A Project to Find the Fundamental Theory of Physics

Book Preface

Weʼre issuing this book to capture the state of our thinking as we launch the Wolfram Physics Project, and to serve as a resource for those who want to understand and potentially participate in the project.

The majority of the book consists of new material specifically created for the launch of the project. But weʼve also included earlier material that traces the evolution of my thinking, and provides additional background. In particular, it includes the key chapter about funda‐ mental physics from my 2002 book, A New Kind of Science. And while weʼve now been able to take the ideas significantly further—and have made some technical modifications—almost everything that was in A New Kind of Science still stands, and now provides the foundation for our new project.

Beyond this book, weʼre making many other resources available on the website for the Wolfram Physics Project, wolframphysics.org, which we hope will see frequent updates and additions as the project progresses.
Join us in what we hope will be the final quest for the fundamental theory of physics

I Never Expected This
Itʼs unexpected, surprising—and for me incredibly exciting. To be fair, at some level I’ve been working towards this for nearly 50 years. But itʼs just in the last few months that itʼs finally come together. And itʼs much more wonderful, and beautiful, than Iʼd ever imagined. In many ways itʼs the ultimate question in natural science: How does our universe work? Is there a fundamental theory? An incredible amount has been figured out about physics over the past few hundred years. But even with everything thatʼs been done—and itʼs very impressive—we still, a�er all this time, donʼt have a truly fundamental theory of physics. Back when I used do theoretical physics for a living, I must admit I didnʼt think much about trying to find a fundamental theory; I was more concerned about what we could figure out based on the theories we had. And somehow I think I imagined that if there was a funda‐ mental theory, it would inevitably be very complicated.
Stephen Wolfram Writings: April 14, 2020

But in the early 1980s, when I started studying the computational universe of simple pro‐ grams I made what was for me a very surprising and important discovery: that even when the underlying rules for a system are extremely simple, the behavior of the system as a whole can be essentially arbitrarily rich and complex.

And this got me thinking: Could the universe work this way? Could it in fact be that underneath all of this richness and complexity we see in physics there are just simple rules? I soon realized that if that was going to be the case, weʼd in effect have to go underneath space and time and basically everything we know. Our rules would have to operate at some lower level, and all of physics would just have to emerge.

By the early 1990s I had a definite idea about how the rules might work, and by the end of the 1990s I had figured out quite a bit about their implications for space, time, gravity and other things in physics—and, basically as an example of what one might be able to do with science based on studying the computational universe, I devoted nearly 100 pages to this in my book A New Kind of Science.

I always wanted to mount a big project to take my ideas further. I tried to start around 2004. But pretty soon I got swept up in building Wolfram|Alpha, and the Wolfram Language and everything around it. From time to time I would see physicist friends of mine, and Iʼd talk about my physics project. Thereʼd be polite interest, but basically the feeling was that finding a fundamental theory of physics was just too hard, and only kooks would attempt it.
It didnʼt help that there was something that bothered me about my ideas. The particular way Iʼd set up my rules seemed a little too inflexible, too contrived. In my life as a computational language designer I was constantly thinking about abstract systems of rules. And every so o�en Iʼd wonder if they might be relevant for physics. But I never got anywhere. Until, suddenly, in the fall of 2018, I had a little idea.

It was in some ways simple and obvious, if very abstract. But what was most important about it to me was that it was so elegant and minimal. Finally I had something that felt right to me as a serious possibility for how physics might work. But wonderful things were happening with the Wolfram Language, and I was busy thinking about all the implications of finally having a full‐scale computational language.

But then, at our annual Summer School in 2019, there were two young physicists (Jonathan Gorard and Max Piskunov) who were like, “You just have to pursue this!” Physics had been my great passion when I was young, and in August 2019 I had a big birthday and realized that, yes, a�er all these years I really should see if I can make something work. So—along with the two young physicists whoʼd encouraged me—I began in earnest in October 2019. It helped that—a�er a lifetime of developing them—we now had great computational tools. And it wasnʼt long before we started finding what I might call “very interesting things”. We reproduced, more elegantly, what I had done in the 1990s. And from tiny, structureless rules out were coming space, time, relativity, gravity and hints of quantum mechanics.

A Project to Find the Fundamental Theory of Physics We were doing zillions of computer experiments, building intuition. And gradually thingswere becoming clearer. We started understanding how quantum mechanics works. Then we realized what energy is. We found an outline derivation of my late friend and mentor Richard Feynmanʼs path integral. We started seeing some deep structural connections between relativity and quantum mechanics. Everything just started falling into place. All those things Iʼd known about in physics for nearly 50 years—and finally we had a way to see not just what was true, but why.

I hadnʼt ever imagined anything like this would happen. I expected that weʼd start exploring simple rules and gradually, if we were lucky, weʼd get hints here or there about connections to physics. I thought maybe weʼd be able to have a possible model for the first 10‐100 seconds of the universe, but weʼd spend years trying to see whether it might actually connect to the physics we see today.

In the end, if weʼre going to have a complete fundamental theory of physics, weʼre going to have to find the specific rule for our universe. And I donʼt know how hard thatʼs going to be. I donʼt know if itʼs going to take a month, a year, a decade or a century. A few months ago I would also have said that I donʼt even know if weʼve got the right framework for finding it. But I wouldnʼt say that anymore. Too much has worked. Too many things have fallen into place. We donʼt know if the precise details of how our rules are set up are correct, or how simple or not the final rules may be. But at this point I am certain that the basic framework we have is telling us fundamentally how physics works.

Itʼs always a test for scientific models to compare how much you put in with how much you get out. And Iʼve never seen anything that comes close. What we put in is about as tiny as it could be. But what weʼre getting out are huge chunks of the most sophisticated things that are known about physics. And whatʼs most amazing to me is that at least so far weʼve not run across a single thing where weʼve had to say “oh, to explain that we have to add something to our model”. Sometimes itʼs not easy to see how things work, but so far itʼs always just been a question of understanding what the model already says, not adding something new.
At the lowest level, the rules weʼve got are about as minimal as anything could be. (Amusingly, their basic structure can be expressed in a fraction of a line of symbolic Wolfram Language code.) And in their raw form, they donʼt really engage with all the rich ideas and structure that exist, for example, in mathematics. But as soon as we start looking at the consequences of the rules when theyʼre applied zillions of times, it becomes clear that theyʼre very elegantly connected to a lot of wonderful recent mathematics.

Thereʼs something similar with physics, too. The basic structure of our models seems alien and bizarrely different from almost everything thatʼs been done in physics for at least the past century or so. But as weʼve gotten further in investigating our models something amazing has happened: weʼve found that not just one, but many of the popular theoretical frameworks that have been pursued in physics in the past few decades are actually directly relevant to our models. Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful