*Ideas in Profile. Small introductions to big topics* is a series published by Profile Books that give short introductions to important socio-cultural or scientific topics. The book under review is the only one so far on a mathematical-physical topic: the theories of everything (note the plural!). This has been a popular, yet undeniably difficult, subject in the media since the successes of Einstein's relativity and the mind boggling consequences of quantum physics originating in the previous century. Frank Close is an emeritus physics professor from Oxford University and he has quite some experience in science communication. So he is the right choice to author a book of this kind.

A theory of everything is a theory that tries to explain everything within the realm of inanimate physics. It should not be speculation but a scientific theory, which means that it should be verifiable in some way by experimental observation. What is illustrated in this book is that the different theories of everything adapt to the scale at which one makes the observation, the scale of the mass, distance, or energy. With more powerful methods usually requiring higher energies, the definition of 'everything' has changed in the course of centuries. We are now even arriving at a point where 'theories' are developed that can probably never be verified by observation since that would require all the energy present in many galaxies. And that is certainly not going to happen in the near future. However, such an 'experiment' has taken place once already, namely at the time of the Big Bang. So our only hope is to rely on cosmic observations. Other theories propose multiverses, and since communication between these is impossible, one could ask whether this can still be called a scientific 'theory' in the usual sense.

Newton's mechanics could explain what happens to men-size objects on earth. His theory of gravity even explains how planets move around the sun or the moon around the earth, but problems arise when more than three bodies are involved. When many particles are involved, this gives rise to thermodynamics, from which follows the notion of entropy which in turn explains the arrow of time. The electric and magnetic theory were unified in the Maxwell equations. With light as an electromagnetic phenomenon, Einstein introduced his relativity theory which linked space and time in a four-dimensional space-time universe where mass and energy are essentially the same.

By joining Maxwell's theory to Dirac's quantum theory the quanta radiating at an atomic scale (1eV) can be described in accordance with general relativity. It took however quantum electrodynamics (QED) to match experiments properly. This insight was only possible after it was understood that terms in a seemingly divergent series cancelled so that it did converge indeed. It is all depending on mathematics after all. While QED describes the exchange of energy, quantum flavourdynamics (QFD) includes the exchange of electrical charge. However, when looking at a subnuclear particle scale (108−109

eV = 100MeV-1GeV), we are dealing with a strong nuclear force, and then the appropriate quantum field theory is quantum chromodynamics (QCD). Like we live in an electromagnetic field, it was conjectured in the 1960's that we are also surrounded by an electroweak plasma. This is only recently proved by the detection of the Higgs boson, which is its quantum excitation. Its energy is about 125 GeV, which is just within reach for the Large Hadron Collider (LHC) in CERN.

This brings us to the so called standard model, and this is where the present theories of everything are conceived. Now we are dealing with the next step up the scale, which is the Planck scale (energy: $1.25\times 10^{19}$GeV, length: $1.6\times 10^{−35}$m, time: $0.5\times 10^{−43}$sec). Both relativity theory and quantum theory have reached their limits here. In the core theory gravity does not matter because it is 40 orders of magnitude less than its electromagnetic counterpart and hence not observable. Observations with this amount of energy are not conceivable and it would imply weird situations, since black holes would be created making observations impossible and quantum theory predicts an unmeasurable space-time foam of black holes. The big challenge to combine quantum field theory and general relativity is to understand dark matter, and to know what prevents the fluctuation of the Higgs field. Possible ways out are string theory (but there turn out to be many), superstring theory (based on symmetry considerations), and multiverses (not verifiable but it would postulate the precise values of the fundamental constants just right for us to exist).

In a final chapter Close hints that some answers could be found in cosmological observations and that the quantum theory, built on the Heisenberg uncertainty principle, is only an approximation. If one could apply energies well above the Planck scale, observations could be made at smaller intervals of space and time and these would decrease indefinitely as the energy keeps increasing. But this is of course speculation as most theories at this scale are for the moment.

Close has done a good job, faithful to the objective of the series. No formulas and no technical details. No mathematics either, although it is clear that it is the driving force in the background of all these theories. I do not think that this is the place where you should learn what relativity theory or what quantum theory really is. When it comes to particle physics, it would be difficult to keep track of all the terminology of the different actors if you never heard of them before. Thus I think, you should not start reading this booklet unprepared. The point that Close makes quite clear is that the quest for the theory of everything is chasing a moving target. As long as one stays within a certain interval of the scale, some phenomena are perfectly negligible, and a theory of everything within that interval can be designed that matches the observations. However close to the boundary of that interval, deviations can be seen and things get mixed up like for example space and time are connected or mass and energy when the speed of light is approached. Then a new, more general theory, has to be designed that explains the phenomena on a much larger interval of the scale. Close guides the reader at a high level to the cliff where we are now standing. The cliff where gravity at a Planck scale has to be incorporated is the competing theories of relativity and quantum dynamics. And he sheds some light on what might be possible roads to a solution.

For those interested in this topic, note that other physicists have published books that were written with the intention. They all explain in their own way to the interested non-specialists the evolution that has brought us from the discovery of relativity theory and quantum physics in the previous century to the current state of the art in mathematical physics. Often these emphasize the personal view of the author. Here are just a few (in alphabetical order).

- Michio Kaku, Hyperspace. A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension (1994)
- Roger Penrose, The Emperor's New Mind. Concerning Computers, Minds, and the Laws of Physics (1989)
- Roger Penrose. Fashion, Faith, and Fantasy in the New Physics of the Universe (2016)
- Ian Stewart, Calculating the Cosmos. How Mathematics Unveils the Universe (2016)
- Max Tegmark, Our mathematical universe. My quest for the ultimate nature of reality (2014)
- Frank Wilczek, A Beautiful Question. Finding Nature's Deep Design (2015)
- Anthony Zee, Fearful Symmetry. The Search for Beauty in Modern Physics (1986)