Gravitational signature of a photon in a double slit experiment

[Herbascious J]

TL;DR

In principal, can the gravitational signature of a photon be used to detect which slit it travels through in a double slit experiment?

I'm trying to think of a how the double slit experiment can detect a photon without interacting with it in theory. In principal (not reality of course) does a photon have a gravitational signature which could be used to detect which slit it traveled through during the double slit experiment? It seems there should always be some kind of gravitational signature, no matter how faint, when energy passes by an observer. Would the detection of this signature 'collapse the waverform'? I apologize for my terminology if it is incorrect.

 

[vanhees71]

There is of course also a tiny gravitational interaction of the photon with the material building the slits, but it's so tiny that you can forget about it completely. The main interaction is electromagnetic and this makes all the phenomena concerning diffraction and corresponding interference effects.

 

[Reggid]

You can make a simple estimate to see that gravitational effects will be far (many orders of magnitude) too small to give a relevant effect.

How could you find out using gravitational interaction which slit the particle was passing through? Well, you could for example place another particle right between the slits, at rest. Then you could argue that if the first particle goes through the upper slit, then our "detector particle" gets a upward momentum kick. If the first particle goes through the lower slit then the detector particle gets a downward momentum kick. So you just look at your detector particle after the interaction and depending on whether it has upwards or downwards momentum you know which slit the other particle went through.

Simple, right?

Well, no. It's not that simple. The devil is in the detail. Especially in the two claims I made about the state of the detector particle before the interaction: "placed between the two slits" and "at rest". Both are important, because if your detector particle was for example placed above both slits, then it would always be pulled down, regardless of which slit the other one passes through. And if it already had upward or downward momentum before the interaction, this could cancel (or even turn around) the momentum kick you actually want to measure. In both cases, your detector would not work

"Placed between the two slits" implies that its position uncertainty $\sigma_x$ in that dimension should be smaller than the distance of the slits $d$.

$$\sigma_x\lesssim d\;.$$

"At rest" should be replaced with "small enough momentum uncertainty in that direction", where "small enough" means that the moment uncertainty $\sigma_p$ should be smaller than the expected momentum transfer $\delta p$ from the interaction of the two particles.

$$\sigma_p \lesssim \delta p\;.$$

Of course the state of the detector particle has to obey the momentum-position uncertainty relation
$$\sigma_x\sigma_p\geq\frac{\hbar}{2}\,.$$.

Putting everything together you find
$$\delta p \gtrsim \frac{\hbar}{2d}\;.$$

This is an estimate of the minimum strength of the interaction (given in terms of the typical momentum kick $\delta p$ that your detector particle gets) in order to get a meaningful which-way measurement.

Plug in some reasonable numbers for the distance of the slits and the strength of gravitational interaction, and you'll see: no chance!

 

[DrClaude]

Wouldn't that simply lead to a change of the phase of the interference pattern? I don't think it would give which-way information.

Observation of Gravitationally Induced Quantum Interference
R. Colella, A. W. Overhauser, and S. A. Werner
Phys. Rev. Lett. 34, 1472 (1975)

We have used a neutron interferometer to observe the quantum-mechanical phase shift of neutrons caused by their interaction with Earth's gravitational field.

 

[f95toli]

Wouldn't that simply lead to a change of the phase of the interference pattern? I don't think it would give which-way information.

Indeed, gravity does not destroy interference in cold-atom interferometers, but it does affect them. Atoms are obviously much more sensitive to gravity than photons.
You can even build extremely sensitive gravimeters this way.

 

[vanhees71]

Indeed, they brought a BEC to the ISS recently in order to avoid disturbance by gravity.

 

[PeterDonis]

Wouldn't that simply lead to a change of the phase of the interference pattern?

The experiment in the paper you linked to is not attempting to detect gravitational which-way information. It is only attempting to test whether the Newtonian gravitational potential can be treated like any other potential in the Schrödinger Equation (and it turns out it can). That is a much, much coarser test than what the OP is asking about.

 

[PeterDonis]

It seems there should always be some kind of gravitational signature, no matter how faint, when energy passes by an observer. Would the detection of this signature 'collapse the waverform'?

If you could detect it, then yes, it would. But, as you can see from the numbers others have posted showing how tiny the effect is, that's a very, very big "if".

 

[Vanadium 50]

Let's take a step back. Can we tell which slit a photon went through without gravity? Yes. No problem. We don't get an interference pattern when we do this, though. So if it were possible to determine which slit gravitationally, what would happen? Nothing that doesn't already happen: the interference pattern would be replaced by two diffraction patterns.

 

[Herbascious J]

...the interference pattern would be replaced by two diffraction patterns.

Ok, this is where I was hung up. Admittedly, this is all theoretical, but something about it seems peculiar to me only because when I imagine the photon passing the slit, i know there is a faint signature from it's gravity albeit undetectable. If the detector (in principle) were to effect the photon, wouldn't also the gravitational fields of just the slits alone also effect the photon and what if we just didn't look at the results or turned off the detector all together? I guess I'm not sure where the breakdown of the wave happens. Is it me looking at the screen of the data results? Is it me turning off the detector? Is it me removing the gravity detector, which has gravity just like the slits do? How far can you push this mind experiment before the wave collapses? Thanks everyone for the input, much appreciated.

 

[PeterDonis]

I guess I'm not sure where the breakdown of the wave happens.

It happens when an irreversible result is recorded. Just the tiny gravitational effect of a photon going through one slit or the other does not do that. Only setting up some kind of measuring apparatus that magnifies that effect into an irreversible result (like a light either lighting up or not lighting up, or a pointer swinging one way or the other) will do it.

 

[andresB]

Ok, this is where I was hung up. Admittedly, this is all theoretical, but something about it seems peculiar to me only because when I imagine the photon passing the slit, i know there is a faint signature from it's gravity albeit undetectable...

Why do you expect know that the photon passes through one slit?

In the double slit experiment the photon is, after passing the slits, in a superposition of "slits" states. Why do you think the gravitational field produced by the photon will not also be in a superposition?

Actually, this is an unanswered question and it isstill hotly debated. So far, we really don't know.

 

[PeterDonis]

Why do you think the gravitational field produced by the photon will not also be in a superposition?

The gravitational effect itself might be (as you say, we don't currently know whether a quantum theory of gravity that could describe a superposition of different gravitational fields exists), but if we have a measuring device that amplifies that effect to produce an irreversible result, as described in my post #11, that would count as a which-way measurement on the photon.

 

[andresB]

The gravitational effect itself might be (as you say, we don't currently know whether a quantum theory of gravity that could describe a superposition of different gravitational fields exists), but if we have a measuring device that amplifies that effect to produce an irreversible result, as described in my post #11, that would count as a which-way measurement on the photon.

In a related experiment, say, neutron scattering, we could determine through which slit the neutron traveled by measuring the magnetic field produced by the neutron's magnetic moment.

However, in the gravitational case I'm not so sure because the proposed measuring device will measure the gravitational field. You are assuming that that measurement will collapse the photon state to one or the other slit. But we do not know if gravity couple that way.

 

[PeterDonis]

In a related experiment, say, neutron scattering, we could determine through which slit the neutron traveled by measuring the magnetic field produced by the neutron's magnetic moment.

Yes.

You are assuming that that measurement will collapse the photon state to one or the other slit. But we do not know if gravity couple that way.

You're missing the point. If we can measure a "gravitational field" at all, then we can make such a measurement yield which-slit information, the same way the measurement of a magnetic field would.

If gravity "doesn't couple that way", that would mean we could not measure a "gravitational field" at all. It would not mean that we could measure it, but measuring it wouldn't yield which-slit information the way other kinds of measurement would.

 

[vanhees71]

It happens when an irreversible result is recorded. Just the tiny gravitational effect of a photon going through one slit or the other does not do that. Only setting up some kind of measuring apparatus that magnifies that effect into an irreversible result (like a light either lighting up or not lighting up, or a pointer swinging one way or the other) will do it.

One example is to do the experiment with linearly polarized photons (say in $x$-direction polarized). Then put two quarter-wave plates into the slits one at orientation $\pi/4$ the other at $-\pi/4$ relative to the $x$-axis. Then photon going through the 1st slit get left-circularly polarized those going through the 2nd slit get right-circularly polarized. The polarization states then are orthogonal to each other. And this means you can in principle know through which slit each photon came when measuring the polarization state to be either left- or right-circularly polarized. Now, however, you don't measure the polarization but just let all the photons hit a screen. Since now the photons going through slit one are orthogonal to those going through slit 2 due to their polarization state, you won't get an interference pattern, because the interference term cancels due to the orthogonality of the polarization states, i.e., you see the incoherent superposition of two single-slit interference patterns. If you remove the quarter-wave plates the photons going through slit 1 are not distinguishable from photons going through slit 2, and the interference term for photons going through either slit is maximal in amplitude, such that you get a two-slit interference pattern in "full contrast" (with ideally monochromatic photons in the minima you get really 0 intensity).

Note that for the two-slit interference pattern to vanish you don't need to measure the polarization state. It's enough that the photons get labelled through which slit they came by the polarization observable in such a way that with 100% probability a certain polarization states means it came through a specific slit, i.e., you have a full entanglement between which-way information and polarization of the photon.

You can also orient the quarter-wave plates in the slits in any other relative angle than $\pi/2$. Then the polarization states for the photons going through either slit are no longer orthogonal and you get two-slit interference pattern but with lower than maximal contrast. For "full contrast" the quarter-wave plates must be oriented in the same direction. The higher the contrast of the two-slit interference pattern is choosen the less you know through which slit the photon came even when measuring its polarization state.

In Bohr's language this is an example for complementarity: You can either have precise which-way information or a full-contrast interference pattern but never both. In all other setups you get only partial knowledge about which-way information and an interference pattern with correspondingly lower contrast.

 

[Herbascious J]

You can either have precise which-way information or a full-contrast interference pattern but never both. In all other setups you get only partial knowledge about which-way information and an interference pattern with correspondingly lower contrast.

Is there some theorhetical explanation of why the "gravitational detector" (admittedly fiction) would also be physcially limited in this way? The explanation I am currently thinking is that the gravity fields are too faint to detect, therefore practically, it can't be done, but in principal it's still possible. But that doesn't seem very satisfying because the physical principals seem to exist. What I mean is, can't I set up a thought experiment with a magical elf that holds a magic wand that can detect the faintest of all gravitataional signatures in all of the kingdom and if they hold that wand between the slits they can whipser to me in some elven language which slit the photon went through if only I left a cookie crumb after the photon is fired. I can chose to leave the cookie crumb or not, after the results are displayed on the pattern monitor. (groans and eye rolls all around - I get it). My question is, does this experiment not work because there are no such things as magical elves, or is it more satisfying than that. Rather is it because the gravitational field of the wand has now affected the nature of the photon, and so it no longer can interfere with the 'ghost path' it would have taken through the other slit and produce interference? Many apologies for introducing and elven kingdom.

 

[PeterDonis]

Is there some theorhetical explanation of why the "gravitational detector" (admittedly fiction) would also be physcially limited in this way?

Any detector will be limited in the way @vanhees71 described. That's a basic principle of QM and doesn't depend on any of the details of what the detector is detecting.

 

[PeterDonis]

The explanation I am currently thinking is that the gravity fields are too faint to detect, therefore practically, it can't be done, but in principal it's still possible.

See my response to @andresB in post #15.

 

[vanhees71]

Any detector will be limited in the way @vanhees71 described. That's a basic principle of QM and doesn't depend on any of the details of what the detector is detecting.

Yes, and in fact the GW detectors like LIGO/VIRGO are sensitive to the quantum flucutations. AFAIK LIGO also uses quantum effects ("sqeezed light") to enhance their sensitivity further!

 

[PeterDonis]

GW detectors like LIGO/VIRGO are sensitive to the quantum flucutations

If you mean quantum fluctuations in the gravitational waves themselves, no, they're not. Those detectors are way too insensitive to detect quantum fluctuations in the GWs they detect.

LIGO also uses quantum effects ("sqeezed light") to enhance their sensitivity further!

They use quantum effects in the light inside the interferometer, yes. That is not at all the same as detecting quantum fluctuations in the GWs.

 

[vanhees71]

No, of course I didn't mean quantum fluctuations in the gravitational waves but quantum fluctuations of the detectors themselves (uncertainty of the mirrors' positions as well as shot noise due to quantum fluctuations of the light) as detailed in, e.g.,

https://doi.org/10.1088/1464-4266/6/8/008

 

[Aonghus Lynch]

Hi,

Because objects with more mass create more gravity, you would want to go for the largest mass particle/object you can find for the proposed experiment.

And it seems that you should certainly be able to do better than with photons.

The following 1999 paper describes how wave-particle duality has been observed with carbon 60 molecules: https://physicsworld.com/a/wave-particle-duality-seen-in-carbon-60-molecules/

Here is another one from 2013, with other molecules: https://arstechnica.com/science/201...ith-big-molecules-approaches-the-macroscopic/

There may have been larger molecules since then, but the above two are the latest I could find after a modest search.

 

[PeterDonis]

you would want to go for the largest mass particle/object you can find for the proposed experiment

The largest mass of any object for which we have observed quantum interference effects in a double slit experiment is still many orders of magnitude too small for us to observe its gravitational effects with our current technology.

 

[Aonghus Lynch]

Point taken,

But it looks like the effort to improve that current technology for (generally) measuring the gravitation of small masses is pretty active.

- Ref to PRL article from 2014, which demonstrates gravitational forces being measured at very small scales: https://www.nature.com/news/bouncing-neutrons-probe-dark-energy-on-a-table-top-1.15062
- PRL article from 2018, where the smallest size is reported be down to 7mg: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.071101
- Nature article from 2017, looking at the gravitational effect of caesium atoms
https://www.nature.com/articles/nphys4189

Maybe a method can be found soon enough to measuring the gravity of whatever might passing through the slits. It certainly seems like a sensible prediction to expect the breakdown in the waveform in that setup, but even if it broke down, IMO it would be cool see gravity and the wavefunction interacting in this way.

 

[andresB]

Without directly measuring a gravitational interaction, there are might be other possibilities for observing quantum gravitational effects. One possible path is to look for gravitationally mediated quantum entanglement between previously untangled particles.

 

[vanhees71]

I think somewhere in this thread the beautiful measurement of the energy levels of cold neutrons in the gravitational field of the Earth (+total reflection on the bottom) has been already mentioned. The results are precisely as expected from the corresponding result of solving the energy-eigenvector problem (a nice exercise in the QM 1 lecture; hint: it's most easily solved in the momentum representation). This means gravitational interactions (at least on the level of the semiclassical theory where the gravitational field is treated as a classical external field) don't behave different from the other interactions.

 

[f95toli]

Without directly measuring a gravitational interaction, there are might be other possibilities for observing quantum gravitational effects. One possible path is to look for gravitationally mediated quantum entanglement between previously untangled particles.

"Gravitational interactions" are measured all the the time. Gravimeters as well as inertial navigation systems based on cold atom interferometry have been around for a long time in the labs and are now being commercialised (just google "Cold atom gravimeter").

One of the issues with this and many other threads on PF is that people start talking about photons.
In the early days of QM we did not have systems like cold atoms, ion traps or solid state qubits and since photons interact very weakly with their environment they were "easy" to use which is why most of the early demonstrations of QM effect were demonstrated using photonics.

These days all of these "basic" effects have been demonstrated in many, many different systems, but since pop-sci books still use photons as examples people end of worrying unnecessarily things that are specific to photons (typically that they massless) thinking that this is somehow important; but this is a red herring and not at all of fundamental importance.

.

 

[Lord Crc]

So how exactly would you, in principle, go about measuring the which way information? A couple of masses near each slit and measure relative distance to centerline between slits?
From what I've gathered the particle being sent through the slits wouldn't actually radiate gravitational waves, so LIGO-like interferometers are out. Or am I mistaken here?

 

[PeterDonis]

This means gravitational interactions (at least on the level of the semiclassical theory where the gravitational field is treated as a classical external field) don't behave different from the other interactions.

This measurement won't give "which way" information in a double slit scenario, however. All that this measurement, as beautiful as it is, is measuring is whether the Newtonian gravitational potential acts like any other potential in the Schrödinger Equation.

"Gravitational interactions" are measured all the the time.

For much larger objects than the ones for which interference has been measured in a double slit experiment, yes. A "cold atom gravimeter" is not measuring the gravitational effect of individual cold atoms. It is using cold atoms to measure the gravitational effect of something large.