Video Transcript

Hello there! Welcome to lecture 31: light quanta!

At this point, we’ve learned an awful lot about light. We’ve seen how it’s emitted, and we’ve seen how it travels through space and different media. Hopefully you’re convinced that light exhibits many wave-like properties. It can interfere, it can diffract, and it can be polarized.

This video will take that understanding of light and turn it on its head. What if light isn’t only a wave, but also a particle? Hopefully this video will show you how light can be treated as both a particle and a wave in different situations. The quantum nature of light is truly fascinating!

Each of the following concepts will be discussed in this video: quantum physics, wave-particle duality, matter waves, the double-slit experiment, and the uncertainty principle.

Quantum physics

In the late 19th and early 20th centuries, scientists began to discover some strange new phenomena that could not be explained using classical physics. By classical physics, I mean the types of physics we’ve discussed so far in this class: physics that uses Newton’s laws of motion, Maxwell’s equations, or thermodynamics to interpret and quantify. These strange effects occurred when doing science on a very small scale: with light, or with small particles such as atoms, electrons, or protons.

The laws of classical physics work great for objects that are larger than atomic-size: we’ve seen a lot of convincing evidence for that in the demos and labs we’ve done over the past 30 lectures! However, a new type of physics needed to be developed to describe the phenomena that occurs on a very small scale. We call this quantum physics.

At the heart of quantum physics is the concept that properties that we consider to be continuous on the macro scale become quantized when things become extremely small. A quantity that is quantized is something that only takes on certain well-defined values. For example, the number of people in a room is a quantized property. There can be a room filled with 40 people, or 28, but not four and a half people. The number of pennies in a jar is quantized, as is the number of atoms in a person, the charge of an atom, or the energy of electrons in an atom, as we discussed in lecture 30.

The idea is that quantum physics can be used to explain all phenomena: those happening on the very small scale as well as those happening on a very large scale. However, because quantum physics is so mathematically complicated, and because classical physics works so well on the macro scale, there is no need to use quantum physics when calculating quantities on the macro scale. Using Newton’s laws is perfectly sufficient when calculating velocity, acceleration, momentum, and other kinematic quantities for collisions that are large enough for us to see with our eyes.

It’s also important to point out that our current theoretical models to understand the universe, whether it be quantum physics, Newtonian physics, or general relativity, are excellent models that have undergone rigorous scientific inquiry and scrutiny. But that doesn’t mean that these models aren’t subject to adjustment and change as we learn more about the universe.

While this lecture focuses on quantum physics as pertains to light in particular, lecture 32 will expand on this for a more general discussion on quantum phenomena.

Wave-particle duality

At this point, we have seen some convincing evidence that light is a wave: diffraction, interference, and polarization are phenomena that would not happen if light was not a wave. Furthermore, polarization indicates that light is an electromagnetic wave.

In 1905, Albert Einstein published a paper describing a phenomenon that had an astounding implication: that light acts not like a wave, but like a particle! This paper was on the photoelectric effect, and the discovery of this effect was the reason that Einstein received a Nobel prize in 1921.

The photoelectric effect is the emission of electrons when electromagnetic radiation, light, hits a metal. By itself, this observation was not groundbreaking. It’s the details of how the photoelectric effect works that upended our understanding of classical physics and the treatment of light as a wave.

In this demo, a piece of zinc has been loaded up with electrons by rubbing it with a charged piece of plastic. Placing the zinc on the electroscope, which we used in lecture 22, visually demonstrates the presence of these electrons. When I shine a UV light source on the zinc, electrons are ejected from the metal and we can tell that this occurs because the electroscope rapidly goes back to its neutral state.

Classical physics predicts that energy is transferred from the light wave to the electron. It predicts that when a sufficient amount of energy is built up, an electron will eventually be emitted from the metal. This predicts that the intensity of light would be the indication of electron ejection. Strong light would eject electrons quickly, and dim light would eject electrons with a time delay as the electrons gradually build up more energy.

We can test this classical prediction by taking that same piece of negatively charged zinc and illuminating it with a bright white light source. If the classical model were correct, this would also cause the zinc to quickly eject the electrons and cause the electroscope to relax back to its neutral state. When I turn on a bright light source, which is much brighter than the relatively dim UV source used earlier, there is no change in the presence of electrons. No matter how long I wait, the electroscope remains negatively charged.

Einstein’s results must have another explanation. The classical model does not hold up here.

The quantum model states that what happens is that the intensity of the light does not matter: the frequency of the light does. Each individual discrete particle of light that hits the zinc has energy given by Planck’s constant times the frequency. These individual, quantized particles of light are known as photons. In this manner, bright light at the frequencies that are lower than a threshold energy will never cause electron ejection, which is what we observed when shining bright white light on the zinc. Each photon of white light was incapable of ejecting an electron, as white light is composed of frequencies of light that are lower than that of UV light.

Similar to the photoelectric effect is the photovoltaic effect. The photovoltaic effect occurs when a photon hits a material and causes an electron to become excited such that it can now cause current to flow. The photovoltaic effect is used to generate electric power in solar farms.

Both the photoelectric and photovoltaic effects indicate that light is a particle. But effects such as interference and polarization indicate that light is a wave. Wave-particle duality is the concept that sometimes, it is not clear that something like light “IS” a wave or “IS” a particle. Both definitions accurately describe the nature of light in different circumstances. Generally speaking, when light travels through space, it acts like a wave. When light interacts with matter, it acts like a particle.

Asking if light is a particle or a wave is like asking if a spork is a fork or a spoon: it’s both! So is light.

As Einstein stated: “It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.”

Matter waves

An interesting effect of wave-particle duality is that not only do things we commonly consider to be waves act like particles, but things we commonly consider to be particles also act like waves!

As with all quantum properties, particles acting like waves occurs on a very small scale. Macroscopically, the wave-like nature of particles is a negligible effect that we can ignore without affecting the outcome of our experiments or calculations. On the atomic scale, the wave-like nature of particles cannot be ignored.

Matter waves were proposed by de Broglie, and we use the de Broglie equation to calculate the wavelength of matter waves. The de Broglie equation states that lambda equals h divided by p. The wavelength of the matter wave is equal to Planck’s constant divided by the momentum of the object.

Let’s do a calculation of wavelength for both a macroscopic object and a subatomic particle so we can get a feel for what scale these wavelengths have.

Consider a 150 gram baseball, thrown at a fast pitch of 45 meters per second. First we can calculate the momentum of the baseball. Remember that momentum equals mass times velocity, and we need to be careful that our mass is in units of kilograms. 150 grams equals 0.15 kilograms. 0.15 kilograms times 45 meters per second is a momentum of 6.75 kilogram-meters per second.

The wavelength of the baseball is Planck’s constant divided by 6.75 kilogram-meters per second. 6.6 times ten to the negative 34 Joule-seconds divided by 6.75 kilogram-meters per second equals 9.8 times ten to the -35 meters. Considering that a baseball has a diameter of 7.25 centimeters, or 0.07 meters, the size of the wavelength of the baseball is essentially zero compared to the size of the baseball itself. In addition, the wavelength of the baseball is so small that we will never notice wave-like effects such as diffraction or interference.

Now let’s consider an electron, a decidedly subatomic object. An electron has a mass of 9.1 times ten to the -31 kilograms, and let’s assume that it travels at 1% of the speed of light, a very fast 3 times ten to the 6 meters per second. The momentum of the electron is 2.7 times ten to the -24 kilogram-meters per second.

The wavelength of the electron is Planck’s constant divided by the momentum, which is 2.4 times ten to the negative 10 meters, or 0.24 nanometers. While this is definitely a small number, it is equivalent in length scale to the wavelength of x-rays. And considering that the radius of an entire atom is much, much smaller than 0.24 nanometers, the wavelength of an electron is definitely noticeable on this length scale.

The double-slit experiment

What experimental evidence might convince you that subatomic particles such as electrons act like waves? The double-slit experiment provides some evidence, and further demonstrates an effect that cannot be explained by classical models of physics.

As discussed in lecture 29, diffraction of waves occurs any time those waves travel through a small opening. If there are two small openings, diffraction will lead to an interference effect leading to bright and dark spots on a screen some distance away. This PhET simulation demonstrates that diffraction interference pattern with light. This is a very wave-like phenomenon.

Experiments have shown that even when single photons are sent through a double slit, the interference pattern continues to be observed on a screen some distance away. This is an effect that cannot be explained using classical models of physics.

We could expect that if objects that are completely particle-like are sent through one or two slits, that they would create an image that resembles the size and shape of the opening, somewhat like spraying paint through a stencil.

It turns out that when electrons are sent through a double slit, they also generate a wave-like diffraction pattern when measured some distance past the double slit. This is not what we would expect if electrons only acted like particles. And just as with single-photon experiments, when electrons are shot through the double slit one at a time, they will, over time, create an interference pattern. Not only do electrons act like waves, but they do so in a way that cannot be explained by classical physics.

The uncertainty principle

Hopefully by now you’re convinced that all objects are wave-like, and that this wave-like property is especially pronounced on the scale of the subatomic. Inherent in all wave-like systems is the uncertainty principle, which theorizes the extent to how well we can know information about related properties. This is not a limitation of current technology, but a fundamental property of wave-like systems.

For example, position and momentum are linked in uncertainty. The uncertainty principle between these two quantities can be expressed as an equation: the uncertainty in position times the uncertainty in momentum is greater than or equal to h-bar divided by 2. Uncertainty is represented by the capital Greek letter delta. Therefore we can state the product of these two uncertainties as delta p times delta x. h-bar is equal to Planck’s constant divided by two times pi.

Because the product of both uncertainties has a lower limit, there is a limit to the accuracy of any measurements we can make on these two properties. If I know the position of something with a high level of accuracy, then the accuracy to which I can measure momentum will be limited. To the extreme: if I know with perfect certainty the exact location of a wave, then it is impossible to know the momentum of that wave, and vice versa. But uncertainty can never be zero for both quantities.

Two other properties that are linked in uncertainty are energy and the time at which the object had that energy. We can state that uncertainty in these two variables is delta E times delta t is greater than or equal to h-bar divided by 2.

It’s important to point out that uncertainty doesn’t just exist on the quantum scale, but also on the macro scale. However, because h-bar divided by two is so small, this effect is trivial for most objects we can see with our eyes. This doesn’t affect macro-scale experiments in any noticeable way.