Once Before Time - Martin Bojowald [3]
Although the required theory is highly mathematical, many calculations are by now intuitively understood. Intuition is not only useful for explorations in an unknown territory; it also allows broad explanations. As suggested by the Nietzsche passage at the beginning of this Introduction, the aims of this book may be realized without the use of mathematical formalism, except for a single crucial equation in chapter 4. While mathematics cannot be dispensed with if one wishes to discover and fully understand the issues underlying this book, an intuitive grasp is possible without too much effort. One may not always discern why things are supposed to be one way rather than another, but with some trust in the travel guide, connections can be grasped.
A warning is required nonetheless: Many areas of research in quantum gravity are still to be considered speculative. In contrast to the first half of the past century, the period when general relativity and quantum theory were developed, there are as yet no observations to corroborate the theoretical formulations of quantum gravity. What currently propels research is a motley collection of conceptual considerations regarding the incompleteness of general relativity, as well as mathematical consistency conditions in the formulation of equations. For instance, there is no guarantee whatsoever that a combination of certain mathematical methods, as they are used in general relativity and quantum physics, will allow solutions for a reliable description of the universe. The required mathematical tools are indeed so restrictive that formulating a theory with reasonable solutions would in itself represent immense success. Whether there may be other reasonable theories is a different, so far incompletely understood question. This shows the fragility of the pillars on which quantum gravity presently rests. But optimism does prevail, for many independent indications such as those in this book point in the same direction. What’s more, it is expected that cosmological observations made in the not too distant future could reveal phenomena predicted by quantum gravity. Such potential observations, which are also described in this book, would finally render quantum gravity an empirically tested theory.
1. The philosopher’s stone melts away. What counts as certain knowledge may, upon further examination, turn out to be in need of correction. Evaluating the results or promises of science must always take into account its limits. Often, such limits are even more important than established results, for they show the way to new insights. (Sculpture by Gianni Caravaggio: Spreco di energia assoluta [Absolute waste of energy], 2006. Photograph: Robert Marossi.)
As of now, the status of quantum gravity resembles the earliest stages of claiming a new territory. Mathematics is the pioneer who opens up new areas beyond established frontiers. In our case, these frontiers are literally those of the universe and of time. Mathematics also serves to explore newly won lands; but in an empirical science such as physics, these lands can be claimed and secured only by observations. This remains to be accomplished for quantum gravity, which thus resembles territory still full of danger, where one can all too easily get lost or be swallowed up in swamps of speculation.
Such a land demands a humility toward nature that is not always shown. The language of physicists often sounds very determined (and sometimes even shows signs of hubris), but concerning a law of nature one must bear in mind, “It may be accurate, it may be faulty. If it is not accurate, the scientist, not nature, is to blame.”1 A physicist constructs laws of nature, but is the one responsible if they are broken. Nobody is a physicist’s subject, least of all Nature herself. This is true in particular for theoretical sketches such as quantum