Based on the uncertainty principles of quantum mechanics and the general theory of relativity, there is no reason that spacetime needs to be fundamentally smooth. Instead, in a quantum theory of gravity spacetime would consist of many small, ever-changing, regions in which space and time are not definite, but fluctuate in a foam-like manner.
In quantum mechanics, and in particular in quantum field theory, Heisenberg uncertainty principle allows energy to briefly decay into particles and antiparticles which then annihilate back to energy without violating physical conservation laws. As time and space are being probed at smaller scales, the energy of such particles, called virtual particles, increases. Combining this observation with the fact that in Einstein's theory of general relativity energy curves spacetime, one can imagine that at sufficiently small scales the energy of these fluctuations would be large enough to cause significant departures from the smooth spacetime seen at macroscopic scales, giving spacetime a "foamy" character.
Ordinarily, however, quantum field theory does not deal with virtual particles of sufficient energy to curve spacetime significantly, so quantum foam is a speculative extension of these concepts which imagines the consequences of such high-energy virtual particles at very short distances and times.
With an incomplete theory of quantum gravity, it is impossible to be certain what spacetime would look like at small scales. Also, our understanding of the quantum foam will necessarily be ambiguous as long as there are many competing proposals for a theory of quantum gravity.
The MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) telescopes have detected that among gamma-ray photons arriving from the blazar Markarian 501, some photons at different energy levels arrived at different times, suggesting that some of the photons had moved more slowly and thus contradicting the theory of general relativity's notion of the speed of light being constant, a discrepancy which could be explained by the irregularity of quantum foam. More recent experiments were, however, unable to confirm the supposed variation on the speed of light due to graininess of space.
Constraints and limits
The predicted scale of spacetime foam is about ten times a billionth of the diameter of a hydrogen atom's nucleus, which cannot be measured directly. A foamy spacetime would have limits on the accuracy with which distances can be measured because the size of the many quantum bubbles through which light travels will fluctuate. Depending on the spacetime model used, the spacetime uncertainties accumulate at different rates as light travels through the vast distances.
X-ray and gamma-ray observations of quasars used data from NASA’s Chandra X-ray Observatory, the Fermi Gamma-ray Space Telescope and ground-based gamma-ray observations from the Very Energetic Radiation Imaging Telescope Array (VERITAS) show that spacetime is uniform down to distances 1000 times smaller than the nucleus of a hydrogen atom.
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.
Random diffusion model
Chandra's X-ray detection of quasars at distances of billions of light years rules out the model where photons diffuse randomly through spacetime foam, similar to light diffusing passing through fog.
Relation to other theories
The Casimir effect is related to quantum foam in a sense that it is also understood in terms of the behaviour of virtual particles in the empty space between two parallel plates.
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