Quantum Paths: Third Lesson

In this lesson we see the first practical application of these paths and phases, the double slit expirement. History on double slit here.

In this simulation we are actually examining two different processes that are linked together. As the electron goes from the source to a final point on the screen it can go through either the left or the right slit. If we block either one off we can a roughly flat distribution. So, if we have both slits open, we would expect that we would again get a roughly flat distribution. In fact, we get regions of zero probability interwoven with regions of unusually high probability. The reason for this lies at the heart of quantum mechanics, the phase which we have spoken about so much before. Individually, the phases for the processes through each slit are irrelevant, but when two processes of the same probability have different phases the probability of the two processes put together is not a linear sum of the individual probabilities. The phase dictates how probabilities add.

If the phases for passing through each slit are the same, then the two vectors line up and the total probability it at a maximum. If, however, the phases correspond to vectors in opposite directions, the vectors will cancel out and we get a region of zero probability. Even thought there are some paths to that particular point on the screen, the sum over all the paths perfectly cancels out to leave a zero probability for that point. This is how we know about phase and why it is so important in quantum mechanics.

Additionally, we should note that we can't say which slit the electron actually travels through. In fact, it is essentially as if the electron simultaneously travels through both. Yet, what if we look at the electron to see which slit it travels though, with a photomultiplier perhaps. Then the quantum mechanical interference breaks down, and we get the flat distribution we got from blocking off one of the slits. In essence, if we force the elctron to actually pick a slit, it can no longer interact with paths through the other slit. These thoughts lead us to two of the major ways in which quantum mechanics violates our physical intuition. First off, by looking at or observing something we actually change it. That is, we can't speak of a physical reality independent of observers. Secondly, as has been mentioned before, we can't actually say through what mechanism a process occurs, the reason being that in fact all of them occur simultaneously.

One final point to note as you play with the simulation below is how the distance between the slits affects the probability distribution on the screen. As you make the slits farther apart, does the length ofthe vector oscilate slower or faster?

Click anywhere on the display in the upperleft corner to select an endpoint on the screen. Click the "Left" or "Right" buttons to have the point on the screen move in the corresponding direction, and press "Stop" to stop the movement. The "Block Left Slit" and "Block Right Slit" buttons can be used to open and close the left and right slits respectively. The "Closer Slits" and "Farther Slits" buttons can be used to change the distances between the slits by either clicking once or clicking and holding. Finally, the "Show Path Vectors" button toggles on and off whether the individual path vectors will be displayed or just the final vector for the process.