## SchrödingerIn 1939 Erwin Schroödinger reasoned that if spacetime is curved as general relativity demands, then its effects on quantum processes must not be dismissed without careful investigation. Using the equations of relativistic quantum mechanics, Schroödinger proved that quantum wave functions coevolve with the curved spacetime of the closed Friedmann universe.Schrödinger found that the plane-wave eigenfunctions characteristic of flat spacetime are replaced in the curved spacetime of the Friedmann universe by wave functions that are not precisely flat and that have wavelengths that are directly proportional to the Friedmann radius. This means that the eigenfunctions change wavelength as the radius of the universe changes and the quantum systems they describe follow. In an expanding universe quantum systems expand. In a contracting universe they contract. From this quantum mechanical perspective Schroödinger confirmed the changes in both photon and particle momenta well known from general relativity, giving confidence in the logic of each approach and in the tie of Friedmann spacetime geometry to quantum processes. These changes in quantum systems may equivalently be viewed as a logical consequence of the fact that the energy and momentum of an “isolated” system can change in general relativity when the spacetime geometry of the universe changes. Schroödinger’s arguments are general and have applications beyond just photons and single particles. His reasoning applies to all quantum systems. It applies to meter sticks and clocks. Schrödinger found the missing link that Einstein knew needed to be there.
"We thus find that in order to describe the properties of Matter, as well as those of Light, we must employ waves and corpuscles simultaneously. We can no longer imagine the electron as being just a minute corpuscle of electricity: we must associate a wave with it. And this wave is not just a fiction: its length can be measured and its interferences calculated in advance."
Louis de Broglie, Nobel Prize 1929 |