Equivalence principle and gravitational neutron diffraction

[luxxio]

In Modern Quantum Mechanics, Sakurai say that at quantum level the gravity is no more geometrical because the Schrödinger equation depend on the fraction \frac{m}{\hbar}. Can someone explain better this claim or link me some detailed paper on this argument?

 

[George Jones]

In Modern Quantum Mechanics, Sakurai say that at quantum level the gravity is no more geometrical because the Schrödinger equation depend on the fraction \frac{m}{\hbar}. Can someone explain better this claim or link me some detailed paper on this argument?

I'm not sure what Sakurai means, maybe just that quantum gravity is not needed for this situaution. An experiment that showed quantized energy levels for neutrons moving under the influence of gravity was performed a few years ago,

http://physicsworld.com/cws/article/news/3525,

http://arxiv.org/abs/hep-ph/0306198.

 

[luxxio]

I'm not sure what Sakurai means, maybe just that quantum gravity is not needed for this situaution.

I can explain better. If you write the Schrödinger equation for a gravitational potential

\left[\frac{-\nabla^2}{2m}+\frac{G_0 M m}{r}\right]|\psi>=E|\psi>

then you can't eliminate the probe particle mass term. So Sakurai say that gravity at quantum level is no longer a geomtrical property of the space.

 

[jambaugh]

I think we must be careful in interpreting Einstein's Equivalence Principle. I see often stated in texts and on forum posts that "Gravity is simply geometry" or variations there-of.

But we should look at it both ways. The equivalence principle states in effect that we cannot distinguish between geometry and gravitation and this also points out that geometry is not directly observable. What we observe is the dynamic evolution of test particles and via the EP we cannot separate the geometric "free evolution" and the "physical" forces.

As it stands then "geometry" is what's left when we (by convention) choose what is to be considered "free evolution". The purely geometric model of gravitation is beautiful and elegant but it is a model. I cannot help but wonder if thinking that "gravity is just geometry" has inhibited the integration of GR with QM. It certainly has motivated the explosion of quantum string/brane "theories".

 

[jfy4]

I have to wonder the same thing! As far as I know, almost all efforts to bring GR and QM together have assumed gravity as a strictly geometrical phenomena, however, there seems to be some experimental evidence to the contrary...

In Sakurai's book he specifically has a footnote dedicated to preserving the equivalence principle in these gravity/QM experiments, but is not light in pointing out that at this Quantum mechanical scale, gravity exhibits characteristics of not being entirely geometrical. So I guess my question is: Am I missing something here, or are a lot of quantum gravity approaches ignoring these experimental results?

 

[atyy]

I can explain better. If you write the Schrödinger equation for a gravitational potential

\left[\frac{-\nabla^2}{2m}+\frac{G_0 M m}{r}\right]|\psi>=E|\psi>

then you can't eliminate the probe particle mass term. So Sakurai say that gravity at quantum level is no longer a geomtrical property of the space.

But here the Newtonian potential is used, which is not "geometrical".

Anyway, in quantum gravity, at low energies, gravity is a spin-2 particle on flat spacetime (so in that sense, not "geometrical"). This description works well, and the equivalence principle can even be derived from energy conservation, rather than assumed. http://arxiv.org/abs/1105.3735