User:Anthony/Double slit

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http://physicsweb.org/articles/news/9/3/1/1

Keeping this here to work on until the actual paper gets published.

First of all, if you don't know the classic double-slit experiment, read Double-slit experiment. In the classic experiment, we send something (a photon, an election, whatever) through two slits, and plot the number (of photons, electrons, whatever) vs. the position. Now due to the uncertainty principle we know that \Delta x \Delta p \ge \frac{\hbar}{2} , where Δx is the uncertainty of position, Δp is the uncertainty of momentum, and \hbar is a constant (see Planck's constant for more info). So we can derive the formula λ/s=x/D, where λ is the wavelength (of the photon, or the de Broglie wavelength of the electron), s is the slit separation, x is the fringe width, and D is the distance of the slits from the screen.

Now in this new experiment, we send a photon which has a wave consisting of two maxima and one minimum into a cloud of atoms. An electron may be emitted from the cloud and sent to the screen, and we measure the time it arrives at the screen. This electron could have been emitted from the first maxima or the second maxima (ignore the minimum as those electrons get sent to the other screen). If we plot the number of electrons vs time, we should see the exact same interference pattern as with the plot of number of electrons vs. position that we see in the classic experiment ([1], [2], [3]). And the uncertainty principle can also be expressed as \Delta E \Delta t \ge \frac{\hbar}{2} , where ΔE is uncertainty of energy and Δt is uncertainty of time. So now we should find that E/s~x/D (I'm not sure if this is right, and not sure if I'm missing some constants so I used proportional rather than equal here). E is the energy of the photon, s is now the difference in time between the two maxima, x is still the fringe width (though it's now measure in units of time), and D is still the distance between the screen and the (in this case cloud), but I suppose you have to measure the distance in time (the time it takes the electron to travel that distance).

Anyway, this is all a guess, since the actual experiment doesn't seem to be found. If someone sees a glaring problem, please add it to the talk page, or just edit this directly.

  • Fraunhofer pattern