Although I have changed my mind about several ideas and theories, my longest struggle has been with the concept of time. The most obvious and universal aspect about reality, as we experience it, is that it is structured as a succession of moments, each of which comes into being, supplanting what was just present and is now past. But, as soon as we describe nature in terms of mathematical equations, the present moment and the flow of time seem to disappear, and time becomes just a number, a reading on an instrument, like any other.
Consequently, many philosophers and physicists argue that time is an illusion, that reality consists of the whole four dimensional history of the universe, as represented in Einstein’s theory of general relativity. Some, like Julian Barbour, go further and argue that, when quantum theory is unified with gravity, time disappears completely. The world is just a vast collection of moments which are represented by the "wave-function of the universe." Time not real, it is just an "emergent quantity" that is helpful to organize our observations of the universe when it is big and complex.
Other physicists argue that aspects of time are real, such as the relationships of causality, that record which events were the necessary causes of others. Penrose, Sorkin and Markopoulou have proposed models of quantum spacetime in which everything real reduces to these relationships of causality.
In my own thinking, I first embraced the view that quantum reality is timeless. In our work on loop quantum gravity we were able to take this idea more seriously than people before us could, because we could construct and study exact wave-functions of the universe. Carlo Rovelli , Bianca Dittrich and others worked out in detail how time would "emerge" from the study of the question of what quantities of the theory are observable.
But, somehow, the more this view was worked out in detail the less I was convinced. This was partly due to technical challenges in realizing the emergence of time, and partly because some naïve part of me could never understand conceptually how the basic experience of the passage of time could emerge from a world without time.
So in the late 90s I embraced the view that time, as causality, is real. This fit best the next stage of development of loop quantum gravity, which was based on quantum spacetime histories. However, even as we continued to make progress on the technical side of these studies, I found myself worrying that the present moment and the flow of time were still nowhere represented. And I had another motivation, which was to make sense of the idea that laws of nature could evolve in time.
Back in the early 90s I had formulated a view of laws evolving on a landscape of theories along with the universe they govern. This had been initially ignored, but in the last few years there has been much study of dynamics on landscapes of theories. Most of these are framed in the timeless language of the "wavefunction of the universe," in contrast to my original presentation, in which theories evolved in real time. As these studies progressed, it became clear that only those in which time played a role could generate testable predictions — and this made me want to think more deeply about time.
It is becoming clear to me that the mystery of the nature of time is connected with other fundamental questions such as the nature of truth in mathematics and whether there must be timeless laws of nature. Rather than being an illusion, time may be the only aspect of our present understanding of nature that is not temporary and emergent.