[Alekanekelo]

Could you elaborate a bit on your point 1/3? How come the little interest in this subject? Even though it contains no relativistic effects it would seem to have some importance in filling out the complete 'cube' of theories?

[crntaylor]

The equations you end up with are called the Schrodinger-Newton equations [1]. These are the same as Schrodinger's equation, but with an extra term that couples the wavefunction to a global gravitational field via its mass.

I'm not an expert, but possible reasons for the relative lack of interest in these equations include:

1. It doesn't produce many interesting predictions (possible exception: it might be useful for explaining how gravitational effects can induce wavefunction collapse, but this appears to be highly speculative.)

2. There isn't a natural domain of applicability. For example, combining 1/2 (gravity and relativity) has a natural applicability to things that are heavy and move fast (i.e. stars, galaxies, the universe). Combining 2/3 (relativity and quantum mechanics) applies to things that are small and move fast (electrons and other fundamental particles). The domain of applicability of 1/3 would be things that are small and heavy, but move slowly. I can't think of any examples of things that fit the bill (note that 1/2/3 applies to things that are small, heavy and move quickly, i.e. black holes).

When I say "move quickly" here I don't necessarily mean that the object you're modelling must be moving quickly - just that there are speeds in the problem that are appreciable fractions of the speed of light.

[1] http://en.wikipedia.org/wiki/Schr%C3%B6dinger%E2%80%93Newton...

[gus_massa]

There are a few experiments that combine Newtonian gravity and quantum mechanics (1/3).

For example you can split a ray of neutrons, direct each beam throu a different path with different height and then make them collide and see the interference pattern. (The details are in the book of Sakurai "Modern Quantum Mechanics" pp127-129, with data from an experiment of Colella, Overhauser, Werner (1975).)

It is possible to create systems that combine 1/3, but they are almost corner cases and most of the time the other combinations are more useful.