1. Mixing Hot and Cold Tea: Can Throwing It Into a Black Hole Erase the Evidence?
Let us start with a familiar experience. If you mix hot tea and cold tea, you get lukewarm tea. Can you separate that lukewarm tea back into hot and cold parts? No, you cannot. Why does this happen? It feels obvious, but the reason is important. Think about flipping 10 coins. There is only 1 way for all 10 coins to land heads up. However, there are 252 ways for 5 coins to land heads and 5 to land tails. If you shake coins and scatter them, they usually end up mixed. Getting all heads is possible, but the chance is 1 in 1,024. The "ordered state" has few possibilities, while the "mixed state" has overwhelmingly many. It is not that ordered states are forbidden. They are just unlikely. This is a key point to remember.
The same applies to tea. The arrangement where hot molecules and cold molecules are neatly separated is extremely rare. The arrangement where they are mixed is extremely common. Therefore, they mix. They do not return to being separate because it is forbidden, but because there are almost no ways for them to return to being separate. This measure of the number of possibilities is called entropy in physics. Ordered (few possibilities) means low entropy. Mixed (many possibilities) means high entropy. This is why entropy is often explained as "disorder" or "messiness." A messy room has many more arrangements than a tidy one. Nature always moves toward the state with more possibilities. This rule is called the Second Law of Thermodynamics. It states that entropy (the number of possibilities) never decreases in the whole system. It is one of the hardest laws to break in physics. Everything that follows comes from this idea. For now, just remember that mixing has more possibilities.
In 1971, at Princeton University in the United States, a physicist named John Wheeler was present. He is the person who popularized the name "black hole." Before continuing, let us confirm what a black hole is. It is an incredibly heavy celestial body. Everything that gets close falls inside. Even light cannot escape. This means there is no way to know from the outside what fell in. One day, Wheeler told his graduate student a story. He said: mixing hot and cold tea increases the entropy of the universe. That cannot be reversed. But what if there is a black hole nearby? If you throw both mixed teas into it, they become invisible from the outside. Could the increased entropy be erased, as if it never happened? [1]
2. Bekenstein's Answer: A Black Hole's Entropy Is Its Surface Area
Months later, the graduate student, Jacob Bekenstein, returned with an answer. He said: "The increase in entropy cannot be avoided. It has just moved to another place. Black holes themselves have entropy. When they swallow objects, their entropy increases by that amount." [1] The clue he found was a quantity that never decreases. He focused on the area of the event horizon. The event horizon is the boundary beyond which nothing can escape. At that time, Stephen Hawking had proven an important theorem. The area of a black hole's event horizon never decreases. If it swallows matter, the area increases. If nothing happens, it does not decrease. Here, two "non-decreasing quantities" were side by side. Entropy (from thermodynamics) does not decrease. The area of the event horizon (from gravity theory) does not decrease. Bekenstein believed this was not a coincidence. He proposed that a black hole's entropy is proportional to the area of its event horizon. [2] If you throw tea in, the event horizon expands, and entropy increases. Therefore, the Second Law is not broken. The perfect crime did not work.
Finding similar behavior in completely different fields and assuming a connection is a method repeatedly used in physics. However, similarity does not always mean identity. Because of this, objections followed.
3. Hawking's Calculation: Why He Opposed Bekenstein and Then Changed His Mind
Stephen Hawking strongly opposed Bekenstein’s claim. His reason was clear. If there is entropy, there must be a temperature. If there is a temperature, it must emit heat as light. But black holes emit nothing. Therefore, the claim must be wrong. This was a logical criticism. So, Hawking began his own calculation to prove the error. He carefully applied quantum mechanics to the curved spacetime around black holes. In 1974, the result was the opposite of his prediction. From far away, black holes appear to emit a slight amount of light or particles. [3] Moreover, the amount was consistent with Bekenstein’s prediction. Hawking published a paper stating that his calculation overturned his own claim. In 1974, the title of his paper in the journal *Nature* was "Black hole explosions?" This radiation is now called Hawking radiation. It bears the name of the person who originally opposed the idea.
This is how science works. When the answer differs from your prediction, you could hide the calculation. But he published it.
4. The Black Hole Entropy Equation: Linking Entropy, Area, and Physics Constants
The equation that came from this story is: S = kB c³ A / (4 G ħ). S is entropy, and A is the area of the event horizon. You do not need to know the details inside. Look at which symbols are included. The constants in the equation are: kB (Boltzmann constant) from the world of heat; c (speed of light) from the world of relativity; G (gravitational constant) from the world of gravity; and ħ (Planck constant divided by 2π) from the world of quantum mechanics. The equation contains constants from the worlds of heat, relativity, gravity, and quantum mechanics.
5. The Information Problem: Does Hawking Radiation Carry Away What Fell In?
From here, an unsolved problem appears. Hawking radiation looks like smooth, heat-only light. It seems to carry no information about what originally fell in. This causes a problem. Suppose a black hole keeps emitting radiation and eventually evaporates completely. Where did the information of the swallowed objects go? In quantum mechanics, information is supposed to never disappear. But in this picture, it does. This is the Black Hole Information Paradox. In 1997, a famous bet was made about this problem. Hawking and Kip Thorne bet that information is lost. John Preskill bet that information is not lost. In 2004, Hawking conceded the bet at a conference and gave Preskill a baseball encyclopedia, meaning "a book from which you can retrieve information whenever you like." Thorne was not convinced and did not concede at that point [4]. Conceding the bet is not the same as solving the problem: how information could come back is still being studied.
6. Bekenstein and Hawking: What Happened to the Two Scientists
What happened to the two main figures in this story? Jacob Bekenstein held onto his idea even when almost everyone opposed him. Hawking’s calculation eventually supported his claim. Today, the formula is called the Bekenstein-Hawking entropy, named after both of them. The idea that he pushed through despite opposition from many people is now the starting point for quantum gravity research.
Stephen Hawking was diagnosed at age 21 with a disease where nerves controlling muscles stop working. He was told he would not live long, but he continued research for more than 50 years. When writing calculations on paper became difficult, he is said to have moved geometric shapes in his mind to think. [5] He died in 2018. His ashes are placed in Westminster Abbey in London. The location is between the graves of Newton and Darwin. [6] On his gravestone, an equation is carved. It is the equation for the temperature of a black hole, which is the Hawking radiation equation. [6] The equation born from a calculation he started to prove he was wrong was finally carved in stone with his name. He published a calculation that differed from his own claim, and that is how he left his name.
7. A Home Experiment: Watching Food Coloring Spread in Water
The entry point of this article was mixing tea. You can do a similar experiment at home. Drop one drop of paint or food coloring into a glass of water. It spreads and mixes. Try to separate it back into one drop. You cannot. Mix cold water and hot water to make lukewarm water. Think about whether you can separate it back into hot and cold parts. This obvious fact that you "cannot return" is the story of entropy. From there, we reached the conclusion that black holes glow.