The Subjectivity of Objects

Objects are everywhere. Houses, trees, windows, computers, people. Our language revolves around objects. We conceptualize the world in terms of objects. And today, I’m going to go full-on philosopher, and ask, “What are objects?”

Platonic Forms

In Ancient Greece, Plato described objects in terms of the theory of Forms. It was said that, for every type of object—house, door, cat, human—there is a perfect version of it, its Form. The Forms were said to exist non-physically and timelessly. Thus, reality was thought to be made of objects attempting to mimic their corresponding perfect Forms.

The theory of Forms may be useful in some contexts, but it doesn’t do well at describing physical reality. In the relatively static ancient world, it made sense, but in modern times with historically rapid technological and scientific progress, not as much. Has there always been a Form of a spaceship? A cell phone? The internet? What about the way some languages have words for objects that others don’t? It seems much more likely that Forms only exist as concepts within our minds, not in external objective reality.

Reductionism and Holism

In the era of science, another theory has arisen: reductionism. We observed that things are made out of parts, and those parts are made out of smaller parts, and the chain continues quite awhile. Finding the fundamental building blocks of the universe became a goal of modern physics, and some came to the belief that these building blocks are the true reality, and everything emergent from them is just our perception, less real or not real at all. This view is called reductionism.

Counter to reductionism, there is holism, the view that any system that functions as a whole and has properties that are different from the properties of its parts is a real object. Some stronger versions of holism even claim that certain higher-level emergent objects are more real than the parts they are made of.

Reductionism and holism are both perspectives and metaphysical theories. As perspectives, whether they are valid or not depends on the context. Today, we are examining them as metaphysical theories.

Associative Equivalence

Which is true, reductionism or holism? Are higher-level objects real, or are only the smallest, most reducible parts they are made from? To explore this question, let’s take a detour into math. Consider the following expressions:

3

1 + 2

2 + 1

(1 + 1) + 1

1 + (1 + 1)

1/2 + 2 + 1/2

What is the difference in the ideas each of these expressions represent? The answer: nothing! They all represent the number three, divided into arbitrary pieces.

Let’s take this analogy to physical reality. If we cut a sandwich into four pieces, does it become four sandwiches? If we put four full-sized sandwiches together at the corners, do we get one big sandwich? The answer is not a question of metaphysics, it is a question of semantics. It only depends on how we decide to define the words.

Just like how the number of numbers we divide a math expression into does not change what it represents, neither does reductionism describe a different reality than holism. Holism is merely putting the parentheses in different places (and, as we will see in next week’s quantum physics discussion, reductionism ends up doing that too). As metaphysical theories, neither reductionism nor holism measure up. They are both equally valid descriptions of the same reality!

Thus, we come to a profound realization: the universe is not inherently made out of objects; objects are human constructions. The universe is one thing, and it is infinitely many things. There is no difference. It’s all up to how we look at it.


For me, to see a door as a door, and as wood, and as wood cells, and as organic molecules, and as atoms, and as subatomic particles, and as interacting quantum fields, and to know that all of these are equally true, and none is more or less true than any other, is awe-inspiringly profound. To see myself as one person, and as two halves of a brain, and as a trillion cells, and as a part of the universe where the boundary between me and everything else is just a mental construction; that is nothing short of spiritual.


A Scientist’s Fiction is featured on Feedspot’s list of top 50 science fiction blogs! If you have some free time, and are interested in science and science fiction, why not check out some of the other creators there?

Your Brain is a Virtual Reality Machine

What is the difference between reality and virtual reality? At first, the answer seems obvious: reality is real and virtual reality is made up. It’s right there in the definitions of the words. But when we get down to the nuances of the meanings of these terms, we will find out that there may not be nearly as much of a difference as we first think.

Teasing Apart Reality and Perception

Being human, we have an instinctive intuition about what reality is. We look around, and we see it. We hear it, touch it, smell it, orient ourselves within it. Our senses tell us what reality around us is like, and in our consciousness, we perceive it. This instinct is called naive realism.

To make naive realism concrete, we look at an ancient theory of vision: eye beams. Back before the days of modern science, people believed we saw things by emitting invisible beams from our eyes. Anything these beams touched, we perceived in our vision. Perception was thought to take place out at the location of the things we perceive, and thus, our perceptions showed us reality.

Modern science has shown us that, to the contrary, perception happens in the brain. Our eyes do not emit beams. Instead, light bounces off the objects and brings information about their colors and textures into our eyes. Our eyes receive that information and translate it into electrical signals, which travel up our optic nerves into our brains, where our brains take the information and construct a representation that makes sense to us. The same is true for the rest of our senses.

Thus, what we think of as reality is not actually reality; it is a representation of reality created in our brains out of the information brought to them by our senses. When you see an apple, you see something red, round, and delicious over there. But “redness,” “roundness,” “deliciousness,” and “over there-ness” are just concepts created in your mind; they are not real qualities! Sure, there is something out there corresponding with each of these qualities, but it is different from the qulia that represent it. This theory of perception and reality is called representational realism.

Brains, Reality, and Virtual Reality

What is virtual reality? Those of us who have tried it have the experience of putting on a headset with screens in the eyepieces so close to our eyes we can’t tell they are there. These screens produce images that give the illusion that we are in a different place. The things we see in virtual reality are not material objects, they are illusions fed to us by a computer.

There’s an old thought experiment that asks, how do you know you aren’t a brain in a vat of nutrients, and that everything you perceive isn’t just being fed to you through your sensory nerves? Well, according to science, you are! The vat is your skull. Your brain is being fed electrical signals through your sensory nerves, which are translations of information received by your sensory organs.

Reality, like virtual reality, is made of information. The ultimate information in reality is a set of relationships between mathematical constructs, which we think of as matter and energy. The ultimate information in virtual reality is a set of relationships between mathematical constructs, which we call electrical signals in the computer. The concept and image of an apple in your brain is not like the electrical signals in the computer. But neither is it like the information making up the material apple. It is an equally false, and equally true, representation of both.

Thus, the only difference between reality and virtual reality is the type of information that exists “out there.” In terms of what we naively think of as reality, the images and sounds and colors and spaces and all that stuff, there is no difference! This “reality” created in our brains is a virtual reality, generated to help us process the information coming from our senses so that we can survive and thrive. There is one major difference between a material apple and a virtual apple: you can eat a material apple. But as to the question of which is more real, they are both mental constructs made from real information out there.

Broadening our Perspectives with Game Theory

Toolbelt of Knowledge: Theories
Darwinian Evolution
Game Theory

It’s been awhile since we’ve added to the Toolbelt of Knowledge, perhaps because there is so much we can explore in the space of ideas with what we’ve already covered. Today, I’ve decided to add to the longtime-lonely Theories category with another theory that can show us a new perspective on behavior, actions, and ethics: Game Theory.

What is Game Theory?

By its name, we might think Game Theory is a theory of games. It’s not, though. Most commonly, Game Theory is described as a theory of goals, outcomes, and strategies, though it can also be thought of as a theory of acting in accordance with our values. Game Theory is a theory of choices and consequences, actions and effects. The reason it is called “Game Theory” instead of “Strategy Theory” or “Choice Theory” is that games are structured with rules and goals for the players, and so it is easy to apply Game Theory to games. In this blog post, any time we mention “games,” we mean game theoretic systems, unless it is obvious by the context that we are talking about games in the fun-and-games sense.

There are three elements to a game theoretic system: Agents, the people, animals, AI programs, etc. who make decisions; the choices available to them; and the predicted outcomes of each combination of choices. The outcomes are usually written as a list of numbers, such as (3, 10, -1, …). Each number represents how satisfied each person is with the results.

You might see a problem here: in a game, this can represent the number of points each player ends up with, but how does it apply to the rest of life, where outcomes are not so easily quantified?

The answer, in my view, is that Game Theory should not be considered a theory of winning, but a theory of actions and consequences. Instead of numbers, we might put emojis representing how each person feels about the results. Or, we might directly represent the outcomes, rather than trying to quantify them. This can make it more difficult to compare the outcomes, but there are still times when we can comfortably say A is better than B, such as if A includes intense happiness and B includes despair.

Let’s look at some of the concepts of Game Theory, and some of the systems we can apply it to.

Positive-Sum, Negative-Sum, and Zero-Sum

There are three possible ways the total amount of “points” at the end can compare to the total amount at the beginning. If there is more at the end, it is a positive-sum resource; if there is less at the end, it is a negative-sum resource; and if the amount at the end is the same as the beginning, it is a zero-sum resource.

A note on terminology: you have probably heard the terms “positive- etc. sum game” instead of “positive- etc. sum resource.” A _____-sum game is more tied to the way the agents look at the game. For instance, if we say someone is “playing a zero-sum game,” it means they are trying to gain more by taking from others, rather than trying to increase the pot for all.

To illustrate each of these resource types, let’s look at the economy of a hypothetical island nation. This nation is self-reliant, it doesn’t trade or interact with anyone else.

The people of this island want to make it thrive. So they work the farms, build houses, mine for minerals, chop down and plant trees, educate their children, and all the other things a society needs in order to thrive. At the end of the year, they have more seeds, more knowledgeable people, more metal and wood and other resources than when they started with, and they are ready to start the next year and continue to reap increasing returns. This is a positive-sum game.

The land on the island is a zero-sum resource. There is a fixed amount, so if every acre is owned by someone, the only way for a person to acquire more is to get it from someone else.

And finally, the island’s coal supply from the coal mine is a negative-sum resource. The best use for coal is to burn it for electricity, but the more the nation uses, the less there is left to use. In order to continue to thrive in the long term, they must get off the negative sum game of coal power and find a positive sum game with renewable energy sources.

Short, Long, and Infinite Games

There are essentially three ways to strategize about a game-theoretic scenario. Short games are where we try to score as many points (metaphorically or literally) as possible as quickly as possible. A 100-meter dash is a short game; the goal is to get to the finish line before as many of your competitors as possible.

In a long game, the idea is to bide your time, waiting for the right moment to make the pivotal move. In a long game, we make short-term sacrifices for long-term payoffs. Chess is the archetypal example of a long game, as the ultimate goal is to trap the king, and it is common practice to sacrifice one’s own pieces in order to trap the other player in a snare.

An individual person’s life is a long game. The ideal life, according to present-day America and some other places, is to work hard at education, take out some loans for college, get a job, take out some loans for a car and a house, and slowly work off our debts until we break net positive and start accumulating wealth later in life.

An infinite game, on the other hand, is one that doesn’t end. The goal of an infinite game is to stay in the game as long as possible. Those who score points in infinite games are not people, as people have finite lifespans, but longer-lived things like countries, religions, and social causes.

Wars may end. Civil rights may be won. Oppressive regimes may be toppled. But their ripple effects continue, and in order to understand the way things are in the present and move toward a better future, we must study the past. Though the threads of history change, none of them end. History is a collection of infinite games.

Dominant Strategies

Sometimes, a single action can lead to positive results for all possible outcomes. These are called dominant strategies. Let’s look at a few examples.

Suppose we have a scenario where there is one choice: to light a candle or not to light it, and one risk: the candle might fall over. There are four possible scenarios.

1. We do not light the candle, and it does not fall over.
2. We do not light the candle, and it falls over.
3. We light the candle, and it does not fall over.
4. We light the candle, and it falls over.

If the fourth outcome happens, the house catches on fire, but in the other three outcomes it does not. We notice that if we do not light the candle, there is no outcome that results in a house fire. So if our goal is to not have a house fire, the dominant strategy is to not light the candle.

Another example can be found in cooking. If we are cooking a pan full of food, such as stir fried vegetables, we want to cook every piece equally on all sides. The surefire way to do this is to flip each piece individually. But if we do that, it takes too long, and by the time we’re done with the last piece, the first one is burnt. A better way to get it all cooked evenly is to stir the whole pan, making all of the pieces tumble around. Instead of having to plan each time exactly how to deal with each piece of food, stirring the pot or pan works every time. It is a dominant strategy.

Of course, in real-life situations it is often hard to find dominant strategies, since there are usually a very high number of factors and choices. Still, we can use this concept to look for strategies that have high probabilities of leading to good outcomes for a wide variety of ways a scenario might go.

Instrumental Goals and Ultimate Goals

There are two types of goals we might have in game-theoretic scenarios. An ultimate goal is what we are after, the outcome that would give us the most satisfaction from the game. Along the way, we pick up instrumental goals, things that help us achieve our ultimate goals.

Suppose my ultimate goal for today is to finish writing a blog post. In order to do that, I pick up a number of instrumental goals. I make coffee, because caffeine helps me think faster and more clearly. I eat food for similar reasons. I cross the street carefully, because it would be very difficult to finish my post if I am in the hospital or dead.

Of course, there are other reasons to do these things; other games being played. I’m playing the long game of life, in which writing is my major marketable skill, and finishing blog posts is an instrumental goal in service of the goal of making a living as a freelance writer, which is an instrumental goal in service of the goal of pursuing my passion as a science fiction author, which is . . . You get the picture. It’s not always clear what one’s ultimate goals are, or if their web of instrumental goals loops back on itself, or goes on forever.

The distinction between instrumental goals and ultimate goals comes from artificial intelligence research, not Game Theory. But they are useful in the same way as the rest of the ideas we’re looking at today, so I thought it made sense to add them to the Game Theory bundle.

Prisoner’s Dilemmas

Most of us are taught that being selfish is bad, and that we should share and be kind to others. Game Theory has several mathematical models supporting these ideas, the most well-known among them the prisoner’s dilemma. Abstractly speaking, a prisoner’s dilemma is any situation in which people acting in their best interests at the expense of others makes things worse off for everybody.

I won’t use the famous prison example today; you can find a million explanations of it with a quick google search. Instead, let’s look at another example: water rationing. Suppose there is a drought, and a town that usually has plenty of water for everyone starts to run low. The water supplier puts out a public notice, telling everyone that if they don’t limit their water consumption, the supplier will have to start temporarily shutting off the water for several hours at a time.

Each person is faced with the following conundrum:
1. Limit water and there is no shutdown.
2. Limit water and there is a shutdown.
3. Do not limit water, and there is no shutdown.
4. Do not limit water, and there is a shutdown.

In either case, whether or not there is a shutdown, an individual gets to use more water if they don’t limit their own consumption. Therefore, the dominant strategy is to ignore the public advice and use as much water as they want.

However, if too many people make this choice, the water will be rationed by the supplier, making things worse for everyone than if they had all limited their own water consumption. Hence the dilemma: the best possible outcome requires everyone to make the choice that is not the best for themselves.

The way to deal with prisoner’s dilemmas is through trust and self-sacrifice. We have to make the decision that is bad for ourselves, trusting the others to do the same. This is one of the reasons why it is important to treat others well and build relationships, even for people who only care about themselves. If everyone makes the hard choice to do the right thing, everyone ends up better off than if someone makes the selfish choice.


When considering things like political issues, our plans for our own lives, how we treat others, and stuff like that, it can be helpful to consider the questions from a game theoretic perspective. I may feel like this choice is right, but will its consequences actually line up with my values? Am I treating this situation like a zero-sum game, when it could be taken as a positive-sum game? Could a little sacrifice and trust on my part lead to a better outcome for everybody? These questions put things in a new perspective, and can lead to wiser choices and better outcomes.

The Six Critical Elements of Story Crafting

In my journey to become a published author, I have heard a lot of advice on story crafting. There’s so much it’s hard to keep track of it all, and the parts that spread the most readily are not necessarily the best. So this week I thought I would take a break from the science and philosophy and talk about the six major elements I focus on while writing a story, and which determine for me how good a story is. And also to plug some of the good books I’ve been reading lately. Let us begin.

Presence

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Every medium for stories has its strengths and weaknesses. A book or short story’s only tool is words, and the strength of words lies in their power over the readers imaginations. To achieve the element of presence, a writer must paint a picture with those words so vivid that the readers forget they are looking at paper and ink, and instead feel like they are there with the characters.

I felt present in stories a lot more when I was a kid, perhaps because my imagination was more active in filling in the gaps. As an adult, I haven’t felt this as much, although it may be more prevalent in the more literary genres. Of those I have read, H. P. Lovecraft was a master of presence in his horror stories crafting the entire experience of each around a mounting sense of dread. On a more adventurous note, Dune by Frank Herbert has quite vivid presence, if I recall.

Immersion

Subtly different from presence, the element of immersion is how believable the story is. Not necessarily how realistic it is, but how well the world and characters fit together and feel like something bigger than what is written on the page. Immersion breaks when the characters act uncharacteristically or too one-dimensionally, when laws of science or magic are carelessly broken, when the economic or social systems make no sense, and when there are plot holes.

The great fantasies, such as The Wheel of Time by Robert Jordan, A Song of Ice and Fire by George R. R. Martin, and The Stormlight Archive by Brandon Sanderson, excel at immersion. For near-future sci-fi, David Brin is a master of immersion in Earth and Existence.

Aesthetic stimulation

Concept art for the Avatar movies by Dylan Cole

Writers are not limited by trivialities like funding or the laws of physics. We can make statues a mile high, space ships the size of continents, the most gorgeous natural environments imaginable, exotic aliens, plants, and animals, and everything and anything we can imagine. I personally like messing with space and gravity. I am of the belief that even with our culture of today immersed in science fiction and fantasy, we have still barely scratched the surface of the aesthetic potential of our imagination. I’m including emotional stimulation in this category.

Pioneers into literary aesthetics include Shad Brooks in Shadow of the Conqueror, as well as Brandon Sanderson in The Stormlight Archive, particularly book 3, Oathbringer. On the older side of things, Hyperion and The Fall of Hyperion by Dan Simmons had their moments of incredible aesthetics.

Intellectual stimulation

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I love to think, and stories are a great playground for thought. The element of intellectual stimulation includes themes, moral dilemmas, scientific and philosophical concepts, and new perspectives on things we’ve come to take for granted.

Intellectual stimulation is important, but as we all know, stories are not essays. If the description or dialog waxes on about a scientific or philosophical idea, it’s boring. Stories have the unique ability to explore ideas through setting and the actions of the characters, and keep readers engaged that way.

Science fiction is great for intellectual stimulation. First and foremost, Earth and Existence by David Brin each put a large number of the struggles of our present society and contemporary philosophy into accessible story-rich juiciness. Ursula K. Le Guin paints a fantastic social thought experiment in The Left Hand of Darkness. Iain M. Banks set his Culture series in a galactic utopia, exploring a lot of the questions we easily overlook in our present societies as our attention is occupied by other things. And along those lines, I’ll throw in a TV show too: Star Trek is all about exploring the spaces of mind, meaning, and humanity.

Structural Coherence

Novels are collections of scenes and beats, and these all have to go together in ways that make sense when viewed as a whole. There is a lot of craft that goes into the element of structural coherence, including pacing, the ordering of the scenes, and which scenes are included and which left out. At the end, a structurally coherent story has everything it needs, no more and no less.

Most successful novels are good at structural coherence, so it’s especially jarring to find one that isn’t. We might find extra scenes or conversations bogging down the flow and which should have been cut, or topics that did not receive as much attention as they needed. A set of stories that do structural coherence surprisingly well are the I Am Not a Serial Killer series by Dan Wells. These book feel like they wander, but when we get to the end, we see how every scene has been deliberately used to serve the plot and the character development.

Payoff

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Themes, character arcs, plot threads, major features of worldbuilding, and flavors of the story should all be explored in many dimensions, and come to a culmination at the climax. It is not only at the climax where this matters, but all of the foreshadowing and development along the way as well. The payoff may be the most critical of the elements, as it is what will determine the emotions the readers leave the story feeling, whether they are inspired to look at life differently, and how psyched they will be to read more of the author’s stories.

The Wheel of Time had some of the best payoff of any story I've read at the end of the series, though it lacked a little during the middle. Most of Brandon Sanderson’s books have great payoff, particularly regarding the development of the magic systems. Ender’s Game by Orson Scott Card is a masterpiece of payoff through and through. And Artemis by Andy Weir makes very good use of many dimensions of its setting in a moon colony.

These six elements are the breath of life for a good story. Pacing, characters, setting, prose, the reason all that stuff is important is to serve these elements. Stuff like the three-act structure, the hero’s journey, and tropes and archetypes are, I believe, tools of analysis of finished stories, not things that are necessary to worry too much about when constructing them. For me, a story is good if it feels present, immerses me in the world, stimulates aesthetically and intellectually, is structurally coherent, and pays off on all the things that make it unique. Any rules, models, and guidelines are, in my view, meant to support these things.

So What Actually Is Quantum Physics?

Quantum Physics:
Fields, Waves, and Particles
Multi-Particle Waves

You may have heard the saying, “No one understands quantum physics.” This is, quite frankly, a lie. When Richard Feynman said the quote, he did not mean no one understood the theory; it is mathematically robust, and makes the most precise predictions out of any theory in science. What Feynman meant is that no one understands its implications on the underlying metaphysical structure of reality, i.e. which interpretation of it is correct. If we are just talking about the physical theory, experts in the field understand quantum physics very well, and I believe you can too. That’s why I’ve started this series explaining quantum physics in a streamlined top-down approach.

What you get out of this series will be up to your expectations. If you go into this with a “can’t understand” mindset, you will not be able to understand it. Failure is a self-fulfilling prophecy. You can understand quantum physics. It may be difficult, and you may not get it on the first read-through, but with enough persistence and perhaps some help from other resources, you can get to the point where you can brag to your friends that you know quantum physics.

Unless you took quantum physics classes, what you know of quantum physics is probably wrong

There are two main things holding people back from understanding quantum physics. First, its reputation for being incomprehensible, which, as I just mentioned, is false. Second, most people’s exposure to quantum physics comes from either science fiction movies or spiritual gurus, both of which use “quantum” as a modern substitute for “magic.” Stories and mystics want to invoke alternative histories, portals to other realms of existence, psychic powers, time travel, and all kinds of uncommon phenomena.

Back in the day, people were more generally open to the existence of the supernatural, and we could get away with calling it magic. If a story had a magic mirror that took curious wanderers to a bizarre world, a reader might entertain the notion that such a mirror might exist somewhere in the reaches of the world untouched by modern society. Nowadays, a magic mirror would be seen as a children’s fancy, not something to be taken seriously in adult fiction. A quantum mirror, on the other hand, crosses the boundary back into the fringes of believability, and it feels like it may be invented someday, or perhaps already has been by some alien civilization out in the universe somewhere.

A timeline-hopping quantum mirror as seen in the Stargate SG-1 episode, “There But for the Grace of God.”

Background Knowledge: Fields and Waves

Before we get to quantum physics, we need to lay a foundation of supporting knowledge, so that the concepts of quantum physics will come more naturally. To start off, let’s look at the concept of a field. In everyday language, a field is a wide open area of land, usually covered by a certain kind of plant or combination of plants. A physical field is similar. It is anything that fills all of space and has some numerical value everywhere.

Temperature, for example, is a field. Pick any spot in the universe, and it has a temperature. Gravity is a field. Pick any spot in the universe, and the total gravity from all masses will have a single direction and strength. The same is true for the electric field. Any spot in the universe has a direction and strength of the electric field from all charged particles added together.

You might have been taught in physics classes that charged objects each create their own electric field, which interacts with other charged particles to cause static electric forces. Similarly, magnets create magnetic fields. However, it is more correct to say there is one electromagnetic field throughout all the universe, and charged particles and magnets create perturbations in this single field. Just like the rest of us, scientists tend to use the language that is most useful for the problem at hand, not necessarily what is most true.

Next, let’s talk about waves in the fields. For an easy example, think about tossing rocks into a lake. From where the rock lands, ripples spread out. The water does not move horizontally, just up and down. Also, aside form the initial splash, the surface doesn’t break.

Physical fields can have waves too. Just like the water’s surface, physical fields don’t “break.” When a point in a field is perturbed, it tugs on all the points around it, and is tugged back in return. This causes a ripple through the field as each point is tugged and tugs on the points after it in turn. Unlike the water’s surface, which is two-dimensional, physical fields fill all three dimensions of space.

What direction is the field pulled in? After all, the surface of a lake is pulled in the third dimension, upward and downward. Fields, on the other hand, are not pulled in any dimension. Rather, they are pulled in the level of their strength. Heat doesn’t have a direction, it has a temperature. A wave of heat is a front of increasing temperature. An electromagnetic wave, also known as light, is a wave of increasing and decreasing electric and magnetic field strength.

Now that we understand fields and waves, we are ready to get quantum.

Definition of Quantum: Limited Allowable Quantities

The word, “quantum,” seems mysterious. But it has a simple meaning: A quantity is quantized if it has a limited number of possible values. A quantum is one of those values. Okay, maybe that doesn’t sound so simple at first glance, but once we start seeing examples it will start to make sense.

One type of quantum is a number of pixels. There is no smaller piece of visual information your screen can produce than a pixel. It cannot display half a pixel, and it cannot display a pixel and a half; the number of pixels it can display is limited to the natural numbers (0, 1, 2, 3, …). Therefore, a natural number of pixels is a quantum of computer graphics display.

Pixels are also a nice example of degeneracy. Degeneracy is when there are multiple possible states for a given quantum level. Again, examples will make this clear. If there are 0 pixels, there is only one state: off. 0 pixels is non-degenerate. For 1 pixel, there is also one state: on. At the 2-pixel level, however, there are two states: one on top of the other, and beside one another. The 2-pixel level has a degeneracy of 2. The 3-pixel level has a degeneracy of 6, as is shown in the diagram below.

Particles: Excitations in Quantum Fields

Now that we have all the background knowledge we need, we can start to learn quantum physics. Let’s begin by putting aside all our notions of matter and particles, and imagine a vast region of empty space with only fields inside it. These fields can interact with one another, but only in certain amounts at once; in other words, the fields are quantized. They are quantum fields.

These fields, like the fields we discussed before, can have waves. But for each wavelength, there is a smallest possible excitation; if you try to put less energy into a quantum field than its smallest possible excitation, nothing will happen.

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In the electromagnetic field, the smallest possible excitation is called a photon. In the electron field, the smallest possible excitation is an electron. In the quark fields, the smallest possible excitations are quarks. What we are getting at here is that fundamental particles are the smallest possible chunks of wave in quantum fields. All forms of matter and energy in the universe are made up of these field excitations and their interactions with one another.

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Let’s look at this in more detail. Imagine a place where the electron field is zero. The field is there, there just aren’t any electrons. Now we put energy into a point on the field, perhaps by shining a high-energy photon through it. If the photon has enough energy, at least twice the amount of energy of an electron’s mass as given by E=mc², then there is a chance it will interact with the electron field, giving up its energy, and creating two particles, an electron and an anti-electron.* If the light pulse has less energy than that, it will not give any energy to the electron field, because an electron is the smallest possible excitation of the electron field.

If the photon has a lot more energy than necessary to create an electron/anti-electron pair, it will stimulate the second quantum level of the electron field, creating a muon/anti-muon pair. If its energy is anywhere in between, the excess is given to the electron and anti-electron as a burst of speed.

Particles or Waves? The Wave Function

Most of us picture particles as infinitesimally small dots that zip around bumping into things, and waves as ripples that spread out to unlimited size and affect everything they touch. When it comes to fundamental particles, however, both of these pictures are incorrect. Fundamental particles are something new; they move like waves, and interact like particles.

First, let’s talk about the wave part, using electrons as a case study. In empty space, an electron spreads out as a wave in the electron field. As the wave approaches something it can interact with, the probability it will interact correlates with the amplitude of the wave. Where the wave is highest and lowest, the electron has the highest probability of interacting, and where the wave crosses zero, the electron has no probability of interacting.

Now we don’t need any math for the concepts we discuss today, but we should at least mention the Schrödinger equation, because it is an icon of quantum physics. You don’t need to be able to solve the equation, or even understand it, but you should be able to recognize it when you see it.

The most important part of the Schrödinger equation is the wave function, ψ. The wave function is a mathematical representation of particle waves, their peaks and valleys, and how they move through space and time.

Every behavior of quantum physics, from the double slit experiment to the quantum eraser behave as expected when the correct values are fed into this equation. It also explains, when understood, why many values are quantized rather than continuous.

Particles or Waves? Exclusive Interactions

As I mentioned above, fundamental particles spread out like waves, but interact like particles. As a wave, it has a probability of interacting everywhere, correlated with its amplitude at that point. But when it interacts, it interacts fully at one location. At that moment, it becomes impossible for any other part of the wave to interact. This is called the collapse of the wave function. After the interaction, the particle once again spreads out as a wave from the point of interaction, ready for its next interaction.

This is where the interpretations come in. The reason people say “no one understands quantum physics,” is because no one knows what happens to the parts of the wave function that don’t interact. If they just disappear, it is called the Copenhagen interpretation. If the interaction causes a split in the universe, and every part of the wave function interacts in one of the branches, it is called the Many-Worlds interpretation. There are other interpretations too, but those are the main contenders.

Summary and Conclusion

Let’s recap what we’ve learned today. Space is filled with substance-like things called fields, including the electromagnetic field, the electron field, and others. Particles are quanta of excitation in these fields (smallest, second-smallest, third-smallest, and perhaps more). These particles behave like waves until they interact, whereby they interact all at once. This causes the wave to collapse and spread out again from the point of interaction.

That’s the basics of the basics in a nutshell. It’s not enough to understand most experiments and technology that use quantum physics—that will have to wait for part two—but it should be enough that when you hear the word “quantum,” you know it relates to subatomic wave-particles and discrete levels of smallest-possible things. It has absolutely nothing to do with love, telepathy, willpower, perception, or anything like that. That’s just misusing the word “quantum” as a substitute for magic.

Next time in the quantum physics series, we will talk about multi-particle waves, finishing up the foundational knowledge necessary to understand quantum physics-based experiments and technology, and taking a glimpse into how atoms work. I hope to see you then!

*Another name for an anti-electron is a positron. For reasons we may talk about in a future blog post, in order for a particle of matter to be created in a quantum field, a particle of antimatter must also be created.