Mystery 2: Quantum Mechanics and General Relativity are Fundamentally Incompatible!

Physicists have a big problem: two of our favorite theories, General Relativity (GR) and Quantum Mechanics (QM), are fundamentally incompatible with each other.  This is not a minor disagreement; they are infinitely incompatible, and the usual tricks physicists use to make infinities go away (renormalization) do not work here, because there are an infinite number of these infinities. And you thought you had a lot of problems…

There are many ways to express the incompatibility between GR and QM. General Relativity is a classical theory while Quantum Mechanics is, well, a quantum theory. All efforts to quantize GR to date have failed. Here is one way to understand the incompatibility: the quantum vacuum is not empty, it is filled with virtual particle-antiparticle pairs, and according to GR, these virtual particles should curve spacetime. In fact, they should curve spacetime so much that the Universe should have collapsed an instant after it was created. Obviously, it did not, so either there is some miraculous cancellation, or our understanding of GR and/or QM must be wrong. How miraculous? The observed curvature of spacetime is some 120 orders of magnitude smaller than expected. This has been called the worst prediction in physics!

However, if antimatter has antigravity, then virtual matter-antimatter pairs will have no gravitational charge, so they would not curve spacetime. Furthermore, if virtual pairs do not gravitate, it would invalidate the current indirect measurements that limit the difference in the gravitational charge between matter and antimatter because these measurements rely upon measuring the virtual antimatter content in matter.