LEGO & BELL’S

It begins as a typical children’s cartoon movie: a struggle between good and evil, mildly interesting characters trying to overcome personal insecurities to ‘be all that they can be’, a love triangle of course, some witty, adult oriented repartee, and lots and lots of action.

But The Lego Movie is much, much more than this! As we shall see, this movie includes a huge twist (spoiler alert to follow), and that ‘twist’ reveals that the fundamental ontology of this film is not Classical (Euclidean/Newtonian) but Quantum Mechanical. But to appreciate this twist, we need to review the movie’s plot line.

The Story

As the film opens, we see characters existing in a world built entirely out of Legos; they are Lego pieces themselves and everything they do is done with Legos. Their tools, their weapons, all made of Legos! There is every reason to believe that this World is entirely self-contained, that it is Universe.

As the film progresses, we learn that Lego World has many realms, including Old West, Viking’s Landing, Pirates’ Cove, Middle Zealand and Cloud Cuckoo Land; but most of the action takes place in Bricksburg, a thriving metropolis dominated by a crushing culture of conformity. The dominant ethic of Bricksburg could be summed up on a bumper sticker: “Follow instructions!”

Under the influence of ‘Lord Business’, construction workers, ‘micromanagers’, robots and cops work together to nurture and, if need be, enforce the conformist ethic. But under the radar, a tiny group of Master Builders harks back to a time before Lord Business when Lego World was free and full of possibility.

In Bricksburg, everyone builds according to plans, blueprints, instructions; but not the Master Builders! They build free form. Even better, they build their creations quickly and in real time to confront immediate, real life challenges. Philosophically, they are William James Pragmatists. But they are also society’s artists and magicians. Only Master Builders are capable of introducing true novelty into the world and impacting the course of events.

But “Lord Business, who you know as President Business” has diabolical plans for Bricksburg. Lord Business plans to unleash a fully weaponized Kragle on Taco Tuesday to end the world as we know it. ‘Taco Tuesday’, a typical government program of bread and circuses designed to co-opt and distract the populace, is cover for President Business’ plan to activate the super weapon (Kragle), which will freeze Bricksburg, effectively destroying it.

The central theme of the movie is the Master Builders’ struggle to derail Lord Business’ scheme. Because of a prophesy from the blind wizard Vitruvius, they believe that their success depends on finding the “Special”, a savior foretold by Vitruvius who will locate the “Piece of Resistance” (piece de resistance), the one ‘piece’ that can disable the Kragle, and use that piece to thwart Lord Business’ plans.

When we are introduced to the Piece of Resistance, it is quite unassuming. An elongated cube, open at one end, it looks slightly out of place in Lego World…and it is (but more on that later).

The Special is simply the most important, most talented, most brilliant, most interesting, most extraordinary person in the universe…at least according to the prophesy. But surprisingly, the Piece of Resistance is found accidentally by a construction worker named Emmet who turns out to be a paradigm of the mindless conformity that dominates Bricksburg. “We all have something that makes us something and Emmet is…nothing.”

As the Master Builders learn more and more about Emmet, they trust him less and less. Even if he is the Special, he lacks the skills necessary to complete the mission. He is not even a Master Builder and he shows no hint of creativity. Something is terribly wrong but nobody knows quite what.

Nonetheless, Emmet gets a chance to plead his case at a gathering of Master Builders “in the secret realm of Cloud Cuckoo Land.” Princess UniKitty welcomes the Master Builders to Cloud Cuckoo Land and explains its unique social order to Emmet: “Well, we have no signs here, no rules, no government, no bedtimes, no baby-sitters…And there’s also NO consistency.”

Emmet introduces himself to the august assembly: “…I may not be a Master Builder…I’m not all that smart. And I’m not what you’d call a creative type. Plus I’m generally unskilled. I know what you’re thinking. He’s the least qualified person in the world to lead us. And you are right.”

Before Emmet can complete his ‘pitch’, all but a few of the Master Builders desert him. But later on, as the situation worsens and some of the Master Builders return to Emmet’s side, his experience in Cloud Cuckoo Land stands him in good stead.

“What is the last thing Lord Business expects Master Builders to do? Follow the instructions. You’re all so imaginative and talented. You can build things out of thin air. But you can’t work together as a team. Just imagine what could happen if you work together. You could save the universe!”

And so Emmet proposes a ‘third way’. In contrast to mindless conformity or anarchic creativity, he suggests a middle course: conscious, intentional, voluntary cooperation. For the remainder of our adventure, this is the strategy that Emmet and the Master Builders adopt in their crusade against Lord Business.

But even that is not enough! Nothing the Master Builders do can derail Lord Business’ plan to end the world. To make matters worse we learn that Vitruvius made up the prophesy in the first place “because I knew that whoever found the piece could become the Special, because the only thing anyone needs to be special is to believe that you can be.”

Perhaps Vitruvius was right after all. In the course of leading the Master Builders against Lord Business, Emmet does indeed become a Master Builder himself. A Master Builder “sees everything”; he understands that every piece has the potential (actually, is the potential) to participate in the creation of more complex structures. Master Builders share the vision of Aristotle (matter is pure potentiality) and Alfred North Whitehead (every being is potential for a new becoming).

So far, we have a good story with some interesting philosophical and sociological insights but nothing more…yet. Then something amazing happens.

Spoiler Alert!

Separated from the Special by Lord Business, the Piece of Resistance falls out of Lego World entirely. Who knew that was even a possibility? Who knew Lego World had borders, that there was anything beyond Lego World?

The Piece of Resistance is gone…and now all is certainly lost! But the transformed Emmet refuses to give up. He follows the Piece of Resistance right out of Lego World. He falls freely toward all but certain annihilation; but amazingly, he instead lands in another world, a world entirely beyond his wildest imagination, a world far removed from any of the realms of Lego World. He finds himself in the basement of a house where a boy named Finn is playing with a gigantic Lego set that nearly fills the room.

Then we hear Finn’s father’s footsteps ominously descending the cellar stairs. Finn’s father is “the man upstairs” we’ve heard references to throughout the movie; we discover that he is using these Legos to create a model for a major real estate development project. He has repeatedly instructed his son not to play with these Legos. Yet that is exactly what Finn is doing.

At the beginning of the movie, perhaps before Finn was even born, Vitruvius issued another prophesy, “He is coming. Cover your butt.” It seems likely that ‘ancient’ prophesy referred to just this moment. A confrontation between the boy and his father ensues and in the process the movie is decoded.

It’s Tuesday night and Tuesday night is Taco night in Finn’s family (‘Taco Tuesday’). But Dad (aka Lord Business) has a tube of Krazy Glue (Kragle: Kra Gl e) and tonight is the night when he plans to superglue all the Lego pieces together to solidify his model. Once the superglue takes hold, Lego World will be frozen solid.

Throughout the movie, we are told that Lord Business plans to “end the world”. Now we understand what that means. According to Alfred North Whitehead, “…it belongs to the nature of a ‘being’ that it is a potential for every ‘becoming’.” By that standard (as we saw above), Lego pieces are paradigmatic ‘actual entities’ (beings). What is a Lego piece but the potentiality to participate in the formation of novel, complex structures? But once Lord Business ‘freezes’ Lego World with his weapon of mass destruction (Krazy Glue), all potentiality will vanish. The Lego pieces will no longer be actual entities (beings) and Lego World will effectively cease to exist.

Until now, we have assumed that the Special must overcome Lord Business by force and use the Piece of Resistance to destroy the Kragle. But now we realize that we, and our Lego characters, have misunderstood the true mission of the Special. It is not to overcome Lord Business by force of arms; it is to persuade him by force of argument to abandon his plans to freeze the world. The Piece of Resistance turns out to be the cap to the Krazy Glue tube and it must be voluntarily re-attached by Lord Business himself if Lego World is to be saved.

Finn argues that it is totally unreasonable to expect a boy his age not to play with a huge Lego set in his basement. “We bought it at a toy store,” and he points out that the instructions on the box read, “Ages 8 to 14”. But Dad is less than impressed by Finn’s legalistic argument. For a moment it looks as though Vitruvius’ initial prophesy may be fulfilled.

But after some further give and take, the ‘man upstairs’ decides to give his son another chance to present his side of the story and to argue for the future of Lego World. This time, however, he invites Finn to present his case through Emmet, the Special. Using Emmet as a less vulnerable intermediary, Finn is empowered to take a different approach:

“You don’t have to be the bad guy. You are the most talented, intelligent, extraordinary person, capable of amazing things. You are the Special…and so am I. The prophesy was made up…but it’s still true. You still can change everything.”

At that moment Lord Business walks toward Emmet and gives him a hug…just as Dad walks toward Finn and hugs him. Finn and Emmet succeed and Dad/Lord Business decides to use the Piece of Resistance for its intended function, to cap the tube of superglue. Lego World is saved.

The Ontology

Thanks to this surprise ending, a good story becomes great. But how are we to understand the ontology that makes this outcome possible? What is the relationship between Finn’s World and Lego World?

One is tempted to say, “Simple! There is no ‘Lego World’ per se. It is just a part of Finn’s world. Lego World has no independent reality. Thoughts, words, actions ascribed to the Lego characters are really just Finn’s thoughts, words, actions.”

This is certainly the Classical view…but it is not the position of the film itself!

According to the Classical view, events in Lego World are entirely dependent on events in Finn’s world. There can be no conflict between the worlds because there really is only one world, Finn’s world, and Lego World is just part of it. In the language of pre-20th century philosophy, we would say that events in Lego World are completely determined by events in Finn’s World. In the language of mathematics, we would say that Lego World is a proper subset of Finn’s World.

According to the Classical hypothesis, all consciousness, all awareness resides in Finn (and his dad). The Lego characters have no independent mental activity. Therefore, there can be no displacement between Finn’s consciousness and the consciousness of the characters he creates and directs.

For the most part, the movie does not contradict this view. In most scenes, the apparent consciousness of the Lego characters can be understood merely as a projection of Finn’s consciousness. But unfortunately for the Classical view, there are exceptions to this generalization…more than enough exceptions to invalidate the hypothesis.

For example, looking back through the movie, we see that there were several early clues that Lego World might be embedded in some larger reality. But because these clues pointed to things far beyond the experience of the Lego characters, and because at that point we were experiencing events solely through the eyes and ears of those Lego characters, we missed those clues.

There was Vitruvius’ initial prophesy: “He is coming, cover your butt!” A warning undoubtedly intended for Finn (sometime in the future) but the Lego character who overhears the warning, a guard, merely says, “Cover what?”…and looks around, confused. The warning has no meaning in the context of the guard’s own experience (Lego characters apparently don’t get spanked).

At various times in the movie, President Business (Finn’s dad) speaks in a manner that seems intended to resonate in both worlds…but with slight differences of meaning for each. For example, he says, “Let’s take extra care to follow the (my?) instructions or you’ll be put to sleep (bed?).” Emmet hears (or mishears) the warning and reacts: “Wait, did he say ‘put to sleep’?” But he gives it no further thought; the warning makes no sense in Emmet’s world. (Lego characters apparently don’t get sent to bed early either.)

According to the Classical model, warnings directed at Finn would be perceived by Finn and only by Finn and he would have understood them. But that is not what happens here. Instead, we see that the information is spread between Finn’s World and Lego World and is understood differently, and incompletely, in each world. The two worlds share information but in the process of sharing, its meaning is diluted.

Bricksburg includes a collection of odd items that belong to Lord Business, items that seem out of place in Lego World. The Lego characters understand them as purposeless ‘relics’ but we later come to understand that they are really human artifacts, detritus of the organic world (Band-Aids, golf balls, etc.), that have somehow made their way into the Lego complex.

The ultimate relic is the Piece of Resistance itself, a superglue cap that is certainly out of place in Lego World (as we noted earlier); but the anomaly is unappreciated by the Lego characters.

The Lego characters have an awareness of these relics but because the relics are completely foreign to the Lego characters’ experience, they cannot appreciate their significance or understand their purpose or their origin. For example, they mistake the Krazy Glue cap for some kind of explosive weapon.

Toward the end of the movie, when he falls out of Lego World into Finn’s cellar, Emmet is genuinely startled. He sees Finn but does not understand his relationship to the boy: “What in the world is that? It’s adorable.” Later Emmet refers to Finn (in contrast to his dad) as “smaller creature”. Finn, of course, recognizes Emmet immediately and welcomes him by name, completely bewildering Emmet. There is an imbalance in their relationship caused by an asymmetrical distribution of information between the two heroes.

Most convincingly, Emmet remains completely conscious even though he is outside Lego World and, initially at least, outside of Finn’s awareness. In fact, Finn is so totally unaware of Emmet’s presence in his basement that he actually steps on him. There is no way to account for this if Lego World is merely a proper subset of Finn’s World. Emmet’s independent consciousness clearly falls outside of Finn’s World.

In fact, it is now Emmet who takes control of events in Finn’s world. Emmet endeavors to get Finn’s attention and direct that attention toward the Piece of Resistance that is lying, previously unnoticed on the basement floor. The asymmetrical distribution of information between the two heroes now favors Emmet. There is no way to account for this if Lego World is merely a projection of Finn’s consciousness.

Finn notices Emmet’s gesture, reunites Emmet with the Piece of Resistance and inserts Emmet back into Lego World: “It’s up to you now Emmet.”

So we have two worlds, related to one another yet independent of one another. Clearly, some information is shared by both worlds; just as clearly, each world has information that the other world lacks.

The two worlds share a common timeline but their event narratives are quite different. Yet in the end, when the story line demands that they produce a single result, they both arrive at exactly the same conclusion at exactly the same moment in time. What kind of universe can account for these strange features? Certainly not the Classical universe presupposed in the orthodox hypothesis!

Bell’s Theorem

In 1964, the great Irish mathematician, John Bell, asked about the information content of a simple system consisting of 2 ‘entangled’ quantum particles (e.g. two quantum particles with a common origin). He already knew that measuring the state of one entangled quantum would give us reliable information about the state of the other quantum. But if the particles are distinct and independent, why should this be and how could it be?

Bell considered various classical explanations for this phenomenon but found that they did not precisely account for the phenomenon he sought to model. He then developed an alternative, non-classical theory that did account for the phenomenon in question.

He reasoned that a pair of entangled particles must possess a finite amount of information. While that could be any amount, for our purposes let’s ‘normalize’ the quantity and call it 1.

So let “1” be the total information content of the system, denoted as “T” in the equations below:

T = A + B (where A and B represent the two quanta)

Now, if T = 1, then A and B must add up to 1. So, for example, A could equal 0.5 and B could equal 0.5, and that would be a perfectly valid model so long as A and B are entirely independent of one another.

But that model doesn’t fit the data for entangled particles. The model allows for no sharing of information and therefore there should be no significant correlation between measurements on A and measurements on B. But in fact such a correlation exists so this model contradicts the demonstrated facts of Quantum Mechanics.

So Bell constructed an alternative model (Bell’s Theorem) that he believed would better model the theoretical and experimental results. For that model, he turned to a very simple formula called the “Sum of Squares”. (Most of us first encountered the Sum of Squares as the “Pythagorean Theorem”.)

T² = A² + B²

Now if T = 1, T² = 1 as well. Then A² + B² must also equal 1. Suppose A² = 0.5 and B² = 0.5. What does that mean for A and B?

A = .7 and B = .7 (approximately). Now if we add A + B we find a combined information content of 1.4 (i.e. the square root of 2). But that’s also a problem because how can the information content of the parts exceed the information content of the whole? That would contradict the principle that information is always conserved.

So Bell came to the only possible conclusion. The extra 0.4 quantity of information is actually shared by the two particles; it exists in two places at once. So A has its own information content equal to 0.3 and B has its own information content equal to 0.3 and A and B share information content equal to 0.4.

0.3 + 0.3 + 0.4 = 1

Each particle has 70% of the total information content of the system but because 40% of the total information content of the system is shared information, the total information content of the system remains equal to 1.

Because information is shared by two particles separated by an indefinite distance, the universe modeled by Bell’s Theorem is called non-local. Events in such a universe do not happen in one place at a time. Instead, events happen in at least two places at a time and those two places can be as far apart in space as you wish (that’s why it’s a non-local model of Universe).

The Lego Movie

What does Bell’s Theorem have to do with The Lego Movie? Everything! Bell’s phenomenon is exactly what we experience when we watch the film. The total information content is distributed between Finn’s World and Lego World. But it is not neatly divided in half like a candy bar. Instead, some resides in Finn’s World and some resides in Lego World and some resides in both places at once.

In our example, here’s how it works: of the total information content (1), 30% resides solely in Finn’s World (F) and 30% resides solely in Lego World (L) but 40% resides both in Finn’s World and in Lego World. It’s no wonder that both Finn and the Lego characters misunderstand so much of the information they are given; each sees only 70% of the total picture.

Bell’s Theorem, derived from the science of Quantum Mechanics, is the best approach to understanding The Lego Movie. What confirms this use of the Bell Model is what happens at the end of the film. Both Finn and Emmet attempt to influence Dad/Lord Business. Initially, their efforts are independent and in fact quite different. Gradually, however, the two approaches converge and ultimately they merge completely. There is no way to be certain what the outcome will be…but it is absolutely certain that it will be definite and the same in both worlds.

In Quantum Mechanics, when it is no longer possible to maintain several possible outcomes at the same time, we say that “the wave function collapses”. That is exactly what happens in The Lego Movie. Finn’s World and Lego World offer radically different accounts of the same events and, so long as that persists, the outcome is undetermined. But once an outcome is required (whether by external measurement or observation…or by the story line itself), the wave function collapses and the two worlds become one with a single, definite outcome.

The predictions made by Quantum Mechanics (QM) are more accurate than those of any other theory in the history of science. That QM works is virtually beyond dispute; but why and how QM works is still a bit of a mystery. As a result, there are many different “interpretations of Quantum Mechanics”; here, we will deal with just three.

Early Quantum Mechanics interpreted the data using probability theory. Just as there is a probability that a craps player will roll a 7 and a reciprocal probability that she will roll some other number, so there is probability of finding an electron at point A and a reciprocal probability of finding it someplace else. This interpretation gave us the paradox of Schrödinger’s Cat. The cat is locked in a box inside a hermetically sealed room; no contact with the outside world is possible. The cat’s life (or death) is dependent on a subatomic event that has a finite probability.

Is the cat alive or dead? We can’t know without opening the box and according to this interpretation of Quantum Mechanics, the cat is both alive and dead until such an observation is made.

Hugh Everett suggested an alternative possibility. His “Many Worlds Interpretation of Quantum Mechanics” suggested that the cat was alive in one world and dead in another. At every quantum junction, the world bifurcates into two (or more) worlds corresponding to the different possible outcomes. The bumper sticker for this view reads, “Whatever can happen does happen..somewhere!”

The third interpretation comes from Richard Feynman. His “Sum over Histories” interpretation bridges the gap between Schrödinger and Everett. Feynman proposes that the electron does indeed follow all possible paths simultaneously but that the final result is the sum of all such paths weighted by the relative probability of each. With Feynman, we keep ‘one world’ but that one world reflects contributions from all possible path or outcomes.

Which of these interpretations underlies our film? In The Lego Movie, there were two possible outcomes, either one of which might have occurred, but only one of which actually did occur. Finn’s and Emmet’s pleas could not have led to inconsistent results. Lord Business could not have acceded to Emmet at the same time Dad was denying Finn, or vice-a-versa. Dad and Lord Business could only come to one and the same conclusion regarding the fate of Bricksburg, whatever that conclusion might be. Bricksburg could not be both glued and unglued. So Schrödinger’s model doesn’t work.

Likewise, we have already seen that Lego World and Finn’s World, while different, and not totally independent; throughout the movie they influence one another, however subtly. Ultimately, the two worlds actually merge, so Everett’s interpretation doesn’t work either.

Feynman’s Sum over Histories is the QM model that The Lego Movie demonstrates. Separate but related events occur in the two worlds but the outcome is simply the sum of the histories of these two worlds. If there were only one world, Lego or Finn’s, the end result would probably have been different that it was. Neither Emmet nor Finn could have swayed Lord Business/Dad alone. It is because the unique histories of both worlds converge that we get the happy finale.

 

THE LEGO MOVIE written by David Cowles

(Note: Toward the end of the movie, Finn explains to his dad that Legos are for kids ages 8 to 14. It says so on the box. But Dad says, “That’s just a suggestion!” Same here. This is written for kids ages 8 t0 14…but that’s also just a suggestion. Interested adults are welcome too.)

If you’re reading this, I know you’ve seen The Lego Movie at least once. How surprised were you the first time you saw Emmet fall out of Lego World into Finn’s basement?

Before that, did you have any idea that there was anything beyond Lego World? Probably not! There were a few clues, like Lord Business’ “relics”, but they were pretty hard to figure out because we were looking at them through the eyes of the Lego characters and Lego characters don’t know anything about Band-aids or Krazy Glue.

For the first hour of the movie, we thought that Lego World was all there was. Then suddenly we realized that there was another world, “Finn’s World”, and we immediately wondered, “How do these two worlds fit together? Are there really two worlds…or just one?”

Most adults would probably say, “That’s easy. Finn’s World is real and Lego World is just make-believe; there’s only one world, Finn’s World.” If you look at them funny when they say that, they might go on, “Finn was just playing with the Lego characters. Everything the characters thought and did came from Finn.”

That’s easy alright, that’s an easy answer; but is it the right answer? Is it what the movie itself says about the two worlds?

I don’t think so. When Emmet falls out of Lego World, Finn doesn’t even notice him for a while. Finn isn’t playing with Emmet then because Finn doesn’t know where Emmet is. In fact, he steps on him. But even without Finn, Emmet continues to think and act.

For his part, Emmet doesn’t know Finn and has no understanding of Finn’s role in Lego World. He doesn’t even know Finn’s name; he calls him “adorable” and “smaller creature”.

A minute later, when he is lying on Dad’s work bench, Emmet notices the Piece of Resistance all on his own. He manages to wriggle himself off the table (with no help from Finn) in the direction of the Piece of Resistance. Emmet’s gesture catches Finn’s attention. Only then does Finn reunite Emmet with the Piece of Resistance and, when Dad is not looking, return them both to Lego World.

Emmet thinks and acts independently of Finn, at least some of the time, so there has to be more to Lego World than just Finn’s imagination.

For the most part, events in Lego World run parallel to events in Finn’s World but they are not exactly the same. Toward the end though, the two worlds do begin to come together. When Finn pleads with his father for the future of Lego World, Emmet pleads with Lord Business. At first, Finn and Emmet make separate arguments but then Dad (Lord Business) invites Finn to speak to him through Emmet and he does. Now Finn and Emmet are one. The argument Finn makes through Emmet works. Dad (Lord Business) gives in, places the cap back on the tube of Krazy Glue and saves the universe.

At the climax, when Dad/Lord Business puts the cap back on the tube, the exact same event happens in both worlds at the same time. Now there is just one World!

So we’re back to our original question, “Two worlds or one?” Surprisingly, the answer is, “Neither!” It’s not one world and it’s not two worlds; it’s something else altogether.

What! How is that possible? How could it be something else? Either a world exists or it doesn’t. In what sort of universe can a world partially exist? Well, it’s the sort of universe that was imagined by a mathematician named John Bell back in 1964.

Dr. John Bell

Dr. Bell wasn’t thinking about The Lego Movie. He was thinking about our universe, the universe we live in. In our universe there are tiny particles called atoms and much, much tinier particles called electrons. Stop me if you know this already.

Dr. Bell thought about what would happen if two electrons were produced as a result of a single atomic reaction and sent off in opposite directions. Are these electrons one thing or two things? Neither, he reasoned. They are two electrons but they are not totally independent of one another. Each carries a memory of their common birth. The technical term for this is entangled: the two electrons are entangled with one other. No matter how far away from one another they get, they’re still entangled. One electron on Mars, the other on Venus, still entangled.

Think of these electrons as a bit like identical twins, two people sharing the same genes. We know that twins are independent people but we also know that are entangled in ways that other folks aren’t. Even if they are separated at birth and raised by totally different families, they usually have a lot in common. If one likes rap music, chances are the other one does too.

Then Dr. Bell posed a question. If something happens on one electron, could that tell us something about what is happening at the same time on the other electron? He went on to prove by math that the answer is “Yes!” Later scientists tested this conclusion in laboratory experiments and those experiments confirmed that he was right.

How could that be? How could something happening on one electron tell us something about what is happening at the same time on another electron far away?

Two possibilities come to mind. Maybe one electron sends a signal to the other electron telling it what to do. But that’s impossible. Signals travel through space at a certain speed and that speed can’t be faster than the speed of light. But we are observing these two electrons one right after the other so there’s not enough time for one to get a message to the other.

There’s another possibility. Maybe there was actually just a single event that happened when the electrons were still together in the original atom. When we observe the two electrons at a later time, we are just seeing evidence of what happened earlier when the electrons were together. In that case, there’s no mystery at all.

This is what Albert Einstein believed but in 1964 John Bell proved Einstein wrong. The idea that there was one event at the birth of the electrons and that is what we see later when the electrons are widely separated doesn’t fit the facts. It can’t be right either.

To understand how John Bell discovered this we can take an example from everyday life, something that could easily happen to you and actually may have happened to you.

Your Mother’s Vase

Imagine your mother comes home from the store and finds her prized blue vase broken on the kitchen floor and you and your sister standing over it with your mouths open. She also notices the cat up on the counter and a ball in a corner of the room. She is determined to find out what really happened to her vase but she knows if she asks, you’ll answer first and your sister will back up whatever you say. So in a split second, she devises a plan: she sends your sister to her room and then she asks you alone, “What happened to the vase?” And you tell your story.

Then she tells you to stay in the kitchen and she goes upstairs and asks your sister the same question. Will she get the same story?

If you’re counting on somehow getting a message to your sister telling her what to say, that won’t work, will it? She’s too far away. Your answer and her answer will have to be totally independent of one another. So it’s likely that your mother is going to hear two very different stories. Bad news for you and your sister!

But there is another possibility. Maybe you and your sister quickly agreed on a story before your mother came home. In that case, you mother will hear the same story from her that she heard from you…exactly the same story…assuming you can trust your sister to follow the plan.

Of course, there is a third possibility: you both could just tell the truth. In that case, your stories would probably differ in some minor details but overall they would be the same. So there are actually three possibilities:

(1)   Your stories are totally different from one another which means that at least one of you is not telling the truth.

(2)   Your stories are exactly the same which means that they were likely made up and rehearsed and probably not true either. (Why rehearse a true story?)

(3)   Or your stories could differ in a few details but be the same overall. In this case, it’s highly likely that you’re both telling the truth, at least to the best of your ability.

Your mother is looking for the truth. If your stories don’t agree at all, she knows she’s not getting it. And if your stories agree too closely, she’s probably not getting the truth either. But if your stories differ a little bit but agree over all, that’s what she’s looking for; and that can only happen if you both decide on your own to tell the truth.

Your mother turned out to be pretty smart and so, as we shall see, was John Bell.

Bell’s Theorem

Following the principles of a science called Quantum Mechanics, John Bell asked how often an observation of one electron would match the same observation of the other electron. Like your mother, he knew the answer he was looking for.

Using math, he showed that if the electrons were entirely independent, observations wouldn’t match closely enough. That’s like you and your sister each telling a different story.

On the other hand, he showed that if the electrons were just carrying information from the time they were first separated, observations would match too closely. This is like you and your sister rehearsing a story before your mother comes home.

So neither of those possibilities could be true!

What’s left? What other possibility is there? Sherlock Holmes says that once you’ve eliminated all other theories of a crime, whatever is left, however bizarre, must be true. Perhaps without realizing it, John Bell followed Sherlock’s instructions.

Dr. Bell realized that the only other possibility is that the same event is happening on both electrons at the same time. It’s kind of like when you and your sister both decide, on your own, to tell the truth. (Actually, it’s a little different than that because when you and your sister make your decisions, it’s actually two decisions. Plus you are guided by the actual event you both observed. But In the case of the electrons, there is only one decision and it is being made on both electrons at the same time with nothing to guide it. It just happens that the stories agree most of the time.)

What does this mean? It means that a single event is taking place in two widely separated places at the same time. People like to say that they can’t be in two places at once. Apparently, that’s not true…at least not if the two people happen to be electrons.

John Bell proved that a single event can happen in two places at once. In fact, it turns out that single events usually happen in two places at once. Most of the events that make up the universe occur at the sub-atomic level. Although we’re not aware of it in everyday life, most sub-atomic particles (like electrons) are entangled.

Does this blow your mind? If not, you haven’t totally understood what I’m saying. We’re not talking about one event here and another event just like it someplace else. That’s still two events and that sort of coincidence happens all the time. We’re talking about one single event that doesn’t happen here or there but happens here and there.

An event happens on Earth and at exactly the same time that exact same event is happening on Mars. An event happens in the Milky Way and at exactly the same time that exact same event is happening in the galaxy Andromeda. Incredible!

Scientists call a universe where events happen in just one place at a time, “local”. Our universe is not local. Events don’t always happen in just one place at a time. 30 years earlier, the great Albert Einstein had called this idea (the idea that the universe isn’t local) “spooky”. But John Bell turned out to be right and Albert Einstein wrong. The universe we live in is spooky after all.

The Lego Movie

What does this have to do with The Lego Movie? It describes perfectly what goes on between Lego World and Finn’s World. Like Bell’s electrons, these two worlds are independent but entangled.

If Lego World were just a part of Finn’s World, there would only be one story, like the story you and your sister rehearsed before your mother came home. But if Lego World were completely separate from Finn’s World, then there would be two stories with only accidental similarities between them, like the stories you and your sister told when you didn’t have time to talk before your mom questioned you.

But neither of these things is true, is it? Lego World has a story and Finn’s World has a story. The two stories are related and they lead to the exact same conclusion but the details along the way are very, very different.

This is like when you and your sister each decide on your own to tell the truth…except that in the case of The Lego Movie, there is no ‘truth’; the truth gets made up along the way. The movie could have ended in any one of a number of ways, but it actually ended just one way. All movies, all stories, end in just one way, but we don’t know which way until we get to the end.

It’s just like that with John Bell’s electrons; there is no event on either electron until someone observes or measures something on one of the electrons. But when that happens, the same event happens on both electrons at the same time.

The Math

What kind of a universe is this? Events happen in two places at once and two stories, completely independent of one another, follow the same path even though there is nothing to guide them?

Is there a way to describe this sort of universe? Yes, there is!

Can you describe it? That depends on how much math you know.

Do you know fractions and percentages (percentages are really just fractions too)? Do you know exponents (sometimes called “powers”) and square roots (square roots are just a kind of exponent)? If you know just these two things, you know everything you need to know to make the same discovery John Bell made 50 years ago, a discovery that Henry Stapp, a famous physicist, called “science’s most profound discovery”.

You have all the tools you need to demonstrate that things happen in two places at once! Want to try? (But if you don’t know about fractions or exponents or if you just don’t like math, you can skip to the next section if you want.)

It turns out that there are many, many different ways to demonstrate what John Bell figured out, but they all come to the same conclusion. I’ll explain his reasoning in terms of Legos instead of electrons but it’s the same thing.

Let’s start by assuming a universe that is made up of just two worlds: Lego World and Finn’s World. Whatever’s in Lego World is in Lego World only and whatever is not in Lego World is in Finn’s World. Finn’s World is everything that is outside of Lego World.

So John Bell thought, in a universe like this I can add the information I get from Lego World and the information I get from Finn’s World together and it will equal 100% of the information in this universe. Another way to write 100% is just 1. For example, 100 cents and 1 dollar are the same thing, aren’t they? If your mom gives you a candy bar and says you can eat 100% of it, then you have 1 candy bar. You don’t have to split it with brothers or sisters.

So if adults are right and Finn’s World is the only real world and Lego World is just a made-up part of Finn’s World, then only Finn’s World contains any real information. Therefore, Finn’s World = 1 and Lego World = 0. If we add the two together we get 1 + 0 = 1.

On the other hand, if Finn’s World and Lego World are both real and if they are totally independent of one another, then whatever is in Lego World is not in Finn’s World and whatever is in Finn’s World is not in Lego World. Part of all the information in the universe is in Finn’s Word and part of it is in Lego World.

Another way to say this is that a fraction of the universe’s information is in Lego World and a fraction of the universe’s information is in Finn’s world. The two fractions can be anything you want them to be as long they add up to 1. The easiest thing to do is make then both ½. Another way to write ½ is 50%. A half dollar equals 50 cents.

In this case, 50% of the universe’s information is in Lego World and the other 50% is in Finn’s world: 50% + 50% = 100%.  Now there are two completely independent sets of events, like when you and your sister each tell a completely different story.

But neither of these things describes what’s going on in The Lego Movie, does it? In the movie, Finn has a story and Emmet has a story. They’re different but they’re also related. Some information exists only in Lego World and other information exists only in Finn’s World but some of the information is shared.

To use John Bell’s words, Finn’s World and Lego World are separate but entangled. There is more going on here than just one simple story but we’re not hearing two totally unrelated stories either.

In a universe where Finn’s World and Lego World are separate but entangled, some information would still be in Finn’s World and some would still be in Lego World. We can still write our equation as 50% + 50% = 100%. But it turns out that according to the science of Quantum Mechanics, when things are separate but entangled, we have to do addition a little differently. In the case of The Lego Movie, instead of writing

(Finn’s World) + (Lego World) = (Universe),

we need to write:

(Finn’s World)² + (Lego World)² = (Universe)²

An equation like this is called the “Sum of Squares”. If you’ve ever heard of the Pythagorean Theorem, you’ve seen this kind of equation before. You can use it find out things like “If I walk 1 mile east and then 1 mile north, how far away am I from where I started?” Hint: you’re less than 2 miles away from where you began but more than 1 mile away.

If we use the Sum of Squares to do our addition, will we get a result that looks like what we see when we watch The Lego Movie? Let’s see.

(Finn’s World)² + (Lego World)² = (Universe)² is the same thing as (50%)² + (50%)² = (1)².

Now what? First, (1)² = 1. We know that has to be true because even though Finn’s World and Lego World are separate (but entangled) their stories both have the same happy ending. They come together and give us the same information, which is 100% of all the information in the universe, so 1 is the only possible right answer. So far our model is working!

Now look back at the left side of the equation. If Finn’s World and Lego World both have the same amount of information and the “sum of their squares” equals 1, how much information is in Finn’s World and how much is in Lego World?

Well, (Finn’s World)² has to equal 50% and (Lego World)² has to equal 50% so that together they can  add up to 100% or 1. Right? But now looks what happens!

If (Finn’s World)² = 50%, what does Finn’s World equal? If (Lego World)² = 50%, what does Lego World equal? The answer to both questions is 70%. 70% is the square root of 50% (approximately). So now, if we add the information in Finn’s World (70%) to the information in Lego World (70%), the total amount of information in both worlds is 140%, more than all the information in the universe.

But that can’t be, can it? Something’s still not right. Remember what Sherlock Holmes said earlier: once you’ve eliminated all other theories of a crime, whatever is left, however bizarre, must be true. But what is left? We know that in The Lego Movie there is more than just one world but we also know that there aren’t two totally independent worlds. We also know that there can’t more information in the two worlds than there is in the entire universe. So what other possibility is there?

Here is where John Bell, like a real life Sherlock Holmes, was brilliant. He said, what if the extra information is actually shared by Lego World and Finn’s World? What if some of the information happens in two places at once? What if Lego World has 70% of all the information in the universe and Finn’s World has 70% but 40% of each is actually shared information?

In that case 30% of all the information in the universe would be only in Lego World and 30% of all the information in the universe would be only in Finn’s World and 40% of all the information in the universe would be both in Lego World and in Finn’s World. Now the equation is:

30% + 30% +40% = 100%.

Up to 40% of the information in an entangled universe exists in two places at once. It’s important to understand that the shared information in Lego World is not just a copy of information in Finn’s World. We’re not talking copies here. The information itself really is in two places at once and that’s what makes it possible for events to happen in two places at once.

Conclusion

So congratulations! If you made it this far, you’ve demonstrated John Bell’s great idea, known as Bell’s Theorem, “science’s most profound discovery”. You know that Finn and the Lego characters share a lot of information in common. But you also know that Finn has some information that the Lego characters don’t have and that the Lego characters have some information that Finn doesn’t have.

Now you’re able to explain The Lego Movie to your parents. Here’s how that conversation might go:

“You see, there are two worlds, Lego World and Finn’s World. They are independent worlds but they are also entangled, you know, like a ball of string can get all tangled up. Events in the two worlds follow one another but they are also very different from one another. The two worlds share some information in common but each world also has some information that the other one doesn’t have. At the end though, one event happens in both worlds in the same way at the exact same time and at that moment the two worlds become one again.”