# Equivalence principle and gravitational neutron diffraction

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

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luxxio said:
In Modern Quantum Mechanics, Sakurai say that at quantum level the gravity is no more geometrical because the schrodinger 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.

George Jones said:
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 schrodinger 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.

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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".

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?

luxxio said:
I can explain better. If you write the schrodinger 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

## 1. What is the Equivalence Principle?

The Equivalence Principle is a fundamental concept in physics that states that the effects of gravity on an object are equivalent to the effects of acceleration. This means that an observer in a uniformly accelerated reference frame cannot distinguish between being in a gravitational field and being in an accelerated frame of reference.

## 2. How does the Equivalence Principle relate to gravitational neutron diffraction?

The Equivalence Principle plays a crucial role in understanding gravitational neutron diffraction. This phenomenon occurs when a beam of neutrons is directed through a gravitational field, causing the neutrons to bend due to their mass. The amount of bending is dependent on the strength of the gravitational field, which follows the same principle as the bending of light in a gravitational field.

## 3. What is the significance of gravitational neutron diffraction in physics?

Gravitational neutron diffraction is significant because it provides evidence for the Equivalence Principle and helps us understand the behavior of particles in a gravitational field. It also has practical applications in fields such as geology and astrophysics, where it can be used to study the properties of neutron stars and other celestial bodies.

## 4. Can the Equivalence Principle be tested experimentally?

Yes, the Equivalence Principle has been tested and confirmed through various experiments, including the famous Eötvös experiment and more recent experiments using atomic clocks. Gravitational neutron diffraction is another way to test the Equivalence Principle and has been observed in experiments using neutron beams passing through a gravitational field.

## 5. How does the Equivalence Principle relate to Einstein's theory of general relativity?

The Equivalence Principle is a fundamental concept in Einstein's theory of general relativity and serves as the cornerstone of the theory. It is the basis for the principle of equivalence between gravity and acceleration, which is central to the understanding of space-time and the behavior of objects in a gravitational field.

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