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See What are cosmological "firewalls"?.

Alice is in freefall in her spacecraft just above the horizon of a gigantic black hole. She measures whether or not the near modes of the horizon contain a firewall. The computer settings of the computer autopilot have been programmed in advanced as follows: If a firewall is detected, let the craft continue falling into the black hole. If none is detected, fire the rockets and leave the black hole before it's too late! No one, including Alice, can tamper with the preprogrammed controls.

What will happen? Will a firewall be detected or not? Or would some mysterious disturbance always happen, like an (apparently) unlikely malfunction of the computer or the detectors?

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Can you be more explicit about what you find paradoxical? –  kleingordon Nov 16 '12 at 8:51
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It's more illuminating to embellish the story a bit.

There are four observers, FREFOS, FIDOS, Alice and Bob. A main spaceship is in freefall above the black hole, and it measures the existence of a firewall before plunging through the horizon. Just before crossing the horizon, but after making the measurements, a smaller escape craft fires off to escape to safety far outside the black hole just in time.

FREFOS pilots the main spaceship, while FIDOS pilots the escape craft. Prior to the experiment, both Alice and Bob are undecided as to which craft to join. However, they have decided that if no firewall is detected, Alice will join FIDOS while Bob will join FREFOS. If a firewall is detected, Alice will join FREFOS while Bob will join FIDOS.

Before the experiment, these four observers decided to celebrate by holding a philosophical tea party. During the heated debates which ensued, the topic of philosophical zombies came up. Philosophical zombies are sentient intelligent observers who think they're conscious when they're "really" not. They have no "actual" subjective experience, even though they're automatons who protest loudly that they have inner subjective experiences. The question was raised as to whether or not Alice might be a zombie, and she protested loudly that she "really" has inner subjective experiences because she can "feel" them "directly". Others countered that she might merely be an automaton spouting off these delusional emotional claims.

According to black hole complementarity, FREFOS will detect no firewall, while FIDOS will detect it.

At the end of their lives, every conscious observer will report their memories to the Census Taker.

FREFOS' memory dump to the Census Taker at the singularity

No firewall was detected. So, Bob joined me in crossing the horizon, while Alice joined FIDOS in getting away. Before parting, all of us chanted "There is no firewall!".

FIDOS' memory dump to the Census Taker at the end of the universe

A firewall was detected. So, Bob joined me in getting out, while Alice joined FREFOS in crossing the horizon. Before parting, all of us chanted "There is a firewall!".

Poor Alice never reported to the Census Taker because she turned out to be a zombie after all. How can she experience a grandfather paradox when there is no one to experience them?

Bob's memory dump to the Census Taker

Probability p (at the singularity)

No firewall was detected. So, I joined FREFOS in crossing the horizon, while Alice joined FIDOS in getting away. Before parting, all of us chanted "There is no firewall!".

Probability 1-p (at the end of the universe)

A firewall was detected. So, I joined FIDOS in getting out, while Alice joined FREFOS in crossing the horizon. Before parting, all of us chanted "There is a firewall!".

What's the value of p?

If no firewall is detected, Bob will become One with FREFOS. If a firewall is detected, Bob will become One with FIDOS.

Does the firewall "exist"? Is existence subjective or objective?

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