Foundations of physics, and what follows from them

Richard Feynman once said that nobody understands quantum mechanics. More than a hundred years after it was first proposed, Feynman’s remark still holds. One of the most puzzling aspects of quantum mechanics is its apparent incompatibility with the assumption that an objective reality exists independently of an observer. One can produce quantum states in the laboratory whose joint probability distribution for all measured quantities does not exist. This means that if we assume an unmeasured observable exists, we arrive at absurd conclusions. It is therefore often said that measuring a quantity does not reveal its value but creates it.

The nonexistence of joint probability distributions for quantum observables is even more puzzling for states composed of particles far apart from each other. In the 1930s, Albert Einstein, Boris Podolsky, and Nathan Rosen (EPR) created a famous thought experiment in which two particles are prepared in an entangled state and then moved far apart. The state is such that when we measure a property of one particle, we immediately know it for the other. Since nothing can be immediate, some “element of reality” common to the particles’ past had to be responsible for the observed values while they were far apart. Those elements of reality were later shown to be incompatible with experimental results. Empirical evidence suggests instead that quantum systems are nonseparable: there are systems whose properties cannot be considered separately. Data, in other words, seems to restrict our metaphysical worldviews. We cannot think of particles as individually separated objects; even when far apart, they still belong to a single whole, the quantum state.

Quantum nonseparability raises many questions. How can we tell whether a quantum system is separable? Does separability imply that quantum systems can be holistic? Can we create nonseparable systems that are classically correlated? Are there other ways in which quantum mechanics restricts our worldviews, and how does this relate to the structure of spacetime? Can we find situations that would distinguish ontological, non-local interpretations from the standard interpretation? What does quantum mechanics tell us about the ontology of our world, and does that ontology present problems for emergent properties such as the mind?

I approach these questions in two complementary ways. The first is through extended probability theory, described below. The second, in collaboration with Décio Krause and Federico Holik, uses quasi-set theory to describe indistinguishability and non-identity in a quantum ontology. Our main question is whether the lack of identity for quantum particles leads to new ways of thinking about quantum contextuality and nonlocality. If we assume quantum particles have no identity, for instance, we can show that Kochen–Specker-type contradictions are not entailed. The same may hold for nonlocality, but this still needs to be investigated.

When examining whether a quantum state is separable, one may check for the existence of a joint probability distribution instead of checking for hidden variables, since the two are in a sense equivalent. This raises a question I have pursued for many years: can extended probability theories offer insights into quantum mechanics that standard probabilities do not?

A sizable part of my research in physics touches on the foundations of mathematics. My interest there began as an undergraduate physics student and continued through my graduate work at the Brazilian Center for Research in Physics under the supervision of Francisco Antonio Doria and Antonio Fernandes Teixeira. While working with Doria I also had the privilege of being co-advised by, and collaborating with, Newton da Costa, considered the father of paraconsistent logic.

More recently I have been interested in quasi-set theories and negative probabilities as mathematical formalisms for representing contextuality, working on these topics with Décio Krause, Gary Oas, and Federico Holik.

Understanding the brain is one of the most fascinating current endeavors in science. In recent decades, with modern experimental and computational techniques, physicists have increasingly helped to decipher some of the brain’s learning mechanisms. Yet much remains to be determined about how it processes and learns information. Despite the many models of brain processing, there are no detailed systematic efforts to fit them to experimental behavioral data, and little attempt is made to connect such data with emergent phenomena such as consciousness.

In collaboration with Pat Suppes, Claudio Carvalhaes, and Gary Oas, we set out to bridge the gap between behavior and brain. We began with models for behavioral stimulus–response theory, which has a solid mathematical foundation and whose central concept of conditioning generalizes easily to the more complex idea of association. That makes it an ideal starting point for connecting psychology experiments with neural modeling. The goal is to set constraints from macroscopic signals, narrowing down the characteristics of the underlying model for brain processing. We modeled stimulus–response theory with neural oscillators, for instance, and compared our results with experiments in the literature.

Another question, investigated in collaboration with Zyg Pizlo, is the relation between perception and minimization theorems. It is well known that most of modern physics can be derived from variational principles: minimizing the action leads to the equations of motion. Our question is whether similar ideas apply to perception. In visual perception, minimizing a cost function leads to the three-dimensional reconstruction of objects. Would this idea and its consequences, such as Noether’s theorem, apply to other problems of perception? If so, what would we learn from it, and what further problems would it suggest?

Finally, I have long been interested in the relationship between brain and mind. How can the mind be an emergent concept formed from the brain’s interconnected network of neurons? Since neurons are made of quantum particles, how can the mind’s identity follow from matter that lacks identity itself? Is there a relationship between the underlying quantum world and how it feels to be ourselves? These questions are part of my research in collaboration with Carlos Montemayor.

For roughly a decade, much of my work in physics applied the causal — Bohmian — interpretation of quantum mechanics to quantum cosmological models: the singularity problem and the issue of time in quantum cosmology, non-singular quantum cosmologies with dust and radiation fluids, the conformally coupled scalar field, quantum gravity corrections to the evolution of a scalar field and to inflation, Bohmian trajectories for evaporating black holes, and the tunneling probability for the birth of an asymptotically de Sitter universe. A related strand was a renormalization-group study of the higher-derivative conformal scalar model. This work was done largely with Nelson Pinto-Neto, Ilya Shapiro, and colleagues in Brazil.

Aware of the need for changes in physics instruction at my previous university (UFJF), I began researching physics education. From my own experience, I believe we learn by becoming members of a community of practice, where newcomers model their work on that of experts and gradually learn to use shared vocabularies, techniques, and concepts. That belief led me to research active-engagement and inquiry-based methods that would let students work in small groups reproducing the dynamics of the scientific community. Our research showed a significant improvement in students’ conceptual understanding and logical reasoning, and led to a widespread change in introductory physics instruction at the Federal University at Juiz de Fora.

I have also been interested in students’ epistemological views. Informal interviews with pre-service and in-service physics teachers suggested a fragmented epistemology, with three distinct knowledge systems about physics: the “college-level physics” needed at exams, the “high-school physics” taught at schools, and the “real physics” applied to everyday phenomena. The difference between them was not one of difficulty or sophistication but of different concepts and laws. One student, for example, correctly used Newton’s Third Law in his exams while teaching his own pupils, incorrectly, that weight and normal forces were Third Law pairs. This epistemological fragmentation poses a problem for departments involved in teaching certification programs.

To better understand how students form their epistemological views, we began a program of mapping students’ reasoning skills and their relationship to those views. We gave introductory physics students a series of tests: for epistemological views, the Colorado Learning Attitudes about Science Survey (CLASS) and the Maryland Physics Expectations survey (MPEX); for reasoning skills, Tobin’s Test of Logical Thinking (TOLT) and a test we created to examine students’ ability to reason with formal logic. Preliminary analysis showed almost no correlation between epistemological views and reasoning. We also found that senior students’ reasoning skills did not change significantly — substantial problems with common logical fallacies remained — while their epistemological views approached those of an expert. Their “expert” views as measured by those tests did not, however, prevent them from holding an actually fragmented epistemology of physics.

Later in this work I became concerned with how to teach science to pre-service teachers in a way that demystifies it. More and more people see science as a form of indoctrination — à la Feyerabend — and, like any indoctrination, as not necessarily carrying an element of truth. I believe science teaching needs to address the misconception that science is only for a few initiated scholars by focusing on the process through which science constructs knowledge.