What Black Holes Teach Us About Identity
What can black holes uncover about the nature of identity? More than you might think.
A beautiful hidden thread connects the brilliant thinkers Leibniz, Newton, and Chandrasekhar to the metaphysics of our universe, the logic of identity, and the astrophysics of black holes. To begin this story, we must first ask:
Is it possible for there to be two truly identical objects?
A common response to this question is: Yes, look at the fundamental particles of our universe. Two electrons will share all of their properties and still be distinct — this is true. But what about macroscopic objects? This is where things get interesting.
To the above question, the 17th and 18th-century polymath Gottfried Wilhelm Leibniz answered: No, it is not possible. He didn’t see how two macroscopic objects could logically or metaphysically share all their characteristics while still being independent. He believed that no two things in the universe can be distinct objects while still having all the same properties. Perfect similarity is metaphysically impossible. But does this make sense?
Leibniz was a brilliant thinker. The French philosopher Diderot likened him to Plato, writing, “…perhaps never has a man read as much, studied as much, meditated more, and written more than Leibniz” (Oeuvres Complètes). This praise is underscored by the fact that Leibniz invented calculus at the same time as Isaac Newton — Newton simply beat him to the press and received all the credit!
However, genius often comes with quirks and eccentricity. Leibniz believed, for example, that this world is ‘the best of all possible worlds,’ a theodicy grilled by Voltaire in Candide, and that the universe’s true building blocks are not atoms but monads — immaterial, soul-like entities that create the illusion of reality. Strange.
You can’t have brilliance without a bit of madness.
For this reason, let’s set aside Leibniz’s sketchy metaphysics and theology in favor of his logic of identity — controversial and interesting enough as it is. Regarding identity, Leibniz says that if two objects have all the same properties, they are identical and cannot be two separate objects. This is called the Identity of Indiscernibles, and it might seem like an intuitive statement; however, it is actually the inverse of this principle that is uncontroversial and intuitive.
There is in fact a difference between, “if two objects share all of their properties, they are identical” and “two identical objects must share all of their properties”. The former is the Identity of Indiscernibles, and the latter is the Indiscernibility of Identicals. This is why people hate philosophy!
The Indiscernibility of Identicals is a logical necessity, so few philosophers dispute it. What we’re interested in is the Identity of Indiscernibles: if two objects share all their properties, then they are identical and cannot be two separate objects.
Can two identical objects be distinct?
Let’s investigate this with an example: take two tennis balls made by the same company at the same time. To a tennis player, these two balls seem identical. They serve the same purpose: bounce and be yellow. Even tennis balls from the same factory are unique because, for example, their atomic structures differ; they are not the same ball. According to Leibniz, if they were the same, down to atomic structure, they would have to be the same ball. His idea boils down to this: no two objects can share all their properties and still be separate.
But there is one instance where identicalness might be possible: black holes.
In his book, The Mathematical Theory of Black Holes, the Nobel prize-winning astrophysicist Chandrasekhar wrote, “The black holes of nature are the most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time.” To understand why Chandrasekhar said this and how it relates to identity, we must first understand what black holes are and where they come from.
Massive stars are the seeds of black holes. These stars come to be in stellar nurseries like the Orion Nebula: giant clouds of gas and dust found in the colorful spiral arms of galaxies. Gravity — the same force that keeps our feet on the ground — can make denser pockets of the clouds collapse in on themselves. This collapse causes the gas to become dense, heat up, and spin — until eventually there is enough energy to ignite nuclear fusion.
This is the engine of the star: smashing lighter elements like hydrogen and helium together to create larger elements like carbon and oxygen, producing quite a lot of energy. Fusion is what keeps the star going for millions or billions of years — but not forever.
Eventually, the massive star will run out of fuel, and when it does, it will begin to puff out its outer layers to become a red supergiant. Because these stars are so massive, gravity will take over and the star will collapse and explode. This is called a supernova.
Supernovae are some of the most energetic events in the universe, and they are how elements heavier than iron are made — including precious metals that humans have killed and died for, like gold and silver. If a star is massive enough, the intense energy from this explosion leads to the formation of black holes. This explosion rips a hole in spacetime, as the stellar core collapses into an infinitesimal singularity.
When black holes form, the history of their formation is lost and all that is left behind is the pit in spacetime. All that exists is spacetime and the hole that has been torn into it; any trace of the previous star’s characteristics is erased. You might see where this is going…
This is why Chandrasekhar said black holes are perfect: they are remarkably simple, as their only ingredient is spacetime. Everything else is lost forever behind the event horizon — the point at which the escape speed is greater than the speed of light. All data is lost…except for three things.
The No-Hair Theorem states that a stationary black hole can be completely described using only three characteristics: mass, electric charge, and angular momentum. Unlike normal objects, black holes have no internal complexity; their entire identity is wrapped up in those three measurements. A tennis ball is orders of magnitude more complicated than a black hole. Perplexing.
Because of the relative simplicity of black holes, to create identical but discernible black holes — against what Leibniz would think is possible — you would only need to match three properties…right?
Well, there’s one thing we forgot: spacetime coordinates. For two black holes to be truly identical, they would need to share all the same properties — including the same location in time and space. This is part of why Leibniz thought true identicalness was impossible: it involved the same position in time and space, which would make two identical objects one.
That is, unless we get creative. The British-American 20th-century philosopher Max Black did just this. He said: imagine an empty universe with two identical iron spheres; each sphere is one mile in diameter, made of pure iron, and positioned two miles apart. Are they discernible? Yes, you would clearly be able to see two spheres. Do they have all the same properties? Let’s think about this.
By definition, they have all the same physical properties: the same mass, structure, and composition. In this regard, they are identical. But they don’t have the same location in space, right?
In an empty universe, the location of each sphere can only be described relative to the other. It is completely symmetrical, and there are no other reference points on which to base a coordinate system. So, in space, one ball is two miles away from the other, and the other is two miles away from the first ball. According to Black, they share the same locational properties, so this counterexample challenges the Identity of Indiscernibles: two distinct objects can indeed be identical, proving Leibniz wrong.
Just like the tennis ball, you might be thinking that it would be impossible to create truly identical spheres — and you are right. But we don’t have to: nature can do this for us. Black holes are nature’s real-life version of Black’s iron spheres — in our universe. They are perfect macroscopic objects, so it is metaphysically possible for two black holes to be physically identical and discernible.
The real issue in our quest to prove Leibniz wrong lies in the nature of our own universe: it is not empty. The problem is not the physical identicalness of black holes; it is spacetime coordinates. In our universe — full of planets, moons, stars, and galaxies — we have a proper coordinate system.
To completely describe something in our universe, we must know its spacetime coordinates: x, y, z, and t. So, for any two macroscopic objects to share all their properties, they would need to have the same coordinates in space, which is impossible. Two objects cannot have the same x, y, z, and t — so within our universe, on macroscopic scales, it appears Leibniz was right. Even though black holes are remarkably simple, any two of them cannot share all of their properties without sharing the same time and space in our universe.
What does this mean for the nature of identity?
Perhaps the most fundamental characteristic to describe an object is its location in time and space.
Something else could have the exact same physical properties but it would not be identical because it has different coordinates. You are you because of your spacetime coordinates: they are unique to you.
Identity, then, ultimately distills down to x, y, z, and t — when and where we find ourselves in this universe we call home.
