Under what conditions will quantum effects become important for gravity?
Either very strong gravity fields (see BH and all similar phenomena) or very high energy particles/interactions in particle physics...For now,in accelerators and colliders gravity effects are too small to be considered,and that fact would be impossible,because we lack a renormalizable quantum theory of gravity.Quantum effects can be neglected in GR,as long you consider large scale phenomena,like planetary/galactic motion.Once you get into cosmology,things are not that simple...
What would the effects be caused by the strong gravitaional fields and the energy particles?
gravitational redshift; for one
It is believed that quantum gravity effects are responsible for the inhomogeneities in the Universe. There are even calculations in agreement with CMB spectrum and Large Scale Structure.
It is not commonly realized that even differences in earth's gravitational potential produce detectable phase shifts in the wavefunction of quantum particles.
This was first established experimentally in the so called COW experiments,( after the authors, Colella, Overhauser, and Werner, 1975) using neutron interferometry.(Phys. Rev. Lett. 34, p.1472 - 1474 (1975))
See here: http://prola.aps.org/abstract/PRL/v34/i23/p1472_1
Further 'COW' experiments are on-going.
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