# 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.

### Online video

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.

### Essays

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.

## Shape Dynamics

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.

## Development of my Ideas Since 1999

This note has been prompted because a Polish translation of my The End of Time is being published by the Copernicus Press early in 2018 with a preface that outlines some of the changes in my thinking since the English publication in 1999. The main points together with references to technical papers relate to a possible resolution of the central problem addressed in my book: given rather strong indications that the universe is fundamentally timeless, whence comes our extremely strong impression that time does exist and carries us relentlessly from the past, through a fleeting present and into an uncertain future? This has been a major problem in theoretical physics since the discovery of the second law of thermodynamics in the early 1850s.

In The End of Time I outlined a possible solution to the problem based on the apparent incompatibility between the way time is treated in the two most fundamental theories we currently possess: Einstein's general theory of relativity and quantum mechanics. My proposal relied heavily on the basic structure of quantum mechanics. To my surprise a potential answer to the problem having nothing to do with quantum mechanics and already explicable in very simple terms of Newton's theory of universal gravitation occurred to me in 2012. Tim Koslowski, Flavio Mercati and I developed the idea in a paper published in 2014 in Physical Review Letters. Links to this and a follow-up can be found in Papers. There's an account of the idea in lay-person terms in the video The Mystery of the Arrow of Time and this article.

The new insight itself had much to do with the development, with a variety of collaborators, of the notion of shape space described in Box 3 of The End of Time. Shape space is a refinement of the notion of Platonia that plays a central role in that book. The difference is related to the one between shape and size. This can be seen especially clearly in the case of a triangle; its shape is determined by two internal angles and is intrinsic, but to define a size for it one needs an external measure. If, as I am, one is seeking to describe the universe, which by definition contains everything, the fundamental arena should be defined purely intrinsically. This leads to shape space. The new perspective that shape space offers turned out to reveal the completely unexpected possibilities discussed in the two technical papers cited in the previous paragraph. The post-2000 research papers trace the development with my collaborators of the theory of shape dynamics, based on the notion of shape space.

To conclude this note, I list the key ideas developed in The End of Time in which I still have confidence and the one main thing about which I have doubts. First, I still adhere to the idea of an 'arena of the universe': Platonia. Mathematically, the notion is closely related to configuration space, which is one of the most basic concepts in physics. However, I now think Platonia should definitely be considered along with shape space. There is a subtle connection between the two.

Second, I retain considerable confidence in the technique of best matching. This was first developed as ‘the intrinsic derivative’ in the 1982 with Bruno Bertotti and then extended by me to scale transformations with the more appropriate name best matching in the 2003 paper "Dynamics of pure shape..." and then significantly further in the 2005 paper "The physical gravitational degrees of freedom".

Third, I remain very hopeful that the notion of time capsules will prove to be helpful in understanding how a universe that, as a mathematical entity, is timeless nevertheless exhibits so many profound aspects that we experience as temporal.

Finally, throughout The End of Time I took the Wheeler–DeWitt equation seriously as a candidate outline of how general relativity and quantum mechanics should be unified. This was by no means universally accepted among theoretical physicists at the time I wrote my book; it remains controversial. The new ideas that have flowed from consideration of shape space do increase doubt in my mind about the status of the Wheeler–DeWitt equation. It is possible that shape space suggests some replacement and with it a deeper quantum explanation of time's arrows than the current purely classical proposal developed by Tim Koslowski, Flavio Mercati and myself.

## Recent Short Videos and a Documentary

Short videos (shot in July 2017) about my home and work can be viewed at:

- The Ideas behind Shape Dynamics
- An Invitation to Quantum Physicists
- The Mystery of the Arrow of Time
- A Colony of Swifts and Kepler's Planets
- The Dominion of Law
- One Big Thing Isaac Newton Did Get Wrong