Time is Pressing?

The black hole is a concept which fascinates- the density of a gravitational field becomes so great that it effectively forms a one-way membrane, an ‘event horizon’, from which, once engulfed, no information can ever escape, since the escape velocity of the singularity exceeds that of light. So the theory goes.

Consider, if you will, an astronaut piloting a spacecraft close to the speed of light. According to Einstein, (and repeated experimental verification), an object approaching the velocity of light increases in mass, from the perspective of an outside observer at a nominal ‘stationary point’ by a quantity M[1-(v^2/c^2)]^(-1/2), where M is the ‘rest mass’ of the spacecraft, v is the velocity of the spacecraft (relative to the ‘stationary’ observer) and c is the velocity of light. A moment’s consideration of this equation reveals that the mass of the spacecraft tends towards infinity as light speed is approached (relative to, and from the point of view of, the stationary observer).

Another peculiarity of General Relativity is that the spacecraft approaching light speed undergoes ‘Lorentz Contraction’, an apparent compression, as viewed from the point of view of the stationary observer, in the direction of motion. The length of the spacecraft as viewed by the stationary observer is then L[1-(v^2/c^2)]^(1/2), where L is the ‘rest length’ of the spacecraft. Length then, tends to zero, as velocity approaches that of light. The spacecraft’s dimensions perpendicular to the direction of relative motion are unaffected.

In summary then, as viewed by the ‘stationary’ observer, as the spacecraft approaches light-speed, it’s overall dimensions, and hence its volume, decreases, while its mass increases. A steady increase in mass and decline in volume necessarily equates to an increase in density- also tending to infinity. Inevitably then, the density of the spacecraft, as it accelerates, will reach the point that it finds itself inside its own event horizon, and is therefore a black hole, by definition. As such, no information from within the spacecraft can ever be communicated back to the wider Universe.

The ‘stationary observer’ whom we defined earlier however, is an arbitrary concept. One can just as easily define the pilot of the spacecraft as the stationary observer. In that case, from his perspective, he never moves, and the wider Universe appears to become contracted. The pilot may at any point decide to reverse thrust and reduce his velocity back to zero, relative to our previously defined ‘stationary observer’. In that case, he will apparently have gone from being a spacecraft, to being a black hole, back to being a spacecraft, conflicting with the notion that once formed, an event horizon can never communicate information back to the rest of us.

As long as one accepts that information lost to a black hole can never be retrieved, there appears to be a paradox.