A Second Peek at Quantum Mechanics: The Double Slit Experiment

 

The double slit experiment is justifiably considered among the most simple, elegant and profound experiments in science.

In this experiment, we show first that light acts like a wave. This was first done two hundred years ago.

To see this you need to know that waves in the same place interact by adding up together. This is called “interference.”

If you take the peak, or crest, (the highest part) of one wave and add it to the peak of another wave, that is, if both waves (whether water or light or a mathematical wave on paper or in computer bits) are in the same place, you get a peak that is the sum of both waves. That is, the combined peak is as tall as both wave peaks added together. If the two waves are the same size it is like adding +1 + 1 to get +2. Similarly the troughs (the lowest part also add up to get deeper troughs, like adding -1 and -1 to get -2. So add two waves of the same size in the same place, perfectly aligned, and you get a wave that is twice as big (both peak and trough).

If you add the peak of one wave to the trough of a wave of the same size aligned in the same spot, they cancel each other out.  Adding the peak and trough of waves of the same size that are aligned peak to trough, it is like adding +1 (the peak) and -1 (the trough) to get 0.

There are also times where there are in between parts of the wave or waves of different sizes where the + and – numbers may not be the same, or cases where waves of the same size  are not exactly lined up. In fact it gets quite complex and to do it right you need calculus (Fourier analysis). A simple example is shown in the image below. The red wave is what we would measure or  “see” (say if these were visible light waves, or hear if they were sound waves) by adding the two smaller gray waves. this may be easiest to see where the two grey waves cross in the middle of the illustration; that point in the center where the gray waves cross is half the height of the red wave at that location.

 

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So waves in the same place add up (constructive interference) or subtract from one another (destructive interference).

The set up for the double slit experiment  is a board with two small slits. Send a light through only one of the slits, and you will see the light in a pretty discreet area approximating the slit on the wall opposite the slit. Same would happen if you send light only through the other slit. Like a flashlight through a window. Now open both slits. You get a pattern of bars of light and dark because waves from the two slits interact. Where crests of the two waves hit the wall at the same time, they add up to a bright spot. Where the crest of one wave and the trough of the other wave lines up they cancel each other out.

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This image shows how the series of waves wave to the left hits the wall and then part of the waves go through each slit. After going through the slits the waves radiate out in ever larger concentric circles, the two now expanding waves overlapping as they progress to the right.

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In this  schematic we are looking down on the experiment, with the peaks of the complex wave on the right labelled “wave intensity” indicating where the peaks of the two expanding waves overlap after passing through the two slits and would be seen as bright areas on the wall opposite. Note that the brightest, or highest, peak is in the middle of the area labelled “wave intensity.” This highest/brightest peak is BETWEEN the areas of the wall opposite the two slits. This is exceedingly strange in that when allowing light to go through either one slit or the other, this area would have had little light.  The light from the individual open slit would have been either to the right or left of this central area, across from whichever single open slit the light went through.  This is like shining flashlights through each of two windows and finding the brightest light on the opposite wall not across from each of the windows but between the spots on the wall where the light from each window would hit the wall. This drives home show different light coming from two slits is from just combining light from two slits. It really can only be explained in terms of waves.

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This image shows what you see in an actual experiment using red laser light. The top image is what you see with one slit open,the slit to the right,  a somewhat smeared out single spot. The bottom image shows the interference pattern with the two slits open, again with the brightest spot in the middle and other spots extending way to the right and left of where the light was from the individual open slit.

Now, light is also a particle.

If you send one photon (the smallest discrete unit of light) at a time through a double slit and have a VERY sensitive device  opposite the slits that will register one photon at a time, you will see individual pings, individual particles, in discreet areas. If you have one slit open, the pings will be all in the area opposite that slit. Open both slits and you still just see individual pings, but over time they will form the same interference pattern as the waves of light did. Of course the waves of light were made up of vast numbers of photons, but sure, they could in aggregate act as waves; maybe each has “waviness” that becomes a property of the whole when they are together like that. Maybe it is an “emergent” phenomenon of vast numbers of photons interacting.

Nope. We can send one photon or other particle (or atom or even collection of atoms) through the slits at a time and see that isn’t true.

 

 

 

 

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In the top image we see schematically one green particle (atom or photon or “Bucky ball” molecule of dozens of carbon atoms) is going through at a time through two slits. Again, we would expect, if they are like little pellets, to result in a pattern we see here with two bars indicating that the pellets hit the screen opposite the slit they went through. But what happens is that over time they form the interference pattern just like a wave would even though one particle at a time went through one or the other slit. Note that in the lower image the bands start with random appearing dots but a patter evolves over time (and we see bands here that are oriented horizontally; just make it vertical in your mind if that confuses you; if it were the experiment with the green pellets/particles these bands would be vertical of course; or you can picture one horizontal slit above the other instead of next to each other. I’ll update this later with better diagrams) In panel a there are a few seemingly randomly placed white”hits” on the detector (here the photons register ass white against the black background). Similarly in b there is little to no pattern yet despite hundreds of hits. But c-e show increasing refinement of the pattern and loss of apparent randomness.

Here is the really cool part. The part that has physicists, mystics, Zen teachers and philosophers buzzing. It doesn’t matter how much later the next particle (or atom or molecule) goes through. Or when then the next one after that goes through. You can wait an hour or a year between particles if you are patient enough. And they don’t form the pattern in a way that is predetermined. Each time the order and location of the individual pings will be different: just where the first, and second, and trillionth particle lands won’t be the same in subsequent trials, but however random it seems, they will land so that the wave interference pattern forms.

Like with our spin L and R adding up to no horizontal spin over time when we send U or D particles along in the post of our first peek at quantum mechanics, we again see that our idea of time space and object permanency is a bit, really quite a bit, off. Where does the pattern reside?  How does an abstract mathematical function, a wave, translate into the behavior of particles, which themselves are energy patterns? How does each particle “know” where it is needed to be to keep the pattern?

It even gets better. If you measure, in any subtle way, which particles go through which slit, you lose the wave interference pattern. The act of observing changes it! The magic is gone, the particles lose their “memory.”

Physicists have been debating for a hundred years what this means. For now, let us just savor it.

 

(PS I will keep working on this to make it clear as I can with more illustrations and less repeating, but I thought worth getting it down and seeing what is clear and what isn’t to people)

 

 

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