Hello, and welcome back to MPC! Last week, we analyzed the double-slit experiment with waves. This week, we will continue looking at the double-slit experiment, but with a twist!

Recall from last week’s post our experiment involving a wave passing through a wall with two slits in it:

Figure 1: The double-slit experiment with a wave

More specifically, recall the strange pattern that the wave in Figure 1 forms:

Figure 2: The pattern created by a wave in the double-slit experiment

(image source: http://www.sciencephoto.com/image/157198/530wm/C0094585-Double-slit_Experiment-SPL.jpg)

As we have already described, this pattern is the result of two wave phenomena:

The diffraction of the wave at the two slits

The constructive and destructive interference of the waves

Let’s try something else now. We’ll keep the same setup from last week, but instead of passing a wave through the wall with two slits in it, what if we just fire electrons at the wall?:

Figure 3: Firing electrons at a wall with two slits in it

How many electrons will hit the back wall (i.e. the wall with no slits in it) and where will those electrons land on the back wall?

Based on Figure 3 the answer seems obvious — zero electrons will hit the back wall! This is simply because the electrons are heading straight for the space between the two slits:

Figure 4: The electrons appear to be heading straight for the center of the wall

Not very interesting! However, maybe our experiment is a little too idealized. No matter how hard we try, we cannot make all of the electrons go precisely forward (some will move at an angle; no equipment is perfect). So, because the two slits are so close together, perhaps a few electrons will be able to make it to the back wall:

Figure 5: The motion of the electrons will not be straight forward (each electron’s motion will be slightly angled)

Now, in this case, how many electrons will land on the back wall and where will they land?

We do not know the exact number of electrons that will hit the back wall, but we should expect a few to hit. Moreover, those that do hit the back wall should be hitting it (approximately) in line with the two slits:

Figure 6: Electrons should hit the back wall in line with the locations of the slits on the front wall

In other words, we would not expect an electron to somehow hit the top of the back wall or even the center:

Figure 7: There are some locations on the wall that electrons should not be able to hit

**Note: The blue, dashed lines represent the straight line path an electron would have to take to reach the indicated positions. These lines are crossing through the wall, so an electron should never be able to reach the two illustrated positions.**

In order for an electron to hit the spots indicated in Figure 7, it would have to pass through the front wall — not the slits on the front wall, the front wall itself (see the dashed lines in Figure 7)! Of course, this cannot happen because electrons are particles and particles do not just pass through walls (you can try throwing a baseball at a wall if you want to “prove” this, but do so at your own risk!).

**Note: In a few weeks, we will actually be talking about a situation in which particles can seemingly pass through walls. However, for now, we will not be considering this phenomenon (known as quantum tunneling).**

Alright, so we have established that all of the electrons that do hit the back wall should hit it directly behind where the slits are located:

Figure 8: Locations where electrons should hit the back wall (expectation)

**Note: The red areas are locations where the electrons should hit the wall.**

If you were to look at the back wall in Figure 9 straight on (as is shown for the wave case in Figure 2), you would see something like this:

Figure 9: Locations where electrons should hit the back wall (expectation)

**Note: The red areas are locations where the electrons should hit the wall.**

So, that’s settled!

Or is it? As has been a common theme with quantum mechanics, experiments contradict our expectations. Indeed, scientists found that, when they fired electrons at a wall with two slits in it, the electrons hit the back wall in a variety of places:

Figure 10: Locations where electrons do hit the back wall

**Note: The red areas are locations where the electrons do hit the wall.**

Are the electrons passing through the front wall itself somehow (as is shown in Figure 7)?

That is a possible explanation for Figure 10, but things get more interesting when we look at the back wall straight on (as is shown for the wave case in Figure 2 and the predicted electron case in Figure 9):

Figure 11: Locations where electrons do hit the back wall (illustrated)

**Note: The red areas are locations where the electrons do hit the wall.**

Figure 11 is just an illustrated representation of the pattern obtained from this experiment, but the real pattern would look something like:

Figure 12: Locations where electrons do hit the back wall (photograph)

(image source: http://www.sciencephoto.com/image/157198/530wm/C0094585-Double-slit_Experiment-SPL.jpg)

**Note: In Figure 2, the red lights actually represent light (i.e. that is what you would see on the back wall if you were to conduct the double-slit experiment with waves). However, here, the red lights simply represent areas where the electrons are hitting the wall (i.e. the electrons are not actually generating the light seen here).**

That pattern looks familiar! It looks just like the pattern we got when we passed a wave through two slits (see Figure 2)!

Something strange is going on! The pattern in Figure 2 is a result of two waves interfering constructively and destructively. In the case of Figure 12, though, we just have electrons approaching the wall. Electrons are particles — they cannot interfere constructively and destructively!

Here’s an idea — what if, just how light has particle-like and wave-like properties, so do electrons? Although we commonly see the particle-like properties of electrons, what if electrons are concealing some strange wave-like nature (that involves interference)? This is exactly what we explained two weeks ago with the concept of matter waves. We finally have experimental evidence to back up the strange theory of matter waves!

You may still be confused. For instance, how can electrons even interfere? They don’t have crests and troughs! We’re going to have to dig a little deeper for a reasonable explanation. This is exactly what we will do next week when we start discussing wave functions. See you then!

One last thing: have a great Thanksgiving!

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For more information, be sure to check out these resources: https://plus.maths.org/content/physics-minute-double-slit-experiment-0, http://www.iop.org/news/13/mar/page_59670.html

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