Wavefunction collapse and gravity

Question

If gravity can be thought of as both a wave (the gravitational wave, as predicted to exist by Albert Einstein and certain calculations) and a particle (the graviton), would it make sense to apply quantum mechanics (which I understand only applies to mass/energy) and therefore wavefunction collapse to gravity? In other words, does gravity exhibit wave-particle duality as light does, and thus is it susceptible to wavefunction collapse? If so, what would the implications of the wavefunction collapse of a gravitational wave be?

To better sum up my question: could a gravitational wave be described as a wavefunction?

I would appreciate it if anyone could help me understand if this is a valid concept, or if there are any other theories and concepts that would help me understand gravity and quantum mechanics combined (quantum field theory?).

Answer 1

To better sum up my question: could a gravitational wave be described as a wavefunction?

At the moment the only candidates for describing a quantized gravitational field and at the same time embed the standard model of particle physics, are string theories . There is no quantization of gravity alone, as following the recipe for quantizing other fields leads to infinities due to the spin 2 of the proposed graviton. Quantisation of gravity is a field of active theoretical physics research.

We have experimental evidence that general relativity holds. We do not have experimental evidence that a graviton exists. We can assume it does and then theorize about interactions of the graviton as wave/particle with other fields and wave functions, but it is just an imaginary exercise at this level.

And yes, you would need as prerequisite quantum field theory to start understanding string theory.

P.S. The collapse of the wavefunction concept is misleading, as the wave itself is not a wave in the field. It is a probability wave for finding a particle in an (x,y,z,t) location.

Answer 2

First, we have serious theoretical reasons to believe that gravitation is mediated by a particle named graviton. From the theory of gravitons we can obtain gravitational waves as an approximation --somehow as we obtain electromagnetic waves as an approximation to a quantum theory of photons--. The wave formulation is not equivalent to the graviton formulation, but only an approximation.

Second, quantum mechanics applies to 'everything', not only to mass-energy. Quantum mechanics applies to entropy, angular momentum, speed, electric field... Therefore, quantum mechanics also applies to gravitation, although nobody has still obtained a complete quantum gravity theory that convinces to everyone else. As a consequence, all the concepts of quantum mechanics, including wavefunction collapse, also apply in a gravitational context. As @AnnaV correctly notices the wavefunction of quantum mechanics is not a wave, but an unobservable function.

Light is a wave. Light is made of lots and lots of particles called photons. Light behaves as a wave and each photon behaves as a particle. Wave-particle duality is an old misconception of quantum mechanics. Klein site explains why.

Gravitational waves are... waves. The theory says us that those gravitational waves are made of lots and lots of particles called gravitons. As remarked above, the gravitational wave theory can be obtained from the quantum theory of gravitons. Steven Weinberg in the section "8 Quantum theory of gravitation" of the chapter "10 Gravitational radiation" of his textbook on "Gravitation and cosmology" gives a bare introduction to the relation between gravitational wave theory and gravitons.