Let us assume that we are studying the position of a light photon traveling in space. We've shown that this photon has a wavefunction as introduced by Schrodinger equation. The wavefunction peaks at the position of the photon. Now if this photon encounters a half-silvered mirror, tilted at 45° to the light beam (a half-silvered mirror is a mirror, which reflects exactly half of the light, which impinges upon it, while the remaining half is transmitted directly through the mirror), the photon's wavefunction shall splits into two, with one part reflected off to the side and the other part continuing in the same direction in which the photon started. The wavefunction is said to be "doubly peaked." Since each "part" of the wavefunction is describing a position that may be light-years away from the other position given by the other "part" of the wavefunction, we can conclude that the photon has found itself to be in two places at once, more than a light-year distant from one another!
Someone might say that this previous assessment is not real. What is happening really is that the photon has a 50 percent probability that it is in one of the places and a 50 percent probability that it is in the other? No, that's simply not true! No matter for how long it has traveled, there is always the possibility that the two parts of the photons' beam may be reflected back so that they encounter one another, for a much awaited "reunion". If it was a simple matter of probability, the photon would be either on one position "OR" the other, and there would not be any need for "reunion" with the other probability.
So as long as there is any possibility that the wavefunction will be reduced to one peak again (as it was before the photon hit the half-silvered mirror), the photon in question shall behave as one photon in two places at the same time!

In the experiment presented here, a light beam encounters a half-silvered mirror angled 45° to the light beam, splitting the beam into two. The two parts of this light beam is brought back again to the same point (where a second half-silvered mirror is placed) by using a pair of fully-silvered mirrors .Two photocells (A & B) are placed in the direct line of the two beams in order to find the where about of the examined photon. What do we find? If it were merely the case that there were a 50 % chance that the photon followed one route and a 50 % chance that it followed the other, then we should find a 50 % probability that one of the detectors registers the photon and a 50 % probability that the other one does. However, that is not what happens. If the two possible routes are exactly equal in length, then it turns out that there is a 100 % probability that the photon reaches the detector A, lying in the direction of the photon's initial motion and a 0 % probability that it reaches the other detector B (the photon is certain to strike detector A).

What does this tell us about the reality of the photon's state of existence between its first and last encounter with a half-reflecting mirror? It seems inescapable that the photon must, in some sense have actually traveled both routes at once! For if an absorbing screen is placed in the way of either of the two routes, then it becomes equally probable that A or B is reached; but when both routes are open (and of equal length) only A can be reached. Blocking off one of the routes actually allows B to be reached! With both routes open, the photon somehow "knows" that it is not permitted to reach B, so it must have actually felt out both routes.