Maybe if the point of contact of the light beam was noted and called point B. If the light arriving at point B triggered a second light to beam back in the direction of the stone, and the stone was dropped from twice the height of the light, they would both touch down at the exact same time?? Maybe:-)

@BrianBishop But you can't send the return signal from where the outgoing signal arrived, you're already on the ground. The return signal needs to leave from somewhere else, so you're screwed ;) (you might try and contrive some situation where you can send the return signal from where the outgoing arrived - it won't work, but you're welcome to try!)

I mean send the return signal from the original height just above the light impact point.

So you need some time to get the message saying "go" from the arrival point to the return-departure point, no?

Hypothetically no. If it left at that exact instant

@BrianBishop how?? This is relativity, you can't just allow information to travel instantaneously and then expect to draw conclusions that are physically valid!

How is not important is it? Let's just visualize that it did. Is that unreasonable in this instance? I'm not sure myself to be honest

It's crucial. One of the central results of general relativity is that it's meaningless to compare times unless they are compared at the same place. So saying "when signal A arrives at location 1, send signal B from location 2" because at 2 you can't know about timing at 1

you may have some information, like you can order events in time under certain conditions

but at the same time is poorly defined, because you can come up with different definitions for "time" depending on the path you take from 1 to 2

you can meaningfully define local time, but not a global time

it's hard to get your head around, but if you try and ignore this rule, you get to incorrect conclusions

no

or hmm

right, no

if you do that, you send the beam back to where it started, but you need to send it back to where the rock will land to make a comparison

might work if you reflect the beam "halfway" along the path

but even then, I don't think there's enough symmetry to make it work out

No mirror needed. We just accept that a beam of light is sent back, from the same original height, at that exact moment. Mathematically it doesn't matter how

Kyle, you're on a different level than me, I don't understand your last comment, so I suspect I'm wrong, I'm not factoring in certain things

you can't just accept that the beam is sent back at that exact moment, because exact moment is undefined

if you ask observer Bob, he might tell you the beam left too early, while Charlie insists is left right on time, and they will both be right