atyy said:Hossenfelder wrote a nice post about an experimental demonstration of neutron wavefunctions in gravity: http://backreaction.blogspot.com/2007/06/bouncing-neutrons-in-gravitational.html" .
bcrowell said:Atyy didn't quite say so explicitly, but the answer to the OP's question is yes.
The De Broglie wavelength shift in gravitational fields is a phenomenon that occurs when a particle with a certain wavelength travels through a gravitational field. The particle's wavelength is affected by the curvature of space-time caused by the gravitational field, resulting in a change in its wavelength.
The De Broglie wavelength shift in gravitational fields was first proposed by French physicist Louis de Broglie in 1924. He suggested that particles, such as electrons, could exhibit both wave-like and particle-like behavior, and that this behavior would be affected by gravity.
The equation for calculating the De Broglie wavelength shift is λ' = λ(1 + GM/rc²), where λ' is the shifted wavelength, λ is the original wavelength of the particle, G is the gravitational constant, M is the mass of the object creating the gravitational field, r is the distance between the particle and the object, and c is the speed of light.
No, the De Broglie wavelength shift can occur in any gravitational field, as long as the particle's wavelength is small enough to be affected by the curvature of space-time. However, the effect is more noticeable in strong gravitational fields, such as those found near black holes.
The De Broglie wavelength shift supports the idea of wave-particle duality, which suggests that particles can exhibit both wave-like and particle-like behavior. It also provides evidence for the theory of general relativity, which explains how gravity affects the curvature of space-time. Additionally, it has implications for quantum mechanics and the behavior of particles at the quantum level.