2.3 Strings or loops?2 Quantum Gravity: Where are 2.1 What is the problem?

2.2 What is the problem? The view of a relativist

For a relativist, on the other hand, the idea of a fundamental description of gravity in terms of physical excitations over a background metric space sounds physically very wrong. The key lesson learned from general relativity is that there is no background metric over which physics happens (unless, of course, in approximations). The world is more complicated than that. Indeed, for a relativist, general relativity is much more than the field theory of a particular force. Rather, it is the discovery that certain classical notions about space and time are inadequate at the fundamental level; they require modifications which are possibly as basic as the ones that quantum mechanics introduced. One of these inadequate notions is precisely the notion of a background metric space, (flat or curved), over which physics happens. This profound conceptual shift has led to the understanding of relativistic gravity, to the discovery of black holes, to relativistic astrophysics and to modern cosmology.

From Newton to the beginning of this century, physics has had a solid foundation in a small number of key notions such as space, time, causality and matter. In spite of substantial evolution, these notions remained rather stable and self-consistent. In the first quarter of this century, quantum theory and general relativity have deeply modified this foundation. The two theories have obtained solid success and vast experimental corroboration, and can now be considered established knowledge. Each of the two theories modifies the conceptual foundation of classical physics in an (more or less) internally consistent manner, but we do not have a novel conceptual foundation capable of supporting both theories. This is why we do not yet have a theory capable of predicting what happens in the physical regime in which both theories are relevant, the regime of Planck scale phenomena, tex2html_wrap_inline2492 cm.

General relativity has taught us not only that space and time share the property of being dynamical with the rest of the physical entities, but also -more crucially- that spacetime location is relational only (see section 5.3). Quantum mechanics has taught us that any dynamical entity is subject to Heisenberg's uncertainty at small scale. Therefore, we need a relational notion of a quantum spacetime in order to understand Planck scale physics.

Thus, for a relativist, the problem of quantum gravity is the problem of bringing a vast conceptual revolution, begun with quantum mechanics and with general relativity, to a conclusion and to a new synthesis. Popup Footnote In this synthesis the notions of space and time need to be deeply reshaped in order to take into account what we have learned with both our present ``fundamental'' theories.

Unlike perturbative or nonperturbative string theory, loop quantum gravity is formulated without a background spacetime. Loop quantum gravity is thus a genuine attempt to grasp what quantum spacetime is at the fundamental level. Accordingly, the notion of spacetime that emerges from the theory is profoundly different from the one on which conventional quantum field theory or string theory is based.

2.3 Strings or loops?2 Quantum Gravity: Where are 2.1 What is the problem?

image Loop Quantum Gravity
Carlo Rovelli
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