According to special relativity, nothing can travel faster than the speed of light – an object with mass would require more and more energy to accelerate closer and closer to the speed of light without actually reaching it. However, theoretical approaches can extend relativity to include particles and observers moving faster than the speed of light. Not only it is possible to do that without causing paradoxes, but there are some intriguing consequences for physics both slower and faster than the speed of light.

Relativity describes the universe with something called a metric – in the case of our cosmos, which is a 3+1 space-time continuum, with three space dimensions and one time dimension. There are other metrics out there that physicists can play with. In the standard one, the only difference between space and time is a minus sign in some of the equations. There are also some other important requirements: The fact that the speed of light in a vacuum is constant, but also that the laws of physics are the same and all the inertial observers are equal.

Would that work if an observer was moving faster than the speed of light? It turns out that theoretically that is possible, but with a caveat. The metric would have to feature a single dimension of space and three dimensions of time. So, from the point of view of such an observer, a regular particle moving through our three-dimensional space will be actually “aging” in three different directions of time.

Now that seems like some sci-fi gobbledygook, but the equations not only are consistent and don’t create paradoxes, but they also end up reproducing some crucial descriptions of quantum mechanics. The particles, from their point of view, simply behave according to the principle of superposition. It doesn’t require the speed of light in a vacuum to be different, just that superluminal observers exist (at least theoretically).

"For a superluminal observer, the classical Newtonian point particle ceases to make sense, and the field becomes the only quantity that can be used to describe the physical world," Professor Andrzej Dragan, from the University of Warsaw and the National University of Singapore, said in a statement.

"Until recently it was generally believed that postulates underlying quantum theory are fundamental and cannot be derived from anything more basic. In this work we showed that the justification of quantum theory using extended relativity [...] can be naturally generalized to 1 + 3 spacetime and such an extension leads to the field-theoretic formulation of the quantum theory. This justifies, or at least provides a plausibility argument, why this extension is not just an eccentric thought exercise, but reflects something fundamental about symmetries of laws of physics," write the authors in the publication.

This intriguing connection between relativity and quantum mechanics is definitely worth exploring more, as might provide new insights into either field of study. The work is clearly theoretical and the applications are not about finding some particles that can move faster than the speed of light, unfortunately.

"The mere experimental discovery of a new fundamental particle is a feat worthy of the Nobel Prize and feasible in a large research team using the latest experimental techniques. However, we hope to apply our results to a better understanding of the phenomenon of spontaneous symmetry breaking associated with the mass of the Higgs particle and other particles in the Standard Model, especially in the early universe," explained professor Krzysztof Turzyński.

The work is published in the journal Classical and Quantum Gravity.