Double-slit experiment and gravity

[Ookke]

If the particles used in double-slit experiment were massive enough and/or our equipment sensitive enough, could we use gravity to spy what path the particles take even before they hit the detector? Would this kind of "measurement" destroy the interference?

 

[phinds]

ANY measurement destroys the interference.

I don't see how you could "use gravity" in the sense you are saying. What would you do, stop the particles, put them on a scale, then send them on their way. I'll bet that would destroy the interference for sure

 

[bahamagreen]

I think Ookke is thinking the opposite way, phinds... using the gravitational dislocation of resting test masses to infer the path of the massive particle going through the slits - a kind of indirect weak measurement.

Imagine we discovered a stream of microscopic black holes entering the solar system and set up the test for their arrival using Ricci ring deformations to measure the little BH paths through the apparatus

 

[Nugatory]

Would this kind of "measurement" destroy the interference?

Yes. It's a historical accident that the words "measurement" and "observation" are so widely used here, when "interaction" might in hindsight have been less misleading. A detectable gravitational interaction, like any other detectable interaction, will suffice to eliminate the interference.

 

[bhobba]

I think Ookke is thinking the opposite way, phinds... using the gravitational dislocation of resting test masses to infer the path of the massive particle going through the slits - a kind of indirect weak measurement.

Weak measurement or no weak measurement QM is unequivocal - if you know the path interference is destroyed

Imagine we discovered a stream of microscopic black holes entering the solar system and set up the test for their arrival using Ricci ring deformations to measure the little BH paths through the apparatus

A string of miniature black holes - well assuming such actually existed QM is clear - you know the path - interference disappears.

Thanks
Bill

 

[Ookke]

A detectable gravitational interaction, like any other detectable interaction, will suffice to eliminate the interference.

Ok. As there is always some gravity present in double-slit experiments on Earth, and the particles e.g. electrons (I suppose) interact with the gravity field, there must be some threshold so that tiny gravitational effects do not eliminate the interference. This threshold must be something fundamental and not really depending on the accuracy of our measuring equipment.

 

[bhobba]

Ok. As there is always some gravity present in double-slit experiments on Earth, and the particles e.g. electrons (I suppose) interact with the gravity field, there must be some threshold so that tiny gravitational effects do not eliminate the interference. This threshold must be something fundamental and not really depending on the accuracy of our measuring equipment.

Nugatory was referring to interactions that 'observe' the path - such, for example, would be placing a detector in one of the slits.

Gravity is not a which path observation.

Over the size of your typical double slit experiment on Earth gravity is effectively constant so has a path independent effect - assuming it actually has a measurable effect on a double slit experiment - which it doesn't - its far too weak to affect electrons in any significant way.

Thanks
Bill

 

[Ookke]

Nugatory was referring to interactions that 'observe' the path - such, for example, would be placing a detector in one of the slits.

Gravity is not a which path observation.

If there was no limit for the accuracy of our equipment, we could put test masses at left and right side of the room, release an electron and see if there is any difference. I would expect that the electron creates tiny gravity field around it and interacts more with left side test mass, if it goes through left slit, and the same with right side.

its far too weak to affect electrons.

Sure, but in principle. And the particle could be more massive than electron.

 

[bhobba]

If there was no limit for the accuracy of our equipment, we could put test masses at left and right side of the room, release an electron and see if there is any difference. I would expect that the electron creates tiny gravity field around it and interacts more with left side test mass, if it goes through left slit, and the same with right side.

Why do you think that's a double slit type experiment where the electron goes through one slit or the other? I think you need to specify your exact set-up, what you expect to happen, and why.

Just so you understand what is meant, and why we get interference effects, see the following:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

The reason you get an interference pattern is the state behind the screen is the superposition of the state going through each hole. If you know which hole it went through ie it goes through one hole, it's not a superposition and you do not get interference.

Precisely how do you propose 'gravity' to force it through one hole or the other, and not be a superposition of both?

Thanks
Bill

 

[vanhees71]

It's pretty hard to study the effects of gravitation on subatomic particles, because it's the weakest of all the fundmental interaction. It's weaker by a factor of about $10^{40}$ or something in this order of magnitude compared to the electromagnetic interaction.

Nevertheless, nowadays one can check a gedanken experiment with "cold" neutrons. Besides photons (which are difficult to study on the beginner's level, because they are massless and thus always ultrarelativistic, and you need pretty advanced math to really understand them right) neutrons enable us to make the most precise measurements on the foundations of quantum theory.

The most simple thing is to study non-relativistic neutrons in the (homogeneous) gravitational field of the earth. This is a problem usually treated in quantum mechanics 1 as an example for an energy eigenvalue problem (time-independent Schrödinger equation) solvable in momentum space, leading to Airy functions as solutions.

At the Institut Laue Langevin in Grenoble the experimentalists put neutrons above a neary ideal mirror (mirror for neutrons of course) such that the neutrons in the gravitational field got bound. You can evaluate the corresponding discrete energy eigenvalues analytically and compare to the measured values, which are in the peV (pico-electron volts, i.e., $10^{-12} \; \text{eV}$.

Here are the two papers about the experiment (for the first one, I couldn't find a publicly available source, which is due to the restrictive copyright politics by Nature):

http://www.nature.com/nature/journal/v415/n6869/abs/415297a.html

Phys. Rev. D 67, 102002 (2003)
http://arxiv.org/abs/hep-ph/0306198

 

[Ookke]

Why do you think that's a double slit type experiment where the electron goes through one slit or the other? I think you need to specify your exact set-up, what you expect to happen, and why.

I didn't mean an experiment that forces the particle to appear at either slit, but something where we compare tiny gravitational effects at different places to get hint of the path that particle goes. This is somewhat analogous to cellular network that is able to (at least roughly) get phone location by comparing phone signal at different nodes. Or something like that a submarine does with its passive sonar.

Maybe this wouldn't work even with ideal equipment, but this was based on intuition that the particle must create gravitational field even in interfered state. If the field is stronger somewhere, this is probably where the particle is near. And if the field is uniform everywhere, this would be important result too, supporting the idea that particle (in its interfered state) has no specific location unless it's forced to appear. But that's true I need to study this more.

 

[bhobba]

I didn't mean an experiment that forces the particle to appear at either slit, but something where we compare tiny gravitational effects at different places to get hint of the path that particle goes.

So you are talking about a hand-wavy very vague experimental set-up that somehow measures the path of the electron. QM is clear - you measure that path - interference disappears.

but this was based on intuition that the particle must create gravitational field even in interfered state.

Why do you believe you can view a non localised particle as point particle with a field? In other words why do you think your classically formed intuition applies to QM?

Its wrong BTW - QFT says the field of an electron is not like that - intuition is a very poor guide to QM.

Thanks
Bill

 

[StevieTNZ]

A similar experiment is proposed - http://www.nature.com/ncomms/journal/v2/n10/pdf/ncomms1498.pdf?WT.ec_id=NCOMMS-20111018

 

[vanhees71]

I think the idea is the following (speaking in terms of Newtonian gravity, because relativistic QFT in a curved background space-time is a very tricky business): You use a double slit with horizontal slits. Then in principle the particles moving through the lower slit has a lower energy than the particle running through the upper slit, supposed you have a particle beam hitting the slits with a very well defined momentum. Of course, this is practically very unlikely to be achieved, because you can not make the distance between the slits pretty large if you want to see interference fringes, and the energy (momentum) difference of the particles due to the gravitational field of the Earth is negligibly tiny and for sure not measurable within the accuracy limits you can prepare the particle's momentum to begin with.

In any case the which-way information has to be established by entangeling it with some intrinsic property of the particles (or photons). E.g., in the famous quantum eraser experiment one uses the photons' polarization to gain which-way information. To gain complete which-way information you must make sure that the polarization of the photons running through slit 1 is perpendicular to the polarization of photons running through slit 2, and thus you don't see interference effects anymore, because the corresponding polarization states are orthogonal and thus the interference term vanishes. If you make only a "weak measurement" of which-way information, you only get less contrast in your interference pattern but have a corresponding uncertainty in the which-way information.

The proposed experiment in Nature uses gravity to provide the entanglement between the way the particles go and some internal degrees of freedom providing a "clock". It's not clear to me, how they concretely want to realize the clock. I guess one has to follow the paper carefully and check the references. I wonder whether it's practically possible to make such a measurement, but with neutrons there may be some chance, because they can be handled with utmost precision.