You can do plenty of experiments to see if you are falling, e.g. hitting the surface of a planet you are falling towards. The event horizon is a surface like any other with a location in space and you can definitely see when you hit it (it's the bit where no light is coming out). And once you've crossed it, literally no EM radiation can move further from the singularity
Well, I disagree. Light literally can't move in a direction that makes it further from the singularity once inside the event horizon. I don't see what space being flat or not locally has to do with that. Check https://en.wikipedia.org/wiki/Event_horizon#/media/File:BH-n... for an example.
If your head is further from the singularity than your feet then you can't see them.
Happy not to discuss further!
So when will we be able to just run general relativity numerical simulations on our desktop machines? So that you could set up Observer A at some point, and Observer B at some other point and and mass distribution, etc, then just crunch the numbers to see what each observer could see/measure as time evolves for each observer. Seems like the differential equations are straight forward enough(?). Is the possibility of singularities at the center of a black hole the hard part? What if you just simulated something that was 99.99% of the density needed to get a black hole? I suppose that you'd need a 4 dimensional matrix to hold the simulation (three space coordinates plus a time coordinate)? Is it that we just don't have enough RAM and storage yet in consumer machines? If your simulation did a 1,000 points in ever dimension, that would be 1e12 points. If there are 10 components of the tensor at each point and we are using 64-bit doubles per parameter, that means our simulation takes up ~80 TB. Or is it a that we don't have enough processing speed? Or are there still some philosophical issues that need to be decided when you program up the simulator? How many lines of code is a numerical general relativity solver using something like Euler's method? Is the core of a naive version less than, say 500 lines of C? I can see an optimized CUDA version being significantly larger of course.
I was considering a stationary observer inside the event horizon, but that’s not possible. ldunn is correct that a free-falling observer will catch up with the photons reflected from their feet.
Space being flat locally is important because if the gravitational gradient is too high (i.e. you get too close to the singularity) your feet will be accelerated much faster than your head.
I agree that if you are freely falling and then you are suddenly not freely falling because you hit the surface of a planet and experienced a huge acceleration, you will notice. That doesn't have anything to do with anything I said, but it is undeniably true.
An event horizon is not like the surface of a planet - you will not be accelerated as you pass through it.
It is, once again, irrelevant that light cannot propagate outward once you're behind the horizon because, again, you are falling towards the center, and in particular you are falling through the future light cone of your feet. Please look at some spacetime diagrams if you do not believe me, preferably ones in Kruskal-Szekeres coordinates.
In GR spacetime is locally flat and for an inertial observer special relativity applies, up to tidal corrections which can be made arbitrarily small at the horizon by considering a suitably large black hole. This is a deep and important fact about GR. The idea that falling through the horizon causes you to suddenly not be able to see your feet anymore appears to obviously violate this basic principle, so if you think your assertion is true you should be able to explain why either this principle of GR is actually not true, or why your assertion does not actually violate this principle.