So similar, so different: BioShock Infinite and quantum physics

I could write many more quotes from real and fictional people, revealing and illustrating the features of quantum physics and the BioShock setting, but I think that they won’t say anything new to those who understand it. And they won’t say anything to those who don’t understand it (and that’s the majority of them).

So, to begin with, I will try to explain as clearly as possible what the essence of quantum physics is.

Quantum physics at your fingertips

So, what do we even know about physics from school?? First of all, that physics is the science of what and how happens in our world. She studies the laws by which objects interact.

Let’s say a couple of objects are flying and collide. What happens next? The laws of conservation (of momentum, energy, mass, etc.) say that they cannot suddenly fly in the opposite direction (since the momentum cannot simply change). Similarly, colliding objects cannot fly apart at higher speeds or stick together. More precisely, they can, but only if some kind of reaction occurs inside them, otherwise there is nowhere for the kinetic energy to come from and nowhere to go. And even if the objects react and disintegrate, the total mass and energy of all the resulting particles will not change.

However, conservation laws, although they place limits on what can happen, do not tell us exactly what will happen. In order to know this, we need to know about the internal structure of the objects themselves. For macroscopic (that is, the size we are used to) objects consisting of more or less homogeneous matter, the equations of Continuum Mechanics are used, which tell us exactly how the object is deformed during a collision, whether two objects can stick together, and so on. But this is not suitable for elementary particles. After all, according to the MSS, two objects cannot, for example, pass through each other, but in reality electrons, protons and even atomic nuclei often do this.

Therefore, the behavior of elementary particles is considered by quantum field theory. And this behavior, according to the equations (and experiments confirming them) has more in common with electromagnetic waves than with solids (the so-called wave-particle duality). That is, from the point of view of quantum physics, each particle is a disturbance of electromagnetic and other fields. Essentially, it is a wave of complex configuration that arises in some region of space and spreads. In the case when two waves find themselves in the same area of ​​space-time, they “interfer,” that is, they are transformed into a new wave of an even more complex configuration.

However, no matter how complex these same waves are, they must always satisfy a number of conditions. Firstly, the mentioned conservation laws. And secondly, common sense. Agree, it would be strange if the equation of wave motion depended on the coordinate system, the name of the particle, or some other conventions we chose.

Without going into details, I will say that the search for equations that would be applicable to any situation is still ongoing (they are needed for the Theory of Everything). But for a small special case, when particles have zero spin and their speeds are much less than the speed of light, in 1926 Erwin Schrödinger found and published the equation. Then several more scientists (Klein, Gordon, Dirac, and so on) refined this equation for particles with half-integer spin. In other words, so far it has been possible to accurately calculate the behavior of particles only for a few special cases.

The Schrödinger equation describes the behavior of a particle in a potential field V. But only if its speed is much less than the speed of light, and its spin is zero.

The Dirac equation describes the behavior of particles with half-integer spin, such as the electron. By the way, it is relativistically invariant – that is, it takes into account the various effects of the theory of relativity. Therefore, it can also be used at near-light speeds.

The Klein-Gordon-Fock equation is a generalization of the Schrödingen equation that is consistent with relativity, but without an arbitrary potential field. If the particle speed is negligible compared to the speed of light, then the solutions to the equation will be the same as the solutions to the Schrödinger equation if V=0

Euler-Lagrange equation. Describes the behavior of particle systems in the most general case. You only need to substitute the corresponding value of the Lagrangian L for a specific particle system. If, for example, we substitute the Lagrangian of a free electron, we get the Klein-Gordon-Fock equation.

I won’t explain what exactly the different symbols in these equations mean. It’s too long, and besides, if you want, you can go to Wikipedia and see for yourself. These formulas are provided simply as examples. The main thing you need to understand is two things.

Firstly, all these equations are a consequence of the most ordinary laws of physics (in particular, the Klein-Gordon-Fock equation is derived from the relationship between energy and momentum). And therefore, all the coefficients in them (in particular, the Hamiltonian H and the Lagrangian density L) are determined by the physical characteristics of the particles (mass, charge, etc.) for which a specific equation has been compiled.

Secondly, the solution to these equations is the function Ψ(t,x). This is the wave function that determines which particle is where and when. In the case of several particles, its value at each point is, of course, a vector, each component of which is the location of the particle at that point.

Here the average person may have a question – “How is it possible?? After all, if the graph of this function looks like a sine wave or a Gaussian curve (and such solutions actually exist in special cases), then at one moment the value of the wave function for one particle can be equal to one in one place, zero in another, and somewhere in between ½ or 0.7! Not to mention the fact that at one point in space and time there can be several particles, and with different magnitudes of this very “location”. Is this really possible??»

Yes it’s possible. Moreover, this is usually what happens. Of course, this situation can best be understood by programmers or people familiar with computer games. Let’s say you have a hero in the game and a rocket is flying at him. What happens when a rocket hits a hero? I don’t mean on the screen, but inside the game itself. After all, the rocket, like the hero, is actually just coordinates in level space and sets of instructions. These instructions say that when a rocket flies within a certain distance to the hero, the program calculates the position of the hero’s body and the rocket and looks to see if they are touching each other. And if they touch, the rocket explodes, that is, there is an interaction between the rocket and the hero. However, please note that in-game calculations do not necessarily have to match the graphics. On the contrary, when calculating a hit, a character model is most often taken, consisting of so-called hit boxes, which generally follow the contours of the character, but more roughly. As a result, a rocket, for example, can easily pass through a cloak, but explode over the hero’s head, because one of the programmers made a hit box with a reserve for a high hairstyle.

To be precise: In fact, in addition to hit boxes, each object also has a bound box. That is, a cubic area that obviously limits the object with all its hit boxes. Therefore, to put it as precisely as possible, the region of the object’s “non-zero wave function” is precisely the bound box. And hit boxes are already areas where the “wave function value” (that is, the probability of interaction) is close to one.

In fact, in addition to hit boxes, each object also has a bound box. That is, a cubic area that obviously limits the object with all its hit boxes. Therefore, to put it as precisely as possible, the region of the object’s “non-zero wave function” is precisely the bound box. And hit boxes are already areas where the “wave function value” (that is, the probability of interaction) is close to one.

And in tactical games, https://non-gamstopcasino.uk/ for example, instead of clearly calculating geometry, they often use random. The closer a missile is to a combat unit at a certain point in time, the higher the likelihood that it will hit it at that very moment and explode. And it doesn’t matter that they will be separated by several meters on the screen. For an algorithm that will calculate the interaction of objects, the space occupied by equipment or a person will be exactly the area where a missile can hit it.

The same is true for the wave function of a particle. Points in space where its value is not zero are those points where this particle can interact with others. And the higher the value at a specific point, the higher the probability of interaction at that point. Of course, nothing prevents hit boxes from intersecting in the game, on the contrary – the intersection of hit boxes is precisely the trigger for the game algorithms that calculate the interaction of objects. Similarly, in reality, the appearance of a region where the density of the wave function for several particles is not zero means the possibility of interaction for these particles.

However, that’s not all. According to the equations, the components of the wave function corresponding to different particles depend on each other. Obviously? Of course, the probability of the appearance of particle C depends on the probability of the interaction of particles A and B, as a result of which it appears. The only problem is that the further movement of particle C also depends on the movement of particles A and B! That is, imagine – an electron and a positron annihilate, and, figuratively speaking, the resulting photon moves as if the particles that formed it still exist. And the above-mentioned man in the street is again at a loss: “How is it possible??! I always see only one possible option! Either the particle is there or it isn’t!».

Scientists have thought about this question for a long time and debated a lot. Suffice it to say that none other than Albert Einstein played the role of that common man. What to do, the man didn’t believe in quantum physics and wave functions. However, several possible explanations have been found.

Two interpretations of one phenomenon

The first explanation, which came to be called the "Copenhagen interpretation", is based on the introduction of such concepts as observer, observation and wave function collapse. After all, what does “we see a particle” mean?? This means that we launched a beam of light (aka a beam of photons) into the experimental area and, having interacted with what was in this area, some of the photons were reflected and hit our eye. This whole procedure is called “observation”, and we, accordingly, are the observer in it. And the essence of the “Copenhagen interpretation” is that when an observer makes an observation, he causes the wave function to collapse, turning it from a wave into a set of specific particles that are in a specific state. And as long as the wave function exists, it is a superposition of any possible states of the system.

However, not everyone liked this definition. Yes, there are no purely mathematical contradictions here, but somehow strangely it turns out that the state of the system depends on some outside observer. There was a wave, and some Vasya came and everything turned into particles. What’s so special about this Vasya? That he is a man? What if Vasya is a cat? Will he also cause a collapse?? Or turn into “Schrödinger’s cat”?

Trying to find contradictions in the theory of quantum mechanics, Schrödinger imagined what would happen if a living cat was placed in the experimental area. For greater clarity, he imagined that there was also a device there that, having caught a photon, released a cloud of poisonous gas. Thus, if an electron and a positron annihilated and emitted a photon, then the cat will die, if not, then it will remain alive. But as long as the wave function contains components of all three particles (electron, positron and photon), then the wave function of the cat in the experiment should contain both states – two particles did not interact and the cat is alive, two particles annihilated and the cat is dead.

In general, first Hugh Everett and then Bryce DeWitt (yes, the same one after whom Booker was named) proposed a different theory, where there was no collapse of the wave function, and the state of Schrödinger’s cat did not depend on whether we looked at him or not. This theory was called the "many-worlds interpretation" because it assumed that since there was no collapse. And since there is no collapse, then all states of the wave function exist, it’s just that each of them is a separate world.

Let me explain with an example of double nesting. There is an experiment with elementary particles in which they can collide and react, or not. Next there is a cat who will either die (if the particles react) or not. And finally, here we are – standing next to the box and getting ready to find out whether the cat is alive or not.

When we open the box, then, according to the many-worlds interpretation, we will not collapse the wave function of the cat, but rather our wave function will bifurcate into us, seeing a living cat, and us, seeing a dead cat!

Science is resting

So what does all this have to do with BioShock Infinite?? To be honest, very distant. Yes, different states of a particle system can be represented as different worlds, but the point is that these worlds are different states of the same particle system. This means that it is at least incorrect to use the word “displacement” in the context of this theory.

Let me explain using Booker DeWitt as an example. When baptized, a particle system called Booker DeWitt can go into two states – B.X.Comstock (if Booker is baptized) and Booker DeWitt who has not been baptized (in order to reduce confusion, let’s call this state L.Shepherd). Let me draw your attention once again: Shepherd and Comstock are two states of the same particle system – Booker DeWitt. From the point of view of the many-worlds interpretation, each state corresponds to a separate world, which means that the Shepherd and Comstock, by definition, cannot exist within the same world.

If pure terminology is not enough for you, then think about this:. If Shepherd and Comstock are one particle system, Booker DeWitt, then its characteristics, in particular mass, should be like those of one particle system. That is, even if Booker DeWitt is somehow in two states within one world, then his mass and energy in this world are still the mass and energy of one person. Imagine that we put Comstock and Shepherd on the scale at the same time – their total weight will be the same as that of one person, which means each individually should weigh half as much!

Moreover, at one time an article was published on the Edge portal (now it is on the Polygon website). In it, the scientific consultant explained the nature of some of the effects in the game, comparing Shepherd and Comstock to a neutron that moves along two trajectories in a quantum interferometer. Correct comparison, but trying to prove the “scientific” nature of what is happening in the game, she kept silent about one important point. Having detected (that is, simply seen) a neutron flying along one trajectory, we will automatically find ourselves in a world (I remind you that we are arguing in terms of the many-worlds, and not the Copenhagen interpretation), where the neutron doesn’t fly along a different trajectory. And that means neutron flying along this other trajectory we will not see in this world. And if we think similarly within the framework of BioShock Infinite, then Comstock’s soldier, who received an order from him to find and destroy the False Shepherd, will never see this shepherd.

Just in case, to avoid misunderstanding, I’ll explain it again more clearly. Here is a hydrogen atom:

Inside, at the very center, is the nucleus of the atom, consisting of. doesn’t matter though. Outside, around the nucleus – electron. Yes, everything on the outside, shaded in gray, is an electron. Because, although it is said that the electron “rotates” around the nucleus of the atom, in fact (which is what quantum physics is talking about) it is simultaneously in all states around the atom in which it can be, according to the conservation law. BUT, although it is simultaneously in all possible states, it can only interact with particles that fall into it once.(this is exactly that part of wave-particle duality, where a particle-corpuscle behaves exactly like a particle, and not a wave) If two photons fall into the “electron cloud” at once, only one of them interacts with the electron (for example, changing its energy), and the other flies past. Similarly, an electron can interact with the gravitational field in only one unique way. It doesn’t matter what size the “electron cloud” is – it can be small in a hydrogen atom or large, for electrons in the outer “orbits” of heavier atoms – the mass and weight of the electron will remain the same.

All the same reasoning applies to Schrödinger’s cat. Here is a cat that is both alive and dead at the same time:

Yes, the cat is in two states, BUT still remains one object. This means it interacts with the Earth’s gravitational field (weight) and photons (visibility) as one object.

There is, of course, one caveat – a cat consists of many atoms, which means many electrons and other elementary particles. Therefore, if we (mentally) decompose a cat into these elementary particles, then each of them will be in two states (in a living cat and in a dead one), and interact only in one of them. And if we assume that the cat particles interact with other particles independently, then it turns out that the two states of the cat can really be seen. But they will only look translucent, as in the picture, because those atoms of the cat’s skin that reflect photons from a dead cat will miss photons falling on a living one. Well, as for the weight, since it is the sum of the weight of all particles, it will always be the weight of one cat, regardless of the exact state in which the particles “weigh”.

It should also be noted that considering a cat as a collection of atoms, we will still have to answer the question of how exactly these atoms interact with each other if they “jump” between its several states. Here’s how this is shown in one sci-fi series:

At the 35:45 mark it roughly shows how a person in two quantum states at the same time should feel.
You can draw a conclusion about how possible this is in reality by simply calculating the probability of how 10 to the thirtieth atoms chaotically moving in space (approximately) can form two cats.

But the game also has gaps, through which heroes, as well as various objects, “move” from one world to another. Just how can they do this if the Booker DeWitt particle system is one for all worlds?? The particles that make up the main character/villain are, by definition, present in all versions of the Universe, it’s just that in each of them the state of these particles is different. Accordingly, “moving” is not really moving at all, in the sense that even if the False Shepherd left “his world,” his particle system (Booker DeWitt) still remains there. How can this be? The answer to this question (like all previous ones) clearly lies beyond the scope of all existing scientific theories.

What if.

But, perhaps, I’m still too harsh on Irrational Games. In the end, almost all science fiction (even that which is classified as “hard”), upon careful examination, does not stand up to scientific criticism. On the other hand, even field theory is just a theory, which, moreover, cannot explain everything. Today, scientists are trying to connect together all the interactions between matter and derive universal equations, thus creating the Theory of Everything. But this is still far away, and even M-theory (a generalization for superstring theory) and the theory of quantum gravity are just sketches of speculative postulates. They haven’t even yet derived equations that would describe physical phenomena without contradictions.

So, let’s try to come up with a theory (albeit unrelated to science, but at least logically consistent) that would explain what is happening in the game.

Let’s start with the "breaks". How does “moving” through them happen?? It can be assumed that the system of particles, which represents a “moving” object, simply disintegrates in the world from which the object is moving. Or, for example, stops interacting with the outside world. There was a box with first aid kits, but it became a beam of photons. At the same time, in the world where the object “moves”, it seems to be assembled from those particles that should have composed it in the original world.

Yes, unfortunately this does not look like the portal that we see at the end of the game, but it coincides 100% with the mechanics of the game. After all, when Elizabeth takes something out of the gap, it appears in the “world” where we are immediately, completely and in the same place where it was in the other “world”.

But in reality it works like this. Note the Anna/Elizabeth particle clusters. Their existence is an important fact related to the quantum nature of worlds – after all, the particles that make up, for example, Elizabeth’s head in one world must necessarily exist in another.

In relation to Booker, however, such a theory has problems. Indeed, in this case, Comstock should have completely turned into the Shepherd, but instead the particles find themselves in two states at the same time. Although, who knows, maybe the same thing happens with other objects, we just don’t see it. That is, somewhere there, the boards that were supposed to be the box that Elizabeth takes out of the gap lose some of their energy, and the box itself is not connected to these boards, like Booker and Comstock.

The most difficult moment to explain is the very possibility of interacting with two states of one object at the same time. One state – one world. This is the essence of the “many-worlds” interpretation of quantum mechanics. Moreover, we are talking not only about the state of some fixed system of particles, but also about the state of all particles that are associated with this system (in scientific terms this is called quantum entanglement). Let’s say Booker the Shepherd emerges victorious from a shootout with enemies. If he hadn’t shot them all, he’d be dead. This means that in any world where he appears, all these enemies must also be dead, otherwise the Shepherd must be dead. Wait a minute though. after all, in the game this is precisely what is shown when a hero who defeats enemies in one world appears in another, and the enemies there also die. That is, they die, it turns out, not from the very fact that Booker killed them in another reality, but from the fact that, having appeared in this one, Booker-Shepherd “brought with him” their death.

Only if everything was according to science, then the enemies would already be dead upon arrival. And in the game they seem to split into two and the states in which they should be in different worlds are mixed.

Mixing worlds is the most unscientific, but at the same time the most logical explanation of what is happening. After all, if we assume that due to some side effect of the Lutes machine, all the people around (not just Elizabeth) began to see several options for the state of the world – everything falls into place. And the existence of doubles who are in different but overlapping worlds, and the mixing of memories. At the beginning of the game, the Shepherd sees a statue of Lutece, which is either a statue of Rosalind or Robert – such “glitches” are exactly what should happen when the human brain somehow observes a world consisting of two realities.

That is, in the end we get that the game has different worlds (where Booker sold Anna, where Booker became Comstock, where instead of Columbia there is Rapchur). And these worlds, in turn, are themselves a superposition of several subrealities. For example, the world in which the first half of the game takes place (from the beginning to the transition to the world where Chen is alive) consists of the subreality of the Shepherd, Comstock, Robert Lutes, Rosalind Lutes, and so on. Moreover, if the states of one person in all realities coincide, then within the framework of the world he is one person. And if the conditions are different, then all sorts of side effects begin. Moreover, they are aimed at reducing the differences between these states. In particular, the memories of Comstock and the Shepherd are brought to a common denominator; people who are dead in the Shepherd’s memories die.

Yes, I understand that my reasoning is far-fetched, but what can you do if Irrational Games came up with a story about a typical classic journey between parallel worlds, and then just added the word “quantum”. Everything would be much simpler, of course, if what was happening was explained by magic, but then the game’s setting would not be labeled “science fiction”. So Levin decided to invite a scientific consultant to add phenomena from quantum mechanics to the game, or at least something similar to them. After which he said, “Gentlemen, players, we don’t have fantasy, but one hundred percent science.”! You see what kind of things are happening here – these are all effects from quantum physics.». Of course, since the vast majority of players are not familiar with quantum physics, everyone fell for this statement.

And don’t get me wrong – I don’t deny that BioShock Infinite’s story is actually interesting and deep. And I’m ready to forgive Ken for throwing dust in his eyes for one of the most unconventional plots of recent times. It’s just that exclamations like “Hey, look!! There is an unrealistic moment in the game." or "Oh, can you imagine?! The developers mixed up scientific terms!». Well, congratulations! You found an unnoticed hole. in a sieve called “a scientific explanation of what is happening in BioShock Infinite”.

But let’s return to our pulling of the owl onto the globe. The last thing I want to look at is the Lutes technology that keeps Columbia in the air. Yes, its action is explained in the game (on one of the voice phones), but from a scientific point of view this explanation is complete nonsense. “The atom just doesn’t fall” – how is this even possible??! That is, it is clear that in theory this means that the atom hangs in a certain position relative to the Earth. But how does it work? Quantum physics or not, Newton’s laws apply everywhere. The action force is equal to the reaction force, and the impulse is always the integral of the force over time. If we walk along the Columbia pavement, we put pressure on it with our mass. This means we give it an impulse in the direction of the Earth. And in order for it to stay in place, the same force is needed in the opposite direction. It must come from somewhere!

It can be assumed, for example, that “Lutece particles” are repelled by the surface of the Earth itself. After all, we know that in fact the wave function of a particle (that is, the region where it interacts with other objects) can extend very far. So it is quite possible that “Lutece particles” are simultaneously in two states – inside the container and outside it. And Lutes technology actually allows these two states to interact. When the container is active, particles, whose wave function can be non-zero at a distance of many kilometers, interact with the surface of the Earth (or in this case the seabed) and receive upward momentum from it. And then they communicate this impulse to the container itself.

Of course, nothing in this explanation prevents momentum from being received in any other direction, so statements like “Columbia can’t move because the particles are hanging motionless relative to the ground." – not at the cash register. By the way, they would not be useful in any other case, because “hanging motionless” can be done relative to any object, including a moving one (the Earth also moves).

What’s behind all the doors??

As you can see, it is extremely difficult to link what is happening in the game with the real theory of quantum physics. And this applies even to the very basics. What can we say about the plot itself with its “abstruse” ending?. If you don’t limit yourself to simply borrowing terms, but try to really look at the game universe from the point of view of a many-worlds interpretation, then the reasoning will take almost as long as all the previous ones.

What motives drive Elizabeth and the Lutes?? How are the events of the game connected with Booker’s inner world?? What place does the game mechanics have here?? What is left behind the scenes and are the events of Clash in the Clouds important for understanding the authors’ intentions?? I’ll make a separate post about this.

In the meantime, you can discuss what has already been written and express your ideas about science in BioShock Infinite.