B Gravitational signature of a photon in a double slit experiment

[Herbascious J]

TL;DR Summary

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 Schrodinger 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 Schrodinger 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.

 

[PeterDonis]

what I've gathered the particle being sent through the slits wouldn't actually radiate gravitational waves

It could, in principle, since its motion through the slits would, in principle, involve a time-varying acceleration due to interaction with the material around the slit. However, the gravitational waves produced by any object for which we have detected interference in a double slit experiment would be much too weak for us to detect.

 

[Lord Crc]

It could, in principle, since its motion through the slits would, in principle, involve a time-varying acceleration due to interaction with the material around the slit.

Ah yeah that makes sense. Would the energy radiated cause a slight decrease in frequency of the photon then? Not that I expect that to be measurable either, just curious.

However, the gravitational waves produced by any object for which we have detected interference in a double slit experiment would be much too weak for us to detect.

I know we are in fantasy land here, but has the magnitude and frequency of such a wave been calculated, for a photon or say a buckyball? Just curious how far into fantasy land we are here.

If the frequency is very high then AFAIK a LIGO style detector would be severely limited by quantum effects (shot noise), which would be a double whammy.

But yeah, just curious.

 

[PeterDonis]

Would the energy radiated cause a slight decrease in frequency of the photon then?

You mean energy radiated by a gravitational wave? It would in principle affect the photon's wave function, yes, and in principle the effect would be to slightly lower the expectation value of the photon energy. However, in practice this effect would be far too tiny to detect.

but has the magnitude and frequency of such a wave been calculated, for a photon or say a buckyball?

Not that I know of. I am basing my heuristic estimates on the general rules for the relative magnitude of such effects, as compared to the total energy of the object or system and the time variation of the system's quadrupole moment.

a LIGO style detector would be severely limited by quantum effects (shot noise), which would be a double whammy.

This might well hamper any attempt to detect such an effect.

 

[DrChinese]

To answer this - at least partially - no detector is really needed... impossibly sensitive or not!

The experiment is performed every time a double slit experiment is run. And the answer is NO... there is no collapse of the wave function. Or more precisely: the interference is not affected by gravitational force. Otherwise we'd never see any interference in any experiment... obviously. So here's the catch. We use the term "which slit detection" as a shortcut to the more correct analysis. That has already been mentioned (see for example @vanhees71 post #16, and others), but I will describe again.

We have a double slit photon setup with a polarizers in front of each slit. There is no detector of any kind. When the polarizers are aligned parallel (setup A), there IS interference. When the polarizers are aligned perpendicular (setup B - orthogonal) there is NO interference. The reason for the difference is that there cannot be interference between the orthogonal paths that the photons take. Again, we are comparing 2 different setups, A vs. B, and no detector is necessary. It's all in the setups.

So for a gravitational version of the double slit: we need some way to switch from an "A" setup to a "B" setup. It's pretty easy to see that this cannot be done - no "B' setup (where there is NO interference) can be created. You need there to be "some way" distinguish paths taken through one slit from paths taken through the other. The detector is NOT important at all, no more than it was relevant in the previous example. How to do this? For the gravitational force, we would need something that would delay/distort the paths on one side - but not delay/distort equally on the other side. That would need to create a torque so large that the paths effectively become orthogonal (rather than parallel which is effectively the default). So we need a massive object to be present on one side, very close to the slit. Obviously, the difference in the gravitational "distortion" between an object being diffracted between 2 slits - when we have a distance between the slits on the order of magnitude of the wavelength of the object - will be much smaller in comparison. You cannot create that much gravitational differential (as best I know anyway) at such a small scale. It will be miniscule.

Clearly: regardless of whether gravity is a relativistic phenomena (distortion of spacetime by mass) or whether it is a quantum phenomena (coupled to a quantum field): there is no discernible effect for an "A" setup (full interference, nothing to distinguish the paths). That being what we see in an interference experiment of any kind. If there was, we wouldn't see any interference at all in the first place. Or... it could be that the effect is so slight it is not noticeable. After all: "which slit" setups can be varied from 0 to 100% with any amount in between. I am not aware of any rigorous studies purporting to demonstrate how perfectly interference effects adhere to theoretical predictions. (I.e. whether there is some background effect due to the Earth's gravity that we haven't previously noticed. I.e. that gravity does cause a small amount of "collapse" in typical double slit studies.)

 

[PeterDonis]

The reason for the difference is that there cannot be interference between the orthogonal paths that the photons take.

"Paths" is not really correct here. Changing the polarizer settings does not change the amplitude for a photon coming from a particular slit to travel a particular path through space. What it changes is the phase the photon has when it hits the screen after traveling a particular path through space. Changing the phase relationships between the photon paths from the two slits to particular points on the screen is what changes the amount of interference that is observed.

Also, what you are describing, as you say, is not a "which slit" measurement made on the photon. But there are other measurements that could in principle be made on the photon that are. In terms of the basic math of QM, a true "which slit" measurement does not affect further results by changing the relative phases of the two paths (one from each slit); it eliminates one path entirely, by providing a macroscopic, irreversible record of the particle taking just one of the two possible paths (i.e., going through just one slit). No such record is created in the polarizer version.

To put it another way, the truly correct meaning of "which slit" is that an actual measurement--in the sense of "something that forces you to apply the Born Rule to calculate probabilities and then collapse the wave function once you know the result"--must take place. That doesn't happen with the polarizer version with photons. But as I understand it, the OP is asking about whether one could have some kind of device that would make it happen--would amount to an actual measurement of which slit the photon went through, without destroying the photon itself--by detecting the gravitational influence of the photon.

I am not aware of any rigorous studies purporting to demonstrate how perfectly interference effects adhere to theoretical predictions. (I.e. whether there is some background effect due to the Earth's gravity that we haven't previously noticed. I.e. that gravity does cause a small amount of "collapse" in typical double slit studies.)

Based on the experiments that have been done with neutrons, the Earth's gravitational potential can be treated as a potential just like any other in the Schrodinger Equation, which means it should have a (tiny) effect on the phase of photons. So if the two slits were oriented vertically in the Earth's gravitational field, so the gravitational potential was slightly different from one to the other, then there should be a tiny relative phase shift that would eliminate a tiny amount of interference. I have not tried to calculate just how tiny, though. And of course if the two slits are oriented horizontally (as I would imagine is typically the case), the gravitational potential is the same at both, so it would not cause any relative phase shift and would not affect interference at all.

 

[anuttarasammyak]

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

Gravity affect momentum and energy, so direction and wave length of light.
Say we emit light horizontally on Earth under gravity g. Set the standing double slits (a) side by side (b) up and down. Even if it is too small to observe in the actual experiment, their interference patterns differ theoretically. For example peak of interference (a) corresponds to the center of the slits (b) bend down from the center. Interference peak distances (a) are constant (b) differ according to the height.

However, we can not make use of these differences to say which slit a photon travels.

 

[vanhees71]

"Paths" is not really correct here. Changing the polarizer settings does not change the amplitude for a photon coming from a particular slit to travel a particular path through space. What it changes is the phase the photon has when it hits the screen after traveling a particular path through space. Changing the phase relationships between the photon paths from the two slits to particular points on the screen is what changes the amount of interference that is observed.

I'd rather explain it differently. It's the setup I've described already in a posting above in this thread.

You make the incoming photons horizontally polarized in $x$-direction (the slits are in the $xy$ plane) moving in $z$ direction (i.e., FAPP plane waves moving in $z$ direction) and put two (ideal, i.e., non-absorbing) quarter-wave plates oriented in $+\pi/4$ and $-\pi/4$ direction relative to the $x$ direction. Quantum-mechanically these represent unitary operators transforming the incoming H-polarized wave into left- (L) and right-handed (R) polarized photons, respectively. Now these two polarization states are orthogonal to each other and thus the polarization state of the photons after passing the slits uniquely determines through which slit the photon came (note that there's necessarily only 1 photon behind the slits, either L- or R-polarized). In other words the observable through which slit the photon came is not entangled with the polarization state of the photon behind the slit.

Since the polarization part of the photon state (NOT WAVE FUNCTION!) for a photon going through slit 1 is perfectly orthogonal to the polarization part of that of the photon going through slit 2. There is no interference between these two possibilities anymore at a point on the screen sufficiently far away from the slits (so far that without the quarter-wave plates, where all photons going through the slits stay in the H-polarization state and thus you cannot distinguish the photons going through slit 1 from those going through slit 2 in this setup, you get two-slit interference fringes) there are no two-slit interference fringes anymore but only the incoherent superposition of the slingle-slit interferences fringes coming from both slits.

This example shows that you can have either which-way information or (full-contrast) interference fringes. If you tune the quarter-wave plates to any other relative angle than $\pi/2$ (as in my example above) you get "partial which-way information" (i.e., by measuring the polarization state of the photons behind the slit you can say with some probaility $>50\%$ that it went through, slit 1) but also some two-slit interference, but the fringes don't show the full contrast.

In this sense which-way information and two-slit fringe contrast are complementary features of the photon. Note that we don't need to really read out the which-way information by measuring the polarization of the photon to destroy the interference fringes. It's sufficient that this information can be found by measuring some observable of the photon, i.e., if this information is available due to the photon's preparation.

 

[DrChinese]

1. Changing the phase relationships between the photon paths from the two slits to particular points on the screen is what changes the amount of interference that is observed.

2. Also, what you are describing, as you say, is not a "which slit" measurement made on the photon.

3. Based on the experiments that have been done with neutrons, the Earth's gravitational potential can be treated as a potential just like any other in the Schrodinger Equation, which means it should have a (tiny) effect on the phase of photons. So if the two slits were oriented vertically in the Earth's gravitational field, so the gravitational potential was slightly different from one to the other, then there should be a tiny relative phase shift that would eliminate a tiny amount of interference.

1. If that wasn't clear from my post, that is what I am saying precisely. The relative relationship controls interference, as we know from both experiment and theory.2. And that's true too... because a "detector" makes NO difference to the observed interference (some or none). This answers the OP's question. If you had a suitably sensitive detector, and it registered that the particle went through a particular slit, there would be NO OBSERVABLE change in the pattern.

Restated: For the pattern to change, something must occur to cause the relative phase to change. That won't happen just because you registered a blip on a magically sensitive detector. Something else needs to happen too.3. Yes, this was the point I introduced - there needs to be 2 setups (A and B). The A setup is what existing experiments demonstrate - there is no gravitational collapse (or it is too mild to detect). The B setup is what you suggest as using the Earth's potential to create a difference between the slits. That differential always affects things much less than the observed particles' wavelength; ideally it would need to be so pronounced that the path differential was distorted by 1/2 a wavelength to get the phase effect you refer to.

---------------------

Now suppose we have the magic gravitational detectors and conduct the experiment in the setup A mode where there is no relative gravitational difference between the slits. What would we see? Would we see one blip for one or both slits every time a particle passes by? Would we only rarely see blips (with that subset of events showing no interference)? That we will need to guess about for a while longer.

 

[DrChinese]

In this sense which-way information and two-slit fringe contrast are complementary features of the photon. Note that we don't need to really read out the which-way information by measuring the polarization of the photon to destroy the interference fringes. It's sufficient that this information can be found by measuring some observable of the photon, i.e., if this information is available due to the photon's preparation.

And the same would apply to a gravitational version of the experiment. If there was information available that indicated the target particle was in a state sufficiently different than if it had traversed the other slit, then there would be NO interference.

I say that no gravitational setup can create enough differential to be measurable even with our hypothetical sensitive gravitational disturbance detector. (Not without the entire lab getting sucked into a black hole...)

 

[PeterDonis]

The B setup is what you suggest as using the Earth's potential to create a difference between the slits.

Thinking this over again, it might be that orienting the slits vertically wouldn't eliminate any interference, it would just shift the interference pattern slightly in space.

Now suppose we have the magic gravitational detectors and conduct the experiment in the setup A mode where there is no relative gravitational difference between the slits. What would we see?

If it is possible to build a "gravitational detector" at all, we would see one blip at one slit each time a particle passes by. That's the definition of a "gravitational detector". (More precisely, we would see one blip at one slit each time a particle passes by, and no interference, with a perfect "gravitational detector"; with an imperfect one we would either see one blip at one slit, or no blip at all, and the former set of runs would show no interference while the latter set of runs would show interference.)

The fact that we don't currently have a good theory of quantum gravity, and aren't even sure that one exists, means we can't say for certain that it's even possible to build a "gravitational detector" at all.

 

[DrChinese]

If it is possible to build a "gravitational detector" at all, we would see one blip at one slit each time a particle passes by. That's the definition of a "gravitational detector". (More precisely, we would see one blip at one slit each time a particle passes by, and no interference, with a perfect "gravitational detector"; with an imperfect one we would either see one blip at one slit, or no blip at all, and the former set of runs would show no interference while the latter set of runs would show interference.)

No detector is necessary (to distinguish setups). We already established that, and I don't think we have a difference of perspective on that. Since interference is always present, obviously gravity does not factor, so no gravitational detector will ever change the results we already obtained. Unless we could find a way to create a suitably large gravitational difference between the slits, which is probably impossible. And even then, no detector is necessary.

 

[PeterDonis]

No detector is necessary (to distinguish setups).

Yes, agreed; you can do that by the difference in interference patterns, without requiring any measurement at the slits themselves.

no gravitational detector will ever change the results we already obtained.

Here I disagree; if a gravitational detector could be built and one such detector were put at each slit, the set of experimental runs where the detector at one slit registered a blip would show no interference, regardless of any other settings (for example, it wouldn't matter whether the slits were oriented horizontally or vertically).

 

[PeterDonis]

Unless we could find a way to create a suitably large gravitational difference between the slits, which is probably impossible. And even then, no detector is necessary.

If this could be done, i.e., if gravity could be used to create a large enough phase difference between the paths from the two slits (which I agree is probably impossible, although I suppose putting the whole setup in a rocket hovering close enough to a black hole's horizon might do it, I haven't done the math), I agree this could eliminate interference without having a gravity detector at either slit, just as appropriate relative orientations of polarizers at each slit can eliminate interference without any kind of detector at either slit.

However, this does not in any way contradict my statements about what happens if we do put a gravity detector (assuming it is possible to build one) at each slit. These are simply different experimental scenarios.

 

[vanhees71]

Of course, the gravitational field of the Earth has some influence though for light it's completely negligible. It would also only shift the interference pattern as a hole. I thought you were discussing a probable influence of the gravitational interaction between the light and the slits in the way Einstein and Bohr discussed during this famous Solvay conference. This is of course totally negligible due to the orders-of-magnitude large influence of the electromagnetic interaction. Even the em. interaction causing a recoil of the slits due to interaction with the photons is completely negligible.

What was a bit a hype in the media in connection of these questions was that they brought a trapped gas BEC experiment to the ISS to get rid of the gravitational field of the Earth which limits the lifetime of the BEC in the trap, so that the setup in the "microgravity" of the ISS is of advantage.

 

[DrChinese]

Here I disagree; if a gravitational detector could be built and one such detector were put at each slit, the set of experimental runs where the detector at one slit registered a blip would show no interference, regardless of any other settings...

Interesting. I say there is no such set, and if there were, there would BE interference. The only way there would NOT be interference if the gravity differential between the slits (one vs. the other) was so great that it effectively encoded a phase shift or similar between slits.

But it is also certainly possible that the subset you are specifying would NOT show any interference, just as you say. That being because the subset is so rare/small that it is lost in the background of typical events (that don't meet your criteria of a single blip).

 

[PeterDonis]

I say there is no such set

I'm not sure what you mean. Are you saying you are certain that no "gravity detector" that would register a blip when a photon passed is possible, even in principle? If you accept that such a detector is possible, then putting one at each slit in a double slit experiment would provide the kind of set I describe.

That being because the subset is so rare/small that it is lost in the background of typical events

Here you appear to be saying that, even if such a "gravity detector" could be built, it would register a blip on such a small fraction of photons passing it that the set of "blip" events would be a negligible fraction of the set of all runs of the experiment.

While this would certainly be the case with today's technology (and I have said so already in this thread), I am not aware of any argument that it must be the case in principle, no matter how much our technology advances in the future. And since we are discussing a thought experiment, the relevant criterion is what is possible in principle, not what is feasible given our current technology.

 

[PeterDonis]

if there were, there would BE interference

This seems to me to obviously contradict basic QM. Basic QM says that if we can measure (as in, do something that requires applying the projection postulate to obtain the correct post-measurement state for predicting future measurement result) which slit the particle goes through, there will not be interference at the detector screen. I am simply applying this general principle to the case where a "gravity detector"--something that register a blip, a macroscopic, irreversible record that constitutes a measurement and requires applying the projection postulate, based on detecting the gravitational effects of a passing particle--is the thing doing the measuring.

 

[PeterDonis]

The only way there would NOT be interference if the gravity differential between the slits (one vs. the other) was so great that it effectively encoded a phase shift or similar between slits.

I think you are conflating two different experimental scenarios. Your description applies to the gravitational analogue of the polarizers, using the gravitational potential of an external massive object (the Earth) to produce a phase shift. But I am talking about having a "detector" at each slit that detects the (miniscule) gravitational effect of the particle itself. That is different from what you are describing.

 

[DrChinese]

I think you are conflating two different experimental scenarios. Your description applies to the gravitational analogue of the polarizers, using the gravitational potential of an external massive object (the Earth) to produce a phase shift. But I am talking about having a "detector" at each slit that detects the (miniscule) gravitational effect of the particle itself. That is different from what you are describing.

No, but there are 2 setups though. I am trying to present what I think we know about these 2 cases.

Setup A: there IS interference because there is no differential applied on a particle traversing one slit versus the other. The presence/absence of a detector sensitive enough to feel the gravitational effect of a particle going by will make no difference (your bolded statement). That's true because this experiment has essentially already been performed (that's the one where there is no phase shift/differential between the slits, and no detector of any kind). If such detection were even possible, then we would never have interference in *any* classic double slit experiment. So what you are asking of a detector, to recognize the miniscule effect of the particle itself, either i) cannot be possible or ii) does not produce the result you might expect. If it is the ii) case, then we would know the which-slit answer but there would still be interference. (In your post #47, you say that defies basic QM. Not sure that is the case, but I understand why you say that.)

In Setup B, there is a profound gravitational shift/differential of some kind so that a particle traversing one slit is accelerated/retarded differently than one going through the other slit. So much so, we're allowing it to be identified as such. I don't think this is possible because the slit separation must be on the order of magnitude of one De Broglie wavelength. The amount of gravity necessary to create sufficient shift to do that would probably eat the planet. (OK that last part is perhaps a bit of hype as I haven't done anything on the back of a napkin yet. But we can imagine how great an gravitational effect would need to be to create a sheer effect over on the general order of magnitude of a nanometer for neutrons.)

https://www.oeaw.ac.at/fileadmin/In...tical_experiments_with_very_cold_neutrons.pdf

In other words - there might be 2 ways to detect the gravitational signature of a particle going through the slits. One won't change anything; and the other is impossible to test.

 

[PeterDonis]

there are 2 setups though

No, there are actually three total. There are the two you describe, and there is the third one I have described, which is different from either of yours.

The presence/absence of a detector sensitive enough to feel the gravitational effect of a particle going by will make no difference

Yes, it will; it will prevent the interference. This is basic QM. Let me go ahead and write down a schematic description of how QM models each case.

(1) Your case: two slits and a detector screen after them, no gravity detector at either slit. The photon wave function goes through both slits, amplitudes from each slit are added at the detector screen for each individual run, and interference is produced over many runs.

(2) My case: two slits, a detector screen after them, and a gravity detector at each slit that makes a macroscopic, irreversible "blip" when it detects the gravitational influence of a particle. The projection postulate is applied at the slits, with the photon wave function being projected into whichever component corresponds to the slit whose gravity detector registered a blip. Because of the projection, there is only one amplitude at the screen for each individual run, and no interference is produced over many runs.

If you disagree with the above, please specify exactly what you disagree with. If you don't disagree with the above, I fail to see how you can claim that my case (2) will make no difference as compared to your case (1).

this experiment has essentially already been performed

No, it hasn't. Nobody has even tried to put a detector sensitive enough to detect the gravitational influence of a single particle into any such experiment.

If you disagree, please say specifically what, in all double slit experiments actually done to date, plays the role of the "gravity detector" in my case (2) above. If your answer is "the individual atoms around the edge of each slit", that is not a viable answer. Why? Because if they were able to play that role for the gravitational influence of the particle, they would be many, many orders of magnitude more able to play it for the electromagnetic influence of the particle, since the latter is many, many orders of magnitude larger than the former.

In other words, if your argument were correct, it would also mean that we could never have observed any interference at all in double slit experiments because photons interact electromagnetically with atoms. Which of course is obviously false: we can design slits that allow interference even though photons interact electromagnetically with atoms. And if we can do that, then those same slits are even more capable of allowing interference even though photons interact gravitationally with atoms, by many, many orders of magnitude. So the "gravity detector" I am talking about cannot be simply a matter of the interactions that we already know are there in experiments we have already run. It has to be a matter of designing a new detector that amplifies the gravitational effects of a single particle to the point where they can be macroscopically observed and recorded.