1.1: The Double Slit Experiment

What is the nature of light? You may have learned light is electromagnetic waves propagating through space. Also, you may have learned that light is made of a rain of individual particles called photons. But these two notions seem contradictory, how can it be both?

The debate over the nature of light goes deep into the history of science. The eminent physicist Isaac Newton believed that light was a rain of particles, called corpuscles. At the beginning of the nineteenth century, Thomas Young demonstrated with his famous double-slit interference experiment that light propagates as waves. With Maxwell's formulation of electromagnetism at the end of the nineteenth century, it was generally accepted that light is propagated as electromagnetic waves, and the debate seemed to be over. However, in 1905, Einstein was able to explain the photoelectric effect, by using the idea of light quanta, or particles which we now call photons. The consequences of this are explained in the video below

Similar confusion reigned over the nature of electrons, which behaved like particles, but then it was discovered in electron diffraction experiments, performed in 1927, that they exhibit wave behavior. So do electrons behave like particles or waves? And what about photons? This great challenge was resolved with the discovery of the equations of quantum mechanics. But the theory is not intuitive, and its description of matter is very different from our common experience.

To understand what seems to be a paradox, we look to Young's double-slit experiment. Here's the set up: a source of light is shone at a screen with two very thin, identical slits cut into it. Some light passes through the two slits and lands upon a subsequent screen. Take a look at Figure \(\PageIndex{1}\) for a diagram of the experiment setup.

First, think about what would happen to a stream of bullets going through this double slit experiment. The source, which we think of as a machine gun, is unsteady and sprays the bullets in the general direction of the two slits. Some bullets pass through one slit, some pass through the other slit, and others don't make it through the slits. The bullets that do go through the slits then land on the observing screen behind them. Now suppose we closed slit 2 . Then the bullets can only go through slit 1 and land in a small spread behind slit 1 .

Figure \(\PageIndex{1}\): Double- and single-slit diffraction. Notice that in the double-slit experiment the two paths interfere with one another. This experiment gives evidence that light propagates as a wave.

If we graphed the number of times a bullet that went through slit 1 landed at the position \(y\) on the observation screen, we would see a normal distribution centered directly behind slit 1 . That is, most land directly behind the slit, but some stray off a little due to the small amount randomness inherent in the gun, and because of they ricochet off the edges of the slit. If we now close slit 1 and open slit 2, we would see a normal distribution centered directly behind slit 2.

Now let's repeat the experiment with both slits open. If we graph the number of times a bullet that went through either slit landed at the position \(y\), we should see the sum of the graph we made for slit 1 and a the graph for slit 2.

Another way we can think of the graphs we made is as graphs of the probability that a bullet will land at a particular spot \(y\) on the screen. Let \(P_{1}(y)\) denote the probability that the bullet lands at point \(y\) when only slit 1 is open, and similarly for \(P_{2}(y)\). And let \(P_{12}(y)\) denote the probability that the bullet lands at point \(y\) when both slits are open. Then \(P_{12}(y)=P_{1}(y)+P_{2}(y)\).

Next, we consider the situation for waves, for example water waves. A water wave doesn't go through either slit 1 or slit 2 , it goes through both. You should imagine the crest of 1 water wave as it approaches the slits. As it hits the slits, the wave is blocked at all places but the two slits, and waves on the other side are generated at each slit as depicted in Figure \(\PageIndex{1}\). The pFET simulation below shows wave interference. Click on each of the rectangles (Waves, Interference, silts, diffraction) to see difference demonstrations

 

When the new waves generated at each slit run into each other, interference occurs. We can see this by plotting the intensity (that is, the amount of energy
carried by the waves) at each point \(y\) along the viewing screen. What we see is the familiar interference pattern seen in Figure \(\PageIndex{1}\). The dark patches of the interference pattern occur where the wave from the first slit arrives perfectly out of sync with wave from the second slit, while the bright points are where the two arrive in sync. For example, the bright spot right in the middle is bright because each wave travels the exact same distance from their respective slit to the screen, so they arrive in sync. The first dark spots are where the wave from one slit traveled exactly half of a wavelength longer than the other wave, thus they arrive at opposite points in their cycle and cancel. Here, it is not the intensities coming from each slit that add, but height of the wave. This differs from the case of bullets: \(I_{12}(y) \neq I_{1}(y)+I_{2}(y)\), but \(h_{12}(y)=h_{1}(y)+h_{2}(y)\), and \(I_{12}(y)=h(y)^{2}\), where \(h(y)\) is the height of the wave and \(I(y)\) is the intensity, or energy, of the wave.

Before we can say what light does, we need one more crucial piece of information. What happens when we turn down the intensity in both of these examples?

In the case of bullets, turning down the intensity means turning down the rate at which the bullets are fired. When we turn down the intensity, each time a bullet hits the screen it transfers the same amount of energy, but the frequency at which bullets hit the screen becomes less.

With water waves, turning down the intensity means making the wave amplitudes smaller. Each time a wave hits the screen it transfers less energy, but the frequency of the waves hitting the screen is unchanged.

Now, what happens when we do this experiment with light. As Young observed in 1802, light makes an interference pattern on the screen. From this observation he concluded that the nature of light is wavelike, and reasonably so! However, Young was unable at the time to turn down the intensity of light enough to see the problem with the wave explanation.

Picture now that the observation screen is made of thousands of tiny little photo-detectors that can detect the energy they absorb. For high intensities the photo-detectors individually are picking up a lot of energy, and when we plot the intensity against the position \(y\) along the screen we see the same interference pattern described earlier. Now, turn the intensity of the light very very very low. At first, the intensity scales down lower and lower everywhere, just like with a wave. But as soon as we get low enough, the energy that the photo-detectors report reaches a minimum energy, and all of the detectors are reporting the same energy, call it \(E_{0}\), just at different rates. This energy corresponds to the energy carried by an individual photon, and at this stage we see what is called the quantization of light.

ADAPT \(\PageIndex{1}\)

 

Turn down the intensity so low that only one photo-detector reports something each second. In other words, the source only sends one photon at a time. Each time a detector receives a photon, we record where on the array it landed and plot it on a graph. The distribution we draw will reflect the probability that a single photon will land at a particular point.

Query \(\PageIndex{1}\)

Logically we think that the photon will either go through one slit or the other. Then, like the bullets, the probability that the photon lands at a point should be \(y\) is \(P_{12}(y)=P_{1}(y)+P_{2}(y)\) and the distribution we expect to see is the two peaked distribution of the bullets. But this not what we see at all.

What we actually see is the same interference pattern from before! But how can this be? For there to be an interference pattern, light coming from one slit must interfere with light from the other slit; but there is only one photon going through at a time! The modern explanation is that the photon actually goes through both slits at the same time, and interferes with itself. The mathematics is analogous to that in the case of water waves. We say that the probability \(P(y)\) that a photon is detected at \(y\) is proportional to the square of some quantity \(a(y)\), which we call a probability amplitude. Now probability amplitudes for different alternatives add up. So \(a_{12}(y)=a_{1}(y)+a_{2}(y)\). But \(P_{12}(y)=\left|a_{12}(y)\right|^{2} \neq\left|a_{1}(y)\right|^{2}+\left|a_{2}(y)\right|^{2}=P_{1}(y)+P_{2}(y)\).

Logically, we can ask which slit the photon went through, and try to measure it. Thus, we might construct a double slit experiment where we put a photodetector at each slit, so that each time a photon comes through the experiment we see which slit it went through and where it hits on the screen. But when such an experiment is preformed, the interference pattern gets completely washed out! The very fact that we know which slit the photon goes through makes the interference pattern go away. This is the first example we see of how measuring a quantum system alters the system.

Here the photon looks both like a particle, a discreet package, and a wave that can have interference. It seems that the photon acts like both a wave and a particle, but at the same time it doesn't exactly behave like either. This is what is commonly known as the wave-particle duality, usually thought of as a paradox. The resolution is that the quantum mechanical behavior of matter is unique, something entirely new.

What may be more mind blowing still is that if we conduct the exact same experiment with electrons instead of light, we get the exact same results! Although it is common to imagine electrons as tiny little charged spheres, they are actually quantum entities, neither wave nor particle but understood by their wavefunction.The truth is that there is no paradox, just an absence of intuition for quantum entities. Why should they be intuitive? Things on our scale do not behave like wavefunctions, and unless we conduct wild experiments like this we do not see the effects of quantum mechanics. The following sections describe in more detail some of the basic truths of quantum mechanics, so that we can build an intuition for a new behavior of matter.