The Crab Nebula.
Image Source: Hyperphysics.
One of the most general expectations of quantum gravity is that space-time is not the smooth background of General Relativity, but instead a wildly fluctuating, bubbly, foamy mess. Seeing the quantum properties of space-time directly is not presently possible, but what we can see is whether the quantum gravitational behavior affects the way particles travel through space-time.
One way this could happen is by distorting paths so that photons of different frequency (energy) move at slightly different speeds. Such an effect is referred to as ‘dispersion’. Next to dispersion there is dissipation, which is basically energy loss into the background. While quantum gravitationally induced dispersion has received substantial attention during the last decade, dissipation hasn’t received as much love.
In a nice and straight-forward recent paper dissipation finally got some love from Liberati and Maccione
Astrophysical constraints on Planck scale dissipative phenomena
Stefano Liberati, Luca Maccione
arXiv:1309.7296 [gr-qc]
They start with a general hydrodynamic ansatz that assigns space-time the properties of a fluid, notably a viscosity, which causes dissipation. The microscopic theory that would give rise to such a hydrodynamic behavior they leave unspecified and just ask what observable consequences a non-vanishing space-time viscosity would have. With this ansatz, they make an expansion of the dispersion relation and collect the dissipative (imaginary) contributions.
Then they look at observations of highly energetic photons from a distant source, the Crab nebula. If space-time was viscous, the photons would lose energy during their travel. Already the rather conservative estimate that the photons of the highest observed energies shouldn’t have lost more energy than they have left at arrival leads to very tight constraints. If the photons lose energy faster than that, the spectrum we receive on Earth would be highly distorted and pretty much incompatible with our knowledge of astrophysics.
This constraint from existing data clearly rules out Planck scale effects, ie effects that plausibly have a quantum gravitational origin, at first order. Better constraints can be obtained by drawing upon concrete astrophysical models for the typical energy of photons that are emitted, so it seems likely that in the future we will see even better constraints on this.
Much like with violations of Lorentz-invariance this is a case where nothing has been found. Yeah, Einstein was right, again. But this doesn’t mean that nothing has been learned. We’ve learned that any model for an emergent space-time that does not have a very small, almost vanishing, viscosity is clearly incompatible with observation.
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