In special relativity, sqrt(x^2 + y^2 + z^2 - ct^2) is invariant between any two events. Greg Egan wrote a science fiction trilogy in which it is instead sqrt(x^2 + y^2 + z^2 + ct^2) that is invariant between any two events. Note the single change of sign. He has worked out in great detail lots of consequences of this "tiny" change. He assumes that as much physics as possible remains unchanged. The series is of course set in a different universe. (That is surprisingly rare in science fiction.) The characters live on a planet that orbits a star, and are just starting to understand physics. The first novel, aptly named, is _The Clockwork Rocket_. The rocket is controlled by clockwork not because they're too primitive to have discovered electricity or steam, but because neither electric current nor liquids exist in their universe. Their planet is gravely threatened by a natural phenomenon. It would take far too long to develop the necessary science and engineering to solve the problem in time to save their planet. So they build an immense rocket designed to travel at an infinite (!) speed. People on board will live for generations and do research, and return to their home planet with the solution. By the planet's clocks this will be a very short time after they left. In our universe it would take an infinite amount of energy for a spaceship to travel at the speed of light. In their universe it would take an finite amount of energy for a spaceship to travel at an infinite speed. The novel also deals with their interpersonal relationships, and with political intrigue. There's even a saboteur aboard their giant rocket. But for me the most interesting part is watching them plan and conduct observations and experiments to figure out their physics (and their chemistry, and their biology). The second novel is _Eternal Flame_, the third is _The Arrows of Time_. The titles are minor spoilers for the physics. They can get unlimited energy by radiating equal amounts of positive and negative energy. And time travel is possible. There are some very interesting scenes set on a time-reversed planet they take a side trip to. Shortly after landing and taking a look around that lifeless planet, one of them sees something unexpected and wishes he'd been trained in time-reversed archeology. They were published in 2011, 2012, and 2013 respectively. For me, much of the fun was working out the physics for myself. For instance I discovered that if you were to accelerate at a uniform rate, you would eventually return to your starting point. Not just in space, but also in time and in velocity! For a real mathematical challenge, work out their version of Maxwell's equations. If you're curious about the physics, too lazy to work it out for yourself, and too cheap to buy the novels, there are spoilers for the physics (but not for the plot) at http://gregegan.net/ On this list, Egan is perhaps best known for the short story "Luminous" and its sequel "Dark Integers," based on the premise that no theorem is ever true of false until it makes a difference to some physical system (if only a mathematician's brain), that during the Big Bang, inconsistencies in math formed and got frozen in, and that by doing lots of proofs near the border between our math and the rival math it's possible to move the border. Bad guys want to get ahold of the secret location (in math-space) of the inconsistencies so that they can make a fortune, presumably by breaking arithmetic so that their bank balances add up to much larger numbers, heedless of the enormous risk to others. But have no fear, lots of things are very different in the Orthogonal universe, but their math is exactly like ours.