Whether we are considering world trade, new technologies, or scientific research, everything seems to become more complicated over time. In the past, Polymaths has been familiar with a wide range of fields and has made important contributions to each one. But today it is much more difficult for a person to be superior in multiple domains. This is for greater specialization.
This is not a rumour that “everything was getting better before.” It’s just a plain observation. The world was simpler. And that also applies from a mathematical perspective. Physicist and philosopher Ludwig Boltzmann admitted this in 1872.
Boltzmann studied the behavior of gases and liquids, among other things. Just a few decades ago it was proposed that everything in the world is made up of small building blocks, especially atoms and molecules.
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If you want to explain the behavior of liquids and gases, you need to track all the particles. Boltzmann knew this was infeasible. Therefore, he developed an equation that explains on average the movement of particles. However, this led to mystical insights. Individual atoms and molecules seem to follow a completely different law from their assemblage. How about this?
The direction of time
Show me a short video of the ball collide several times and rolling along a magical, frictionless billiard table. (Imagine that there are no holes in the table for the purposes of this thought experiment.)
Now I ask you, “Did I play the video forward or backward?” It is impossible to actually answer my question.
Newton’s Law of Movement, explaining the effect of billiard ball resilience, is independent of the direction of time. They produce the same results both forward and backward. In the 19th century, experts assumed that the particles that make up a gas or liquid also moved like small balls, like the billiard balls mentioned above, as they would always slam against each other and slam against each other according to Newton’s law of movement.
Today we know that the truth is more complicated. Atoms and molecules follow quantum mechanics, which is much more complicated. But, interestingly, quantum mechanics is Also It is often assumed The unchanging time reversal. So, like our hypothetical billiard balls, at atomic and subatomic scales like gas molecules, it doesn’t make a difference whether you look at the process forward or backward.
However, on a macro level, things look quite different. When you zoom out this microscopic representation, the direction of time plays a critical role. Imagine pouring milk into coffee. Different substances mix over time to form a uniform liquid. You can’t reverse that process. You cannot remove milk from coffee.
This fundamental difference between the micro and macro worlds was Boltzmann’s main concern. How can invariant equations representing the movement of individual particles and invariant under time inversion cause irreversible behavior? Why can’t milk be separated from coffee if all collisions between individual particles can be theoretically reversed?
The phenomenon can be explained intuitively. Particles in a gas or liquid collide over and over again. This slows down faster particles and accelerates slower particles. If you wait long enough, at some point, equilibrium will arrive and all particles will travel at the same speed on average. There may be individual outliers, but on average, the particles are distributed evenly across space at roughly the same velocity.
What does “complex” mean?
Boltzmann was able to express this part of action in an equation now named after him. This so-called Boltzmann equation shows how the velocity and distribution of particles in space change depending on time and place. He also introduced “collision operators” that take into account the effects of elastic collisions on particles, depending on conditions such as density and temperature.
The Boltzmann equation is a differential equation. This means that it includes derivatives, among other things. Such equations are usually difficult to solve. Nevertheless, Boltzmann was able to use this equation to prove that our world is becoming increasingly complex.
To do this, he had to first define the meaning of the term “complex.” A homogenous mixture of milk and coffee does not seem particularly complicated at first. But from a mathematical and physical perspective, that is true. There are countless different ways in which microscopic particles in the mixture can move and operate, each of which can produce the same macroscopic results. This means that even if the temperature, density, volume and mixing ratio of a mixture are known exactly, it is not possible to accurately infer how the molecules are arranged or what the velocity of each is. Many different microscopic conditions lead to the same final result.
Boltzmann called this complexity “entropy.” The higher the entropy of the system, the There is more possibility for that microscope component It causes the same macroscopic phenomenon. When milk and coffee are separate, the complexity of the system and therefore the entropy is low. This is because the milk molecules are still separate from the coffee molecules. If the liquids are poured together, they gradually mix more and more. Therefore, the complexity and entropy of their systems steadily increase over time. As soon as equilibrium reaches its state of balance, the entropy remains constant.
Both Boltzmann explained this qualitatively and mathematically derived it in his equations. Therefore, he has undoubtedly proven that the complexity of the system increases on the path to equilibrium.
This principle applies to our entire universe. Overall, nothing in the universe is in equilibrium, and even the universe itself continues to expand. This means that entropy, and therefore complexity, constantly and relentlessly increases over time.
This article was originally published Spektrum der wissenschaft Reproduction with permission.
