Atomic surfing: Riding the unpredictable wave of reality.
In multiple previous blog posts of mine I have mentioned stuff like “The behavior of atoms” and “unpredictable” and “The wave equation”, but what the heck exactly do I mean when I say them? Well, I feel inspired today to explain the whole topic of the behavior of atoms, including what exactly I mean when I say stuff like that. Just for disclaimer though, I recommend you abandon your connection and logic to reality, and just let your mind be free and wander, as the world of the quantum is incredibly whack.
Right, so, the humble atom. Despite its humbleness it is filled with a lot of mystery, and phenomena that defy our conventional understanding and logic. But what exactly do I mean when I say that? Well, how about this, two atoms can be seemingly “connected” to each other and share information, even though they are light years apart. Or what about this, an atom can “teleport” through walls? Makes you potentially go “What?” while reading this right? Well it gets weirder, let’s keep going.
So what exactly is the first thing I described? What I described was something called quantum entanglement, what is that? Quantum entanglement very basically, is the concept that describes, that two atoms or whatever other elementary particles that interacted with each other with equal and opposite force, must share identical characteristics like momentum, spin, angle, etc. even across vast distances, otherwise the law of conservation of momentum would be violated. Imagine this: you take two balls and roll them diagonally across a surface with equal speeds. However, their trajectories intersect, and they bounce off each other. If you sent them both with equal speed towards each other, then naturally they should bounce off each other and continue along their trajectory in pretty identical manners right? Try to imagine that scenario again but instead of that happening, one of the balls for example bounces off the other and starts going off at a 45 degree angle, however the other ball just comes to a dead stop and goes straight forwards, makes absolutely no sense. So we say that both of the balls, or in this case, elementary particles are “Entangled” with each other, if the word “Entangled” is a bit hard to understand, then how about “Indirectly connected”, indirectly because they are not literally connected with each other, but by measuring the state of one of the balls, you will know the state of the other ball, it HAS to be equal and opposite right, so their behaviors are connected with each other. This same exact behavior governs elementary particles, and I will explain why and how that is quite special. They are also not literally sharing information, but it appears like they are because if both of the balls remain undisturbed, and they simply carry on their merry way, but imagine that one of the balls decides to change direction for no reason, we know that the other ball has to have done that too, it appears like the two balls are sharing information via phone call or something where one of them goes like “Hey, I am going to change direction now, you do that too okay? On my mark, 3, 2, 1, go.” so to speak, but of course again that’s not exactly the case, it just appears like it.
And the second thing I described is called quantum tunneling. Which basically speaking, describes that elementary particles can travel through obstacles which are in front of them, given that they are thin enough, so they can overcome it. To put it into a bit of a blunt an unusual analogy, I don’t really know why my brain just came up with exactly that analogy, it just popped into my head, but imagine yourself running into a brick wall over and over again. Obviously you’re just going to keep bouncing off and the brick wall will remain where it’s at and untouched right? However, now after every time you run at the brick wall and bounce off of it, make it a bit thinner, and keep doing that until eventually, your energy in speed is enough to overcome that of the brick wall, so you end up running straight through it. In my analogy the brick wall gets destroyed, but of course that doesn’t happen in the quantum realm, still illustrates the point though. I will include a little picture down below which describes it very well and in a less….violent manner. Which on that note, that very thing is the exact reason why we cannot endlessly shrink transistors, which make up the processors in your computer, whether it be the central processor or the CPU, or the graphics processor or the GPU. And to apply more technological stuff, the previous paragraph where I described quantum entanglement, that exact thing is used in quantum computers. But how exactly do you take advantage of something which by its very nature is uncontrollable? It indeed is INCREDIBLY hard to do so, however the many different ways scientists have figured out how to do that is genuinely mind boggling but beyond the scope of this post, I might make a future one about it though.
An image describing how stuff behaves in quantum physics, vs our more familiar classical physics, in the quantum example the folium ball instead of rolling back up and over the hill how you’d expect it to, it just sort of noclips through the hill like it wasn’t even there.
But it gets even weirder still, what if I were to tell you that elementary particles also have wave-like properties? Which is also why the title of this post is what it is. Let me introduce you to a person who’s one of the few people who we can thank for essentially laying the groundwork for quantum physics as we know it today, Erwin Schrödinger . Namely, Schrödinger came up with something called “The wave equation”, also know as “Schrödinger’s equation”, and its purpose is to describe how atoms or other elementary particles behave when unobserved, as a wave that is spread out across space, with the “wave” itself consisting of nothing but the probability of the particle being at any point which is covered by that wave. You can imagine this along with the animation below, as being in the sea and picking a stone out from under the surface, that is your point-like particle which you can see, however, once you stop observing it, like close your eyes and then drop the stone back into the sea, after it falls in, open your eyes. What you see are nothing but waves left behind, and you can think of the area the waves reach as the probability of finding the stone you dropped in that area, and the further out those waves go the smaller that chance becomes reflected by the waves becoming weaker and weaker and eventually dissipating entirely. Enter superposition.
An animation of elementary particles behaving like a wave when unobserved, it also features an event where the particle is measured, which is when it collapses from its wave-like state into a point, the particle itself which we can see. It’s when that narrow and sharp yellow spike suddenly appears, after which the particle is unobserved once again and resumes its state as a wave. Along with the full wave equation used to describe it all.
The term “Superposition” describes the concept of an elementary particle being in multiple places all at once, and the wave function is a way of quantifying it without actually observing the particle itself, which is exactly why it’s such a magical equation. Imagine being able to accurately describe and predict the state of something which is inherently unpredictable, with your eyes closed, it sounds literally magical doesn’t it? To try to illustrate superposition in an easy manner, which is incredibly hard to do. Here is another very unusual analogy I came up with, but this time it might just be funny. So imagine your friend says that he will go into the toilet right, now it’s your task to try to accurately predict and describe what he is doing there, number 1 or number 2? And you have no other information to work with besides him telling you that he went into the toilet. You could always just open the door and look, but until you do that, according to the laws of quantum mechanics, he is doing both number 1 and number 2 all at the same time, insane and absolutely illogical right, well this is just how quantum mechanics is by nature, it is what it is. And then even without any usable information, you somehow come up with an equation like the Schrödinger equation which can somehow describe accurately the probability / chance of him doing either one or the other, without you having to look.
Thankfully…we have a way of describing it which is less cringe however it’s a bit more sad, and it’s from none other than Schrödinger himself! Enter the “Schrödinger’s cat” thought experiment. Basically, take a box and a cat, now take a radioactivity detector with a hammer, a vial of poisonous gas, and a radioactive atom. Now put all of them in the box, and close the lid. If the radioactive atom decays and releases radiation as a byproduct, the detector detects it and breaks the vial of poisonous gas which kills the cat, or the radioactive atom can also not decay, which results in the cat being alive. As long as you don’t open the box and check, according to the laws of quantum mechanics, the cat is both alive and dead at the same time! And to tie the wave function into this, imagine a slider that moves between 0 and 1 by itself in front of you, which is our wave equation. And you observe that slider to be moving seemingly randomly around between those 2 numbers. Now imagine the middle point, 0.5 being 50% chance of the cat being alive and dead once you open the box, so a coin flip, if the slider is below the middle point, the likelihood of the cat being dead is higher than it being alive if you were to open the box, and vice versa if it were above the middle point. Despite that whole entire system being entirely illogical, unpredictable and uncontrollable, in an insane twist of things, you can use the wave equation and that slider to possibly get a result that you want, which is of course the cat being alive if you’re not insane yourself. So you patiently wait for the slider to move sufficiently high enough towards number 1, and then you decide to open the box, so since the likelihood of the cat being alive were very high, the cat is of course alive (unless you got incredibly unlucky, because it’s still not a 100% chance, since it cannot be.).
Another very intuitive and clever way we can indirectly observe the wave-like properties of particles is the double slit experiment. Take a metal sheet and cut two narrow and vertical holes into it that are very close to each other, and put a wall behind that sheet. Now send say for example electrons through the left slit, you’d expect the electrons to simply go through the left slit and show up on the wall accordingly yeah? Well again, that’s not how particles behave when unobserved, they behave in a superposition of states, where they seemingly go through both the left and the right slit simultaneously. However, it’s easier to understand if we again imagine particles to be, and describe them as waves if they were in a superposition, because a wave can obviously travel through both of the slits at once. So what you get as a result of that is something called an interference pattern, which looks like this.
In this case, a red laser was fired at the configuration of slits, and then this is the result they got on the wall.
And what’s even more fascinating, is those bright spots are the probabilities of the electron, or in this case a photon of light, being in any one of those bright spots. The larger and brighter the spot is, the more likely it is that the electron / photon of light is to be found there. Here is a diagram which better describes the stuff taking place.
The wave source is your source of light or electrons, the middle part is of course your double slit setup, and then the right part is your wall along with the pattern it forms on said wall.
You can also conduct this experiment yourself in real life and see the results, if setting up the whole double slit system and getting a laser pointer is a bit too much effort, then you can simply take two small balls, go to a calm source of water like a pond, and then put the balls next to each other but with a little bit of a gap between them, and then start bouncing them up and down in the water gently with the same rhythm and force. What you get on the water is also identical to how particles in a wave-like (superposition) state would behave in the double slit experiment, and it looks very strange, here is also another piece of media that shows exactly that in action.
When the peaks of the waves collide, they do something that is called constructive interference, where they combine into bigger peaks, visible as the bright spots in the double slit experiment. Where the dark spots are, are where the waves do something that is called destructive interference, so the peak of one wave collides with the trough of another wave, which results in them cancelling each other out, so you get a dark spot, or in the case of this water, you get a point that looks calm and smooth, which is also illustrated in this clip via dark lines cast along those spots. Source: Veritasium
Quantum mechanics are also responsible for an even more insane theory called “Many-worlds”, in where basically, particles themselves do not have wave functions, but the entire universe itself is governed by one massive wave function, since we are quantum mechanical as well, as we are made of elementary particles. And when that wave function is collapsed via for example us observing a quantum mechanical system like the cat in a box or anything else, reality splits into two copies or “parallel universes”, one which contains the reality of you opening the box to find the cat dead, and one which contains the reality of you finding the cat alive. To be clear, that split reality version of you might be an exact version of you, but it is no longer “you”, as in it’s a different person who’s going to be living a different life. So thanks to that, there might well be realities where you are president or whatever else. And I have my own theory to build upon that one. To tie my previous blog post about chaos into this, you can think of that “splitting” of realities as the flap of the butterfly’s wings, that then eventually results in a compounding and way different version of reality where as mentioned, you are president or something. It starts off basically identical to you, but eventually over time it diverges and becomes different more and more.
Let’s also talk about something called “Quantum decoherence”, which is also a key part of the previous paragraph’s many-worlds topic. When a measurement of a quantum system is taken (its collapse), the system is said to go under a process called quantum decoherence, which means that it stops being a quantum mechanical system and transfers suddenly and irreversibly into a system of classical mechanics. In the many-worlds theory, quantum decoherence results in the mentioned splitting of reality into two different ones. It also describes the previously mentioned thought experiments, take for example the Schrödinger’s cat thought experiment. When you open the box to look, that whole system goes under quantum decoherence and then starts being described by predictable and deterministic classical systems, so the cat being either alive or dead, and you can SEE it. Quantum decoherence can also be seen in the above animation of the wave equation, when the tall and sharp yellow spike appears signifying that a measurement was taken and the system was observed, that quantum system of the electron or atom just chilling in a superposition (as a wave) decohered and became an observable system governed by classical and observable mechanics. So essentially, we have two sets of rules, one of them which governs how systems behave when we are not looking (the Schrödinger equation), and another which governs systems when we are looking (classical mechanics). Which on that note, the collapse (decoherence) of the wave function can be described as this equation: Probability(x) = I amplitude(x)I² , or more specifically, the probability of measuring any particular outcome(the symbol x), is given by the amplitude of the wave function (the symbol Ψ) associated with that outcome, squared. So in a scientific manner, the equation would be described as ∣Ψ(x)∣². The Greek letter psi (Ψ) is a symbol that represents the entire wave function of a quantum system, similar to how the symbol * or x is used to denote multiplication in regular mathematics.
Fun fact, Schrödinger himself hated this formulation and equation, and it actually took a second physicist, Max Born to propose how we should interpret the wave equation and apply it to quantum mechanical systems, and he introduced the “probability” part of the collapse of the function into the wave equation. Schrödinger’s displeasure at his wave equation is exactly why he invented his thought experiment of the cat in a box, he wanted to show that quantum mechanics as formulated is wrong, which unfortunately for him is not the case. However even the greatest of minds sometimes struggle to come to grips with the strange ways that reality works. Even I sometimes fall into that pit of “crisis” where I attempt to force logic, reason, and sense onto phenomena that are fundamentally devoid of these three aspects, and it’s just something you have to accept. As I described in my previous blog post about chaos and a couple other ones, if you give up reality’s connection to sense, logic, and determinism, only then it is possible for reality to ironically be this ordered, rich, and seemingly “deterministic”.
