Question: How can you test quantum gravity predictions?
About the article "General relativity", section "Quantum gravity".

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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.
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 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 is encoded in the Hamiltonian constraint, but there is no candidate Hamiltonian.
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).
While there has been a recent proposal relating to observation of naked singularities, 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. 
Quantum foam (also referred to as space-time foam) is a concept in quantum mechanics devised by John Wheeler in 1955.
The "foam" is supposed to be conceptualized as the foundation of the fabric of the universe.
Additionally, quantum foam can be used as a qualitative description of subatomic space-time turbulence at extremely small distances (on the order of the Planck length).
At such small scales of time and space, the Heisenberg uncertainty principle allows energy to briefly decay into particles and antiparticles and then annihilate without violating physical conservation laws.
As the scale of time and space being discussed shrinks, the energy of the virtual particles increases.
According to Einstein's theory of general relativity, energy curves space-time.
This suggests that—at sufficiently small scales—the energy of these fluctuations would be large enough to cause significant departures from the smooth space-time seen at larger scales, giving space-time a "foamy" character.
With an incomplete theory of quantum gravity, it is impossible to be certain what space-time would look like at these small scales, because existing theories of gravity do not give accurate predictions in that regime.
Therefore, any of the developing theories of quantum gravity may improve our understanding of quantum foam as they are tested.
However, observations of radiation from nearby quasars by Floyd Stecker of NASA's Goddard Space Flight Center have placed strong experimental limits on the possible violations of Einstein's special theory of relativity implied by the existence of quantum foam.
Thus experimental evidence so far has given a range of values in which scientists can test for quantum foam. 
  Vacuum catastrophe: Why does the predicted mass of the quantum vacuum have little effect on the expansion of the universe?
Quantum gravity: 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?
Black holes, black hole information paradox, and black hole radiation: Do black holes produce thermal radiation, as expected on theoretical grounds?
Does this radiation contain information about their inner structure, as suggested by Gauge-gravity duality, or not, as implied by Hawking's original calculation?
If not, and black holes can evaporate away, what happens to the information stored in them (quantum mechanics does not provide for the destruction of information)?
Or does the radiation stop at some point leaving black hole remnants?
Is there another way to probe their internal structure somehow, if such a structure even exists?
Extra dimensions: Does nature have more than four spacetime dimensions?
If so, what is their size?
Are dimensions a fundamental property of the universe or an emergent result of other physical laws?
Can we experimentally observe evidence of higher spatial dimensions?
The cosmic censorship hypothesis and the chronology protection conjecture: Can singularities not hidden behind an event horizon, known as "naked singularities", arise from realistic initial conditions, or is it possible to prove some version of the "cosmic censorship hypothesis" of Roger Penrose which proposes that this is impossible?
Similarly, will the closed timelike curves which arise in some solutions to the equations of general relativity (and which imply the possibility of backwards time travel) be ruled out by a theory of quantum gravity which unites general relativity with quantum mechanics, as suggested by the "chronology protection conjecture" of Stephen Hawking?
Locality: Are there non-local phenomena in quantum physics?
If they exist, are non-local phenomena limited to the entanglement revealed in the violations of the Bell Inequalities, or can information and conserved quantities also move in a non-local way?
Under what circumstances are non-local phenomena observed?
What does the existence or absence of non-local phenomena imply about the fundamental structure of spacetime?
How does this relate to quantum entanglement?
How does this elucidate the proper interpretation of the fundamental nature of quantum physics?  
Quantum gravity (QG) is a field of theoretical physics that seeks to describe the force of gravity according to the principles of quantum mechanics.
Our current understanding of gravity is based on Albert Einstein's general theory of relativity, which is formulated within the framework of classical physics.
On the other hand, the nongravitational forces are described within the framework of quantum mechanics, a radically different formalism for describing physical phenomena based on probability.
The necessity of a quantum mechanical description of gravity follows from the fact that one cannot consistently couple a classical system to a quantum one.
Although a quantum theory of gravity is needed in order to reconcile general relativity with the principles of quantum mechanics, difficulties arise when one attempts to apply the usual prescriptions of quantum field theory to the force of gravity.
From a technical point of view, the problem is that the theory one gets in this way is not renormalizable and therefore cannot be used to make meaningful physical predictions.
As a result, theorists have taken up more radical approaches to the problem of quantum gravity, the most popular approaches being string theory and loop quantum gravity.
Strictly speaking, the aim of quantum gravity is only to describe the quantum behavior of the gravitational field and should not be confused with the objective of unifying all fundamental interactions into a single mathematical framework.
Although some quantum gravity theories such as string theory try to unify gravity with the other fundamental forces, others such as loop quantum gravity make no such attempt; instead, they make an effort to quantize the gravitational field while it is kept separate from the other forces.
A theory of quantum gravity which is also a grand unification of all known interactions, is sometimes referred to as a theory of everything (TOE).
One of the difficulties of quantum gravity is that quantum gravitational effects are only expected to become apparent near the Planck scale, a scale far smaller in distance (equivalently, far larger in energy) than what is currently accessible at high energy particle accelerators.
As a result, quantum gravity is a mainly theoretical enterprise, although there are speculations about how quantum gravity effects might be observed in existing experiments. 
As there presently exists no widely accepted framework for how to combine quantum mechanics with relativistic gravity, science is not currently able to make predictions about events occurring over intervals shorter than the Planck time or distances shorter than one Planck length, the distance light travels in one Planck time—about 1.616 × 10−35 meters.
Without an understanding of quantum gravity, a theory unifying quantum mechanics and relativistic gravity, the physics of the Planck epoch are unclear, and the exact manner in which the fundamental forces were unified, and how they came to be separate entities, is still poorly understood.
Three of the four forces have been successfully integrated in a common framework, but gravity remains problematic.
If quantum effects are ignored, the universe starts from a singularity with an infinite density.
This conclusion could change when quantum gravity is taken into account.
String theory and Loop quantum gravity are leading candidates for a theory of unification, which have yielded meaningful insights already, but work in Noncommutative geometry and other fields also holds promise for our understanding of the very beginning.