Special Relativity Redux

  Does the Thread Break? Back Story Bell's Spaceship Paradox is a lesson in formation flying at near light speed. Here's the challenge: Point two spaceships in the same direction and line them up, one behind the other Tether them with a delicate thread and pull it taut Try to get the whole assembly up to speed without breaking the thread On the one hand, the entire assembly is subject to Lorentz contraction so everything, including the thread, should survive. On the other hand, each component of the assembly is subject to Lorentz contraction so the thread should break as the spaceships shrink. It's a conundrum. Here are the worldlines for the ends of the thread from the two perspectives of interest: Rest Length CERN insists that you maintain your geometry in your own reference frame no matter how fast you go or what you’re made of. Otherwise it would be a dead give-away for detecting your own motion at cruising speed with the curtains closed. But the worldline x=L+vt transf...

Lorentz Contraction and Perceptions of Simultaneity Back Story In the Ladder Paradox (aka. Pole-Barn Paradox), we are given a ladder (or pole), which is too long to fit inside our barn when both are at rest. A smart aleck physicist, who knows a thing or two about Lorentz contraction, claims he can make it fit (if only for an instant) by throwing it through the barn at a sufficiently high speed. We presume the ladder is perfectly rigid so it won't be contorted by the force of acceleration. That would be cheating. In fact, let's put rockets on both ends just to be sure. Here we go: Hmmm. What went wrong? We followed the recipe, but the ladder didn't shrink. In fact, just the opposite. In its moving reference frame, the ladder actually thinks it has gotten longer (by a factor of γ .)   Our smart aleck friend is undaunted though because, he says, the rest length of the ladder must be measured from the moving frame of reference. Its prelaunch length is therefore shorter so it wi...

Twin Paradox with Spacetime Curvature None Shall Pass Here's what the Twin Paradox looks like in the vicinity of a Schwarzschild black hole if both twins go walkabout on radial trajectories with equal and opposite velocities. Ages are quoted in terms of bystander time, not observer time (aka. coordinate time.) Note that even the light ray, which emanates from the origin, diverges off towards the end of time without ever reaching the horizon. Escape Plan The takeaway is, anything can escape from the grips of a black hole if you are willing to wait long enough. It's just that the longer an object spends on an inbound trajectory, the longer it takes to emerge after it turns around. However, a black hole is bad news if your personal integrity relies on travellers (or QM wave functions) reuniting at the launch pad at the same time. Terminology As an aside, I was once chastised by a GR expert for describing a black hole as a region in space with an unusually high concentration of mas...