Solving super-luminal Special Relativity without breaking Einstein. We don’t (yet) have any way to test this, but University of Adelaide applied mathematicians are suggesting that an extended version of Einstein’s Theory of Special Relativity also holds true for velocities beyond lightspeed.
The surprising idea: with just two assumptions, an extended version of the mathematics for Einstein's special relativity works just as well above the speed of light as below. “Relativity is about frames of reference,” Professor Hill explains. That is, observers with different velocities see the same event from different frames of reference. “Einstein started working from information where the relative velocity is zero and what we knew about, such as rest mass, kinetic energy and so on. Then he extrapolated what is known in the Newtonian world for velocities lower than c. “Our thinking was -- how do we make use of the essential essence of Einstein’s theory for velocities above c?” What the mathematicians assumed is that for infinite relative velocity, there is a fixed relationship between the velocities of the two observers: where u is the first observer’s velocity, v is the second, the product of the two velocities is always c^2. “What we have is an equivalent theory to Special Relativity that applies for velocities beyond the speed of light. That theory is different from Special Relativity, but it has many of the same characteristics.
And readers with an interest in either physics or maths will be delighted with the vital assumptions: there has to be one, and only one, speed of light; and in all cases, a mathematical singularity occurs at the speed of light. “If you believe what we’ve done,” Professor Hill said, “there can only be one speed of light in a universe. This theory and method of solution is absolutely dependent on the assumption that there is only one speed of light in any universe. If there was a second speed of light, our mathematics wouldn’t work. If there is a second singularity -- the one that occurs at the speed of light in Special Relativity -- it wouldn’t work either."
To get from the theory to any practical test is another matter entirely, and Professor Hill freely admits he doesn’t know how that might be achieved. He hopes, however, that a test can be devised. “If you really don’t believe that faster-than-light is possible, then humans will be limited in space travel forever,” he said.