The thermodynamics of a black hole
The existence of temperature confirms the existence of entropy. In physics, a common textbook definition of entropy is the amount of disorder a system has: the greater the entropy, the ‘messier’ a system is. Mathematically, entropy is characterized as being proportional to the number of ways a particular state can be achieved. An excellent analogy is looking at a sandcastle. If the sandcastle is built perfectly, the individual sand particles (microstates) must be organized carefully, corresponding to low entropy (as low disorder). But if the sandcastle was destroyed and it was just sand lying on a beach (macro state), there would be a lot of disorder hence a high entropy (Prigogine, 1989). It was discovered that the surface area, SA, of an event horizon of a black hole was remarkably like entropy in the universe, it always remained the same or increased (except in the case of Hawking radiation). This remarkable similarity led to the discovery of black hole thermodynamics. Israeli physicist Jacob Bekenstein employed the mathematical formula for entropy to predict how the black hole grew as matter/information fell into it:
Entropy equation (LoPresto, 2003)
In 1973 Bekenstein proposed that entropy was associated with area, and not volume, in his paper ‘Black Holes and Entropy’. The maximum entropy that can be stored in this area is known as the Bousso bound (Peach, 2022). This association was formalized in the equations for black hole entropy and led to entropy being regarded as a function of area.
Entropy of black hole (LoPresto, 2003)
These discoveries led to new ways of thinking about information (Preskill, 1992). What if the matter that went into the black hole, the information, was copied onto the surface, 3-dimensional information stored on a 2-dimensional plane, like a hologram? It is important to remember that in this theory, even though information is stored on the surface, the information still goes into the black hole. The reason the information can be duplicated onto the surface is because of a theory called black hole complementarity. Published in 1993, Susskind argued in his paper that, since you cannot observe the inside and outside of the black hole simultaneously (Caltech, 2020), information can be duplicated once it crosses the event horizon.
Following on from last section, this section will explore the holographic principle, and how this idea can then develop into the holographic universe. While the theory is incredibly complex, this explanation is incredibly rudimentary and simplifies much of the maths behind it.
3.1
Holographic principle
As Bekenstein discovered, the entropy of a black hole is proportional to the surface area of the event horizon. This reasoning can then be applied to information, as both quantities measure equivalent properties, and just as entropy is stored on the surface, the same could occur for information.
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