Ideas
Machian dynamics
When Newton created dynamics, he claimed that the phenomena of the universe, especially inertial motion, unfold in an infinite invisible absolute space. In the 19th century, Ernst Mach argued that all motion is relative and advanced the revolutionary idea that inertia does not arise from the guiding effect of absolute space but from the dynamical effect of the entire universe. This idea, now known as Mach’s Principle, was the biggest single stimulus to Einstein’s creation of his general theory of relativity. However, the precise extent to which Mach’s idea is implemented in general relativity has proved to be controversial. This has been a major research topic for me (papers).
The end of time
Closely related to this work is my study of time. Mach remarked “It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive through the changes of things.” Thus, time as such does not exist but only change. Much of my research has been devoted to the implications of this insight. I have shown how, alongside the relativity of motion, the notion of time as change can be built into the foundations of dynamics. In fact, this idea is contained in a hidden form within general relativity. Its potential consequences for the yet to be found quantum mechanics of the universe are profound. The quantum universe is likely to be static. Motion and the apparent passage of time may be nothing but very well founded illusions. This is the thesis of The End of Time (books), which is aimed both at the general reader and physicists.
Film
A Dutch television film, Killing Time, made in 1999, does a remarkably good job of explaining the ideas of The End of Time in a non-technical way. The film (24 minutes, English with Dutch subtitles) is now available on YouTube.
Essay
A relatively simple Machian reformulation of classical dynamics can illustrate how time, or precisely duration, is redundant as a fundamental concept. Duration and the behaviour of clocks emerge from a timeless law that governs change. This is the subject of my winning submission (pdf) to the FQXi essay competition on the nature of time.
Dynamics of pure shape
In the last few years, Niall Ó Murchadha, several students, and I have explored the implications of the relativity of size (current research). If all distances in the universe were doubled over night, nothing would tell us this had happened. We therefore believe that absolute space is irrelevant and that relativity of size should be built into the foundations of dynamics. Strangely, Einstein’s general relativity just fails to implement perfect relativity of size. This is what allows the universe to expand in his theory. The Big Bang violates relativity of size. Most cosmologists accept this without even realising that it is an issue. We have created a scale-invariant theory very like general relativity but with perfect relativity of size. However, our construction is not yet satisfactory, and the search continues for a better alternative. Relativity of size is such an attractive principle, I believe that a dynamics of pure shape will one day be found.