Is the speed of light constant?

In 1887 one of the most important experiments in the history of physics took place. American scientists Michelson and Morley failed to measure the speed of the Earth by comparing the speed of light in the direction of the Earth's motion with that perpendicular to it. That arguably most important zero measurement in the history of science led Einstein to postulate that the speed of light is constant and consequently to formulate his theory of special relativity.
This theory implies that all laws of physics are the same, independent of the relative motion between observers — a concept known as Lorentz invariance.
Meanwhile, quantum theory has been developed, with Lorentz invariance at the heart of all its theoretical frameworks, in particular quantum field theory and the Standard Model of Particle Physics. The latter is the most precisely tested theory ever developed and has been verified to incredible precision.
So why doubt Lorentz invariance after 115 years of uninterrupted success?
The answer once again starts with Albert Einstein—this time with his theory of general relativity, which describes gravity as a deformation of geometry. A theory which has also proven to be extremely successful, having been tested to great precision in many circumstances ranging from weak to very strong gravity.
The problem lies in the fundamental incompatibility between the probability wave functions of quantum field theory with their movement through curved geometry and at the same time their modifications of spacetime curvature. Most attempts to reconcile the two theories into a common framework of quantum gravity have resulted in the need to break Lorentz invariance, albeit only slightly.
Thus, Michelson and Morley’s quest continues today, aided by modern laboratory experiments carried out with vastly improved technology.
One prediction of several Lorentz-Invariance-Violating quantum gravity theories is a dependence of the speed of light on photon energy. Any deviation from a constant speed of light must be extremely small to remain compatible with current constraints, but may become detectable at the very highest photon energies, known as very-high-energy gamma rays.
A team of researchers led by former UAB student Mercè Guerrero and current IEEC PhD student at the UAB Anna Campoy-Ordaz, with the participation of Robertus Potting from the University of Algarve and Markus Gaug, lecturer at the Department of Physics of the UAB and also assigned to the IEEC, has now tested Lorentz invariance to unprecedented precision with the help of astrophysics.
This is possible because tiny differences in the group velocity of photons may accumulate into measurable arrival-time delays on Earth if the photons were emitted simultaneously from a source located at a very large distance.
The team combined a collection of existing bounds from astrophysical measurements of very-high-energy gamma rays using a new statistical method to test a series of Lorentz-invariance-violating parametres, currently favoured by theoreticians, of the Standard Model Extension (SME).
The researchers hoped to prove Einstein wrong but, like so many others before them, did not succeed. Nevertheless, the new bounds improve upon previous limits by an order of magnitude.
In the meantime, the quest to experimentally test the predictions of quantum gravity theories continues, with next-generation instruments just around the corner—such as the Cherenkov Telescope Array Observatory—designed to greatly improve performance on the detection of very-high-energy gamma rays from distant sources.