Max-bounds on information travel speeds

You know how the light we see from stars was emitted ages ago and we’re only seeing the past because of the distance. How do you find out whether a star exists at this moment in time? Because information can’t travel faster than the speed of light, we are fundamentally constrained.

Let’s talk about the sun because it’s closer to us, and more intuitive to think about. The sun is 499 light-seconds away from us (what an annoying number) and we want to find out if the sun actually exists now or if something happened to it in the 499 seconds since it last emitted light. One thing we could do is to send someone up to the sun and report back with real time updates (ignore the fact that the sun would burn up this person, or if you can’t ignore it, imagine a heat-proof sensor or something). But this fails because the fastest way the person would send us the information would still be slower than the speed of light.

After more failed thought-experiments, I thought of one that I can’t seem to refute. Tie someone to a rope that is exactly the distance between the sun and the earth and fly them out to the sun. When they reach the sun, the rope will be taut. Now, when the sun disappears, all this person has to do is to pull on the rope which will instantly alert us, 499 seconds before things actually go dark suddenly. Obviously, I’m ignoring something, because nothing actually can travel faster than the speed of light.

What am I missing? The only thing I can think of is that pulling on the rope doesn’t transmit forces instantaneously as I hope, but why would it not be instantaneous? It’s a rope, why will the length or anything else matter? I’m being incredibly myopic about something, but can’t figure out what.

Update: It takes time for an impulse to travel along a physical object. This can be seen with high-speed differential cameras. I feel like I’ve won the Nobel Prize for Stupid.