The laws of quantum mechanics seem to tell us that there is a fundamental random component to the universe. But Gerard ’t Hooft, who received the Nobel Prize in 1999 for his work on gauge theories in particle physics, is not convinced that physicists have to abandon determinism.
In his new book, The Cellular Automaton Interpretation of Quantum Mechanics (Springer, 2016), ’t Hooft suggests that we may simply be lacking the data that would turn quantum probability distributions into specific predictions. Reviewer Stefano Forte praises it as a “beautifully written, entertaining, and provocative book” that “will dwarf all other contributions ’t Hooft has given to science” if correct. The book is also open access, available as a free e-book on Springer’s website.
Physics Today recently caught up with ’t Hooft to discuss his theory, its reception, and what’s next on his research agenda.
PT: In the first chapter, you write that your book was “born out of dissatisfaction with the existing explanations” of the fact that “our universe appears to be controlled by the laws of quantum mechanics.” What, precisely, did you find unsatisfying about existing approaches?
’T HOOFT: I do not believe that we have to live with the many-worlds interpretation. Indeed, it would be a stupendous number of parallel worlds, which are only there because physicists couldn’t decide which of them is real.
In practice, quantum mechanics merely gives predictions with probabilities attached. This should be considered as a normal and quite acceptable feature of predictions made by science: different possible outcomes with different probabilities. In the world that is familiar to us, we always have such a situation when we make predictions. Thus the question remains: What is the reality described by quantum theories? I claim that we can attribute the fact that our predictions come with probability distributions to the fact that not all relevant data for the predictions are known to us, in particular important features of the initial state.
PT: What is the cellular automaton interpretation, and how does it address your dissatisfaction?
’T HOOFT: A cellular automaton is a computer model of a dynamical system that consists of cells arranged in a multidimensional grid, often two- or three-dimensional. Each cell contains a number of bits of data; furthermore, there is a time variable. As time proceeds, all cells are updated by some algorithm, where the updated data in a cell depend on the previous data in the same cell and its nearest neighbors.
Now, the way I devise such models is completely deterministic, so there is no Hilbert space or Schrödinger equation, just classical algorithms. But we can introduce Hilbert space mathematically, defining its basic elements to correspond to all possible configurations of the automaton. It is not hard to define a Schrödinger equation with a Hamiltonian such that, at integer time values when the cells have been updated, the contents of all cells are accurately reproduced.
For all practical purposes, then, this is a quantum model that reproduces the data of the classical automaton. The catch here is that even if the automaton’s algorithm only refers to nearest neighbors, the quantum system emerging from here seems to lack locality. Since the real world appears to be described by a local quantum field theory, it remains to be explained how locality can be restored. For some of my opponents, this seems to be inexcusable, but I am not worried by this apparent contradiction. There are interesting ideas to cure this apparent shortcoming.
PT: How have fellow researchers responded to your theory?
’T HOOFT: The response has been very mixed. Many other researchers are clearly very skeptical. They should be, because there are important unanswered questions. Others have expressed their interest and support. What concerns me is that I haven’t yet found colleagues who completely understand my approach. And also, of course, I don’t know what they say behind my back.
PT: What are you currently reading?
’T HOOFT: I have my hands full with my mail. And I do calculations most of the time. There are very important questions to which I want better answers than what I have at present.
PT: What is your next project?
’T HOOFT: When I am not working on this theory, I return to a related problem: the quantum mechanics of black holes. Most researchers seem to think that their theories—often string theory or related approaches—tell them everything one might want to know about black holes, but I disagree. First, I do not agree with the usual ways people describe black holes—typically as a stack of branes or something like that in string theory. Standard theories are simply wanting, to a significant extent, when it comes to describing black holes. To me this is important news. We are not doing things quite right.
Now, my own theory about black holes is very simple: Just take the most basic quantum gravity description, consisting merely of perturbative gravity with some forms of matter, and examine how that handles the data of particles and fields inside a black hole. Subsequently, examine where things go wrong. The answer is staring me in the face: We hadn’t understood the topology of the Schwarzschild metric. There’s only one way to do it right, and that is to assume that the topology of the horizon is a projective sphere—all points on the horizon touch their antipodes. This was not known; nobody besides me gives it any attention, and it is extremely important. So I want to understand this thing better than I do now.
