Einstein's field equations describe gravity as smooth, continuous spacetime curvature, while the Schrödinger equation describes reality as discrete, probabilistic quantum waves; these two most successful physics theories are fundamentally incompatible and both break down mathematically (producing infinities) in extreme conditions like black holes and the Big Bang, where a unified theory of quantum gravity is needed but remains undiscovered.
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General relativity vs Quantum Mechanics - The Two Equations That Shouldn't Exist (Part 2)Hinzugefügt:
These are the two most successful equations in human history and they hate each other.
On the left, Einstein's field equations.
Gravity is the curvature of space-time, smooth, continuous, geometric. On the right, the Schrodinger equation. Reality is a fuzzy probability of waves, discrete, jumpy, statistical.
Most of the time, this is fine. Gravity matters for big stuff like planets.
Quantum stuff matters for tiny stuff like electrons. They never overlap, except they do in two places, inside black holes and at the Big Bang. Both theories are required.
Both produce nonsense answers, infinity, division by zero. The math actually just stops working.
So, somewhere out there is a deeper theory, one that contains both smoothly.
We just haven't found it.
And the search is the most interesting thing in physics.
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