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Double slit experiment violates triangle inequality?

  1. Aug 20, 2012 #1
    Imagine a light source, double-slit, and a curved screen in vacuum, shaped so that all parts of the interference pattern are created simultaneously. Define distance as proportional to the time light requires to reach a point. Detectors at each slit can be operating or not. Call the source S, the slits A and B, a point of constructive interference at the screen C, and a point of destructive interference at the screen D. With the detectors at slits on, one can say that the photon traveled (for example) from S to A to D, destroying the destructive interference there. The distance from S to D is given then by d(S,A) + d(A, D). However, with the slit detectors off, no light arrives at D. This implies that d(S,D) is infinity (light does not arrive in any finite time.)

    The above shows a violation of the triangle inequality. d(S,A) + d(A,D) is finite, thus less than d(S,D).
    Therefore I conclude that spacetime is not metrizable with this metric. However, there seems to be no reason why this metric should be any less valid than many equivalent ones in use.

    The idea of spacetime not having a metric is understandably uncomfortable. Obviously, something that acts much like a metric must arise on the large scale of classical objects. We do have a perception of distance. However, it cannot be a true metric. I think this idea is usually rejected on the suspicion that all of physics would collapse if it were true. There are two closely linked ideas here which I consider important to separate.

    1. “We must be able to ignore the price of tea in China while measuring the mass of an electron.” The separability of the universe into distinct non-interacting parts is essential to the functioning of physics. We cannot consider everything in the universe, we have to be able to ignore most data in order to perform any effective analysis.

    2. “Spacetime locality must not be violated.” This is I suspect justified using #1, but is actually a separate assumption. Spatiotemporal proximity is not the only possible means of separation of the universe into analyzable parts.

    I think we have a challenge in geometry and topology, not philosophy. I'm in the minority of people who see no reason to flirt with abandonment of the notion of reality, nor that of logic. Therefore, as John Bell proved, spatiotemporal locality must go. I have attempted to construct various models of “distance” that do not satisfy the requirements of a metric. I regret my skills are not equal to those of a typical Ph.D. in physics. I offer my idea for better minds to follow if interested.

    But I must ask--is this widely known? Is it part of the “oral culture” of the physics community which never gets written down? Or have I made an original contribution? I am a physics grad school dropout, because I never really understood how the physics community operates nor what I had to do to be part of it. Anyway, I have been unable to find any material that seems to follow or refute this reasoning. Please let me know what I have missed. Thank you.
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  3. Aug 21, 2012 #2


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    I do not see how one could draw that conclusion. First, you will get a different interference pattern for every possible wavelength of light you could possibly use giving you a wavelength-dependent distance which is odd. Second, the mere fact that no intensity is arriving at some point in space does not mean that no light field arrives there. The electromagnetic field will arrive at that point - destructive interference is already a proof for that - which invalidates your reasoning.
  4. Aug 21, 2012 #3


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    What does the interference of waves have to do with a triangle inequality about the distance between the source, slit, and screen?
  5. Aug 21, 2012 #4
    Actually, Cthugha, I would say a zero field means no field. No light, no field at that point. Energy density zero. That's the point.

    You are correct that every wavelength would have different places it cannot go. I don't see how that is any weirder than diffferent particles passing through the same point at different velocities end up in different places. You are quite correct that it says something important about how spacetime is stitched together.

    Drakkith, it is an operational definition of distance: proportional to the time required to get directly from point S to point D without observation in the meantime. Since it never gets there, the time is infinity, or if you don't like that, even one second is plenty of time to show the triangle inequality is violated. By observing in the middle, you are *shortening* the distance, which metrics do not allow.
  6. Aug 21, 2012 #5
    If an airplane crossing the Atlantic falls into the ocean, does that mean that the distance between Paris and NYC is infinity(airplane does not arrive in any finite time in NYC)?

    "Optics: Destructive interference - Where does the light go?"

    Last edited by a moderator: Sep 25, 2014
  7. Aug 21, 2012 #6


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    No, that is exactly not the point. Zero field does not mean no field. If you modify the light field - say by introducing a phase shift somewhere, modifying the intensity ratio going to the slits or whatever - any change will still arrive at the point in question with some speed. This is the important quantity.

    According to your reasoning you could just put some screen somewhere and a light source in front of it. As no light reaches the back side of the screen, the distance will be infinite according to your definition. This is an external perturbation and not a matter of the metric.
  8. Aug 21, 2012 #7
    If you introduce a relative phase shift between the slits then the point of destructive interference will move. If you introduce a phase shift in both, no light continues to be no light, and a non-event propagates at the speed of light, is that what you are claiming?

    And yes, Cthugha, that is exactly my point--if you have a light on one side of a screen, light does not get to the other side. The *direct* distance from the source to the back of the screen is infinity. You can get light back there, but only by using a mirror, which use can be detected--and then you're not going directly there any more, you are measuring *two* distances, not one. My point is that they don't add up in accordance with the triangle inequality.

    As for "external perturbation"--that's interaction. That's changing the measurement from direct distance to the sum of two different distances. It is all about the metric. The metric does not behave in the way people assume. That is my point.

    Maui: The *direct* distance between Paris and NYC is infinite, yes. Because you can't go straight there, you have to go around the earth.
  9. Aug 21, 2012 #8


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    The triangle equality doesn't take into account effects like interference. But so what? It's about geometry, not wave mechanics, right?
  10. Aug 21, 2012 #9
    Drakkith, I am saying that we are using the wrong math to describe distance as covered by actual particles. Quantum mechanics is weird because there is something weird about spacetime.

    If you watch a play, and the first actor to come out on stage slips and falls, you think they are clumsy. If every other actor in the play also slips and falls when they come out on stage, you begin to realize that the stage is too slippery. Likewise, if one quantum particle showed interference, that would be a weird particle. But since *all* of them do it, it seems to me that that means it isn't the particles, it's the spacetime they are trying to move through. Interference phenomena of single particles I believe are consequences of the small scale structure of spacetime.

    It has been obvious for a long time that some sort of "spooky action at a distance" is going on, and I think it is because distant points of space are closer than we think. Now if you try to work with a metric and don't use the triangle inequality, you slide down a slippery slope where all distances become zero. I have not found a way around that yet, because I'm not a good enough mathematician. I have toy models, so I can see there are possibilities.

    Is this really a new idea?
  11. Aug 21, 2012 #10


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    Could you elaborate on why you think interference of single particles is "weird" and why you believe it requires different math?
  12. Aug 21, 2012 #11


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    I am claiming that already the first part about moving the point of destructive interference shows that the change in the light field will arrive at the point in question and your definition of distance is not a sensible measure of physical distance.

    So by using a screen which only transmits some wavelengths, you get a wavelength dependent metric again? If you get a time-dependent shutter you get a time-dependent distance? What about gravitational influences which travel at the speed of light, too? Do these have a different distance? This is just not a sensible concept of physical distance. Physical distance is regarded as a property of space. Making it a property of the whole setting is not really tenable. You can come up with effective distance measures as much as you like, but how does that contain any progress besides shifting the physics happening into a strange, complicated and wavelength-, time- and interaction-dependent metric?

    There are semimetrics and premetrics which do not fulfill the triangle equality. However, I am not aware of any sensible attempt to attribute these to physical distances. They are instead used in rather abstract notions of distance like in complex networks (I have seen them used in neural networks or social network analysis).
  13. Aug 21, 2012 #12
    Funny you should mention that, I was just partying with two chicks east of Vegas the other night :)
  14. Aug 21, 2012 #13
    Drakkith, last I checked everybody thinks interference of particles is weird--it's just that most people have given up on trying to explain or understand it. That's why we had the long debate between Bohr and Einstein which is now carried on by others. Many like to pretend there is no problem, or handwave and call it "the measurement problem" and follow that up with deafening silence. But there is always going to be a strong minority of physicists working on the problem because solving things like that is the whole *point* of physics for us.
    Look into Bell's Theorem if you're unfamiliar with any of this.

    Cthugha, I accept that I have not sufficiently made my case; I guess I will have to try to get more results on my own before I try again to present this. The answers to most of your case questions are "yes", btw. I'll have to work on my explanations; honestly I was mostly expecting to hear either "well, duh, everybody knows that" or "Oh, why didn't I see that?"

    I hadn't realized that I had created YAPIOQM--Yet Another Personal Interpretation of Quantum Mechanics--as I call the many worlds, the transactional, many histories, etc.
    As far as I can see, having the "fabric" of spacetime be woven with a complicated "stitch" seems far superior conceptually to the mystical gibberish and arbitrary restrictions on "allowable" questions I find in all the textbooks.

    And spacetime already interacts with matter--that's general relativity. Distance is already defined with geodesics followed by light. I honestly didn't think I had much new here.

    As far as I am concerned, distant entanglement, to say nothing of spin 1/2, means that our concepts of spacetime are fundamentally broken, and the need to fix that is the elephant in the room that most of the physics community seems to be ignoring--or to be fair, many of them probably made a few attempts and saw it was really hard and decided to tackle something else. My only beef with them is the way they pretend the problem isn't there and actively pressure people not to investigate it.

    At root, the motivation is understanding, and yes that means a picture or a model. The claim that "no such model is possible" is not only an unprovable assumption but a pessimistic one to boot. And the reason I for one insist on searching for that model is because I don't feel I can trust *any* of the physics I have learned until this gets settled. Why should I study QFT if tomorrow it's going to be shown to be as useless as phlogiston? Can I even trust conservation of energy? Which parts of physics are still going to be standing? How can I ever build an intuition, a feel for problems, when I can't trust any of it except classical physics in the classical regime, and there only approximately?

    I have taken six courses in quantum mechanics at various levels and I don't feel that I understood a thing. I can solve an equation if presented but I have *no idea* how to look at a physical situation and set up the equations in the first place. I don't have this problem in any other area. I can work GR and classical physics just fine, start to finish. I have no intuition for QM and I see no way to build any without a model which does not yet exist.

    Sorry if that was overexplaining but this is the first time in many years that I have been able to vent that rant to anyone who had a chance of understanding more than one word in three. I am actually very grateful for the feedback and I am not attacking you, just the damned orthodoxy.
  15. Aug 21, 2012 #14


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    I didn't ask what most people think, I asked why YOU think it's weird. Do you think that the universe should work in a simpler way or more intuitive way at the quantum level?

    I don't see how your example deals with this issue. The EM wave still travels to the spot on the screen, it just interferes so we don't see any photons, correct?

    First you need to explain why this is even a problem. What is wrong with entanglement and spin 1/2 particles? Why is this a problem at all? Perhaps this is genuinely what happens.

    Because it isn't always about right and wrong, it is about accuracy and ease of use. Classical physics is obviously wrong, but is still used all over the world for almost everything because it is accurate enough for practically all purposes and is MUCH simpler than more accurate theories and models. Science strives to build more accurate theories and models but unfortunately we run into the problem that what we find does NOT look like what we THINK it should look like, what we are used to dealing with. This doesn't mean that we are wrong, it may mean that we are right! But we don't know. That's why we keep looking.

    Without taking a course in QM I cannot say much on the matter, but it APPEARS to me that you simply never learned how. This is a problem for many people in many different areas in life. I don't see this as being a problem with QM itself or any other theory.
  16. Aug 22, 2012 #15
    Drakkith, you raise a lot of points. Now that I know you have never studied QM, I'll see if I can rephrase and explain.

    Start with the double slit experiment with light. We get an interference pattern, as Young showed in 1811. We know that waves do that, so we interpret light as a wave. Then we developed the ability to register individual photons with CCD counters and such. So light acts like a particle. In short, it travels like a wave, but interacts with the world like a particle. So de Broglie tried in 1927 to describe the situation as a particle having a location, though unknown, and motion guided by the "pilot wave." But this doesn't work because if you turn the light intensity down so far that only one photon per second comes through, the interference pattern still shows up. So it seems that the photon is spread out over the entire wave, right? It has to be in both places at once to be affected by both slits. But now we have a problem when the light wave arrives, because if it hits all parts of the screen simultaneously (we can curve the screen slightly to guarantee this) then if the photon "decides" to arrive at a particular spot on the screen, somehow every other point on the screen *instantaneously* knows *not* to register a photon. So information is going faster than light in what seems to be a violation of relativity, but which always seems to weasel out on a technicality when you try to use it for FTL signalling. It's as if Nature is cheating to keep her books straight, violating her own laws.

    Now, one can ignore this, and "shut up and calculate", as the proponents of the so-called "Copenhagen Interpretation" command, but some of us want to understand what is going on. Is something going faster than light or not? Many say, "well, we can't expect classical thinking to work in the quantum realm," to which I reply, Yes, but we can expect *some* kind of thinking to work, instead of just assuming the answer and refusing to think about it.

    To my mind, the particle is actually spread out over a volume of space in some way, and when it is detected by interacting with the world, somehow all the distant scattered parts of the particle have to instantaneously teleport all into the same spot to get absorbed by the electron or what have you. Suddenly, instantly, there isn't any wave any more, anywhere, because a particle got detected in one spot. I find it a reasonable question to ask "how does it do that? How is spacetime woven such that a particle can spread out all over space and then suddenly all get sucked into one tiny region?" I think it is a geometry problem, and a very hard one, but most people seem to go off into mystical semi-philosophical handwaving and insist that some questions are "improper" but don't provide any way of identifying in advance which questions are "forbidden", which smells suspicious. It is a way to cheat and win every argument--if you don't know the answer, declare the question forbidden. I don't like that one bit.

    It would be one thing if they said, "that kind of question is ill-defined because of this specific feature, and this is what is well-defined in replacement," but instead they say, "well, *sometimes* that question is forbidden and sometimes it isn't," and always seem to forbid it when things get interesting. I don't like theories that claim that some knowledge is impossible when they keep moving the criteria. I find it philosophically offensive, not to mention an unscientific and pessimistic assumption.

    I don't disagree that these things *happen*--the calculations of QM are verified to some huge number of decimal places. The theory works, it gets valid results. But it is a cookbook recipe, not a model, not a way of understanding the world. It is blind magic. And all of my professors and all of my 30+ textbooks on quantum mechanics are incoherent when it comes to giving anything like rules as to how and when to work the magic--hence I can't set up problems because I can't trust any of it. I can solve equations all day long but it's useless if I don't know what they mean.

    QM is a theory written by human beings for human beings, and as such it should be comprehensible to human beings. I'm willing to admit I have blind spots, but I studied physics at MIT, I'm not an idiot, I've been a physics instructor for 19 years and a damned good one by all accounts, and it's not just me. Yes, I didn't learn how, I missed something that all the other students got. But I know pedagogy. I construct many different explanations every day to help students understand. Either every single instructor and author of quantum mechanics is atrociously incompetent, or there is something wrong with the theory. I vote the latter.
  17. Aug 22, 2012 #16


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    Ok. Everyone has their opinion. I don't see what so "incomprehensible" about QM, but perhaps your use of the word is different than mine.
  18. Aug 22, 2012 #17


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    I still do not see your point of putting the physics happening into the metric, but feel free to follow your ideas - though I do not find mystical gibberish in reasonable textbooks.

    The geodesics are those along which changes in the light field travel, not those where intensity arrives. This is a huge conceptual difference.

    I am not a friend of pilot wave theory, but this is incorrect. The guiding wave will go through both slits in pilot wave theory. The photon will not. Those two things are not the same. If it is the ontology you are after, Bohm's approach will at least give you a tenable way of approaching the problem. Other approaches work fine, too.

    Anyway, you somewhat seem to still imagine photons as tiny bullets. This point of view is outdated by at least 40 years. At least with the advent of quantum optics that simple picture became obsolete. Unfortunately, some textbooks from "older times" are still widely used and influential, most prominently the Feynman lectures. If one takes this naive view, one indeed runs into problems with particle-wave duality. However, I do not see why one should even follow that route as duality is just a consequence of taking this wrong approach. Btw, the reality of wave-particle duality is such a common topic around here, that it even got its own FAQ entry: https://www.physicsforums.com/showthread.php?t=511178
  19. Aug 22, 2012 #18


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    Ignoring the problem with photon positions: The point didn't register a photon before you started the experiment and it didn't register one during the experiment. So nothings changes for it. Why do you think this is remarkable?

    "Shut up and calculate" is not really the Copenhagen approach. But I agree that Copenhagen seems more like "shut up and calculate" when compared to other interpretations. In the beginning, I didn't like the Copenhagen interpretation and read a lot about different interpretations. I still don't have a favourite, but Copenhagen is special in one way: it is very close to the scientific method by acknowledging that we get our knowledge by doing measurements. Keeping this in mind, it seems much more rational that measurements may play a special role in a fundamental physical theory.

    The idea that particles are actually spread out over finite volumes is very uncommon even between people who are working on fundamental interpretational questions. It was first advocated by Schrödinger and I don't know much about. Maybe someone else can comment on it. I just wanted to say that starting with a uncommon idea and asking "how does this work" is maybe not the best way to get a grip on the difficult question of interpretation.

    The main problem I see is that comprehension comes from humans interacting with the world. These interactions are described by classical physics, so comprehension really means understanding something in classical terms. This is often possible, but I don't see why we should assume that it always has to be so.
  20. Aug 22, 2012 #19
    Okay Drakkith, thank you for the conversation.
  21. Aug 22, 2012 #20

    Feynman may of help here:

    "If you think you understand quantum mechanics, you don't understand quantum mechanics"
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