For more than a century, physicists have accepted the rules of quantum mechanics as given—strange, counter-intuitive laws that “just work.” Why should nature insist that particles come in discrete packets, that probabilities follow |ψ|², or that light’s speed never changes no matter who measures it?
Until now, the standard answer has been: that’s simply how the universe behaves.
But what if all those mysteries share a single, elegant cause? In the new paper “Quantization and Hilbert Space as Topological Invariants of BCB Information Geometry,” we show that the entire mathematical structure of quantum mechanics—its quantization, probabilities, and even the geometry of spacetime—emerges inevitably once you assume one simple principle: information is conserved.
The Universe as a Flow of Finite Information
Imagine reality not as particles or waves, but as a vast, perfectly balanced flow of information—bits of distinguishability moving through an invisible network. This flow can’t be infinite, and it can’t be lost or created. It must circulate, balance, and conserve.
From that alone, astonishing consequences tumble out:
- Phase becomes a circle: because information can’t accumulate forever, its “phase” must wrap around—forcing quantization into neat integer steps.
- Hilbert space appears naturally: the only way to measure distance between information states, while respecting both probability and phase, is the same inner product quantum physicists use every day.
- Non-commutativity and uncertainty arise automatically: when information has both shape (metric) and flow (symplectic structure), some measurements can’t coexist—just like position and momentum.
- And when you zoom out, spacetime itself emerges, complete with light cones and relativity, as the large-scale pattern of finite-speed information flow.
Why It Matters
This isn’t a new interpretation of quantum mechanics—it’s the foundation beneath it.
BCB (Bit Conservation and Balance) shows that quantization, probability, and relativity aren’t arbitrary postulates—they’re topological and geometric necessities. The universe, it turns out, behaves exactly as it must when information can neither vanish nor exceed its finite capacity.
It means the laws of physics might not be separate laws at all—but different faces of the same cosmic truth:
Reality is conserved, flowing information.
And once you see that, the mysteries of the quantum world no longer seem so strange. They look inevitable.