Aight lads and lasses. Let’s get technical. I want to code more than anything right now, but a certain thought process has been coursing through my veins for the last twelve or so hours, and I need to get it down. If my language gets too technical, it’s your fault for not understanding me. Haha, take that. Nothing like purposefully trying to push my readers away. Here we go!
I’ve written several posts about this, most recently the post about love, but I think the part of physics that is topically most interesting at this moment is the process of analyzing the stability of different systems. I’ll lay out the reason why this is interesting.
One central law in physics is the second law of thermodynamics, which roughly states that the disorder in a global system increases over time (that statement is a shade of the mathematical glory that is a proper study of entropy, but my readers don’t got no time for equations). The simple (and painfully cliché) analogy that is given for this statement is to imagine a new deck of cards. The cards are nicely in order. But the second you start shuffling, the cards quickly become scrambled and disorderly. If you hunker down and examine the probabilities in question, a randomly shuffled deck of cards is far more likely to be “disorderly” than “orderly.”
By applying similarly simple probabilistic theory to physical systems, you basically get the basics of statistical mechanics, which concerns itself with average quantities of systems with a large number of constituents (usually at or above 1023. Gotta love my boi Avogadro). To make a long story painfully short, you can essentially think of a thermodynamic system as a deck of cards that’s constantly “reshuffling” itself, and like a deck of cards, “disorderly” configurations of the system are generally significantly more probable than “orderly” configurations.
Great. So why should you care, inquisitive reader? Well, look at human beings. Human beings are incredibly well-ordered systems of incomprehensible complexity. To perhaps make the point clearer, if you took all the subatomic particles that make up your body and threw them into a box at random, the probability that the particles would end up in the configuration of a human being is disgustingly small. Outrageously small. If you think along this line of reasoning, the probability of humanity existing in our universe is so unthinkably small, it’s a miracle we even happened.
Unless.
I simply refuse to believe that what I’m about to discuss hasn’t been rigorously treated by smarter minds than my own, but I’m going proceed as though these are original thoughts because I enjoy feeling like I’m scientifically innovative.
The fundamental question of this post is the following: Are highly ordered and complex systems probable given the configuration of our universe?
Given what I’ve already stated, your gut reaction to this question is probably: “No, Danny! Stop being dumb.” Hey, reader, watch your mouth. No one’s forcing you to read this, so go shuck a duck.
In order to continue, we ought to have a civil conversation regarding stability, because it’s ever so important. In fact, I think it’s the key.
In the previous example with the deck of cards, let’s change things up a little bit. Imagine that every single time the deck is in new deck order, small magnets engage that keep the deck from being reshuffled. So even though new deck order is statistically unlikely, if you continue shuffling the deck for eternity, the average configuration of the deck of cards is new deck order because once it reaches that state, it can’t be reshuffled.
To get a bit more rigorous, I’ll define a stable configuration of a system to be a configuration that is resistant to change (not super rigorous definition, but it’ll do). As we’ve seen with the “sticky” deck of cards, even is an “orderly” configuration of a system is statistically improbable in terms of possible random configurations of the system, over a large swath of time, the “orderly” configuration is actually probabilistically likely because it’s most stable.
The question now is, what would make any one system any more stable than another? Well, take a helium atom, for example. What makes a helium atom any more stable than a hydrogen atom? Those of you chemistry nerds are probably kerfuffling about orbitals and valence electrons. Hey, chemistry nerds? Y’all can also go shuck some ducks, then go take a proper class on Quantum Mechanics. Or, even better, just read R. Shankar’s The Principles of Quantum Mechanics. What a truly divine textbook. A mathematical masterpiece at the very least. Anyway, I’m not going to even try to explain humanity’s best understanding of the physics of stable orbits, but I can give you a much more abstract answer.
The reason why the helium is a stable configuration of protons, neutrons, and electrons is because these particular particles exhibit a rich set of behaviors when near one another. You probably remember that protons and electrons have opposite electric charges and therefore attract. Our understanding of quantum electrodynamics actually gives a more compelling explanation than that of simple electric fields. In QED, electromagnetic effects are described by an exchange of photons between different particles. Fun fact, QED was the first theory with full agreement between quantum mechanics and special relativity (got that straight from the wiki).
I went down rabbit hole. Regardless of how fascinating QED is, the important thing to keep in mind is that subatomic particles exhibit a rich set of behaviors when interacting with one another. The reason why helium is stable is because of the underlying rules governing the interactions between protons, neutrons, and electrons. If these particles didn’t interact with one another (much like cards in a deck) then there would be no notion of stability, and in those systems, disorder would be statistically likely, even throughout a broad swath of time.
So then, if you want any notion of stability in a system, you want there to exist a rich set of behaviors between the underlying constituents of the system.
Ok, I’m going to go in a slightly different direction now. I want to talk about what constitutes an “orderly” system. I tend to think of a human being as a highly ordered system. Amazon (as in the company) is a highly ordered system. Quartz is a highly ordered crystalline structure.
I think the big thing here is that an ordered system has a fixed set of stable characteristics. Two examples of this: 1) Human beings have arms. On average, a human being will keep both arms all throughout their life. I can reasonably predict that tomorrow morning I will have both arms attached to my body. 2) If someone punches me, I’ll get angry. For the average human being, if you punch them, they’ll probably get angry. I can reasonably predict that if I were punched tomorrow morning, I would get angry.
Ok, so to get a bit more rigorous, (also do know that I’m basically making this up on the fly), the degree to which a system is orderly is proportional to the number and stability of each of the systems characteristics. Cool. One thing to note here is that under this definition, in order for a system to be orderly, it must also necessarily be stable.
Actually, wait. Now that I’m thinking about it more, I think stability and orderliness might be two sides of the same coin. Remember my definition of stability? A system that is resistant to change. Cool, but how do you quantify whether a system is resistant to change? Well, a good first step is to describe the characteristics of a system, and if those characteristics remain the same as time progresses, then your system is stable. But what I just described was my definition of orderliness. Ha! Geisz’s first law: Stability = Order.
Ok, let’s move along. Remember, the big question of this post is whether highly ordered and complex systems (like humans) are probable given the configuration of our universe. What we should talk about next is how stable systems are able to build themselves into bigger stable systems.
What I’m going to talk about next is probably going to be markedly similar to my post about love.
Remember, the recipe for stability is a rich set of behaviors between the constituents of the system. So, an electron and a proton are able to organize themselves into the “stable” and “orderly” configuration of hydrogen because of the underlying interaction between two particles of opposite electric charge.
Hydrogen is all well and good, but I want human beings, I don’t just want hydrogen. How do we get from hydrogen to human beings? In other words, how does one stable system bring forth another stable system.
Remember the recipe. For stability to occur, we need a rich set of behaviors between the constituents of the system. So, if we want hydrogen (and perhaps some other atoms) to build themselves into systems of increased complexity, we need them to be able to interact with one another. Because of the whole business of stable orbitals, certain atoms do interact with one another, and therefore are able to form stable configurations, which we call molecules. On the other hand, helium, while incredibly stable, isn’t able to “help” other atoms create systems of greater complexity (molecules) because it doesn’t interact with any such atoms.
As an interesting side note, even though helium is pretty tame from the perspective of chemistry, it does still interact with other particles in an entirely different context. Because helium is light and stable, in the presence of a dense, gravitationally dominant object, a mixture of helium and other heavier gases will push helium to the top due to helium’s low density. This is a perfect example of a stable characteristic of a system, which means that an atmosphere could be considered a stable and orderly system. So again, any time the constituents of a system exhibit a rich set of stable interactions, there is potential for the system to be stable and orderly.
I think you probably get the idea. I’m at seven pages, so I should probably wrap this sucker up, but I think there should be a big takeaway here. If you want to propagate complexity and order, you want stable systems that exhibit stable behaviors. That’s all for now.