(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.
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.
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.
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.”