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Yet another thought experiment:

So consider an observer $O$ falling directly into a static spherical black hole. Now $O$ can be viewed as a physical system consisting of different parts exchanging information, however once $O$ enters the Event Horizon, any pieces of $O$ cannot send information in a direction that doesn't have positive directional component towards the center of the black hole.

Furthermore suppose we have two pieces of system $O$, $A$ and $B$ such that $B$ is closer to the center of the black hole than $A$, then if $A$ transmits any information to $B$ it can never receive anything from $B$, because such a transmission of information would mean that SOMETHING is moving away from the singularity, yet inside the Event Horizon.

So given that, it's not clear to me if the notion of "3 dimensions" makes sense for observers that have entered a black hole. Since as they are making their transit towards the singularity, any motion in the radial dimension, must necessarily be forward, and cannot be "undone", and so they don't appear to have any mechanism for measuring this 3rd dimension.

But that is just weird for me to consider, so I wanted to ask: if the idea I just considered makes sense, and if this would be a relatively accurate picture of what goes on once is sufficiently deep past the Event Horizon.

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  • $\begingroup$ What makes you think there is a blackhole? $\endgroup$ – machine_1 Aug 1 '16 at 16:05
  • $\begingroup$ @machine_1 It's a thought experiment. Whatever black holes actually are, the thought experiment can still be done with a classical definition of a black hole. $\endgroup$ – userLTK Aug 1 '16 at 16:08
  • $\begingroup$ A and B can still exchange information provided both are moving towards the singularity. What B can't do is send any information to a stationary object it's moved passed, but A isn't stationary. Like 2 falling sky divers playing catch, B can send information back to A where, B, A and the information all take different paths to the singularity. At least, that's my limited understanding. $\endgroup$ – userLTK Aug 1 '16 at 16:31
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What you have forgotten is that your object is falling towards the centre of the black hole. So a light signal sent outwards from $B$ towards $A$ doesn't have to move to increasing $r$. It just has to fall inwards more slowly that $A$ is falling inwards. $A$ can receive signals from $B$ because $A$ in effect catches up and overtakes the light rays $B$ is trying to send outwards.

For more on this see Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?, though the answers to this are somewhat technical.

In fact it's a fundamental principle in general relativity that for a freely falling observer spacetime looks locally flat. If you were falling into a black hole then at least in your immediate vicinity space would look just like normal boring old flat spacetime.

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