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Thread: Double Slit Experiment

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    tom
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    Default Double Slit Experiment

    Is there a need for the wave function collapse to explain the double slit experiment? The way I was looking at it today that the photon goes through both slits and that is just how it works on the quantum level. lets say 50%(probability ) goes through slit A and 50%( probability ) goes through slit B and since they are waves they interfere with each other as they interact with each other.

    If we force the experiment to show that it is either in A or B, that is if we want to see where it is with 100% certainty then by our experiment we need to trap the entire superposition and that is why the experiments show that the photon goes through one slit or the other.

    Is this a valid way to look at it, if not please offer other suggestions.

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    Default Re: Double Slit Experiment

    The photons don't interfere with each other; the photons slits interfere with the photons (more precisely with the fields/atoms at the surfaces of the slits), which re-direct the energy of each photon from its original path configuration at the source. Probability is necessary since one can't precisely observe this interaction because of the uncertainty principle. (One can model the fields in the slit openings as well, or some combination, but the ultimate analysis is simply based on interference "waves" in which these probabilities are characterized as photon densities on the focal plane in terms of linear system theory ....

    One can see interference in water waves in a similar experiment, but one can't see the molecules comprising the waves. Nevertheless, the interference at the slits is linear, and the pattern would be observed even if one sent a single water molecule through at a time (provided the source configuration satisfied linear constraints similar to those for photons).

    (ultimately it is because EM is linear and the masses/fields of the photons/water molecules are invariant (and identical all particles are identical for a given experiment), as well as those in the slits)

    (Changing the slits and/or the frequency/masses changes the interference patterns as well as the angles of impact and the slit size (geometry) and separation.)

    (Would there still be an interference pattern if the slit surfaces were perfect absorbers with no surface fields?)

    I think, anyway, YMMV...
    Last edited by BuleriaChk; 10-14-2015 at 08:01 PM.
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    Default Re: Double Slit Experiment

    The experiment has actually been done where the photons only pass the double slit one at a time. An interference pattern is still built up. Slowly, but surely, one dot at a time.

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    Default Re: Double Slit Experiment

    Quote Originally Posted by grapes View Post
    The experiment has actually been done where the photons only pass the double slit one at a time. An interference pattern is still built up. Slowly, but surely, one dot at a time.
    Yes this is actually what I am talking about. I dont believe that the photon goes through one slit or the other. I believe that it always goes through both. Then when we try to measure it we cant measure probabilities as we are not quantum attuned. So we create experiments that actually force the photons wave to collapse for our measurement.

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    Default Re: Double Slit Experiment

    I am not sure this has anything to do with Einstein at all, only quantum effects. Basically when single photons are fired at the double slit with equal probability of going through either slit an interference pattern is observed on the other side of the slits. If there is a detector in one slit then there will not be interference.

    Does anyone know the type of detector that they use in the slits? Because if photons in one slit is always being absorbed then of course there will be no interference. But I think that was taken into account, possibly with a beam splitter.

    Quote Originally Posted by BuleriaChk View Post
    The issue is complex, and very much depends on the configuration of the experiment - frequency and coherence length in relation to separation of the slits, the thickness of the slit material, the distance of the focal plane from the slit, etc. One can take a spatial Fourier transform on certain configurations to model interference, but one can also set the configuration so that one doesn't see a pattern at all (e.g., the separation of the slits greater than the coherence length).

    The continuous "wave" characterization is that of space-time with massless electromagnetism where Fourier analysis applies, limited by coherence length which "spreads" the samples due to the convolution process w.r.t. the spatial configuration; the "particle" characterization is ultimately quantum mechanical (photons as particles) where the waves are characterized as particle densities interacting with material in the slits.

    If one does see a pattern *unchanging", one is looking at a space transform (a photon density distribution at the focal plane). If one watches individual flashes, one is simply seeing how this distribution is built up over time (photons considered as spatial samples, with intensity the relative number of samples at any one position and time - which is interpreted as a probability of any one photon hitting a given position as time progresses).

    The actual microscopic mechanisms for this (field interactions at the slits) is very complex, and such a description with infinite precision is impossible because of the uncertainty principle (since it involves mass transfers between photons ("kinetic" mass) and the electrons/atoms/fields in the slit material. These actions are what Einstein called "hidden variables" and by adding the concept of mass (as continuous functions, rather than discrete particles), he was attempting to apply GTR at the local level - a photon as a spherical wave modified by interactions with external field media. But only god can ignore the uncertainty principle in quantum physics (observe without interacting) ....

    (Keep in mind that the prescription E= hv applies to photo electrons ejected from a surface (flat or spherical atom), not to changes of state within the atoms themselves (that just eject photons). Nevertheless, these changes in state can be caused by external field excitations impinging on the atoms. So within the atom, one can think of the electrons as changing its effective mass to account for the energy radiated (plus a neutrino to account for the change in the nucleus for a single atom, as opposed to an averaged response from a change in the Fermi level in a material (solid state) lattice) subject to the impinging photon field.

    (That said, observing changes of state caused by electrons within atoms involves comparing them to unobserved states (initial and final conditions) which depend on the relation of electron to nucleus, so in is ultimately a circular description at the Higgs level....

    Bottom line: it actually gets very complex indeed when one tries to characterize the "hidden variables", and there is no one model that covers it all. Different models apply under different configurations of the experiment, and even the "Big Bang" model (impulse-response spatial Fourier transform) model fails if the configuration is greater than the coherence length of the signal.

    (and, like all physics, one eventually needs a blackboard to explain things properly...

    One can only apply models in their "scope of validity"....

    IMO, YMMV, etc, etc.....

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    Default Re: Double Slit Experiment

    Quote Originally Posted by tom View Post
    I am not sure this has anything to do with Einstein at all, only quantum effects. Basically when single photons are fired at the double slit with equal probability of going through either slit an interference pattern is observed on the other side of the slits. If there is a detector in one slit then there will not be interference.

    Does anyone know the type of detector that they use in the slits? Because if photons in one slit is always being absorbed then of course there will be no interference. But I think that was taken into account, possibly with a beam splitter.
    There are no detectors in the slits. A detector at the slit would absorb the photon (a "hit") at the slit, not the detection plane). The "focal" (target) plane is the detector; the photons appear individual as splashes one-at-a-time (quantum particles) or as patterns on the plane (probability/intensity distributions) when many particles are absorbed over time.

    Uh, E=hv? The photoelectric (quantum) effect? Single Photons? What Einstein got the Nobel Prize for? (Special Relativity is the foundation of Quantum Field Theory)

    (the "hidden variable" discussion is Einstein rejecting quantum mechanics (specifically Bohr's probability/correspondence principle) as a "complete" theory), and he devoted his whole life trying to find an alternative via GTR.

    (Interference with who and what?..

    (Interference is a wave phenomenon for photons as "probability" waves, since individual photon phases cannot be observed in quantum theory)

    The "interference" patterns in the spatial interference pattern (which is not a function of time at any given instant after the pattern is established) are usually modeled by convolving a train of Gaussian impulses with the spatial configuration of the slits (which can be extended to infinity in the model for a train that doesn't "cut off").

    Note: I had written much more in this post, but we had a power outage that destroyed it at this point. Oh well, maybe it is just as well.... (it involved some philosophy and a lot of QFT and GTR)

    I hope to expand this topic in the thread I started on "Calculus", but still have a few concepts to clarify to myself.... the math is not so easy....
    Last edited by BuleriaChk; 10-15-2015 at 12:59 PM.
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    Default Re: Double Slit Experiment

    Hi, Tom -

    Double Slit Experiment

    (see the section on path-integral formulation)

    I've been trying to think of a clearer way to explain my take on the double slit experiment. There are a couple of points that are sometimes overlooked in the discussion.

    1. The interference pattern at the sensor changes with the color; that is, the frequency (E=hv), and that is, the temperature (since the photons are not interacting via spin polarization, we use Bose-Einstein statistics. For what, though?

    2. The experiment can (possibly) depend on the nature of the materials and the thickness of the slit material (suppose the slit was infinitely thin, and the target plane was a mirror?) So the appearance of the "spots" on the plane corresponds in some sense to the fact that the wave description is no longer relevant, but the distribution of spots is. (The wave function "collapses" when the photon hits)

    I have to go on my walk, and I don't know if I can get back to this question, but the answer ultimately lies in Feynman's concept of path integrals. The confusion arises because of the aforementioned equation E = hv, i.e. h=E/v If the path length for each photon is measured exactly in terms of wavelengths, then each path will be different at each frequency. Additionally, since h is assigned to each cycle of the "distance", the paths associated with higher frequencies will have higher energies linearly.

    The minute differences in path lengths (each measured exactly in terms of wave lengths) indicates the number of particles with h determined at as a "temperature"; the relative number of wavelengths and their specific h for each path determines the relative intensity at a single point on the target plane.

    (If there were only one path, (an infinitely precise lazer), then the probability (as a relative energy/temperature) would be equal to unity (since the system would have only one path/dimension)

    When one uses a mathematical model to describe the interference pattern, one convolves the physical configuration of the slits with a Gaussian of some sort. (One can also use spatial samples), which is a Fourier analysis that ignores the paths altogether.

    Anyway, I have to get going, but the ultimate answer is that the "Gaussian" used in the convolution is actually the Bose-Einstein distribution in which h has been back-solved so that it depends on the temperature (color). So the "Gaussian" is actually an energy distribution that changes h as a function of color (wavelength), and thus the "path" lengths as measured in terms of wavelengths of individual photons.

    Boltzmann's constant

    Wien's and Planck's Laws

    Hint: experiment with setting the constants equal to 1 or 0 one at a time...

    So for such a distribution, one assumes the source is a blackbody.. or one can think of the source as monochromatic, but the path lengths as measured in photon wavelengths converts the whole system into a blackbody which converts the monochromatic system into an energy spectrum which is resolved (integrated) at each point of contact on the target plane. (Integration of path lengths a la Feynman's path integration)

    Fermi-Dirac statistics take into account spin polarization (if the photon is assumed to have mass), so is not applicable macroscopically. The photons don't interfere with each other. For electrons, one would use F-D statistics, but one would have to model spin interactions with the atoms at each point along the thickness of the slit. No vale la pena....

    Again, each path length is a function of the physical properties of the experimental setup. So the intensity of each spot is the integral of the path-length in terms of wavelength as determined by its color (position in the probability distribution as a function of h(T). For a monochromatic wave, the convolution uses a Dirac delta function as the sampling function (or a train of them, in which case the pattern repeats). There is a cut-off at both the low and the high ends of the probability distribution.

    The physical (atomic) structure of the material can be ignored if one assumes no energy is lost in the interactions at the slit (the material lining the holes are mirrors), and that all the energy of an individual photon is deposited at the point of impact on the target plane.

    This is only a start, and I HAVE to go on my walk, but I'll try to respond if there is any confusion or you need a "fleshing out" of the analysis .....

    Chuck
    Last edited by BuleriaChk; 10-18-2015 at 03:28 PM.
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    Default Re: Double Slit Experiment

    For an even more persnickety analysis, one has to include the thickness of the slit material and the lining of the inner walls of the slit. If the walls of the slit are magic mirrors (so there is no energy imparted to the slit material by the photon), then it might be possible for the photons to bounce back and forth before continuing on their journey to the target plane, which would probably still keep the pattern, but would change its configuration (I'm not sure about this though).

    In any case there would be additional paths to consider, thus changing the "temperature" of the overall system.

    Also, if there IS energy imparted to the walls of the slit, that would also change its temperature, since the photons will have lost energy at each contact. That means the slit material would absorb that energy, so the overall energy of the material (its temperature over time), and the energy of the photon would decrease. Over time there would be equilibrium, and the pattern would be changed (as if the temperature at the source had dropped) Thus the atomic structure of the slit material becomes important, since different energy states in the periodic table come into play, as well as the lattice (sold state) structure.

    Finally, if the photon knocks off pieces of the wall, then the particles would have to be accounted for, both inside the slit material and in the slit itself. This would require a Feynman path diagram, since all photons and particles would need to be accounted for. The infinities in QFT arise because one would have to model the whole experiment to account for all possible paths, in all parts of the model, including the material making up the slit, the material making up the target plane, the particles that were broken off and/or absorbed in all the interactions, all described by creation, destruction, and propagation operators.

    (Obviously one has to make approximations; usually either the Gaussian or Planck's law is enough for all practical purposes.
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    Default Re: Double Slit Experiment

    thanks for sharing this post.

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