In the most common demonstration of wave particle duality, the two-slit interference effect, there is a simple equation which governs the observations of interference. n*(lambda) = d*sin(theta) lambda = wavelength theta = angle from normal d = slit separation In the far field approximation, we get sin(theta) = theta so that n*(lambda) = d*(theta) This analysis is equally valid for photons (optics) and for electrons. Let's consider the case of electrons falling on a distant screen from a two-slit aperture. The electrons are measured in interference fringes that are governed by the above equation. Now, consider adding one simple change to the preparation, we put a mechanism (a loop, a plate , etc.) in front of one slit that causes a delay to one electron pathway. As long as the delay is the correct length (1/2*lambda) then the delay will cause the interference pattern to change the position of its constructive and destructive interference fringes on the screen. This will lead to an exact inversion of the current interference pattern, the destructive interference will be where the constructive inteference was and visa versa. So the average change in position of the electrons on the screen is equal to one half of a fringe spacing (1/2*d*theta). Here is my question: If there is an average displacement of 1/2*d*theta for all electrons in the interference pattern, what was it that caused this displacement? Remember, electrons are massive particles, so in order to get an electron to move a distance of 1/2*d*theta we must have put energy into the system somewhere which causes this displacement. Where is this energy comming from? How is this displacement caused by the simple insertion of a phase delay (which inputs NO energy into the system)? Ah Hah. Look's like I've got you this time!
There's energy provided by a solenoid, but the electrons aren't consuming it. See Ehrenberg and Siday's 1949 paper "The Refractive Index in Electron Optics and the Principles of Dynamics". Here's a screenshot from it: View attachment 6321 See figures 2 and 3. An ordinary lens can refract photons, but it doesn't give them any energy. It's similar for electron optics.
Well, you say half the electrons go this way, and the other half go the other way. the only thing I can think of that affects electrons are conductors and things it interacts with. if it was something other than a conductor or something that affects electrons, then you would have a fallacy.
