2-slit interference in a gravitational field

[Dmitry67]

Lets say I make 2-slit interf. experiment with slow (low enegry) electrons. I make their path as long as possible so they have time to fall in the Earth's gravitational field while they are flying.

So electrons are attracted to the Earth, hence the Earth is attracted to the electron beam. Even it is far beyond the precision of any experiment, it can give a 'which path' info and break the interference.

However, all experiments are made in the Earth's gravitational field, in our slightly curved space-time and it seems that it does not affect the experiments

As an ultimate example: can an interference pattern be obtained from a gravitational lensing? Depending on the path, the central body is attracted to the right or to the left...

 

[gendou2]

If I follow your argument, you suppose the Earth is being tugged in one direction or another the moment the particle passes through the slit.
Thus, we should be able to measure the Earth's change of momentum to find the path.
This seems to me to illuminate an incompatibility of GR and QM.
In order to make QM predictions involving gravitation, we would need a quantum theory of gravity.
The problem is, we don't have one.

To augment this experiment, what if we substitute a beam of heavy neutral particles (neutrons), for the electron beam.
Let's also take it to space so we're in free-fall.
Place a which-path detector; a light object between the slits.
Fire one particle through the slits and wait a while to see if the which-path detector moves in one direction or the other.
If it does move, would conclude the neutron went through the hole towards which it's moving.
I suppose this is still several orders of magnitude away from observable today, but it seems more realistic.

 

[Dmitry67]

Yes, I know, but we can do an experiment. It is possible that interference pattern disappear far enough from the slit because of the interaction with the gravitation field.

P.S.
Just found some links, I will check them
http://www.google.fr/search?sourcei...4-15,GGLD:fr&q=neutron+beam+gravitation+field

Looks like I was not the first who was thinking about it. Farewell, my Nobel prize :)

P.P.S.
Cool: http://backreaction.blogspot.com/2007/06/bouncing-neutrons-in-gravitational.html

 

[gendou2]

Wild stuff. I like your disappearing interference pattern idea. It would be easy to perform, too. Just pull the screen back away from the slits. In a vacuum for better results, I guess?

 

[Count Iblis]

The interference pattern does not vanish (at least not due to the Earth being attracted). The strength of the interference pattern is proportional to the overlap of the two wavefunctions psi1 and psi2, of the rest of the universe, where psi1 is what the wavefunction of the resto of the universe would be if the electron goes to slit 1 and psi2 what it would be if the electron goes through slit 2.

If you have a large body like the Earth, then its wavefunction is very localized in space (we are not talking about the physical dimensions rather about the center of mass position here). This means that in momentum space it has a huge width. Then, if the electron moves through one or the other slit, the mometum of the Earth is affected in different ways, but the difference falls well within the huge width of the wavefunction of the Earth in momentum space.

So, the overlap of psi1 and psi2 is almost exactly equal to 1.

If you had 100% accurate which way information, then that means that there exists an observable such that psi1 and psi2 would be different eigenstates of that observable corresponding to different eigenvalues. Measuring that observable would then tell you through which slit the electron went, regardless of whether you could actually measure that observable in practice.

But since eigenvectors corresponding to different eigenvalues are orthogonal, this means that psi1 and psi2 should have an overlap of zero.

 

[Dmitry67]

1
The interference pattern does not vanish (at least not due to the Earth being attracted).

2
If you have a large body like the Earth, then its wavefunction is very localized in space (we are not talking about the physical dimensions rather about the center of mass position here). This means that in momentum space it has a huge width. Then, if the electron moves through one or the other slit, the mometum of the Earth is affected in different ways, but the difference falls well within the huge width of the wavefunction of the Earth in momentum space.

1 Based on the result of the experiment with a neutron beam yes, I agree with you - looks like the gravitational field does not affect the interference pattern. And this is weird. An interaction of a particle with a macroscopic body full of thermodinamically irreversible processes is a classical case of what is called a "measurement" and it erases the interference in all cases - except the gravitation!

2 I don't understand what is it - "a wavefunction of Earth". Could you explain it differently? I don't think that neutron interacts with the whole Earth. It exchanges a graviton randomly with some of the particles in the Earth. In QM information is never lost, so in principle it is possible to get which-path information

3 What do you think about my example with the gravitational lensing? In that particular case the central body is pushed into the different directions depending on the which-path info.

 

[Hyperreality]

I happen to know two papers which seems to measure the effect of interference due to Earth's gravitational field through neutron interferometry.

1. Observation of Gravitationallly Induced Quantum Interference

http://www2.phys.canterbury.ac.nz/editorial/COW1975.pdf

2. Two-wavelength-difference measurement of gravitationally induced quantum interference phases

http://www2.phys.canterbury.ac.nz/editorial/1997VEP.pdf