B Gravitational signature of a photon in a double slit experiment

[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.

 

[PeterDonis]

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.

Another note might be worth making here: my case is the same regardless of whether you put polarizers or some other phase shifting device after the slits. In other words, the presence of a which slit detector of the type I am describing destroys interference before the polarizers even have a chance to affect the phase of the photon's wave function. So my case (2) is not the same as just putting polarizers or some other phase shifting device after the slits, or even having an external potential that can apply a differential phase shift (such as the Earth's gravitational potential). It is simply a different, separate possibility.

 

[PeterDonis]

there might be 2 ways to detect the gravitational signature of a particle going through the slits

Using an external potential to apply a phase shift does not provide a "which slit" measurement, for the same reason that using a polarizer after each slit and adjusting their relative orientations to eliminate some or all of the interference provides a "which slit" measurement. Shifting the relative phases is simply a different operation from providing a which-slit detector of the type I am describing at each slit. The fact that, with appropriate settings for the relative phase shift, it can remove interference, does not mean it is the same thing as having a which-slit measurement destroy the interference.

 

[vanhees71]

Well, it depends of course always on the strength of the interaction of the photon with your detector, whether you destroy the interference fringes or not and to which degree. Of course, there are always also gravitational interactions involved in any experiment with particles or photons but they are indeed so small that they have no measurable impact and thus can safely be neglected.

 

[DrChinese]

Using an external potential to apply a phase shift does not provide a "which slit" measurement, for the same reason that using a polarizer after each slit and adjusting their relative orientations to eliminate some or all of the interference provides a "which slit" measurement. Shifting the relative phases is simply a different operation from providing a which-slit detector of the type I am describing at each slit. The fact that, with appropriate settings for the relative phase shift, it can remove interference, does not mean it is the same thing as having a which-slit measurement destroy the interference.

I completely agree with this. Setup A and Setup B are essentially different experiments/operations... so differing results would be natural.

A separate question - probably outside the scope of this thread - is whether there exists a "which-slit" measurement that would reveal the slit traversed without otherwise requiring a setup that will NOT produce interference. I am not familiar with anything like that, but would love to hear something new in that regard.

 

[Vanadium 50]

is whether there exists a "which-slit" measurement that would reveal the slit traversed without otherwise requiring a setup that will NOT produce interference.

I don't understand what you mean. If you know which slit, you can't get interefernce, only diffraction. You add intensities, not amplitudes.

 

[PeterDonis]

A separate question - probably outside the scope of this thread - is whether there exists a "which-slit" measurement that would reveal the slit traversed without otherwise requiring a setup that will NOT produce interference. I am not familiar with anything like that, but would love to hear something new in that regard.

This is exactly what I've been describing: put a "gravity detector" at each slit in a setup that, if that detector were not present, would produce interference (such as just two slits and a detector screen).

If you mean a which-slit measurement that can actually be performed with today's technology, it looks like there has been some work done on developing ways to non-destructively detect photons, but I'm not familiar with the details. But that's what would be needed.

 

[vanhees71]

The standard example, I mentioned before in this thread, by putting in quarter-wave plates to label each photon such that you precisely imprint the which-way information in its polarization state is an example for a setup where the photons are not destroyed in the labelling and thus can observed on the screen and you can observe whether there's a an interference pattern or not.

This is of course easily feasible with today's technology and it has been used in the famous quantum eraser experiment by Walborn et al:

https://arxiv.org/abs/quant-ph/0106078

In your thought experiment to use some "gravity detector" in the slits to learn about through which slit the photon came, there's no principle difference: If you could construct a so sensitive a "gravity detector" that it can detect through which slit any photon came, you'd as well destroy the two-slit interference fringes. The point is that you gain this information with certainty by a measurement. If you only gain partial information (like when you put the quarter-wave plates not in perpendicular relative orientations) you also only loose contrast in the two-slit fringe pattern.

 

[DrChinese]

1. The standard example, I mentioned before in this thread, by putting in quarter-wave plates to label each photon such that you precisely imprint the which-way information in its polarization state is an example for a setup where the photons are not destroyed in the labelling and thus can observed on the screen and you can observe whether there's a an interference pattern or not. ...

2. In your thought experiment to use some "gravity detector" in the slits to learn about through which slit the photon came, there's no principle difference: If you could construct a so sensitive a "gravity detector" that it can detect through which slit any photon came, you'd as well destroy the two-slit interference fringes. The point is that you gain this information with certainty by a measurement. If you only gain partial information (like when you put the quarter-wave plates not in perpendicular relative orientations) you also only loose contrast in the two-slit fringe pattern.

1. Yes, and there is no which-slit detector of any kind in these experiments. You don't need to know which-slit for the interference to disappear. It is enough that you COULD get the which-slit information, in principle.

2. Similarly, you don't need an actual detector to determine that no such sensitive gravity detector would change the outcome. This experiment is executed and produces negative results every time the experiment in 1 is run. The negative results might also indicate that such a detector is not possible, in principle.

The only way to see a loss of interference due to a "gravity-based which-slit detector" is to use extreme gravity to induce some marker on the particle in question (say a neutron) in one slit differently than the other. That marker would need to be a lot more than simply something which labels it as going through one slit or the other. Otherwise, there is not enough difference in the quantum phase shift/path differential to eliminate the interference between slits. You would just eliminate such a small fraction that it is not detectible. And we know this because gravity is not a factor in double slit experiments already run.

 

[DrChinese]

The standard example, I mentioned before in this thread...

Just wanted to shout-out to @vanhees71 for achieving 7600 post likes. There is nothing special about that specific number, except that it says a lot about how folks here respect his comments. That is obviously true of our other great mentors and science advisors such as @PeterDonis, @Nugatory , @Vanadium 50 and many others too.

Just wanted to say thanks to all of you for the time and effort you put in here. And for how much your comments mean to me personally, even in the few cases where there might be some difference of opinion.

PS Heck, I liked another of PeterDonis' posts to get him to that magic 10600 number and I noticed Vanadium 50 just crossed over 9000

 

[PeterDonis]

You don't need to know which-slit for the interference to disappear. It is enough that you COULD get the which-slit information, in principle.

In the case of the polarizers, you can't get which-slit information just from the polarizers alone. The polarizers just induce a phase shift in photons passing through by a simple unitary operation, and no entanglement is produced between the polarizers and the photons passing through them. That means nothing takes place at the polarizers that could be subject to decoherence and could produce an irreversible record (even one that is not recoverable by humans, such as a decoherent interaction with an environment) of which slit each photon passed through.

Again, the case of the polarizers is simply different from the case in which there is a which-slit measurement, or even the in principle possibility of a which-slit measurement. The polarizers themselves aren't measuring the polarization of the photons; they are just shifting their phase. (Perhaps "polarizers" is the wrong term to use to describe these devices; I think @vanhees71 used the term "quarter-wave plates", which might be better.)

you don't need an actual detector to determine that no such sensitive gravity detector would change the outcome. This experiment is executed and produces negative results every time the experiment in 1 is run.

No, this is not correct. If this argument were correct, it would also prove that no interference could ever occur at all in a double slit experiment, because the photon interacts electromagnetically with the atoms around the edge of each slit. See the last part of my post #50.