Are Einstein's equations really foolproof? Is there really no way to break the speed of light?

Originally asked on Quora

Yes. An object cannot surpass 299,792,458 m/s ever. However space itself can expand or stretch as fast as it wants. Think of it this way: You are in a rowboat in the ocean. You know that your arms can only propel the boat a little more that 25 mph. However the ocean itself often has waves and windshields greater than 100 mph. The universe is expanding more that twice the speed of light. During inflation it blew up trillions times faster than celeritas. And yes, this does mean that a warp drive (popularised in star trek; shown below) would have the potential to slope or wrinkle spacetime to carry a mass relatively faster than the golden number.

Left: Warp Drive Model, Wikipedia

I say relatively because we are only moving that speed from our own perspective. In the perspective of spacetime we are simply standing still while is stretches or folds. This can be expressed in a thought experiment: A man is in a box wooden box with no windows in space. He is floating in the center of the box due to the lack of gravity. Suddenly, he falls to the bottom of south pole of the box (I cannot say bottom because there is no up or down in space). How could this have happened he wonders? The man must think outside the box (Da dun ch). It could be that the box has entered a gravitational field and the man was pulled down by gravity (assuming heavy resistance on the box) it could also be that someone has attached a rope to the top of the box and the floor was pulled to the man's feet. It is impossible to know which scenario obscured unless the man left the box.

This goes to show that acceleration and gravity (push and pull) are the same forces and leads to the base of special relativity. It is the same case with a mass on a warp drive. Velocity is simply perspective. One relatively common example of faster-than-celeritas travel is a black hole since the sheer mass of the dead star has caused one particle to literally overlap another particle, it creates a warp that is marked as greater than 45 degrees (the speed of light) on a Feynman Diagram. Thus a ball placed near a black hole, upon crossing the event horizon would be traveling over celeritas, relatively speaking, of course.

Another possibility for faster than light travel is called quantum leaping: When a boson (a particle with no integral spin such as a photon or a lesson) is accelerated toward a barrier such as another particle or a graphene wall (a strip of graphene is only one atom thick) it is periodically subject to an anomaly in which the particle glitches through the barrier and lands on the other side without interaction.

It is not yet known why such occurrence occurs. Some have suggested Heisenberg uncertainty may play a role, but when mapped it was found that the wavefunction itself was transposed through the barrier. Only about one in every thousand particles launched does this and probability of the anomaly decreases per every particle diameter as a factor of the wall thickness. In other words if the particle was 1 unit wide and the wall was 2 units, the particle would have a one in two thousand chance of quantum leaping through the wall.

Other than the above options there is no yet discovered way to surpass the speed of light. A simple thought experiment can prove this: Scientists have discovered a way to surpass the speed of light and have built a rocket to do so. The rocket leaves earth and lands on mars, rigging it with explosives. Then it explodes mars and travels faster than the speed of light from the red planet. One it reaches pluto it quickly whips out its telescope. Since the light of the events past has not yet reached pluto the rocket sees itself landing on mars,. It then flies to mars, once again faster than the speed of light and kills its past self. Thus the mars does not explode and thus the rocket did not fly to pluto then fly back and kill itself.

This is called a circular event chain. It is technically not impossible as long as anything can travel faster than the speed of light.