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Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects.
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Hermann Nicolai Director. Email: hermann. Members of the Division. Independent research groups. Publications of the Division. Articles in the Max Planck Yearbook. Nicolai: Quantum gravity and unification. More Articles in the Max Planck Yearbook. News and Events. Nicolai in an interview about Stephen Hawking. More News and Events. Max Planck Partner Groups. Since the contemporary theory of gravity, general relativity, describes gravitation as the curvature of spacetime by matter and energy, a quantization of gravity seemingly implies some sort of quantization of spacetime geometry: quantum spacetime.

Insofar as all extant physical theories rely on a classical non-quantum spacetime background, this presents not only extreme technical difficulties, but also profound methodological and ontological challenges for the philosopher and the physicist.

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Though quantum gravity has been the subject of investigation by physicists for almost a century, philosophers have only just begun to investigate its philosophical implications. Dutch artist M.


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Some of his work, for example Ascending and Descending , relies on optical illusion to depict what is actually an impossible situation. Other works are paradoxical in the broad sense, but not impossible: Relativity depicts a coherent arrangement of objects, albeit an arrangement in which the force of gravity operates in an unfamiliar fashion. See the Other Internet Resources section below for images. Quantum gravity itself may be like this: an unfamiliar yet coherent arrangement of familiar elements.

Or it may be more like Ascending and Descending , an impossible construction which looks sensible in its local details but does not fit together into a coherent whole when using presently existing building materials. If the latter is true, then the construction of a quantum theory of gravity may demand entirely unfamiliar elements. Whatever the final outcome, the situation at present is one of flux, with a great many competing approaches vying for the prize. However, it is also important to note that the prize is not always the same: string theorists seek a unified theory of all four interactions that has the power of explaining such things as the numbers of generations of elementary particles and other previous inexplicable properties.

Other approaches are more modest, and seek only to bring general relativity in line with quantum theory, without necessarily invoking the other interactions. Hence, the problem of quantum gravity can mean very different things to different researchers and what constitutes a possible solution to one group might not qualify as such to another. Given that quantum gravity does not yet exist as a working physical theory, one might legitimately question whether philosophers have any business being involved at this stage.

In such cases, one typically proceeds by assuming the physical soundness of the theory or theoretical framework and drawing out the ontological and perhaps epistemological consequences of the theory, trying to understand what it is that the theory is telling us about the nature of space, time, matter, causation, and so on. Theories of quantum gravity, on the other hand, are bedeviled by a host of technical and conceptual problems, questions, and issues that make them largely unsuited to this kind of interpretive approach.

However, philosophers who have a taste for a broader and more open-ended form of inquiry will find much to think about, and it is entirely possible that future philosophers of physics will be faced with problems of a very different flavour as a result of the peculiar nature of quantum gravity.

Whence the incompatibility? In doing so, they manage to encompass traditional, Newtonian gravitational phenomena such as the mutual attraction of two or more massive objects, while also predicting new phenomena such as the bending and red-shifting of light by these objects which have been observed and the existence of gravitational radiation until very recently, with the direct detection of gravitational waves by LIGO, this was, of course, only indirectly observed via the decrease in the period of binary pulsars-see the Physics Nobel Prize presentation speech by Carl Nordling.

These quantities are represented by tensor fields, sets of real numbers associated with each spacetime point. For example, the stress, energy, and momentum T ab x , t of the electromagnetic field at some point x , t , are functions of the three components E i , E j , E k , B i , B j , B k of the electric and magnetic fields E and B at that point. The metric g ab x , t is a set of numbers associated with each point which gives the distance to neighboring points.

A model of the world according to general relativity consists of a spacetime manifold with a metric, the curvature of which is constrained by the stress-energy-momentum of the matter distribution.

Quantum gravity - Wikipedia

All physical quantities — the value of the x -component of the electric field at some point, the scalar curvature of spacetime at some point, and so on — have definite values, given by real as opposed to complex or imaginary numbers. Thus general relativity is a classical theory in the sense given above. The problem is that our fundamental theories of matter and energy, the theories describing the interactions of various particles via the electromagnetic force and the strong and weak nuclear forces, are all quantum theories.

In quantum theories , these physical quantities do not in general have definite values. For example, in quantum mechanics, the position of an electron may be specified with arbitrarily high accuracy only at the cost of a loss of specificity in the description of its momentum, hence its velocity. At the same time, in the quantum theory of the electromagnetic field known as quantum electrodynamics QED , the electric and magnetic fields associated with the electron suffer an associated uncertainty.

In general, physical quantities are described by a quantum state which gives a probability distribution over many different values, and increased specificity narrowing of the distribution of one property e. Likewise, if one focusses in on the spatial geometry, it will not have a definite trajectory. On the surface, the incompatibility between general relativity and quantum theory might seem rather trivial. Why not just follow the model of QED and quantize the gravitational field, similar to the way in which the electromagnetic field was quantized?

Time gets weird

This is more or less the path that was taken, but it encounters extraordinary difficulties. However, these technical problems are closely related to a set of daunting conceptual difficulties, of interest to both physicists and philosophers. The conceptual difficulties basically follow from the nature of the gravitational interaction, in particular the equivalence of gravitational and inertial mass, which allows one to represent gravity as a property of spacetime itself, rather than as a field propagating in a passive spacetime background.

When one attempts to quantize gravity, one is subjecting some of the properties of spacetime to quantum fluctuations. For example, in canonical quantizations of gravity one isolates and then quantizes geometrical quantities roughly the intrinsic and extrinsic curvature of three dimensional space functioning as the position and momentum variables. Given the uncertainty principle and the probabilistic nature of quantum theory, one has a picture involving fluctuations of the geometry of space, much as the electric and magnetic fields fluctuate in QED.

But ordinary quantum theory presupposes a well-defined classical background against which to define these fluctuations Weinstein, a, b , and so one runs into trouble not only in giving a mathematical characterization of the quantization procedure how to take into account these fluctuations in the effective spacetime structure? For example, a fluctuating metric would seem to imply a fluctuating causal structure and spatiotemporal ordering of events, in which case, how is one to define equal-time commutation relations in the quantum theory?

Quantum gravity's tangled time

See the section on the Lagrangian formulation in the entry on quantum field theory. Cao believes that the conceptual nature of the problem demands a conceptual resolution. This approach asks for an analysis of the ontological pictures of the two ingredient theories of quantum gravity, so that their consistency the consistency of the resulting synthesis can be properly assessed. Ontology for Cao refers to the primary, autonomous structures from which all other properties and relations in a theory are constructed.

A fairly simple inspection of the respective ontological constraints imposed by general relativity and quantum field theory reveals serious tension: general relativity discards the fixed kinematical structure of spacetime, so that localization is rendered relational, but in quantum field theory a fixed flat background is part of its ontological basis, from which the standard features of the theory are derived. On the other hand, as we have seen, quantum field theory involves quantum fluctuations in the vicinity of a point, while general relativity involves the use of a smooth point neighbourhood.

Either way, in order to bring the two ontological bases together, some piece of either edifice must be demolished. Cao proposes that the tension can best be resolved by focussing firmly on those sine qua non principles of the respective theories. Likewise, he argues that quantum field theory requires a fixed background in order to localize quantum fields and set up causal structure. But he notes that a relational account of localization could perform such a function, with fields localized relative to each other.

In so doing, one could envisage a diffeomorphism covariant quantum field theory i.

The Story of Loop Quantum Gravity- From the Big Bounce to Black Holes

The resulting synthesized entity a violently fluctuating, universally coupled quantum gravitational field would then be what a quantum theory of gravity ought to describe. While such an approach sounds sensible enough on the surface, to actually put it into practice in the constructive stages of theory-building rather than a retrospective analysis of a completed theory is not going to be easy—though it has to be said, the method Cao describes bears close resemblance to the way loop quantum gravity has developed. The causaloid approach is intended to provide a framework for quantum gravity theories, where idea is to develop a general formalism that respects the key features of both general relativity, which he takes to be the dynamical non-probabilistic causal structure, and quantum theory, which he takes to be the probabilistic nondynamical dynamics.

The causaloid of some theory is an entity that encodes all that can be calculated in the theory. However, it is perfectly possible that both of the input theories break down at higher energies. Not only that, the technical difficulties of setting up the kind of physically realistic diffeomorphism-invariant quantum field theory he suggests have so far proven to be an insurmountable challenge. Of course, they must be relational, but this still leaves the problem very much open. The idea of making progress by isolating appropriate principles of quantum gravity forms the basis of a special issue: Crowther and Rickles, eds, We will look in more detail at how various conceptual and methodological problems arise in two different research programs below.

But first, we introduce some key features of the leading research programs. All approaches to the problem of quantum gravity agree that something must be said about the relationship between gravitation and quantized matter. These various approaches can be catalogued in various ways, depending on the relative weight assigned to general relativity and quantum field theory.

Some approaches view general relativity as in need of correction and quantum field theory as generally applicable, while others view quantum field theory as problematic and general relativity as having a more universal status. Still others view the theories in a more even-handed manner, perhaps with both simply amounting to distinct limits of a deeper theory. It has often been suggested, since the earliest days of quantum gravity research, that bringing quantum field theory and general relativity together might serve to cure their respective singularity problems the former resulting from bad high frequency behaviour of fields; the latter resulting from certain kinds of gravitational collapse.

This hope does seem to have been borne out in many of the current approaches. Roger Penrose has even argued that the joint consideration of gravitation and quantum theory could resolve the infamous quantum measurement problem see Penrose ; see also the section on the measurement problem in the entry on philosophical issues in quantum theory. There are difficulties in distinguishing the gravitationally induced collapse that Penrose proposes from the effective collapse induced by quantum theory itself, thanks to decoherence—Joy Christian has suggested that by observing oscillations in the flavor ratios of neutrinos originating at cosmological distances one could eliminate the confounding effects of environmental decoherence.

By far the two most popular approaches are string theory and loop quantum gravity.


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  • The former is an example of an approach to quantum gravity in which the gravitational field is not quantized; rather, a distinct theory is quantized which happens to coincide with general relativity at low energies. The latter is an approach involving constrained canonical quantization, albeit of a version of general relativity based on a different choice of variables than the usual geometrodynamical, metric-based variables.

    We cover the basic details of each of these in the following subsections. However, it turned out that the theory is not perturbatively renormalizable, meaning that there are ineliminable infinities. The original and still prominent idea behind string theory was to replace the point particles of ordinary quantum field theory particles like photons, electrons, etc with one-dimensional extended objects called strings. See Weingard, and Witten, for overviews of the conceptual framework.

    String theories containing fermions as well as bosons must be formulated in nine space dimensions and one time dimension. Strings can be open or closed, and have a characteristic tension and hence vibrational spectrum. The various modes of vibration correspond to various particles, one of which is the graviton the hypothetical massless, spin-2 particle responsible for mediating gravitational interactions. The resulting theories have the advantage of being perturbatively renormalizable. This means that perturbative calculations are at least mathematically tractable.

    Since perturbation theory is an almost indispensable tool for physicists, this is deemed a good thing.

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    The rationale, according to one kind of duality S-duality , is that one theory at strong coupling high energy description is physically equivalent in terms of physical symmetries, correlation functions and all observable content to another theory at weak coupling where a lower energy means a more tractable description , and that if all the theories are related to one another by dualities such as this, then they must all be aspects of some more fundamental theory. Though attempts have been made, there has been no successful formulation of this theory: its very existence, much less its nature, is still largely a matter of conjecture.

    The link comes about because in a dual pair of theories one has a observable equivalence combined with what appears to be radical physical and mathematical differences.