The thermodynamics of a black hole
Information could be smeared across the event horizon as matter falls into the black hole (Constantinos, 2021).
Therefore, information describing matter that has fallen past the event horizon could be copied onto the 2-dimensional surface (in this case the event horizon). As discussed earlier, information is proportional to the area of a region, hence the information on the 2-dimensional boundary can be thought of as the true information, and the information inside the 3-dimensional interior can be thought of as a fake and a projection of this true information. However, for this projection of information to exist, two further ideas must also be true, a duality and string theory. A duality simply explains how two opposite regions are equivalent. This 3-dimensional volume (black hole interior) and this 2-dimensional area (event horizon) are equivalent (duality), despite them appearing completely different. If a duality existed between two regions, whatever applied in one region had to apply in the other, so if there is no paradox in one region there is no paradox in the other (Bekenstein, 2003). Supposing information could be stored on the event horizon, it could be carried away by Hawking radiation, as the information is already outside the black hole. According to this duality, a set of rules in one region corresponds to the same set of rules in the other region, hence a solution to the paradox in the 2-dimensional boundary corresponds to a resolution of the paradox in the 3-dimensional interior. This idea of a duality of the information on the 2-dimensional surface and 3-dimensional interior is called the holographic principle or holographic conjecture . The reasoning behind it seems very strange and unlike anything we would experience in day-to-day life, but it is important to remember this is purely hypothetical. The most common example of a duality in nature is wave-particle duality. A subatomic particle is both a particle and a wave, while even though they appear different they are equivalent. This idea was theorized by Gerard t’Hooft in 2001, ‘The Holographic Principle’ (t’Hooft, 2001). t‘Hooft proposed that , for a duality to exist, hence conserving information, these black holes had to exist in a universe with different properties to our current model of physics (Luminet, 2016). While the holographic principle is an elegant solution, our current laws of physics prohibit it from existing, implying that either our model of the universe is incorrect, or this theory is incomplete (Dai, 2020). The simplest example of how our current model of the universe prohibits the holographic universe is in the number of dimensions available to us. The universe we exist in is 4-dimensional, 3- spatial coordinates and 1-time coordinate, hence the boundary would be 1-dimensional lower. A universe which would allow this theory to operate, often referred to as a holographic universe, must be 5-dimensional, therefore its boundary would be 4-dimensional (Preskill, 1992).
t’Hooft concluded that , for a duality to exist between a black hole interior and edge, a duality had to exist between the edge of the universe and the inside. The interior would be the universe that we could live in, and the boundary would be the edge or the horizon of the universe.
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