I struggled long and hard to resist the idea that Alice observes nothing special as she falls into the Schwarzschild horizon of a BH. Now, I accept it. The thing that did it for me was professor Susskind's description of deSitter space, and how the math of the metric for the cosmological horizon in de Sitter space was the same as the math of the Schwarzschild horizon of a BH. The same effects of the remote observer Bob seeing Alice dim and red shift apply to both kinds of horizons.(adsbygoogle = window.adsbygoogle || []).push({});

Since every point in spacetime lies on the horizon of some hypothetical observer 46 billion light years away. If Alice is at Bob's cosmological horizon, then Bob is at Alice's horizon. That means that Alice, Bob, and you, and I all sit on someone's horizon. Yet I observe nothing special.

But then Susskind continued discussing the temperature just above the BH horizon. He specified temperature in the sense of average kinetic energy. Whereas the Hawking temperature of a large BH is low, the temperature just above the horizon is very hot. Close to the horizon, it is described by 1/2∏ρ (where ρ is the distance from the horizon, say from one plank length up to 1 cm above the horizon). Then, Susskind said that the same applies to the temperature just short of the cosmological horizon in de Sitter space.

Susskind illustrated with the imaginary experiment in which the remote observer lowers a thermometer on a string to just above the horizon, then reels it back up to read the recorded temperature. Note that the thermometer does not transmit its reading; it records a reading and is then reeled in. Schwarzschild horizon, cosmological horizon; same thing.

Now, I'm struggling again to understand. How can my local sense of temperature differ from my temperature as seen by a remote observer? I imagine the remote observer's thermometer hovering in front of my eyes and I wonder how it can record a temperature different than that I perceive.

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# Local Versus Remote Views of Temperature

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