A freely falling observer far from the hole will detect Hawking radiation, but the particles they receive will be benign, with energies characteristic of an object radiating at the Hawking temperature. This is as expected – it is what Hawking predicted. Another way to understand how Hawking radiation arises from this far away point of view is to think about the tidal gravity of the black hole. Tides on Earth are raised because the gravitational pull of the Moon varies across the Earth. The result is that the ocean surface, and to a very small extent the Earth itself, is distorted by the varying gravitational field. On Earth, tidal gravitational effects are only felt over very long distances – at widely separated points on the Earth’s surface – because they are caused by the difference in the gravitational pull of the Moon in two places. There is no measurable difference in gravitational pull over a couple of metres, which is why the Moon does not raise tides in your bath. Hawking radiation arises because the gravitational pull of the black hole varies across a vacuum fluctuation. For this to be a large enough effect to make the particles real, the vacuum fluctuation must be separated by approximately the size of the black hole. From the distant vantage point, an observer therefore sees a flux of long-wavelength (low-energy) particles.
Each of these three experiences are legitimate descriptions from different viewpoints, yet at first sight they appear to be mutually contradictory. Let us make the point even more starkly. Suppose you jump into a large black hole. From your perspective you are doomed to spaghettification as you approach the singularity, but you will cross the event horizon with no drama. Your friend in a rocket ship outside of the hole will never see you cross the horizon, but they will see you get closer and closer. That much we know from general relativity. They might decide to lower a thermometer down to measure the temperature at your position close to the horizon. The thermometer, hovering above the horizon, will experience the vacuum fluctuations as in case 2 above and will therefore be immersed in a hot bath of real radiation. From this vantage point, the near-horizon region is a scorching hot place. Your friend may conclude that you got burnt to a crisp outside the black hole and never made it through the horizon.
It seems there is little way out here. Should we abandon the Equivalence Principle, the very foundation of general relativity, and conclude that the horizon is a hot and dangerous place? Or should we insist that a freely falling observer must cross the horizon with no drama and conclude that there is something wrong with our quantum physics analysis of the vacuum? If we take one or other of these positions, we are required to ditch a core element of either general relativity or quantum theory.
There is a third way. A beautiful expression of centrism. It is possible that both perspectives are correct. From the outside perspective, the black hole has a scorching hot, impenetrable atmosphere which vaporises everything that approaches. Yet, according to in-fallers, the horizon is a complete non-entity and they pass through unharmed into the interior. A person can be both spaghettified and vaporised: Spaghettified from their own perspective and vaporised according to outsiders. This idea is known as ‘black hole complementarity’.36
From the outside, nothing is ever observed to fall into a black hole. We might say that the interior lies beyond the end of time for someone lurking outside. Stuff just falls into a hot atmosphere where it gets burnt up. From the outsiders’ point of view, it seems that a black hole is not so different to a hot, glowing coal.
According to the black hole complementarity paradigm, none of this is contradicted by the narrative of someone who falls into the hole, although the story they tell is different. They get to explore the interior and meet with the singularity. Crucially, however, they are not able to communicate any of this to the outsiders once they have crossed the horizon. Equally crucially, the outsiders are unable to inform the in-faller that they have been burnt up. A contradiction is avoided because the outsiders and in-fallers never get together to compare notes. This sounds like a proper bodge, to use our native vernacular, but it is a serious proposition.
You might immediately raise the following objection. What if the outsider collects some of the ashes of the in-faller and then jumps in after their friend to show them the evidence that they were incinerated? Being confronted with one’s own ashes would be a disconcerting experience, even for the most ardent advocate of black hole complementarity. The way out of this logical impossibility, according to complementarity, is that it takes time for the outsider to collect the evidence that the in-faller has burnt up. By the time the outsider has gathered the evidence and jumped in across the horizon, their friend has already been spaghettified and cannot therefore be presented with the evidence of their own demise. However bizarre it may seem, the picture we’ve just outlined appears to be essentially correct. The route to this realisation can be traced back to the 1980s and a very simple question.
The information paradox
The title of Stephen Hawking’s initial paper on Hawking radiation was ‘Black Hole Explosions?’ The reason for this eye-catching title is that the temperature of the black hole is predicted to rise as it shrinks, causing it to radiate more fiercely and shrink faster until it completely disappears in a flash of radiation.‡ ‘Faster’ is perhaps the wrong word to use, introducing an unwarranted sense of urgency to the process. You can pop a few numbers into Hawking’s formula to calculate the temperature of a typical stellar mass black hole – let’s say around five times the mass of the Sun. Doing so reveals that the temperature is ten billionths of a degree above absolute zero. That’s very much colder than the Universe today, which has cooled down to around 2.7 degrees above absolute zero in the 13.8 billion years since the Big Bang. At this moment in cosmic time, black holes are more like Wheeler’s iced teacups and, in accord with the Second Law of Thermodynamics, they are absorbing energy as they float in the relatively hot bath of the cosmos. There will come a time, however, as the Universe continues to expand and cool, when they become glowing hot spots in the ever-chilling sky and then they will begin to evaporate. A typical solar mass black hole will have a lifetime of approximately 1069 years, which is a very long time. At first sight, therefore, it might appear that we don’t need to worry about black hole explosions; their lifetimes are surely as close to infinite as makes no odds. If we stopped here, however, we would miss what is quite possibly the most important revolution in theoretical physics since Einstein’s time. The revolution was triggered by the following question: ‘Do black holes destroy information?’
Imagine that a book falls into a black hole. Over incomprehensible time scales, the black hole will gradually evaporate away as it emits Hawking radiation until it vanishes in a final burst of radiation. All that remains will be the Hawking radiation. Crucially, Hawking’s calculation makes a definite prediction about the nature of this radiation: it is thermal, which means that the radiation encodes no information at all. In other words, when the black hole has vanished, it is as if the book never existed. The information it contained has been erased from the Universe. In fact, all the information about everything that ever fell into the black hole, including the details of the collapsing star out of which it originally formed, will also be erased. Instead, all that remains is a bath of featureless, thermal radiation.