Why do we need a Theory of Everything?

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The search for a so-called theory of everything is a deep topic and is perhaps the greatest open question in theoretical physics today. A theory of everything would be an as-yet unknown theory that would allow us to understand our entire universe within one self-consistent framework.

This search can be looked at through the lens of so many topics that there is something for everyone in this search. There are wonderful stories from the history of science, ever better experiments and calculations from the past to projected projects in the future, definitions and arguments within the philosophy of science, discussions of the vastly different interpretations of quantum mechanics, the applicability of quantum field theory, general relativity in the most extreme conditions, studies of the very beginning of the universe, the ultimate fate of the universe, the very meaning and use of the scientific method, and questions about what even qualifies as science. This is all before we even discuss the technical details of a possible theory of everything, what it gets right and what it gets wrong, and how we would know.

A rich topic indeed. My plan is to write a series of articles to discuss virtually all of these topics as I am able. These articles are a spin-off of an introductory course I have been teaching at my college for several years to introduce students to the wonders of the universe in a non-technical and non-mathematical manner. I don’t have a good name for this kind of course, nothing as insulting as “Physics for Poets” or “Rocks for Jocks,” but I like to think of it as a “Theory of Everything for Everyone.”

There are many popular books and magazine articles that attempt to explain these topics, but I have intellectual problems with most of them, not in their details but in their presentation. I am not the only scientist who feels this way, but it would be very fair to say that I am in the minority of opinion. Many of these books and articles are what I call “cheerleading” books that champion a very specific point of view about how close we are to a solution for a theory of everything and how much agreement exists within the scientific community. These books typically skip over the challenges moving forward and moreover what it would mean if the theory was actually correct. And not to pretend otherwise, I understand that this is the whole point of such a book, it is an introduction from a very specific point of view. My aim is to fill in some of these gaps.

However, no matter how interesting the destination, I would like to spend our time today motivating the journey.

Our current understanding of the universe is built upon two theories, quantum field theory and general relativity. Quantum field theory is an extension of quantum mechanics that incorporates the special theory of relativity which allows the description of unstable particles. These two theories together very well describe the four known “forces” and their interactions with matter.

Gravity stands on its own theoretically and seems to be perfectly described by the theory of general relativity. However, not as a “force.” Rather, general relativity is a mathematical framework that takes as its input the distribution of matter and energy in space (as big as the entire universe) and yields a series of equations that, once solved, tells us how objects move in space and time.

There is of course another very useful formulation of gravity that is known as Newton’s law of universal gravitation which does describe gravity as a force. If you have ever taken a physics class, this is most likely what you learned. We continue to teach it in high schools, colleges, and graduate schools today because it is so simple when compared to general relativity. Plus, Newton’s law of gravity is very, very good at doing many, many things and only breaks down and makes bad predictions in very specific situations. If you stay away from these situations, you can use Newton’s much simpler version of gravity. That being said, many scientists still refer to gravity as a force and so will I most of the time, even though I am aware that this is not completely correct.

The other three forces in nature are electromagnetism, the strong nuclear force, and the weak nuclear force which will be explained in detail in later posts. These forces are understood via quantum field theory to an unreasonably high precision. This understanding is encoded in what we call the Standard Model of Particle Physics. The standard model is a model of nature written in the language of quantum field theory. It would be easy to write down other versions of the standard model that would not correspond to what we see in our universe.

Quantum mechanics, and by extension quantum field theory, is a mathematical framework that, as far as we can tell, cannot be changed in any meaningful way without becoming inconsistent both theoretically and experimentally. There are still a few question marks about the exact content of the standard model, but, finding a problem with the standard model is very different from questioning the validity of quantum mechanics. Much like general relativity, we input our understanding of the standard model into quantum field theory which in turn gives us equations that, once solved, tell us about the non-gravitational interactions with great success.

This sounds great! By my count, that is everything being described by a theory. So, where is the problem?

Although these two theories have been verified independently to high precision, they are mutually incompatible with each other. Understanding how we know this, what it means, and how this could be fixed is the search for a theory of everything. So you see, this is more than just a vanity project, more than just an intellectual exercise, we need a new way of looking at the universe because what we have cannot possibly be the whole story.

Dr. Bryan J Field is a theoretical high-energy physicist and Associate Professor. “A Theory of Everything” (MIT Press, Spring 2023). https://www.bryanjfield.com