Greg Egan on Nostr: nprofile1q…ufa4k The stationary observer only gets to see the first falling ...
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The stationary observer only gets to see the first falling astronaut fall as far as the event horizon, but the light from that period is received over an infinite time.
The second falling astronaut not only sees light from the first falling astronaut from a larger span of radial coordinates, they (a) measure different redshifts for any given photon, because of the way they are falling themselves [which explains the initial higher frequencies than those the stationary observer measures], but also (b) once they are falling, they will receive any given photon from the first falling astronaut *sooner* by their personal clocks than the stationary observer, so everything they see occupies a smaller range along the horizontal axis — which is proper time for whomever’s observation is being plotted. So points on different curves at the same horizontal position do not refer to the same photon; the horizontal position is purely about the time course of the observer’s experience.
In the second plot in that section of the web page, the red/green/magenta curves now show the redshift that the first falling astronaut records when looking up at an astronaut who delayed their fall, and for all four curves the horizontal axis is now proper time for a single observer: the first astronaut to fall. The different curves still refer to different photons [in this case, photons received at the same time, but from different sources], but because the different curves now record observations at exactly the same time, in that sense the curves are more comparable ... and now they never cross.
The stationary observer only gets to see the first falling astronaut fall as far as the event horizon, but the light from that period is received over an infinite time.
The second falling astronaut not only sees light from the first falling astronaut from a larger span of radial coordinates, they (a) measure different redshifts for any given photon, because of the way they are falling themselves [which explains the initial higher frequencies than those the stationary observer measures], but also (b) once they are falling, they will receive any given photon from the first falling astronaut *sooner* by their personal clocks than the stationary observer, so everything they see occupies a smaller range along the horizontal axis — which is proper time for whomever’s observation is being plotted. So points on different curves at the same horizontal position do not refer to the same photon; the horizontal position is purely about the time course of the observer’s experience.
In the second plot in that section of the web page, the red/green/magenta curves now show the redshift that the first falling astronaut records when looking up at an astronaut who delayed their fall, and for all four curves the horizontal axis is now proper time for a single observer: the first astronaut to fall. The different curves still refer to different photons [in this case, photons received at the same time, but from different sources], but because the different curves now record observations at exactly the same time, in that sense the curves are more comparable ... and now they never cross.