So imagine a black hole the size of 100 km, and then there is a giant rod that is 50 km and pretends that the rod doesn't get broken due to tidal forces, and also assumes that the rod has a mini-robot on the other end of it. So once the robot end of the rod enters the event horizon, it can never escape. However, the robot can technically exert a force as pre-programmed, inward towards the singularity making the rest of the string or rod fall faster than normal. So if the rod is long enough, this extra acceleration can be interpreted as a message from the robot. And technically this doesn't violate the law that matter or energy can escape because the rod is still falling and in fact is falling faster now due to the added force. And then on top of that there could be something where sideways motion means something else, so some information about the black hole interior can be gotten until the robot and the rod completely get absorbed and broken apart. So how does this not violate the fact that information can not get out because the rate at which matter falls in changing can be seen as information leaving out?
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2But you've programmed the robot to do something, hence you already know what's going to happen...so no information is actually sent out of the black hole. – Triatticus Feb 27 '24 at 00:48
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2How exactly does this overcome the usual story that constrains information to travel in timelike directions? "I assumed that away" does not count as an answer. – WillO Feb 27 '24 at 00:51
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What WillO said. All the timelike paths crossing the EH go inward. Your impossibly strong rod doesn't overcome that. FWIW, a steel rod that long in freefall would snap at 270000 km from a 50 km Schwarzschild radius BH, see https://physics.stackexchange.com/a/631427/123208 – PM 2Ring Feb 27 '24 at 01:43
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@Triatticus It could be something like an artificial intelligence system which can measure and see if there are some unique properties and then relay them through increased downward force which would be from robot pulling down faster or sideways motion. So not everything would be completely programmed. – MiltonTheMeme Feb 27 '24 at 01:43
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@PM2Ring what if the the rod or string is still falling at its usual pace, and is accelerating downwards because then the rod won't experience as much of a force as when the rod is held in place right above a blackhole? What if the rod is falling but there is an additional force from the robot contracting the rod and maybe this could be a signal to the outside world? Because wouldn't the gravitational forces then not be as large and only the tidal forces will be an issue so if there is some kind of super strong material that can withstand that, then there should not be too much of an issue. – MiltonTheMeme Feb 27 '24 at 01:46
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If we posit a super-strong material then we start to run into paradoxes, just like if we use an infinitely rigid rod to transmit signals faster than light. You can't use the laws of physics to analyse a thought experiment if the materials in the experiment don't obey the laws of physics. – PM 2Ring Feb 27 '24 at 01:54
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You might find my H-bomb analogy helpful. https://physics.stackexchange.com/a/696441/123208 Greg Egan analyses a similar situation involving a Rindler horizon https://www.gregegan.net/SCIENCE/Rindler/RindlerHorizon.html This is simpler than a BH because it can be analysed with special relativity. – PM 2Ring Feb 27 '24 at 02:06
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@safesphere you can still see the part of the rod 100 meters above the event horizon falling however, so that extra force from the robot end can still be seen as the rod falling in a bit faster than normal right? – MiltonTheMeme Feb 27 '24 at 02:21
2 Answers
This will not work. Any information that the robot tries to convey will travel up the rod at the speed of sound in the rod. This is far slower than the speed of light. So it will never escape the event horizon.
The inward force would propagate at the speed of longitudinal or compressive waves. The sideways force would propagate at the speed of transverse or shear waves. Longitudinal waves are usually faster than shear waves, but still far slower than light. It simply cannot catch up to the event horizon which moves outward at the speed of light in any local inertial frame.
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So if the robot exerts an extra inward force, the rod would not fall inward faster then? – MiltonTheMeme Feb 27 '24 at 02:22
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1@RoghanArun the end that the robot is on would fall faster. The other end would be unaffected until the sound wave reaches it – Dale Feb 27 '24 at 02:52
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There was actually a good video posted about this recently https://youtube.com/shorts/W1Qyv6EI2hE – RC_23 Feb 27 '24 at 03:11
One thought experiment 'paradox' is to hit the end of very long rod with a very large hammer. If the far end moves at the same instant the near end was hit this would be an example of transmitting a signal faster than light, but in reality that does happen. The impulse signal of hitting one end of the rod has to propagate along the rod before the far end becomes 'aware' of the impulse. This impulse travels at the speed of sound of the material the rod is made of and this is slower than the speed of light, but for your thought experiment with the robot, if this impulse signal travelled at the speed of light, it would still not reach the event horizon. Even light can not travel 'upwards' inside a black hole.
Another thought experiment is to attach a rocket to one end of a very long 'rigid' rod. if the rocket accelerates very rapidly away from the far end, the rod will stretch while the far end remains stationary for a finite period, while the information that the rod has accelerated at the rocket end travels along the rod to the far end. For this reason relativity predicts no rod or material object can be perfectly rigid.
In your experiment, there is absolutely nothing the falling robot inside the black hole can do to affect the motion of the part of the rod still outside the event horizon.
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