Physics & Math / Math

Parallel universes are like different pages in a book, existing independently, simultaneously, and right next to each other.

In what way does time provide a bridge between the two perspectives?
Well, all mathematical structures are abstract, immutable entities. The integers and their relations to each other, all these things exist outside of time.

Do you mean that there is no such thing as time for these structures?
Yes, from the outside. But you can have time inside some of them. The integers are not a mathematical structure that includes time, but Einstein’s beautiful theory of relativity certainly does have parts that correspond to time. Einstein’s theory has a four-dimensional mathematical structure called space-time, in which there are three dimensions of space and one dimension of time.

So the mathematical structure that is the theory of relativity has a piece that explicitly describes time or, better yet, is time. But the integers don’t have anything similar.
Yes, and the important thing to remember is that Einstein’s theory taken as a whole represents the bird’s perspective. In relativity all of time already exists. All events, including your entire life, already exist as the mathematical structure called space-time. In space-time, nothing happens or changes because it contains all time at once. From the frog’s perspective it appears that time is flowing, but that is just an illusion. The frog looks out and sees the moon in space, orbiting around Earth. But from the bird’s perspective, the moon’s orbit is a static spiral in space-time.

The frog feels time pass, but from the bird’s perspective it’s all just one eternal, unalterable mathematical structure.
That is it. If the history of our universe were a movie, the mathematical structure would correspond not to a single frame but to the entire DVD. That explains how change can be an illusion.

Of course, quantum mechanics with its notorious uncertainty principle and its Schrödinger equation will have to be part of the theory of everything.
Right. Things are more complicated than just relativity. If Einstein’s theory described all of physics, then all events would be predetermined. But thanks to quantum mechanics, it’s more interesting.

But why do some equations describe our universe so perfectly and others not so much?
Stephen Hawking once asked it this way: “What is it that breathes fire into the equations and makes a universe for them to describe?” If I am right and the cosmos is just mathematics, then no fire-breathing is required. A mathematical structure doesn’t describe a universe, it is a universe. The existence of the level IV multiverse also answers another question that has bothered people for a long time. John Wheeler put it this way: Even if we found equations that describe our universe perfectly, then why these particular equations and not others? The answer is that the other equations govern other, parallel universes, and that our universe has these particular equations because they are just statistically likely, given the distribution of mathematical structures that can support observers like us.

These are pretty broad and sweeping ideas. Are they just philosophical musings, or is there something that can actually be tested?
Well, the hypothesis predicts a lot more to reality than we thought, since every mathematical structure is another universe. Just as our sun is not the center of the galaxy but just another star, so too our universe is just another mathematical structure in a cosmos full of mathematical structures. From that we can make all kinds of predictions.

So instead of exploring just our universe, you look to all possible mathematical structures in this much bigger cosmos.

If the mathematical universe hypothesis is true, then we aren’t asking which particular mathematical equations describe all of reality anymore. Instead we have to figure out how to separate the frog’s view of the universe—our observations—from the bird’s view. Once we distinguish them we can determine whether we have uncovered the true structure of our universe and figure out which corner of the mathematical cosmos is our home.
Max, this is pretty rarefied territory. On a personal level, how do you reconcile this pursuit of ultimate truth with your everyday life?
Sometimes it’s quite comical. I will be thinking about the ultimate nature of reality and then my wife says, “Hey, you forgot to take out the trash.” The big picture and the little picture just collide.

Your wife is a respected cosmologist herself. Do you ever talk about this over breakfast cereal with your kids?
She makes fun of me for my philosophical “bananas stuff,” but we try not to talk about it too much. We have our kids to raise.

Do your theories help with raising your kids, or does that also seem like two different worlds?
The overlap with the kids is great because they ask the same questions I do. I did a presentation about space for my son Alexander’s preschool when he was 4. I showed them videos of the moon landing and brought in a rocket. Then one little kid put up his hand and said: “I have a question. Does space end or go on forever?” I was like, “Yeah, that is exactly what I am thinking about now.”