Can Spacetime Perturbance Reveal Paths in the Double Slit Experiment?

[greypilgrim]

Hi.

Would it be possible (at least in principle) to use the spacetime perturbance caused by the energy-momentum of a photon (or any other particle) to figure out which way it took in a double slit experiment? Can this question even be answered in today's attempts at quantum gravity?

 

[mfb]

Would it be possible (at least in principle) to use the spacetime perturbance caused by the energy-momentum of a photon (or any other particle) to figure out which way it took in a double slit experiment?

If you can figure out which way it took you don't get interference any more.
It doesn't matter how exactly you can figure it out. You don't need anything exotic, a simple polarizer does the job. This is an experiment you can do in a classroom.

 

[greypilgrim]

Orthogonally polarized beams of light don't create an interference pattern because you can figure out in principle which way a photon took, even if the measurement is not performed. Since we see interference in normal experiments, it shouldn't even be possible in principle to use spacetime perturbance to figure out which way, no matter how good our future measurement devices will be. Why not? As far as I know, GR doesn't allow superpositions of spacetime perturbances that collapse into one when interacting with the measurement device.

 

[DrChinese]

Orthogonally polarized beams of light don't create an interference pattern because you can figure out in principle which way a photon took, even if the measurement is not performed. Since we see interference in normal experiments, it shouldn't even be possible in principle to use spacetime perturbance to figure out which way, no matter how good our future measurement devices will be. Why not? As far as I know, GR doesn't allow superpositions of spacetime perturbances that collapse into one when interacting with the measurement device.

There would need to be a quantum interaction to obtain the which way information. That is not present in GR, but would be in a quantum theory of gravity. The fact that quantum interference is observed in the standard version of the experiment might rule out some candidate quantum gravity theories.

There have been attempts to research this area. Here are a couple that might be up your alley, from some top teams:

https://arxiv.org/abs/1206.0965
Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon traveling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon's coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.

https://arxiv.org/abs/1304.7912
In the last years quantum correlations received large attention as key ingredient in advanced quantum metrology protocols, in this letter we show that they provide even larger advantages when considering multiple-interferometer setups. In particular we demonstrate that the use of quantum correlated light beams in coupled interferometers leads to substantial advantages with respect to classical light, up to a noise-free scenario for the ideal lossless case. On the one hand, our results prompt the possibility of testing quantum gravity in experimental configurations affordable in current quantum optics laboratories and strongly improve the precision in "larger size experiments" such as the Fermilab holometer; on the other hand, they pave the way for future applications to high precision measurements and quantum metrology.

 

[mfb]

The energy is way too low to lead to a detectable signature via gravity. Send Planck energy photons and the result will be different.

 

[greypilgrim]

The energy is way too low to lead to a detectable signature via gravity.

In practice or fundamentally? If the latter, why would there be a fundamental limit?

 

[mfb]

Fundamentally.
Gravity is simply way too weak. Tens of orders of magnitude too weak.

If it would be strong enough the double slit experiment wouldn't work.

 

[Vanadium 50]

Why overcomplicate things? "spacetime perturbance" isn't a thing, but it sounds like you are thinking about general relativity, which is completely unnecessary and just makes things more complicated. Clasical gravity is just fine.

So, how would you go about measuring the gravitational force ("spacetime perturbance") from your beam? (Which can be atoms or molecuules instead of light, if you want to make it easier) Hang a weight and see how far it moves when the beam passes it.

Problem is, just as the beam exerts a force on the weight, the weight exerts a force on the beam. If there is enough force to determine which slit the beam passed through, there is enough force to drive it towards only one of the slits - you will get the same pattern as if it were single slit. If there's not enough force to drive the beam to only one slit there is not enough to determine which slit it went through.

In short, this is a very difficult way to effectively cover one slit.