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.