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B Double slit and randomly functioning measuring devices

  1. Jan 7, 2017 #1
    Hey there!
    This thread started off as a question regarding the impact of blindness on the wave function collapse, ended up thinking of an alteration to the double slit experiment that I think could yield some interesting results.

    So!

    Say the double slit experiment is run with measuring devices that have a constant 50% chance to be either on or off.
    (For lack of better wording) Would the wall reflect both the classical and quantum interference patterns or do the particles not 'risk' being detected in wave and stay in classical mode.
    Is there a major difference in having the probability be 49%/51%? Is there a disproportionately greater likelihood of the particle risking wave form if there is only the 49% chance of being detected? (Likewise for a 25/75 and 10/90... I just feel as though there would be a point where quantum mechanics really gets that we want to understand it, stops being as coy and shows a card.)
    I want to emphasize the usage of 'risk' here as I am envisioning something like having one of these 50/50 detectors on each slit constantly turning off and on, eventually, ideally both randomly turning on at the same time during the time-frame that the particle is in motion going through both slits.
    Even if during this 'being caught out' phase, it does slip back into classical mode, surely there would be some kind of recordable phenomenon occur as it jumps from being both back into being one again.

    [Mentor's note: Speculation in violation of the Physics Forums rules has been removed from this post]
     
    Last edited by a moderator: Jan 7, 2017
  2. jcsd
  3. Jan 7, 2017 #2

    Nugatory

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    You have a basic misunderstanding about the double-slit experiment. The incoming particles do not switch between being waves or particles according to whether a detector is involved or not.

    What's really going on: We calculate the probability of the particle landing at any point on the screen by summing the probability amplitudes for every possible path between the source and the screen. If there are two slits, there are two possible paths. If we close one of the slits, then there is only one possible path. If we put a detector in one of the slits, then we know to not count the path through that slit if the detector doesn't trigger, and to count only that path if it does trigger. But in all cases we're adding the probability amplitudes for all the possible paths between the source and the screen, and we get an interference pattern when there are multiple possible paths whose amplitudes add in a particular way.

    The imperfect detectors just make these calculations more complicated, but the results are unsurprising: as the detector efficiency improves, the contribution of the both-paths-open possibility to the overall probability amplitude goes down and the interference pattern becomes weaker. The experiment has been done and matches the prediction.
     
  4. Jan 7, 2017 #3
  5. Jan 7, 2017 #4

    Nugatory

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    In any reasonable experiment we choose our barrier thickness and material so that that probability is for all practical purposes zero.
    Yes, but again we design our barriers so that the contribution from these paths is small enough to ignore.
     
  6. Jan 7, 2017 #5
    Thank you for your response.
    I appreciate that I can certainly be having a misunderstanding. My understanding is not based off mathematical models, rather the 'for dummies' equivalent as seen at:


    Now, from what I can tell of this, mathematics aside, it is rather straight forward, unobserved the particles hit the back wall with a distortion pattern like ( | | | | || | | | | ), while observed the distortion pattern is like ( || || ). The mathematics involved in working out why this happens to me seems secondary to the factual information of what actually occurred.

    So the experiment has been done with imperfect detectors? Like as stated in the thread with a random possibility of them recording or not? Did the distortion pattern that occurred match what would be expected after correlating when the detectors where on and off? I wasn't able to find anything like that during an online search, or I wouldn't of asked to begin with.
    Did the mentioned event with detectors on both slits both happening to be randomly on as a particle went through a slit, occur? Like I am talking hooking them up to something that has an ongoing, every tenth of a second chance of them changing from off to on and so on.

    Kind regards,
    <3 Phillip
     
  7. Jan 7, 2017 #6

    Nugatory

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    Videos like that are one of the reasons Physics Forums has its rule about acceptable sources. It is terribly misleading - you can search this forum for past discussion of "Dr. Quantum" for more background. But one particular distortion really stands out:
    The pattern appears or not according to whether the interaction between the incident particle and the barrier/slits eliminates one of the two possible paths. Obviously an instrument that records the path through one slit or the other will have this effect, but so will many other interactions. (This might also be a good time to mention that a quantum mechanical "observation" is not at all what the ordinary English meaning of the word suggests - physicists attached that word to what turned out to be a very different concept because of an accident of history a century ago).

    Seeing as how all physically realizable detectors are at least a little bit imperfect.... The experiment has only been done with imperfect detectors. You're really asking how detector effectiveness affects the observed results, and those experiments have been done.
    Two examples:
    1) Place a polarizing filter behind each slit. If the two filters are perpendicular to one another then only one path is available to each photon according to its polarization as measured behind the screen (the probability of finding a vertically polarized photon at a given point behind the barrier receives no contribution from the path through the horizontal polarizer, and vice versa) and there is no interference pattern. If the two polarizers are aligned in the same direction then only photons with that polarization will be found behind the barrier; both paths are equally available to these, and an interference pattern forms. It gets interesting when you align one of the polarizers vertically and the other one at a 45 degree angle from that. Now, 3/4 of the photons behind the barrier will be vertically polarized and 1/4 will be horizontally polarized. The vertically polarized photons receive contributions from both slits but the only path available to the horizontally polarized ones is through the slit with the angled polarizer - we have a setup in which we detect the slit for only 25% of the photons that pass through, and by rotating the polarizer to other angles we can dial that probability up to 100% (polarizers 90 degrees apart as described above) or down to zero (polarizers aligned as described above). We get a weaker or stronger interference pattern accordingly.
    As a historical aside: This interaction between polarizers and the interference pattern was first measured early in the 19th century, a full century before the quantum mechanical explanation was available.

    2) https://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser#The_experiment_of_Kim_et_al._.282000.29 is a modern experiment in which we get interference or not according to whether one or two paths were detected for any given photon. Of course that wasn't the primary purpose of the experiment; it just so happens that to investigate the delayed-choice phenomenon you need an apparatus that lets you compare the two-possible-path and the one-possible-path patterns so it's also relevant to your question.
     
  8. Jan 7, 2017 #7
    Thank you again for your reply, appreciated.

    I do not think I am describing the test I have in mind clearly enough, as I am not actually asking 'how detector effectiveness affects the observed results'. I do not think imperfect detectors is a great description.

    I am picturing two electron microscopes that are actually both perfectly effective and capable of constantly recording each slit. I am then referring to adding an algorithm that has utilizes a random number generator to ensure that every tenth of a second there is a constant 50% chance to shut them off and a tenth of a second later, another 50% chance to turn them back on.

    The best way I can think of to describe why to do it this way is that I feel quantum mechanics is best described in one word as 'Coy'.

    From my understanding of things, there is a huge difference between having there be windows for some of the particles to go through completely undetected due to the measuring devices being turned off, compared to some of the particles going through completely undetected because the device was imperfect.
    From what I understand the technology to even photograph electrons is only about a decade old with the double slit being centuries old. The phenomena I would be hoping this alteration to the test would catch is something like the having the microscopes being randomly off for like half a second and then both simultaneously randomly turning on and randomly capturing a shot of the electron already half into the slit, or ideally, slits.

    Mathematical probabilities aside. Where we able to stop time and look at this one frame at a time, the electron is not just teleporting through the slits, so hence, I think if we where to focus on the process as it reaches the interaction with the slits one frame at a time, eventually going to photograph a single electron interacting with itself, even if having to be rather deliberately, a little cheeky in utilizing randomness to catch it out!

    Kind regards,
    <3 Phillip
     
  9. Jan 7, 2017 #8

    Nugatory

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    That's essentially what the 45-degree angled polarizer is doing. The only difference is that instead of being on for a short period of time and then off for another short period of time, it's randomly choosing to be off or on for each incident particle.

    Why would you expect that to make a difference? Either there is an interaction with the detector and no interference, or there isn't an interaction and there is interference.

    Taking that "photograph" (which we can't do - the "image" formed by a STM is in no way a picture of an electron moving by - but this is a thought experiment so we won't worry about that) is an interaction that measures the position. Without that interaction the electron has no position at all - not "it has a position but we don't know what it is because our camera is off" but "no position", the same way that you don't have a lap when you're standing up. With that interaction, the electron has a position at one slit or the other and there will be no interference.

    Maybe not, but if we don't measure its position (more precisely, if there is no interaction that determines its position) then it has no position and hence no trajectory. It was at the source (emission is a position-determining interaction) and a moment later it was at the screen (making a dot on the screen is a position-determining interaction) but it had no position in between. That might not be so far from what you're thinking when you said "teleporting".
    These continuous position measuring devices exist and have been used routinely for many decades - google for "cloud chamber" and "bubble chamber". If we were to put a double-slit experiment inside one of these, we would see each particle follow a path through one slit or the other to the screen and there would be no interference pattern.
     
  10. Jan 8, 2017 #9
    I no doubt have my numbers off in choosing the tenth of a second timeframe, however, I intended to imply it would a system that could randomly be on when the particle is fired and could then also be randomly off while it is in flight towards the slits and then happen to randomly be back on as the particle has already decided it is not being observed and is half way through the slits.. This is literally going to have a different mechanical effect than a system that is just simply either on or off for each particles journey.. Wanting to catch it out, not give it a warning.
    I guess I risk going too philosophical in my explanation of why I expect this to make a difference. I guess suffice to say, that even as an Atheist, I believe consciousness plays a role in quantum interactions by way of all energy being capable of being conscious. In a brief sentence: Isaac Asimovs 'The Last Question', combined with eternal recurrence.

    Okay, well if you are going to limit this to a thought experiment, work with me, I don't know the name of whatever piece of equipment is capable of photographing electrons. Are we only at the stage of being able to photograph 'stationary' electrons? Surely would be able to just fluke capturing the blur of a moving one at the very least by now? Why not fluke that capture on an electron that was already going through both slits presuming it was unobserved? Is that at least making sense?
    I really do not understand what you mean by the electron having no position without an interaction. After being fired, is there not at least an approximate timeframe until it hits the back wall? Presuming it is going in a predictably straight line, surely the position at any given time can be inferred with absolute precision without an interaction?

    I actually brought up teleporting as closer to a bit of a joke, I want to test the heck out of that 'moment later' timeframe, that is where the magic is happening with regards to the particle being either classical or quantum based on observation. Again, I think the tenth of a second change in on/off status is missleading and could well do with being ramped up to a trillionth of a second type thing to further emphasize the point I am trying to make... Want to give the electron no opportunity to decide on if it is being observed or not until it has already decided and we fluke the randomness of both cameras being at 'on' as the electron is literally inside the slits.
    However, I get the impression that we are currently lacking in the technology to even calculate a random number every trillionth of a second, nevermind actually having a camera capable of photographing electrons switch between on and off that quickly?
    These sound interesting, do these have the capabilities to be 'randomly' turned off so that the particles path could only be tracked at random? Say there was a mathematical anomaly and the tracking was off for a solid minute (At a 50% chance every trillionth of a second to be on), would there be an interference pattern during that minute?

    <3 Phillip
     
    Last edited: Jan 8, 2017
  11. Jan 8, 2017 #10






    One more question.

    1.Can the emitting device be accurate enough to direct the photon/electron with reasonable accuracy toward the left/right slit OR the barrier between the slits?

    I'm not to sure if this is a reasonable assumption since I don't really know how wide apart the slits are in proportion to the "diameter" of the emitting particle.
    How accurate is the emitters direction when pointing it to the slits?
    Are the variations in direction proportional to the width of the slits and diameter of the particle?

    And what would you expect the results on the background screen to be in the different scenario's in 1 above?
     
  12. Jan 8, 2017 #11
    It is very important that it is quite inaccurate in this respect. To obtain an interference pattern there must be uncertainty.
     
  13. Jan 8, 2017 #12

    Zafa Pi

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    I'm not buying that. I think what will happen is that photons behind the barrier will either vertically polarized or or polarized at 45 degrees.
     
  14. Jan 8, 2017 #13

    Nugatory

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    You're right, I was being sloppy with that wording.

    Every particle will either be in the state ##|V\rangle## or ##|45\rangle=\frac{\sqrt{2}}{2}(|V\rangle+|H\rangle)## (did I get the coefficients right?).
     
  15. May 4, 2017 #14
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