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How does a particle interfere with itself?

  1. Feb 10, 2004 #1
    Hello,

    I am a high school senior trying to a project on wave particle duality. I know alot of you are probably going to shoot me because i have no clue (compared to laot of you) what I am talking about. I was searching the net for answeres when i stumbled upon these forums, so somone please help me.

    Basically, my problem is this:

    I understnad how the double slit experiment works. I understand what waves are and how they intereact. I also understand what particlces are and how they behave. After stareing at my computer screen for hours on end, i have finally figured out everything i need to know for my project about the double slit experiment so i can adequetly explain it to me class... Except for one thing:

    When a single photon is fired through a single slit, it produces the pattern on the wall like a bell curve, which is what you would expect from a particle. However when you open up both slits, evan if you fire it one photon at a time you get a wave-like interference pattern on the wall behind the slits.

    If i am correct, this is because somehow the particle is interfereing with itself somehow? I have read all sorts of crazy theorems, although this is quantum physics so alot of them probably arn't as crazy as I think. One of them is that my view of a photon as a partical is wrong and that a photon is actually some energy spread out over a space, and so when you fire a "photon" at the double slits it actually goes through both of them. Another theory is that there are waves of probablility or something that interefere with each other... that one didnt make any sense at all, and i think its wrong anyways. eh.

    SO anywyas i was hopeing somone could offer me a very simple explination as to HOW A PARTICLE IS INTERFEREING WITH ITSELF... in the context of the double slit experiment. if there is no simple explination then please dont even both because I wont understand..for I am but a lowly high school student who really doesn't understand much.

    Please offer me help you geniuses of the physics forum....
     
  2. jcsd
  3. Feb 10, 2004 #2

    chroot

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    You may already understand this, but just to make sure: each individual photon only hits the detector in one place, making one small dot. Only when you fire many photons (even if you fire them one at a time) will you see the interference pattern build up out of the small, individual dots.
    It would be more precise to say that the photon is interacting with the entire apparatus at once -- both slits. It is not localized like a bullet which passes through only one.
    Yes, in a way, that's correct. It's improper to think about a photon as being a bullet which goes through one slit or another. The photon actually interacts with the entire apparatus.

    - Warren
     
  4. Feb 10, 2004 #3
    Yes i undertand that the wave-like interference pattern with having both slits open and only fireing one photon at a time comes only after you fire lots of photons and you collect a scattering of points the photons hit.

    SO are you saying that the idea of a photon just being a chunk of energy localized in a area of space, not a point like a partical is, is right? could you explain a little more please.
     
  5. Feb 11, 2004 #4
    hi!
    it is not the electron( or whatever) that interferes with itself ...it is the possibilities available for the particle, which interfere!

    what i mean is....in classical probability theory, the total probability for A or B,
    ie P(A or B) = P(A)+ P(B)...

    but this is not so in qm...

    in qm, the total probability is given by...

    P(A or B) = {p(A) + p(B)}^2.... (eqn.1)

    where [p(A)]*[p(A)]! = P(A)=probabilty of A occuring (and similarly for B)

    and where, [p(A)]! is the complex congugate of p(A)

    here p(A) is called the probabilty amplitude ,and when multiplied by its complex conjugate , gives the probability for A occuring....similarly for B

    you must have noticed that eqn.1 is the usual equation of adding wave intesities,ie, the intensity of the resultant wave (formed by the superposition opf two waves) is given by the square of the sum of the amplitudes.

    that is what we mean by an electron wave...it doesn't mean that the electron is a wave floating in space...what it means is that the probabilty of finding the electron in a certain state is given by an equation exactly similar to the equation for finding the intensity of a resultant wave (in the classical theory of waves.)

    the probabilty amplitude is similar to the amplitude of a wave in classical wave theory, except that it is a comlpex quantity (for which there are technical reasons)


    if you want to know further, see "feynman lectures on physics Vol.3" ...first 2 or 3 chapters.
     
  6. Feb 11, 2004 #5
    Hey, remember when i said "uncomplicated or dont bother."
     
  7. Feb 11, 2004 #6
     
    Last edited: Feb 11, 2004
  8. Feb 11, 2004 #7
    Ok you have a SINGLE particle that you are going to direct at a Single Hole, if you could peer from the OTHER side you would see a Particle emerging, you have a direct Hit so to speak , (100%)PROBABILITY OF PARTICLE NOT GOING THROUGH THE HOLE=ZERO, all of the particle has emerged from all (100%) of the Hole.

    Now for simplistic terminology you should class the hole as a 100% quantity(event-frame). When you devide the original hole into two pieces you get 100% devided by 50%, thus you end up with TWO HOLES(50%+ 50%), now the particle's 100% is divided equally into both holes, you have really devided the probability into equal halves.

    There are certain other things that have to be taken into considerations, like if you keep deviding the original hole into OTHER holes, what happens when you reach a point where the original hole meets up with all the other divided HOLES? you have increased in magnitude the probability of there becoming a single hole again, albeit a bigger hole than the original, you have created a bigger EVENT SPACE, now certain quantites can TUNNEL through area's that have no holes at all, this is based upon Probability of quantum potentials, and proximity (MAGNITUDES) play important roles for near and far off events.

    The important thing for what you are trying to understand is the initial setup (single particle + one-hole) is a fundemental setup, even for the photon, by introducing another hole, you are giving the photon another option, which it gladly accepts, by giving you the effect of going through both holes, at the same instant!

    One can state that the inteference is the INTRODUCTION of another hole!
     
  9. Feb 12, 2004 #8
    Ok, there's been a lot of good information going around so far, but from what I can tell the best answer to Rabbit's question is that we don't know. We don't know why only one photon still behaves as though it is being influenced by wave interference. Some assume, but there is no commonly accepted truth.

    The most commonly accepted theory is that even a single photon is still a quantity and can still be divided. As long as the photon is not observed, it can maintain a quantum superposition of all possible paths that the photon may travel. When the photon reaches the wall or detector, it is 'observed' so to speak and is reduced to 'normal' physics. This is required in order for the photon to interact with the matter that it hits, otherwise it would remain in a superposition of all possible states. So, in a manner of thinking, the partice is interfering with itself, the same way a wave that splits around a rock and merges again is interfering with itself.

    Another theory says that there is a standing field of 'virtual photons' which interact with the single photon the same way that other photons would, which eliminates the need for quantum superposition to come into play. In this case the photon is not interfering with itself, it is interfering with the virtual photons.

    There are probably other theories too.
     
  10. Feb 12, 2004 #9
    We don't know

    The best answer is that we don't know. A more accurate one would be to say that we have several possible answers, most of which contradict each other and no way of telling which one is right at the moment. Here are some of the answers that have been proposed (it is incomplete as there have been many):

    1. Instrumentalist approach: We don't know and we have no way of knowing. Quantum mechanics is simply a formalism for describing the probabilities that various measurement results occur and it always gives consistent answers. If you add some philosophical mubmo-jumbo to this then you get the Copenhagen interpretation.

    2. Everything is a particle, but there is some kind of weird force that acts on particles to make them follow strange trajectories. The weird force (called the quantum potential) depends on the entire setup of the apparatus and is highly non-local. The most famous explanation of this type comes from Bohmian mechanics.

    3. Waves are real and particles are not, but there is a real physical mechanism that causes the waves to "collapse" in certain circumstances and behave like particles. There have been many proposals for what this mechanism is, but most of them disagree with the predicitions of quantum mechanics. However, the differences can be very small and it is possible that we haven't detected them yet.

    4. Everything is real, a.k.a. the many worlds interpretation. The wave-function of the universe is the only real thing and everything, including the experimental apparatus and you has to be included in it. When a "measurement" occurs and you look at the outcome, the universe seems to split into two pieces. This is very popular with popular science writers and science fiction writers because it is easy to explain, but most physicists can find many problems with it.

    5. None of the above (re-open nominations): Either the question is unsolvable by physics, or the answer will come from some combination of deeper theories, such as quantum gravity and quantum information. These theories take a radically different view of what the universe is like, so they may solve the problem or at least explain why the question has no answer.
     
  11. Feb 12, 2004 #10
    RR, on my website below (at "P-Duality: Quantum Mechanics Inside-Out") I speculate that quanta have both an exterior and interior phase space that interfere with each other. Usually phase space, a mathematical arena for representing dynamics, is considered by quantum mechanics to have a "granularity" minimum of Planck's constant (h) magnitude. So, we have particles and their actions (energy X time or momentum X displacement) no less than ~h.

    My hypothesis states that phase space exists also in reciprocal form, with actions less than ~h. This inverse phase space inhabits particles and enables them to exhibit properties mutual to and unique from conventional phase space, like interference and novel energy states. I surmise that such interference produces fermions, photons and gravitons.

    Remember, inverse phase space should be treated at the moment as pure speculation, but I believe it to be at least equivalent to other interpretations in explaining these phenomena. Sorry for the information overload.
     
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