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Understanding duality

  1. Apr 20, 2010 #1
    I'm thinking about the wave/particle duality and I have a few questions about it.

    Question: How do we know a particle is also a wave if we can't measure it as one?
    Answer: The double slit experiment, for example, allows us to INFERE the wave nature of particles because of the way multiple particles display an interference pattern on the screen. This interference pattern developes even if we shoot only one particle at a time.

    Question: If each particle is being fired only one...at...a...time... then, after each particle hits the screen, it is no longer in the chamber, right? So, how does the NEXT particle interfere with the previous ones, if the previous ones are no longer there to interfere with??
  2. jcsd
  3. Apr 20, 2010 #2
    The particle must be interfering with itself. They can't interfere with each other. Keep in mind that the particle is not a wave, wave is just a word that helps explain part of it's nature.

    It is more accurate to say that the particle has an oscillatory function (a fourier transform) associated with it and this function interferes with itself. The complication lies in this association, there is no explanation for it in spoken words. The function is not observable in any way. We [Humans] found it through a lot of hard work in the field of mathematics and experimentation.
  4. Apr 20, 2010 #3
    But the interference pattern on the screen is made up of single dots, each given by a single particle. Each particle only makes one dot. A single dot is not the result of interference. To be honest, at this point I'm not convinced any interference is happening at all. They just happen to randomly amount to an image similar to waves of interference. I know this isn't correct, but I need some better evidence of a single particle being wavelike.

    Would it help to look at the uncertainty principle? In it, you can know speed or position but not both. If you measure speed are you measuring the wave, while measuring position is measuring the particle? If you measure the speed of a wave, you should be able to do so at numerous different locations simultaneously. This would be good proof of a wave for me.
  5. Apr 20, 2010 #4


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    Ok .. so what is your explanation for the interference pattern then? It definitely exists and can be measured for only single particles passing through the slit. If they were propagating like classical particles, then there is no way for them to produce the measured behavior, right? So it seems there has to be some wave-like character to the indivudual particles, right?

    My point is that the available experimental evidence has convinced the physics community that particles have wave-like characteristic, and we have a theory that predicts this (QM), so things look pretty consistent. You can't demand "other evidence" unless you can explain away the experimentally observed effects some other way. (Well, you can, but no one will take you seriously.)

    I am uncertain (pun intended) what you are trying to say with the above ... it sounds a little like you are saying the wave-like nature of the particles should cause its probability density to be delocalized, according to the HUP. That much is correct, and has been verified experimentally. It's the specification of simultaneity that is troubling me ... I don't understand why it is necessary. As far as I know, such a measurement is impossible according to standard QM ... the probability density of a particle can be delocalized over an arbitrarily large area, however once you make a position measurement, the wavefunction resolves itself to a single point in space. Thus, it should be fundamentally impossible to measure a discrete particle in two places at the same instant.
  6. Apr 20, 2010 #5
    Thanks for the reply, SpetraCat. I definitely need some help here.
    Yesterday, that's what I thought. But after reading through different threads here and looking at the Wikipedia description of the DSE, I've been led to conclude that the interference pattern is NOT displayed from just one particle. It's displayed collectively from numerous particles. I'm just having trouble understanding where the actual "interference" is. If a single particle doesn't display an interference pattern, then why would we say it interferes with itself? The interference pattern is between one particle and others, yet all of those particles are not in the chamber to interfere with each other. Do you understand my confusion?
    Aren't the only "observed effects" a pattern that is displayed on a screen? The pattern may be predictable, but why does that mean it's the result of "interference"? Again, I don't understand where the interference is coming from.
    From what I understand, a "wave" encompasses a wide area, consisting of several congruent points in space. So if a "wave" can be measured without collapsing the function, then why can't we measure it in the same way at more than one location? Maybe with two screens at 120 deg. angles to each other? But this point is minor. I'm just trying to find ways of understanding the duality. My point isn't to come up with new experimental ideas.
  7. Apr 20, 2010 #6
    Each particle interferes with itself. The central mystery of QM is why this happens. Nobody knows.

    Its not enough to say "they're really particles but there is a wave-like behavior to them". It's just as true that quanta are only waves that appear to localize depending on what they interact with.
  8. Apr 20, 2010 #7


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    Ok, that certainly seems wrong. All QM theories assume some postulates to be true ... and working from these postulates it is possible to predict the observed "self-interference" of quantum particles. This can be done in SQM, dBB, MWI, whatever. One might better say that any quantum theory that *cannot* explain the two-slit experiment is wrong.

    Now, if what you meant to say is that "No one knows why the fundamental postulates we take to be true in the theory seem to hold in real life.", then I would tend to agree with that.

    I think I know what you are trying to say, but to nitpick a little, the phrase in bold makes no sense in terms of QM .. in fact, most of that doesn't seem to make sense as written.

    I guess what you were trying to get across is that the classical notions of waves and particles are inadequate to describe quantum phenomena, right?
  9. Apr 20, 2010 #8
    Hi, Antiphon! What I'm trying to find out is how we know that it interferes with itself if it doesn't display that pattern on the screen. It is said that, if a particle is fired at a barrier in which two slits are cut, it can go through both slits simultaneously. How do we know this is happening if there is no interference pattern displayed?

    I know that a quantum "particle" is both a particle AND a wave. I know it, I believe it, no issue there. To me, the dot on the screen is evidence of its particle nature. Now, I need to understand evidence of it's wave nature. I used to think that evidence was displayed as interference on the screen. But now it seems that such interference is not displayed from just one particle.
  10. Apr 20, 2010 #9


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    You are correct, any single particle is detected at a discrete location .. a dot. However, if we shoot a large number of particles through the slit one-by-one, with space-like separations between them so we can be certain they don't interact, then we observe that the collective pattern of dots is an interference pattern.

    So, let's think about how that can arise. We can safely assume that the test particles come from a stream of identical particles with some spread of transverse velocities, so that if there were no slits present, you would see a circular spot with a roughly gaussian radial intensity profile centered around the beam axis, ok? Now, assume you put a single slit in the way of the beam .. for classical particles, they would either hit the screen or be transmitted, and the observed pattern would be a the subset of the original gaussian profile, windowed by the slit .. also ok? Now put another identical slit quite closely spaced to the first slit. You will see the windowed profile described above from each slit .. they may overlap a bit, in which case the intensities will add normally. In other words, there is no interference pattern.

    Thus, the fact that we observe an interference pattern (again, for repeated experiments) *must* indicate that there is something non-classical going on .. hopefully you are convinced of that. Luckily we have "the most successful theory in physics" (i.e. quantum mechanics) available, which predicts this behavior, and explains the observed non-classical pattern as arising from the wave-like character of the quantum particles.

    That last paragraph sums up why it is somewhat hard for me to address your question directly ... to us (i.e. physicists), the wave-like properties are clear as day ... no further evidence or experiments is needed. The fact that you are asking for them tends to indicate that you don't fully understand the theory ... in which case you are in the right place to get help, but perhaps we could go about things a little differently. Do you understand how QM predicts the interference pattern?

    Just as an FYI, we have been focusing on the interference pattern aspect of the two-slit experiment, which is fine, but that is not even the coolest part of that experiment ... the cool part happens when you try to figure out which slit a given particle goes through ... the interference pattern disappears! There are lots of threads in this forum describing that experiment in detail, so I won't rehash it here. I suggest that you read some of those threads, and come back here with questions (or ask in those threads if it seems appropriate).
  11. Apr 20, 2010 #10


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    Right, the particle is detected on the screen as a "dot" - it's the pattern of a large number of particles that is so curious.

    To see what this looks like, check out a video of it. Go to http://www.hitachi.com/rd/research/em/movie.html" [Broken] and click on "doubleslite.wmv".

    Hoku, have you seen Feynman's Messenger lecture on this? I recommend it, and I'll look for a link.

    Edit: oops, it seems the lecture I was looking for is no longer available - sorry. The Messenger lectures are available in print, though.
    Last edited by a moderator: May 4, 2017
  12. Apr 20, 2010 #11
    Thanks for the video clip lisab! It's nice to have an actual video to look at and this one was good. I'll look up the Messenger lecture, also.
    Believe it or not, this "FYI" is EXACTLY what I'm trying to get at. It's really hard when you're a layman because you lack the knowledge to make a confusion clear and easily move a question forward.

    I was content with my understanding of this phenomena before I posted on PF yesterday. But yesterday (including my PF searches on DSE) completely tore down any understanding I thought I had, so I tried to reconstruct a better picture from the ground up. NOW I see that the whole thing was just a big misunderstanding and I think I was fine to begin with.

    The interference pattern shows the wave aspect, and the "not" interference pattern shows the particle aspect, right? Right. *sigh*. That whole concept, which I understood before, was torn down for me and I'm relieved to see it is still there. One of the impressions I was under in the past 24+ hours, was that the only "observation" in effect was the screen detecting the particles. But, obviously, there is ANOTHER observation in play to take the interference pattern away. So, I'll be content to wrap this thread up with only one other question to ask:

    What is the other observing apparatus that changes the state of the particles? One observing apparatus is the screen, what is the other??
  13. Apr 20, 2010 #12
    Hoku: Richard Feynman said, "The basic element of quantum theory is the double slit experiment." Indeed, if you really want to understand quantum theory, you need to thoroughly understand the double slit experiment and its implications. I believe I can help you understand it. First of all, the remakable feature of the experiment is not the interference pattern. Forget the interference pattern. The important fact is that photons or particles such as electrons go through the slits in a different way depending on if one slit is open or both slits are open. Let's say that behind the two slits you placed a photographic film. If you shine a light on the two slits and developed the film, you would see bands of lighter and darker areas (the interference pattern). If you block one of the slits, shine the light again, and devleop another film, you see one bright line behind the open slit, an image of the slit. To Thomas Young, who first did this experiment, this proved beyond any doubt that light was a wave. But Young didn't have the capability of shooting single photons or electrons through the slits one at a time. When physicists achieved this capabilty, a remakable thing was observed; something that shook the foundations of physics. When one slit is open, single photons and electrons pass through that slit and form an image of the slit, as expected. But when both slits are open and single photons or electrons go through either slit, THEY GO THROUGH THE SLIT IN A DIFFERENT WAY to form an interference pattern on the film! But wait! Why should a single photon or electron go through a slit a different way depending on whether or not an adjacent slit was open or blocked? It's as if the single photon or electron KNOWS whether of not the adjacent slit is open or blocked! Impossible! A photon or electron doesn't have a mind! It can't KNOW anything! I'm using too many exclamation marks here! Well, this is the real paradox regarding the double slit experiment, and this paradox led to quantum theory and wave-particle duality. If you want to discuss this explanation in more detail, send me an e-mail (gboothe@charter.net) and I will gladly respound. I hope this was helpful.
  14. Apr 21, 2010 #13
    Gary, thanks for "respounding" on this thread. :wink: I found it educational and got a good chuckle, too (you can call EMA for help. That's, "Exclamation Marks Anonomous").

    It sounds like you're saying the "non-interference" pattern comes about when you block one of the slits. This is confusing because I thought it was only when we tried to see WHICH slit it went through, that the interference dissappeared. In other words, I thought we were still giving the particle options to see what it "chooses". But there's no choice if one slit is blocked. And if one slit IS blocked, it seems natural that the particles would go through the only open one. And since it's not being "separated" it wouldn't display interference. ???
  15. Apr 21, 2010 #14
    You agree that the particle is being separated as it goes through the slits?
  16. Apr 21, 2010 #15


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    You can see that IF you know which-slit - because it is blocked - the pattern is different. There are other ways to detect which-slit as well, and those lead to the same results. There is another video - don't have the link in front of me - which shows the effect of placing polarizers in front of the slits. By varying their relative angle from 0 to 90 degrees - which corresponds with gaining which-slit knowledge - the pattern changes as well.
  17. Apr 21, 2010 #16


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    To make this clear, consider the following two setups A and B, which are identical except for the settings of the polarizers in front of each slit. In each case, the source beam is polarized to 0 degress and the L (left) slit has a +45 degree polarizer. The R slit has a ++45 degree polarizer in the A setup but has a -45 degree polarizer in the B setup. Sorry for the crude drawing...

    A. Inteference IS seen
    .... Source
    ....== | ==
    ........ |
    ........ V
    == /L/ = /R/ ==


    B. NO Interference seen
    .... Source
    ....== | ==
    ........ |
    ........ V
    == /L/ = \R\ ==


    In both cases A and B above, the amount of light that is detected on the screen is the same. And that amount is half of the light that would go through if there were no polarizers in front of the L and R slits. In other words, the polarizers filter out half the light. Quantum mechanics explains the A results based on a superposition of states which gives rise to interference terms. But there are no interference terms when the polarizers are crossed as per B. That is when the which-slit information is available. So QM relies more on a mathematical formalism rather than an "intuitive" description.
  18. Apr 21, 2010 #17
    That is interesting.

    It would be impossible for a single photon to pass through both slits though. It can't be simultaneously 100% polarized in x and 100% polarized in y. It is not so lucid as closing a slit however it is easy to see we are forcing any photons that pass through to only choose one slit.
  19. Apr 21, 2010 #18


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    Well sort of (and not simultaneously 100%, as you say). Clearly, if the slit polarizers are anything LESS than 90 degrees apart they can pass both to a degree - which depends on the relative angle.

    What if the source photons are at 0 degrees and the polarizers are at +45 degrees and -45 degrees relative? How does the part at one side "know" to only allow the other to get through? Predetermination? And yet all photons that are polarized at 0 degrees are otherwise indistinguishable!
  20. Apr 21, 2010 #19
    How about this. As an EM wave reaches a grating (polarizer) the component of polarization that is blocked is done so by another EM wave released from the free electrons in the grating that is exactly out of phase.

    So this should apply to a single photon. As the photon reaches the grating, the x component is removed because of another photon polarized in x (released by a free electron) that is out of phase with the x component of the original photon.

    Now we have two photons heading for the plate. The original one, and one that is working to block out the x polarization of the original. The plate will never pick up the second photon because the original one is our of phase with it and they will reach the plate at the same time.

    We have the exact opposite thing happening when a photon goes through the opposite grating.

    Now I am fuzzy in this part, but because p_x and p_y do not commute with each other these extra polarized photons that are generated are not exactly along one axis, but more of in a cone, and since the cones are opposite couldn't that destroy the interference pattern?
  21. Apr 21, 2010 #20


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    Are you saying that each slit sees "half" a wave? Or an entire wave? Because no matter how you answer, the math doesn't work - eventually. :smile:
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