Editing Loop quantum gravity (section)

== Problems and comparisons with alternative approaches ==
{{main|List of unsolved problems in physics}}

Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.

Many of these problems apply to LQG, including:
* Can quantum mechanics and general relativity be realized as a fully consistent theory (perhaps as a quantum field theory)?
* Is spacetime fundamentally continuous or discrete?
* Would a consistent theory involve a force mediated by a hypothetical graviton, or be a product of a discrete structure of spacetime itself (as in loop quantum gravity)?
* Are there deviations from the predictions of general relativity at very small or very large scales or in other extreme circumstances that flow from a quantum gravity theory?

The theory of LQG is one possible solution to the problem of quantum gravity, as is [[string theory]]. There are substantial differences however. For example, string theory also addresses [[Unified field theory|unification]], the understanding of all known forces and particles as manifestations of a single entity, by postulating extra dimensions and so-far unobserved additional particles and symmetries. Contrary to this, LQG is based only on quantum theory and general relativity and its scope is limited to understanding the quantum aspects of the gravitational interaction. On the other hand, the consequences of LQG are radical, because they fundamentally change the nature of space and time and provide a tentative but detailed physical and mathematical picture of quantum spacetime.

Presently, no semiclassical limit recovering general relativity has been shown to exist. This means it remains unproven that LQG's description of spacetime at the [[Planck scale]] has the right [[continuum limit]] (described by general relativity with possible quantum corrections). Specifically, the dynamics of the theory are encoded in the [[Hamiltonian constraint of LQG|Hamiltonian constraint]], but there is no candidate [[Hamiltonian (quantum mechanics)|Hamiltonian]].{{sfn|Nicolai|Peeters|Zamaklar|2005|pp=R193–R247}} Other technical problems include finding [[off-shell]] closure of the constraint algebra and physical inner product [[vector space]], coupling to matter fields of [[quantum field theory]], fate of the [[renormalization]] of the [[graviton]] in [[perturbation theory]] that lead to [[ultraviolet divergence]] beyond 2-loops (see [[one-loop Feynman diagram]] in [[Feynman diagram]]).{{sfn|Nicolai|Peeters|Zamaklar|2005|pp=R193–R247}}

While there has been a proposal relating to observation of [[naked singularity|naked singularities]],{{sfn|Goswami|Joshi|Singh|2006|p=31302}} and [[doubly special relativity]] as a part of a program called [[loop quantum cosmology]], there is no experimental observation for which loop quantum gravity makes a prediction not made by the Standard Model or general relativity (a problem that plagues all current theories of quantum gravity). Because of the above-mentioned lack of a semiclassical limit, LQG has not yet even reproduced the predictions made by general relativity.

An alternative criticism is that general relativity may be an [[effective field theory]], and therefore quantization ignores the fundamental degrees of freedom.

[[ESA]]'s [[INTEGRAL]] satellite measured polarization of photons of different wavelengths and was able to place a limit in the granularity of space<ref>{{Cite web|url=https://www.esa.int/Science_Exploration/Space_Science/Integral_challenges_physics_beyond_Einstein|title = Integral challenges physics beyond Einstein}}</ref> that is less than 10<sup>−48</sup>m or 13 orders of magnitude below the Planck scale.{{Clarify|date=November 2022|reason= See "Last part about granulation of spacetime is misleading?" in the talk page: "Public relations people at ESA put out a press release making popularized and overly sensationalized and overly broad claims. Someone should correct this."}}