Wave-Particle Duality

De Broglie

Particles like electrons have a wave associated with them. The wavelength with an electron of momentum p will be
λ = 2πh/p. This wave will produce the same interference pattern when you do it with electrons as you did with light. In Newtonian mechanics electron either goes through slit 1 or slit 2. Imagine that in a given time there is only one electron. It cannot collide with itself, and yet it knows two slits are open. So it has such a wave associated with it, and it can go through both slits, and giving the interference pattern. That's the peculiarity of particles; electron also behaves like a particle or a wave. An electron can't go through one particular slit. Imagine putting a light source behind the slit, and you see that electron you catch goes through one slit, and electron which cannot be detected goes through both the slits, and forming interference pattern. Whenever it's not observed it seems to be able to somehow be aware of two slits. We know that light is made of quanta, and each quanta carries a certain energy, and certain momentum. If I want to locate the electron with some waves with some light, I want the momentum of light to be weak, because I don't want to slam the electron too hard in the act of finding it. So I want p to be very small. If p is very small λ which is proportional to 1/p becomes large, and once λ is bigger than the spacing between the slits, the picture you get will be so fuzzy, you cannot tell which slit it went through. To make a fine observation in the optics you need a wavelength smaller than the distances you're trying to resolve, so you got to use a wavelength smaller than these slits. So p should be such that λ is comparable to this slit or even smaller, and then you find the act of observing an electron imparts to it an unknown amount of momentum. Once you change the momentum you change the interference. So the act of observing which is pretty innocuous for macroscopic things (right now all of us are getting slammed by millions of photons,) but for the electron it is not that simple (one collision with the photon is like getting hit by a truck.) The momentum of photon is enormous in the scale of electron. So it matters a lot to the electron. In Newtonian mechanics there is no limit to observe somebody without noticing we can make it gentle by just make the light dimmer, and dimmer. But in quantum mechanics it is not how dim the light is if the light is too dim we can't find the electron cause there are too few photons. In order to detect electron you've got to send enough photons, but the point is each photon carries certain energy, and momentum which is minimum it cannot be smaller than λ=2πh/p which will cause disturbance to the electron collapsing its wavefunction.