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Matter waves are oscillations in what medium?

  1. Nov 8, 2009 #1

    I have been thinking as everything being particles and only appearing wavelike in double-slit experiments because they were in superposition.

    Now I am reading that they are really only waves. Waves in what medium?

    Last edited: Nov 8, 2009
  2. jcsd
  3. Nov 8, 2009 #2
    In space, of course.
  4. Nov 8, 2009 #3
    But aren't waves just vibrations of matter?
  5. Nov 8, 2009 #4
    Not always.
  6. Nov 8, 2009 #5
    But then what are waves?
  7. Nov 8, 2009 #6
    Image patterns. Any complex system needs many points to be visualized. Sometimes images have interference patterns, sometimes not.
  8. Nov 8, 2009 #7
    If you really wish you can give this medium a name. However scientists are fine with just seeing it as abstract numbers. They say the waves are described by the wavefunction.
  9. Nov 8, 2009 #8
    Which describes a space of events.
  10. Nov 8, 2009 #9
    Matter waves are not vibrations at all. They are crests and troughs in the probability that a detector would detect a particle in each region of space.
  11. Nov 8, 2009 #10


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    They are waves in configuration space, not to be confused with ordinary space.
  12. Nov 8, 2009 #11
    Okay, according to the replies I am reading, it seems they are not really waves in anything? But that "wave" just refers to the way a graph of the probable location of a particle?
  13. Nov 9, 2009 #12
    I see articles about matter waves being used in quantum wave optics, being amplified and used in atom lasers etc. How then can these waves still be considered 'abstract', 'not in real space' or whatever (see for example the references mentioned http://www.iop.org/EJ/abstract/0953-4075/33/19/001")?
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  14. Nov 9, 2009 #13
    If someone could explain this they would be answering questions from a great many people.

    There is something very wrong with the illustration of double-slit experiments shown in every book and article.

    They show a top view of the experiment with waves heading towards the screen. Waves in a plane as shown would create a horizontal wavy line on the screen, not the vertical lines produced in the experiment by particles hitting the screen.

    I can imagine how a spray of particles would create vertical lines but not waves.

    Can someone please correctly illustrate what is going on between the holes and the screen?
    Last edited: Nov 9, 2009
  15. Nov 9, 2009 #14


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    The idea of a wave has a specific meaning in physics and mathematics. In normal nomenclature though, most people only think of waves as physical disturbances, vibrations or displacements of matter of a medium.

    When we talk about waves in physics, we mainly are talking about a phenomenon that has certain characteristics. Like periodicity and phase. The properties of phase are important because it allows for interference to occur. These properties apply to physical waves like sound or water waves that we are used to dealing with in the macroscopic everyday world. But a lot of the underlying properties and mathematics that give rise to these phenomenon also occur in the mathematical, abstract, of physics.

    For example, light is composed of electromagnetic waves. However, the oscillations and phase properties are contained in the electric and magnetic field components. There is no physical perturbation here. Matter waves are even more abstract. While with electromagnetic waves we can measure the electric and magnetic fields, we cannot measure the direct properties that make matter waves, waves. We can only observe the consequences of their wave properties. These consequences arise in the probability density of events, described by the wavefunction. We can't measure the wavefunction directly, but we can measure its influence on where a particle can be found for example.

    The idea of a wave picture is just an abstraction of the wavefunction. Most people can understand the double slit experiment with photons. They understand that light is an electromagnetic wave and so they think of it in that context In a more accurate description, we could say that light is a field that permeates space and the photon is a quanta of that field. Whenever the field interacts with something it does through the photon particle, a quanta of energy/momentum. We can only concretely talk about quantum mechanics when we make a measurement, force an interaction. From the time that light is created at a source and hits the detector in the double-slit experiment, we cannot really say what form it is or what it is doing. To make a measurement to determine such information changes the final results, preventing us from "observing" the desired states.

    So in quantum field theory, one way is to think about light being a field. Whenever this field interacts, it does so by the photon quanta. A matter wave is also a field that interacts via its quanta. Except now its quanta are electrons or positrons. There is an electron field, not unlike the electric and magnetic fields (though we describe them with more primitive forms), and whenever the electron field interacts, it does so through a quanta called the electron.

    Somebody has posted links to some papers that suggest teaching this idea at the offset to help clear up the confusion over the matter wave, particle-wave duality stuff.

    Take a look at Art Hobson's papers on the idea:

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  16. Nov 9, 2009 #15
    Born2bwire, thank you very much for your helpful reply and links.

    I understand that we cannot directly measure what is between the emitter and the screen, but that we can infer it.

    I am wondering why the same so obviously flaw diagram is used over and over to show the experiment. The wave clearly does not match the pattern on the wall. The wave iisn't even touching where most of the particle hits are. The illustration is incomplete.

    When I see an illustration for something such as a photon, it is accurate. It shows perpendicular oscillating electric and magnetic fields. I am trying find an illustration showing graphs the shape of the wave.

    For simplicity, lets just focus on a object such a one electron emitted in superposition. Can you explain what an illustration of what that would look like? Once I known the shape of that I can combine multiple ones in the double-slit experiment. I am guessing it radiating outward in a sphere? What and where exactly are the compressions and rarefactions or peaks and troughs or whatever they are that interfere and cause the electrons to hit the wall in pattern of vertical lines?

    I wish someone would create an accurate 3D illustration instead of one I see everywhere that doesn't make sense.
    Last edited: Nov 9, 2009
  17. Nov 10, 2009 #16


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    The problem is, we can't say what happens between its creation and measurement. That's a whole stickling point when it comes to interpretations of quantum mechanics. Some physicists will just completely ignore the idea, since we currently cannot define what happens we do not worry or attempt to define it. We can describe how an ensemble of measurements will look like. We can talk about what will happen when we observe.

    So the wave drawings are a representation of the wavefunction, a representation of what we will find should we make measurements over identical systems at that spot. Even the electric and magnetic fields are not exactly correct when thinking of the photon. The basic elements of the electric and magnetic fields are the potential fields. The measurement of the potential is not possible, but we can indirectly measure it in the electric and magnetic fields.

    Anyway, back to your last question. We can't draw anything about the electron except its wavefunction, which is not a true physical quantity. But the wavefunction is not going to represent what I think you want it to.
  18. Nov 10, 2009 #17
    Born2bwire, hello again.

    Just to make absolutely sure you know what I am talking about:
    http://rst.gsfc.nasa.gov/Sect20/photon_double_slit3.gif [Broken]

    1 - Is that plane of semicircles the wave function? I would expect it to be 3D. Doesn't it extend above and below like a radiating sphere? They way they show it doesn't make sense.

    2 - What I am trying to visualize is for example, with an electron, how one of the forces such as gravity is distributed or how the mass is distributed.

    3 - What are the troughs in the waves exactly that prevent the electrons from striking there? Are there areas where an electron can not strike, or just very few?

    3 - Another question, can the interference pattern be explained by a particle being in many places in superposition and it interacting with itself by bouncing and diffracting off the sides of the slits? If you were to plot the all possible paths and how they would alter each others trajectory would it create that pattern? If so, I can forget about the wave idea, and conclude it is just used for the purposes of calculation.
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  19. Nov 10, 2009 #18
    The electrons carry charges, they may interact with the environment differently.
  20. Nov 10, 2009 #19


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    The picture that CosmicVoyager posted is a good picture to visualize how this happens with waves like light or water. The two-dimensional representation is perfectly valid, just imagine that it extends infinitely in the vertical directions (we assume that the problem is invariant in the normal direction). Why this is a good representation for water waves and a bad one for matter waves is that it makes you think in terms of casuality.

    The water wave is produced at a source, continually for this to occur properly, and we can watch the wavefronts propagate out, through the slits to produce secondary "sources" and finally interfere in constructive and destructive interference. This is nice and perfectly physical. However, this is not the same with quantum field theory waves. When we analyze the double slit problem, there is no propagating wavefront. The wavefunction, that encompasses the wave behavior, is time-independent, it does not propagate out like a true wave. This picture is good for conceptually demonstrating the intereference of waves, but it has no bearing on how the electron actually behaves between its creation and measurement. Again, we have no real idea what happens, we can only describe what happens at the end based upon initial conditions.

    But how does this interference arise. Well, we cannot give it a true physical explaination, but we can explain it in terms of the wavefunction. The probability density can be defined as
    where \phi is our wavefunction (I'm going out of a Feynmen text, normally we use \Psi). Let's say we take our double slit screen and cover a single slit and make measurements. In this case, we get a diffraction pattern denoted by P_1, \phi_1 and P_2, \phi_2 where 1 and 2 denote the slit. Now, what is the final probability of both slits uncovered. This is simply the superposition of the wavefunctions. Thus,
    [tex]P = |\phi_1+\phi_2|^2[/tex]
    This will incorporate the interference because the wave function has a phase dependence. Points were the amplitude of the wavefunction of \phi_1 and \phi_2 are the same but the phase is 180 degrees different will result in destructive interference. What happens if we setup a means to measure which slit the particle actually passed through. We lose the interference and get
    [tex]P = P_1+P_2[/tex]
    This is not the same as before because the phase information has been lost by taking the magnitude of the wavefunctions before the addition.

    Just ignore MikeW. He's going to be annoying for a while. He was on earlier in a different name posting his spam.
  21. Nov 10, 2009 #20
    Feynman is right, a particle makes a field (presence of charge makes EM field which has an electric component in the rest frame of the particle), the field acts on another particle (other charges feel forces when in this field), the field has energy and momentum (think of the energy of a photon, a quanta of the EM field). Nothing is new here, just someone misinterpreting commonly understood particle physics/electrodynamics.

    He is essentially saying you can think of the EM field in terms of photons, nothing to do with electrons being part of the field!
  22. Nov 10, 2009 #21


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    It's just a picture. It's a 2D cross-section. For that picture to be correct though, the slits and source must extend to infinity along the vertical direction. When I mean it is invariant in the z I mean that the problem is the same at any given vertical point. That would make these cylindrical waves. We could do a point source sure, but then the displayed image they have there would be truncated in the vertical direction. Doesn't matter, just a trivial note.

    But there are no oscillations. The fields for a matter wave do not have oscillations in space-time like an acoustic or water wave. The phase property is purely in the wave function, which is not a description of any physical process or property.
  23. Nov 10, 2009 #22
    Okay, do I have this correct?

    - In the illustration, unlike the points of the screen, the wave shown is not a real wave but "representation of what we will find should we make measurements over identical systems at that spot?"

    - We do not have "true physical explanation" of what causes the interference?

    - If we calculate all possible paths that a particle could take including the effect it's counterparts in superposition would have, we would *not* get the interference patten on the screen?

    The source of so much confusion and people not understanding is saying that objects are sometimes particles and sometimes waves as though both were physical things you can measure. It is not a wave, that is it is not something oscillating in space. The wave referred to is a "wave function". There is an inconsistency in the illustrations in that the screen can be an actual photograph of the screen, while the "wave" is an abstract graph.

    I want to create a better illustration. Nothing in the usual ones indicates probability, especially if extending the waves vertically would create cylinders and not spheres. Maybe colors can be used to indicate intensity or higher probability.
  24. Nov 10, 2009 #23


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    Maybe something like this, in which the density of dots indicates relative probability?

  25. Nov 10, 2009 #24
    I mean coloring the waves to indicate probability of finding the particle there.

    If it existed I wouldn't be writing about it, LOL. I have looked through hundreds of illustrations. I am trying to correct a problem that causes much confusion.
  26. Nov 10, 2009 #25
    I hope I can clear this up. In my university I'm in a course which introduces this topic.

    When we say things like "the wave is not a real wave", this is trying to illustrate the fact that nothing is waving in a left-right, up-down, or forward-backward fashion. However we observe wave properties in the phenomenon, and so we know that these objects which we would like to call particles also have wave properties. What properties I don't remember exactly, but phase, wavelength, frequency, energy, and interference are quite important.

    And in fact, we do have a physical explanation for interference. We should go back to the idea that the diagrams in textbooks are wrong. If they explain that the interference shape is a graph of Probability of the electron hitting that place in the wall, they're not wrong.

    If you conduct a double-slit experiment, you're basically watching over a given period of time, how many electrons hit the wall, and where they hit the wall. Assuming the two slits are separated in the horizontal direction, you will find they form vertical bands on this wall. Imagine they were paintballs hitting the wall. You could look at the bright band in the middle and say "paintballs are very likely to hit here", and you could also look at the dry spots on the wall and say "paintballs never hit here". Basically the brightness of any point on the wall is related to the probability of the electron striking that point.

    The physical wave interpretation is this: The wave out of hole 1 is mixed with the wave out of hole 2. When those waves hit the wall, they have to add together. If the waves are in phase, the interference is constructive and we see a bright band. If the waves are out of phase, we see a gap between the bright bands - i.e. darkness.

    To tell where the waves will be in phase and out of phase, just look at the criscrossed wave pattern in the picture you posted. Anywhere in the pattern of white lines you see an X, or the center of a diamond-shape, the waves are in phase at that location.

    When we say we don't have an explanation for what causes the waves, this refers to the fact that quantum mechanics is just a description of the behaviour of matter at this scale, but does not explain the origins of these behaviours.

    Correct. However this is where it begins to deviate from the way we understand the world. A lot of experiments designed to tell the path the particle took in the double-slit experiment reached a problem: If you do anything that should give away the path, the interference pattern disappears. At that instant, the interference pattern will be replaced by a wide bright smear, centered on the most likely point the particle should impact.

    Another related consequence is that if the electron gun's rate of firing is slowed down so much that it only shoots one particle at a time, giving the experimenter time to see where each particle hit, the probability of the electron hitting any spot on the wall STILL follows the interference pattern.
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