Mathematicians from University of Adelaide, Australia, have extended the theory of special relativity to work beyond the speed of light.

Einstein’s theory holds that nothing could move faster than the speed of light. Published in 1905, the theory explains how motion and speed is always relative to the observer’s frame of reference. It connects measurements of the same physical incident viewed from these different points in a way that depends on the relative velocity of the two observers.

“Since the introduction of special relativity there has been much speculation as to whether or not it might be possible to travel faster than the speed of light, noting that there is no substantial evidence to suggest that this is presently feasible with any existing transportation mechanisms,” said Prof Jim Hill of the University of Adelaide’s School of Mathematical Sciences, who co-authored a paper published in the Proceedings of the Royal Society A.

“About this time last year, experiments at CERN in Switzerland suggested that perhaps neutrinos could be accelerated just a very small amount faster than the speed of light; at this point we started to think about how to deal with the issues from both a mathematical and physical perspective.”

“Questions have since been raised over the experimental results but we were already well on our way to successfully formulating a theory of special relativity, applicable to relative velocities in excess of the speed of light.”

“Our approach is a natural and logical extension of the Einstein’s Theory of Special Relativity, and produces anticipated formulae without the need for imaginary numbers or complicated physics.”

The new formulas extend special relativity to a situation where the relative velocity can be infinite, and can be used to describe motion at speeds faster than light.

“We propose here two new transformations between inertial frames that apply for relative velocities greater than the speed of light, and that are complementary to the Lorentz transformation, giving rise to the Einstein special theory of relativity that applies to relative velocities less than the speed of light,” the authors said in the paper. “The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behavior when the relative velocity approaches the speed of light and generating the same addition law for velocities, but, most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide well-defined expressions.”

“We are mathematicians, not physicists, so we’ve approached this problem from a theoretical mathematical perspective,” explained co-author Dr Barry Cox of the University of Adelaide’s School of Mathematical Sciences. “Should it, however, be proven that motion faster than light is possible, then that would be game changing.

“Our paper doesn’t try and explain how this could be achieved, just how equations of motion might operate in such regimes,” he concluded.

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Bibliographic information: James M. Hill and Barry J. Cox. Einstein’s special relativity beyond the speed of light. Proc. R. Soc. A, published online before print October 3, 2012; doi: 10.1098/rspa.2012.0340