Two Photons, One Story – A metaphorical approach to entanglement

Two Photons, One Story

Have you ever heard of the mysterious island called Superposition? This secret island does not appear on any map. Its houses are built not of brick, but of possibilities; its streets are not straight, but have taken on undulating, wave-like shapes, and every night a faint, silvery veil shimmers over the island. A wizard named Hilbert lived on this island. His unique magical power lay in his ability to create light, to stop it, and to influence any of its properties.

One day, due to a massive storm, a lonely fisherman named Albert drifted out to sea and was washed ashore on the island. Exhausted by the journey and the gale, his first act was to sit upon an old, moss-covered stone and rest with a deep sigh. The golden sunlight filtered through the canopy of trees, dappling two tiny spots of light onto the ground, as if the trees themselves had scattered stars into the grass. He watched the world around him in silence. He heard the leaves whispering softly in the wind, saw a butterfly dancing gracefully over the flowers, and smelled the scent of fresh earth and pine resin in the air. The bubbling of a brook accompanied the moment like a gentle melody.

Suddenly, he noticed that these two tiny spots of light had come to life and were performing a strange dance. As a lonely fisherman marvelling at the secrets of nature, he gave the spots names: he called one Alice and the other one Bob. However, their exciting, playful dance confused Albert; if he closed his eyes for even a blink – and he had to blink – the undulating, graceful motion of the two spots caused him to lose track of them. He could no longer tell which one was Alice and which one was Bob. They were so perfectly identical that distinguishing them was a monumental challenge. He could not have known it then, but these two pieces of light were created by Hilbert, the mage.

Albert decided to begin studying these fascinating fragments of light, and because of their identical nature, he gave them the same last name: Photon. "Can I even call Alice Photon and Bob Photon different things at all? After all, they are more perfectly identical than anything I have ever seen in my life. If two things have no differing properties, what makes them distinct? Besides, my naming is only valid between two blinks, and it feels quite artificial...", Albert mused.

Fed up with the situation, Albert designed a peculiar experiment. He separated the two photons using mirrors. Through this spatial separation, he hoped they would become distinguishable forever. He devised a plan to paint one blue with blueberries and the other red with raspberries. However, whenever he walked from one painted photon to the next, the sight of it caused the other to take on colour as well: sometimes the exact same colour, sometimes the exact opposite.

Suddenly, a strange, deep, ancient voice echoed from the sky. The voice was low, slow, and raspy, like the crackling of a warm fire – simultaneously soothing and commanding a sense of deep, inner peace. "The pieces of light you call photons are entangled", whispered the voice of the wise Hilbert. "Think of them as two siblings who were not only born together but were split from a single shared destiny."

"Like twins?", Albert asked.

"Yes, but far stranger. If one of two ordinary twins smiles, the other twin can still choose to be sad. But these quantum twins are not like that. They do not make separate decisions; they are two parts of a single, shared state."

Albert did not understand. How could two separate objects be a single system? Then Hilbert appeared and held up both pieces of light. "This pair of photons does not exist as separate entities, but as two parts of one great whole. If you imagine them as two in your mind, you are already on the wrong path. It is impossible to treat them separately. If you paint one, the other assumes the same – or the other – colour instantly."

Albert was astonished. "And what if one photon is here on the shore, and we take the other to the far end of the island? What will happen then?"

"The experiment will show the exact same behaviour as before", Hilbert replied. "This is quantum entanglement. No visible thread connects them, no energy flows between them. The connection is not spatial, but mathematical and physical: they exist in a shared state. This state can be described as a mathematical entity that merely enables statistical predictions such as: the probability that Alice Photon is blue and Bob Photon is red is 25%."

Albert began to understand. Quantum entanglement is like two characters being part of a single sentence. Just as a musical ensemble's creation cannot be viewed as separate parts, because the experience is delivered by the team as a whole.

Suddenly, a great clap of thunder erupted, and Albert woke up from his dream in his soft, warm bed at home, embraced by his blanket. But by then, Albert knew that in the deepest depths of the universe, it is not objects that wander at magical speeds, but states that interact, carefully bound by rules. It does not matter where something is, but rather in what state and with whom it coexists. Nature’s great secrets were surprising to him, but he realised why Hilbert, the master of light, would not forbid the existence of states that are not bound by space and time – states that refuse to allow the system of light to be described as separate parts. Perhaps this strange feature of the world could be used for so many things...