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.
There are several videos available on YouTube in which I present my ideas, including the Dutch television film Killing Time (English with Dutch subtitles), the Spanish film El tiempo no existe, and an interview with Craig Callender, professor of philosophy at the University of San Diego.
I submitted the essay Bit from It (pdf) to the Third FQXi essay competition (2011) on the subject Is Nature Analog or Digital? John Wheeler's aphorism "It from Bit" is very popular in the quantum information community and among people who argue that information is physical and more fundamental than physical fields. I express doubts about this in my essay and argue that Wheeler's aphorism should be reversed.
In a (winning) submission (pdf) to a previous FQXI essay competition, I show that 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.
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 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 created a scale-invariant theory very like general relativity but with perfect relativity of size. However, our construction was not satisfactory, being unable to explain fundamental observational facts in cosmology. Relativity of size is such an attractive principle, I long believed that a dynamics of pure shape would one day be found, but in the last two years my thinking has changed somewhat. The changed perspective is reflected in the final four papers in Papers before the two on maximal variety. These define a theory of gravity that my current collaborators and I call Shape Dynamics. It retains the essential dynamical core of general relativity while removing in a well-motivated way structure that is potentially redundant and may well be responsible for the difficulties in the creation of quantum gravity. My collaborators Henrique Gomes, Sean Gryb, Tim Koslowski and Flavio Mercati are now working actively on Shape Dynamics and have obtained very interesting and encouraging results, the first of which are already published in two of the four papers just mentioned.