ArticleslgStudy

physics

Loop quantum gravity

Loop quantum gravity is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Loop quantum gravity rather than just read about it. In short: Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Albert Einstein's geometric formulation, general relativity.

Loop quantum gravity — main illustration
Loop quantum gravity — illustration

Key takeaways

  • Loop quantum gravity belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Loop quantum gravity to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Loop quantum gravity from memory before moving on to harder problems.

Reference excerpt

Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Albert Einstein's geometric formulation, general relativity. As a theory, LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale on the order of a Planck length, approximately 10−35 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure. The areas of research, which involve about 30 research groups worldwide, share the basic physical assumptions and the mathematical description of quantum space. Research has evolved in two directions: the more traditional canonical loop quantum gravity, and the newer covariant loop quantum gravity, called spin foam theory. The most well-developed theory that has been advanced as a direct result of loop quantum gravity is called loop quantum cosmology (LQC). LQC advances the study of the early universe, incorporating the concept of the Big Bang into the broader theory of the Big Bounce, which envisions the Big Bang as the beginning of a period of expansion, that follows a period of contraction, which has been described as the Big Crunch.

History

In 1986, Abhay Ashtekar reformulated Einstein's general relativity in a language closer to that of the rest of fundamental physics, specifically Yang–Mills theory. Shortly after, Ted Jacobson and Lee Smolin realized that the formal equation of quantum gravity, called the Wheeler–DeWitt equation, admitted solutions labelled by loops when rewritten in the new Ashtekar variables. Carlo Rovelli and Smolin defined a nonperturbative and background-independent quantum theory of gravity in terms of these loop solutions. Jorge Pullin and Jerzy Lewandowski understood that the intersections of the loops are essential for the consistency of the theory, and the theory should be formulated in terms of intersecting loops, or graphs. In 1994, Rovelli and Smolin showed that the quantum operators of the theory associated to area and volume have a discrete spectrum. That is, geometry is quantized. This result defines an explicit basis of states of quantum geometry, which turned out to be labelled by Roger Penrose's spin networks, which are graphs labelled by spins. The canonical version of the dynamics was established by Thomas Thiemann, who defined an anomaly-free Hamiltonian operator and showed the existence of a mathematically consistent background-independent theory. The covariant, or "spin foam", version of the dynamics was developed jointly over several decades by research groups in France, Canada, UK, Poland, and Germany. It was completed in 2008, leading to the definition of a family of transition amplitudes, which in the classical limit can be shown to be related to a family of truncations of general relativity. The finiteness of these amplitudes was proven in 2011. It requires the existence of a positive cosmological constant, which is consistent with observed acceleration in the expansion of the Universe.

Background independence LQG is formally background independent, meaning the equations of LQG are not embedded in, or dependent on, space and time (except for its invariant topology). Instead, they are expected to give rise to space and time at distances which are 10 times the Planck length. The issue of background independence in LQG still has some unresolved subtleties. For example, some derivations require a fixed choice of the topology, while any consistent quantum theory of gravity should include topology change as a dynamical process. Spacetime as a "container" over which physics takes place has no objective physical meaning and instead the gravitational interaction is represented as just one of the fields forming the world. This is known as the relationalist interpretation of spacetime. In LQG this aspect of general relativity is taken seriously and this symmetry is preserved by requiring that the physical states remain invariant under the generators of diffeomorphisms. The interpretation of this condition is well understood for purely spatial diffeomorphisms. However, the understanding of diffeomorphisms involving time (the Hamiltonian constraint) is more subtle because it is related to dynamics and the so-called "problem of time" in general relativity. A generally accepted calculational framework to account for this constraint has yet to be found. A plausible candidate for the quantum Hamiltonian constraint is the operator introduced by Thiemann.

Constraints and their Poisson bracket algebra

Dirac observables The constraints define a constraint surface in the original phase space. The gauge motions of the constraints apply to all phase space but have the feature that they leave the constraint surface where it is, and thus the orbit of a point in the hypersurface under gauge transformations will be an orbit entirely within it. Dirac observables are defined as phase space functions, O {\displaystyle O} , that Poisson commute with all the constraints when the constraint equations are imposed,

… excerpt ends here. Continue reading the full article.

Illustrations

Loop quantum gravity illustration
Loop quantum gravity: Graphical representation of the simplest non-trivial Mandelstam identity relating different Wilson loops
Graphical representation of the simplest non-trivial Mandelstam identity relating different Wilson loops
Loop quantum gravity: The action of the Hamiltonian constraint translated to the path integral or so-called spin foam description. A single node splits into three nodes, creating a spin foam vertex. N ( x n ) {\displaystyle N(x_{n})} is the value of N {\displaystyle N} at the vertex and H n o p {\displaystyle H_{nop}} are the matrix elements of the Hamiltonian constraint H ^ {\displaystyle {\hat {H}}} .
The action of the Hamiltonian constraint translated to the path integral or so-called spin foam description. A single node splits into three nodes, creating a spin foam vertex. N ( x n ) {\displaystyle N(x_{n})} is the value of N {\displaystyle N} at the vertex and H n o p {\displaystyle H_{nop}} are the matrix elements of the Hamiltonian constraint H ^ {\displaystyle {\hat {H}}} .
Loop quantum gravity: An artist depiction of two black holes merging, a process in which the laws of thermodynamics are upheld
An artist depiction of two black holes merging, a process in which the laws of thermodynamics are upheld
Loop quantum gravity: Representation of quantum geometries of the horizon. Polymer excitations in the bulk puncture the horizon, endowing it with quantized area. Intrinsically the horizon is flat except at punctures where it acquires a quantized deficit angle or quantized amount of curvature. These deficit angles add up to 4 π {\displaystyle 4\pi } .
Representation of quantum geometries of the horizon. Polymer excitations in the bulk puncture the horizon, endowing it with quantized area. Intrinsically the horizon is flat except at punctures where it acquires a quantized deficit angle or quantized amount of curvature. These deficit angles add up to 4 π {\displaystyle 4\pi } .

Worked examples

Example 1 — a first encounter with Loop quantum gravity

Start with the simplest possible case. Write down what Loop quantum gravity claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Loop quantum gravity before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Loop quantum gravity ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Loop quantum gravity

In research
Loop quantum gravity appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Loop quantum gravity in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Loop quantum gravity is common in secondary-school and first-year university syllabi. It links to neighbouring topics Loop quantum gravity, Physics beyond the Standard Model, Theories of gravity, so understanding it makes those chapters shorter.
In everyday life
Look for Loop quantum gravity outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Loop quantum gravity in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Loop quantum gravity means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Loop quantum gravity out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Loop quantum gravity in simple terms?

Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Albert Einstein's geometric formulation, general…

Why does Loop quantum gravity matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Loop quantum gravity?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Loop quantum gravity.

Tags

  • Loop quantum gravity
  • Physics beyond the Standard Model
  • Theories of gravity

Keep exploring