer to think of as somehow isolated from the surrounding environment. Sometimes we accept the total impact of the environment surrounding the system, but more often we choose to accept that the system is isolated. So is true insulation possible? The answer is no, true insulation is artificial.
For example, a crystal is traditionally defined as a solid having an infinitely periodically ordered structure in three spatial dimensions. Even if we admit that such a “perfectly ordered” system can (actually cannot) exist, such a system will actually have finite size.
In this way, it is easy to realize that such perfect structures are indeed very imaginary: crystals as found in nature are not only of finite size, but also contain many imperfections and are many times far from perfect.
Luckily, perfection is a subjective concept, and in physics a crystal is defined by a set of rules, represented in the biçim of equations that gömü repeatable symmetry operations on a set of points representing atomic centers. They describe an infinite, three-dimensional, periodic structure.
These rules are arbitrarily described as “perfect” because they describe patterns that can repeat infinitely and themselves. In this way, any real structure remains quite flawed by comparison.
How can we predict discontinuities and irregularities in a real structure if our model does not allow for flaws? We cannot predict. Thus, the system we describe is labeled as “chaotic” because they cannot be predicted by the “perfect” rules.
Thus, we can conclude that the chaos sorun özgü nothing to do with reality, but rather to human interpretation.
Such “imperfections” can lead to another interesting phenomenon: the fractal geometry of nature, which is also the title of the book by a famous mathematician who studied these ubiquitous structures: Benoit Mandelbrot.
What is a fractal? Fractals are technically geometric structures with fractional dimensions, for example 2,3. To understand this, it would be a good idea to give an example: Suppose you are told to follow a truth. We know from elementary school that a line consists of infinite points in one dimension, and thus a line itself becomes infinite.
Can you draw a really straight line? No, but you can probably draw a segment. A segment is an infinite series of points bounded by two extreme points. If for a line you need to keep track of an entire dimension, for a line segment you need even less than that.
In other words, you need a size between 0 and 1 to follow the segment. Thus, a segment creates a fairly simple but still fractal geometry. Can you predict all possible line segments in a single dimension using the equation of the line (y = a * x + b)? Yes, but such an equation creates an infinite array of values for the coordinates of the endpoints of the segment, which cannot be counted, calculated, and naturally edited.
So we can safely say that nature appears to be fractal, but is it really so? It can be argued that the answer to this question özgü more to do with philosophy than physics and its accuracy. What if fractals are a nascent feature of our innate inability to grasp infinity?
Source: https://bilimfili.com/doga-gercekten-kaotik-ve-fraktal-midir/
