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Double slit and electrons

  1. Jan 13, 2012 #1

    i often heard about the double-slit experiment with electrons and read that it would give the same pattern as the double-slit experiment with photons. so the only difference would be the shorter de-broglie wavelength of electrons compared with the wavelength of ordinary photons.

    but i would say, that the coulomb repulsion of electrons should also have an effect on the pattern. is this true or is it really the same pattern, that photons give?
  2. jcsd
  3. Jan 13, 2012 #2

    Ken G

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    You're right that you have to run the experiment more carefully to avoid the Coulomb repulsion being an issue. But if the slits are uncharged, and the beam density is low enough to avoid interparticle interactions, then you can still get the same pattern as you say.
  4. Jan 16, 2012 #3
    Re: Double slit and electrons

    There is one more difference. While the double slit experiment with photon will have an interference pattern of field intensity of received photons, the same experiment carried out with electrons will have an interference pattern of the number of received electrons.

    Odd thing is electrons go through either of the slits as they comes in lumps. Yet they interfere. :cool:
  5. Jan 16, 2012 #4

    Ken G

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    But that's not really a difference-- photons do the same thing. If you use X-rays, for example, you will detect individual "hits" on the screen, not field intensities. Wave/particle duality is ubiquitous.
  6. Jan 23, 2012 #5
    But isn't it also likely that the duration of this duality is a time-dependent function of how large (ie, massive) the particle is? IOW, if you could shoot progressively bigger and bigger particles/objects through a double-slit experiment, isn't it probable that at some given size you would eventually detect decoherence as indicated by the disappearance of the interference pattern? Not because the particle didn't momentarily take on a wavelike characteristic as do smaller objects like electrons and atoms ...but because that probability wave collapsed much faster due to its larger mass?

    More than a decade ago researchers conducted the double-slit experiment with Buckminsterfullerene ("buckyball") molecules. These particles have a structure much like a soccer ball and have ~60 carbon atoms per molecule. To my knowledge, these are the largest objects ever tested in a DS experiment and the interference pattern caused by quantum superposition was still in evidence.

    The abstract of the paper that the researchers wrote to report their findings said that using objects this size pushed the limits of the interferometry techniques at that time (I don't know what causes those limits if anybody would care to enlighten me). But if we were to imagine for a moment that no such detection limitations existed, my hunch is that as you continued to increase the size (mass) of these "projectiles" you would eventually reach a point where their probability wave would collapse before they reached the slits. It might be informative to know at what point this occurred if true.

    To your knowledge, is there no other method of determining whether an interference pattern exists or not? I suppose physicists haven't pursued such an investigation because for some technical reason it can't be done. But I would be interested in hearing any thoughts you may have about this just the same.
  7. Jan 23, 2012 #6

    Ken G

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    Decoherence is also a wave phenomenon, it's something that waves do. An example is the little bumps or holes they put in ceilings to avoid echoes. Do those bumps turn sound waves into particles? I agree that if you shoot a bullet through a window, you are not going to use wave mechanics to solve that problem-- but you could. Waves do everything that particles do, because they are exactly the same thing in quantum mechanics (our best theory of dynamics in the absence of gravity). That doesn't mean we are always going to avail ourselves of quantum mechanics though.
    Exactly, so we see that we can always treat these objects as dual particle/waves, it's just that if they get large enough we have no particular reason to want to do that. The concept of a trajectory is very useful-- yet it is also something that waves do. Waves can decohere, waves can follow trajectories, waves can get absorbed or reflected or fragmented. Waves do everything that classical mechanics does, the significance of this fact was just not recognized before quantum mechanics. But of course we still need particles, to explain the discretenesses we encounter and to convey the attributes like mass and spin. So we have wave/particle duality-- you never get one without the other, though you often don't need to include both for practical efficacy.
    There are two issues there-- as the energy of the particles increases, their deBroglie wavelengths decrease, and their wave mechanics more and more closely approximates a pure trajectory. Then there's also the effect you refer to-- decoherence among the parts. The entanglements between the parts gets more complicated, and there's more chance of interacting with the environment. None of that makes quantum mechanics not work any more, but it makes it less necessary, and a lot less practical, to use quantum mechanics instead of classical mechanics.
    I don't know about the practical issues for extending detections of interference patterns through that "murky" middle ground where you can still use quantum mechanics but it is difficult. I agree it is an interesting domain to pursue, and perhaps some surprises might live there, maybe there is even evidence for the next theory somewhere in that domain. But the expectation is that quantum mechanics will work fine in that domain whenever it is possible to both calculate and measure, which means that the systems will still be doing something that waves do. I guess my main point is that people often equate "something that waves do" with "something that particles don't do" and vice versa, but this isn't right-- wave/particle duality means that waves and particles are exactly the same things, so waves do everything that particles do (when you include their particle-like attributes), and particles do everything that waves do (when you include their wavelike attributes), all described by quantum mechanics.
  8. Jan 23, 2012 #7
    Ken...first off thanks so much for taking the time and trouble to post your excellent response to my initial inquiry...I very much appreciate the effort. I understand and agree with almost everything you wrote, but I'm struggling a bit with the very last thing you said...

    I'm an aerospace engineer by profession and just a puny little physics layman, so I'd be the first to admit that when it comes to quantum physics there is a ton (make that a black hole's mass worth) of stuff that I undoubtedly have wrong. But just to clarify my original post a little, I wasn't questioning wave/particle duality at all...I was merely wondering if the collapse of the probability wave function might not be dependent on the size (mass) of the particle in question?

    IOW, let's assume that we designed a Super-Duper Double-Slit experiment, along with an interferometer that could resolve interference patterns for any de Broglie wavelength...ie, if there's an interference pattern associated with any size particle we used we'd see it and if there wasn't we wouldn't.

    If we had such a device, is it your contention that we would detect interference patterns for bosons to bullets, and everything in between? I suppose what I'm really asking is it absolutely necessary to invoke either the hideous Many Worlds scenario, or the Copenhagen Interpretation that Einstein found so utterly abhorrent to explain away this phenomenon, or is it possible that there could be a reasonable third alternative...that there is some very real cause-and-effect that forces wave function collapse so that we can avoid either inventing an infinite number of universes or blaming the bizarre results on a pair of prying eyeballs?

    If not mistaken, physicist Roger Penrose suspects that there is a more rational explanation...that gravity somehow plays a role in the appearance of quantum decoherence. I dunno, but as an engineer this possibility just makes a lot more intuitive sense to me and is a much more satisfactory explanation than any of the currently most accepted explanations/excuses.
    Last edited: Jan 23, 2012
  9. Jan 23, 2012 #8
    Let me discuss separately these two things: collapse and interference of particles of arbitrary mass.

    As for collapse, I hate to spoil the fun, but this notion is dubious: “no positive experimental evidence exists for physical state-vector collapse” (M. Schlosshauer, Annals of Physics, 321 (2006) 112-149, http://arxiv.org/pdf/quant-ph/0506199v3.pdf).

    As for interference of particles of arbitrary mass, for what it’s worth, my advice would be: don’t hold your breath waiting for anything new for interference of larger particles. My reasoning is based on the following almost forgotten ideas of Duane (W. Duane, Proc. Natl. Acad. Science 9, 158 (1923)) and Lande (A. Lande, British Journal for the Philosophy of Science 15, 307 (1965)): the direction of motion of electron in the interference experiment is determined by the momentum transferred to the screen, and this momentum corresponds to quanta (e.g. phonons) with spatial frequencies from the spatial Fourier transform of matter distribution of the screen. So I tend to make the following conclusion: when the mass of the incident particle increases, the momentum transferred to the screen remains the same, but the angle of deflection of the incident particle becomes smaller, as its momentum is greater. So the mass of the incident particle is in some sense an “external” parameter for the interference experiment.

    EDIT: By the way, the following article on a classical analog of the double-slit experiment may be of some interest for you: Yves Couder, Emmanuel Fort, Single-Particle Diffraction and Interference at a Macroscopic Scale, Phys. Rev. Lett. 97, 154101 (2006).
    Last edited: Jan 23, 2012
  10. Jan 23, 2012 #9


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    Er... hang on. In a superconducting interference experiment, the "object" here is the whole superfluid, which can be of any arbitrary number depending on the superfluid density. As long as one can maintain coherence, one gets all the quantum effects. This macro particle has already been shown to exhibit such interference and other quantum effects (see the Stony Brook/Delft experiments).

    That, in itself, has falsified what you are claiming above.

  11. Jan 23, 2012 #10
    Dear ZapperZ,

    Maybe I was not clear enough, but I was just trying to say that, in my opinion, interference experiments with larger particles will give the results compatible with the relevant (smaller) de Broglie wavelength, so we should not expect anything new. I don't think this is in contradiction with what you're saying.
  12. Jan 23, 2012 #11
    akhmeteli...thank you for providing that link to a paper on wave function collapse. I'm gonna go read it now, although I'm quite certain I won't understand 95% of it. This stuff is a lot harder than rocket science.

    Many of my questions I'm asking here I've had for a long time, but some of them only recently occurred to me after reading a little article that first appeared back in 2005...


    I know that Penrose has been working with some researchers at Leiden University in an attempt to devise an experiment to test out his hypothesis...but it must be one helluva complicated task because they've been working on it for many years now...


    Anyway, I'd like to thank all you guys for taking some time to submit posts to better help us physics ignoramuses understand this wonderful subject a little bit more...even if it's only just a little.
  13. Jan 23, 2012 #12
    Okie dokie, akh...so far this seems to be a good paper you linked to. Early on...

    Our goal is to show that there is no experimental evidence
    for a breakdown of the superposition principle and
    the related interference effects at any length scale investigated
    thus far. Whenever a decay of such superpositions
    is observed, it can be fully accounted for (both
    experimentally and theoretically) as resulting from environmental
    interactions. The absense of any empirical
    evidence for nonlinear deviations from unitary time evolution,
    combined with the ability to give an empirically
    adequate description of the decoherence of superpositions
    into apparent mixtures, provides good reasons to take the
    universal validity of the Schr¨odinger equation as a working
    assumption and to explore the consequences of this

    I don't think this is what Penrose is conjecturing about. If not mistaken, he speculates that decoherence may result when the mass of particles gets large enough so that gravity begins to exert an influence which eventually somehow causes the loss of quantum superposition that occurs over a finite time duration. The larger the mass, the quicker the collapse occurs.

    This might be thought of as an "environmental interaction" as stated by the paper. Perhaps the effect of gravity is not much different than the interaction with radiation from a detector that causes wave collapse and the disappearance of the infamous interference pattern.

    So to summarize, I don't think Penrose believes that quantum mechanics is necessarily invalid in any size regime...just that there are external environmental effects we don't yet totally understand that may influence the wave/particle duality...be it radiation from a measurement device or naturally occurring gravity in the presence of mass.

    Back to the paper...although I suspect I won't have to go too much further before it totally loses me. But thanks again for submitting it.
    Last edited: Jan 23, 2012
  14. Jan 23, 2012 #13
    I cannot comment on Penrose's work, as I don't know much about gravity.
  15. Jan 24, 2012 #14

    Ken G

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    As you said, Penrose thinks we should look for such a real dynamical collapse, perhaps linked to gravity. My point is only that this requires a new theory-- in quantum mechanics, there is not a dynamical collapse, instead the collapse appears because of how we have chosen to treat the interactions of that system with its environment (the decoherence you mention). So yes, systems that involve complicated enough interactions can be treated by us in a way that results in the collapse phenomenon, without us having a clear dynamical description of just how that collapse occurs (analogous to how thermodynamics treats systems whose detailed dynamics are not tracked). If we instead tried to track it, both MWI and Copenhagen say we would fail, but Penrose thinks perhaps we could succeed (but no one has yet). The MWI approach says the collapse doesn't really occur at all, we only think it does, and Copenhagen says the collapse does occur, but it is not only outside of quantum mechanics, it is outside of physics. Choose your poison-- it's an illusion, it's real but unknowable, or it relies on gravity in some way that few are convinced can reallly work. All these questions must await the next theory.

    But it we stay within quantum mechanics and its standard interpretation, then yes, a system can get complicated enough that the physicist will not choose to treat it completely. In that situation, collapse occurs spontaneously, that's what I meant by the second effect over and above simply having a very small deBroglie wavelength. But it's still something that waves do-- when the wave mechanics gets too difficult for us, we can choose to treat the wave as incoherent, and this generates results similar to particle mechanics (geometric optics is an example here). In wave mechanics (like quantum mechanics), collapse is something that happens in the way we choose to treat the system, but it's still a "wave phenomenon", it's something that waves do within how we are treating them (and that also includes the quanta, we impose that onto the wave mechanics manually, so we impose the wave/particle duality ourselves, just like the collapse). Hence, a completely dynamical accounting for the collapse had better also be able to give a completely dynamical accounting for the emergence of particles from waves (not instead of waves), or else it falls short of its goals.
    Last edited: Jan 24, 2012
  16. Jan 24, 2012 #15
    I would think electrons would act the same as long as they are not influenced by another charge.
  17. Jan 25, 2012 #16
    And this gets back to my original post...that being if we could somehow determine whether or not wave collapse occurs for macroscopic objects (a speck of dust or a mirror of that size) that would tell us a helluva lot about whether this phenomenon is actually real and may be an intrinsic property that manifests itself in a certain size regime that has not really been investigated very closely. It seems to me that in the last century or so, we've gone from the classical physics world of paperclips, people and planets and zoomed right down to the quantum scale of photons, electrons, protons, atoms and molecules...and in the process we shot right past many orders of magnitude...the range in which the two worlds collide and where many interesting things are probably happening. And it is this range where string theory advocates are currently battling the loop gravity proponents in their holy war for the "truth".

    If the guys over at Leiden could ever manage to finalize their tremendously technically challenging experiment they've been working on for years and they observed decoherence not caused by environmental interaction, that wouldn't necessarily prove that Penrose was correct in his speculation that gravity somehow plays a role in wave collapse, but it would nevertheless be a hugely important finding that would beg some explanation as to what causes it. And if they don't observe the disappearance of superposition, that too would be informative.

    I guess which of the current wave collapse theories one leans toward depends a lot on whether or not one's gut tells him it is a real phenomenon or not...


    Penrose's interpretation is just another objective collapse concept, much like the better known GRW theory that arose back in the 70s & 80s. To be sure, this particular set of interpretations have their own unique problems, one of them being nonlocality, I think. But if we believe that current QM theory is somehow flawed or at the very least incomplete, then I'm not too sure that saying this or that new theory can't be right because some aspect of it conflicts with a model that is suspected to be flawed or known to be incomplete is very logical.

    I've been reading up on Penrose some lately, because whenever I hear about a new interpretation or conjecture, I kinda like to know a little about the pedigree of the person making such speculation.


    He has been known to put forth some rather controversial ideas, especially in the area of quantum effects on consciousness, but that doesn't bother me one bit. Given the history of science, new concepts which at first were considered radical by the mainstream often turned out to ultimately be correct. That certainly doesn't mean every unorthodox proposal that comes along is right, and Penrose may very well be wrong here...but given the current state of fundamental physics today, it seems to this layman looking in from the outside that the field most definitely needs a lot of shaking up.

    My conclusion so far is that Penrose is most definitely not a total flake...but rather is just another very smart mathematical physicist who has no idea what the hell is really going on! :smile:

    Take a seat and wait for your number to be called, Roger.
  18. Jan 25, 2012 #17
    As an afterthought, I don't think what Penrose is proposing is an entirely new theory that would either supplement or replace current QM. To my knowledge, even if the Leiden experiment did show wave function collapse that would only suggest that it is possibly an intrinsic and real phenomenon...it would not prove that gravity was the cause nor explain exactly how it occurs. Penrose is offering up something that is nowhere close to a full-blown theory.

    Going off topic a little (or maybe not), I started reading Penrose's book The Road To Reality, and came across an interesting section that I've thought about for many years now...

    When quantum-mechanical ideas were beginning to be introduced early in the 20th century, there was the feeling that perhaps we were now beginning to witness a discrete or granular nature to the physical world at its smallest scales. Energy could apparently exist only in discrete bundles—or ‘quanta’—and the physical quantities of ‘action’ and ‘spin’ seemed to occur only in discrete multiples of a fundamental unit (see §§20.1,5 for the classical concept of action and §26.6 for its quantum counterpart; see §§22.8–12 for spin). Accordingly, various physicists attempted to build up an alternative picture of the world in which discrete processes governed all actions at the tiniest levels.

    However, as we now understand quantum mechanics, that theory does not force us (nor even lead us) to the view that there is a discrete or granular nature to space, time, or energy at its tiniest levels (see Chapters 21 and 22, particularly the last sentence of §22.13). Nevertheless, the idea has remained with us that there may indeed be, at root, such a fundamental discreteness to Nature, despite the fact that quantum mechanics, in its standard formulation, certainly does not imply this. For example, the great quantum physicist Erwin Schrodinger was among the first to propose that a change to some form of fundamental spatial discreteness might actually be necessary:

    "The idea of a continuous range, so familiar to mathematicians in our days, is something quite exorbitant, an enormous extrapolation of what is accessible to us."

    He related this proposal to some early Greek thinking concerning the discreteness of Nature. Einstein, also, suggested, in his last published words, that a discretely based (‘algebraic’) theory might be the way forward for the future physics:

    "One can give good reasons why reality cannot be represented as a continuous field. . . . Quantum phenomena . . . must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory."

    Others also have pursued ideas of this kind; see §33.1. In the late 1950s, I myself tried this sort of thing, coming up with a scheme that I referred to as the theory of ‘spin networks’, in which the discrete nature of quantum-mechanical spin is taken as the fundamental building block for a combinatorial (i.e. discrete rather than real-number-based) approach to physics. (This scheme will be briefly described in §32.6.) Although my own ideas along this particular direction did not develop to a comprehensive theory (but, to some extent, became later transmogrified into ‘twistor theory’; see §33.2), the theory of spin networks has now been imported, by others, into one of the major programmes for attacking the fundamental problem of quantum gravity.

    Do you have any thoughts on this? Specifically, how if space and/or time were really quantized that continuous quantum field theory might come up short in describing something that was ultimately discrete in nature?

    The quotes from heavy hitters like Schrodinger and Einstein are pretty striking, IMO. I have often wondered about this, and after I came upon this passage of Penrose's I started doing a little tangential research which brought me to such things as Digital Mechanics and Cellular Automata Theory...which led me to the early works of Konrad Zuse in the late 60s (Calculating Space)...which then led me to Edward Fredkin in the 80s (Finite Nature)....which then led me to recent work by Stephen Wolfram and gang (A New Kind of Science).

    Some pretty fascinating stuff. You never know where you're gonna wind up when you start thinking about double slits.
  19. Jan 25, 2012 #18


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    Why are we going severely off-topic on this subject? You are welcome to start a new topic, but don't hijack an existing one for such a discussion.

  20. Jan 25, 2012 #19
  21. Jan 26, 2012 #20

    Ken G

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    I'm actually missing why that experiment is telling us anything new, it seems like a perfectly routine application of elementary quantum mechanics. For example, it's well known that if you put polarizers tilted at 90 degrees to each other in the slits, you also have which-way information, and you also have no two-slit pattern. Why is this experiment any different? Quantum mechanics tells us that accessing which-way information ruins the two-slit pattern, essentially because interference is an expression of indeterminacy for quantum fields. Classical fields can interfere even when they are completely determined, but quantum fields require either the indeterminacy of indistinguishable particles, or the indeterminacy in the history of each particle, to produce the interference. Hence whatever can act to remove the indeterminacy also acts to remove the interference (imagine a sum over possible paths as the source of both the indeterminacy and the interference), this is one of the only things about quantum mechanics that actually does make perfect sense.
  22. Jan 26, 2012 #21
    That seems to be the opinion of quite a few people who posted comments to the article. Some thought the experiment worthwhile...others said "yeah, so what?". One thing's for sure...for any MWI aficionados out there, the Italians at least created umpteen new universes for all the electrons that didn't make it through with their wave functions unscathed. Bravissimo, Italia!

    Seems a lot of popular science magazines like to hype a lot, probably to sell copies to laypeople looking to learn a little...


    If not mistaken this one went from "shaking foundations" to "oops, maybe we kinda made a mistake" pretty quick. Physicists are starting to remind me of economists more and more every day.
    Last edited: Jan 26, 2012
  23. May 10, 2012 #22

    I just read this thread, and I found most of the answers missed the central point of the d-slit exp on electrons.

    The question of electron interaction is not relevant for the experiment because the central part of the setup is to make sure that electrons are passed through the slits ONE by ONE. That is the second electron is fired only after the first electron is already absorbed by the detection screen. The interference pattern is a result of build up over time of individually fired electrons.

    1. Merli, P. G., Missiroli, G. F., and Pozzi, G. [1974]: `Electron Interferometry with the Elmiskop 101 Electron Microscope', Journal of Physics E: Scientic Instruments, 7, pp. 729–732.

    2. Tonomura, A., Endo, J., Matsuda, T., Kawasaki, T., and Ezawa, H. [1989]: `Demonstration of Single-Electron Buildup of an Interference Pattern', American Journal of Physics, 57, pp. 117–120.

    If the electrons are fired en mass, the interference pattern would have been much less important, and the result would not have implied a classically impossible state - i.e. quantum superposition. Without such superposition, Quantum Mechanics is rather lame. There would not have been implications on non-locality, Quantum computers, or multiverse theory proposed by David Deutsche.

    Rock on in physics. Regards
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