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I have always been intrigued by what seems to be very similar characteristic of the phenomena of traveling very, very fast, (close to the speed of light , and the Schwartzchild radius. AS a body gets close to the speed of light, (relative to the rest of the local universe), two phenomena occur. First, time dilates. Clocks traveling at a high rate of speed relative to an observer in the body, would appear to run slower and slower, until, at the limit, if a body, (like a photon) reached the speed of light, all other clocks would appear to almost freeze, and stop moving completely. Second, the length of all objects moving at a high rate of speed relative to any frame of reference, (the length in the dimension parallel to the relative velocity of the frame of reference), would appear to shorten, until, again, at the limit, if the relative velocity reached the speed of light, (as it is for a photon), all lengths parallel to the velocity would appear to be zero. This implies that, to a photon, the entire rest of the universe, appears as a two dimensional surface, of zero thickness. And that to a photon, the travel from any point where it is emitted, to the point in the universe where it is absorbed, takes zero time and covers zero distance.

Now consider the Schwartzchild radius. It is a closed, two-dimensional curved surface, which, from the outside has the characteristics, that as a body approaches it, time slows down. To an observer on such a body, clocks far away from the Schwartzchild radius would appear to speed up, to an observer far away, a clock on the body would appear to slow down, until at the limit, as the body touched or crossed the surface, a clock on the body would appear to have stopped completely.

What about objects inside of a Schwartzchild radius (inside a black hole)? If a clock falling through a Schwartzchild radius would appear to have stopped as it crosses this threshold, does this mean that from our position far away from the surface, the object would never actually cross the boundary? Does this mean that all mass that falls into a black hole after it has initially formed, at least from the perspective of an observer far away, exists, forever, within the two-dimensional surface of the Schwartzchild radius? If so, this is remarkably similar to the 2D image I have of what the entire universe looks like to a photon traveling at the speed of light.

Is there any significance to this analogy?

... and does it imply that everywhere within our universe, we are in a black hole of enormous size, and that photons within our universe are traveling on the surface of its event horizon, and that we can "approach" it's event horizon by accelerating to a velocity close to the speed of light?

Qmechanic
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Charles Bretana
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1 Answers1

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Let us compare the travelling close to the speed of light in SR (special relativity) and the approaching to the event horizon of a Schwarzschild black hole.
Here the correspondence is:
SR travelling observer - Schwarzschild approaching event horizon observer
SR stationary observer - Schwarzschild far away observer
1. In SR the stationary observer would measure the clock of the travelling observer to tick slower. However also the travelling observer would measure the clock of the stationary observer to tick slower. SR is symmetrical as for reference frames in relative velocity.
2. In Schwarzschild the far away observer would measure the clock of the approaching event horizon observer to tick slower. Instead the approaching event horizon observer would measure the clock of the far away observer to tick faster. Schwarzschild is not symmetrical.
Therefore there is no analogy between the travelling close to the speed of light in SR and the approaching to the event horizon of a Schwarzschild black hole.
Note:
As for the Schwarzschild far away observer the approaching event horizon observer will never reach the horizon if not at an infinite time. As for the last paragraph it looks like more a philosophical statement than a scientific speculation.

Michele Grosso
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