###### By Steven Gimbel, Ph.D., Gettysburg College

## German theoretical physicist Max Planck’s claim that emitted and absorbed light is quantized and the application of this concept to the photoelectric effect by his contemporary and friend Albert Einstein presented a tricky question: Is light a particle or a wave?

### Particles and Waves Are Objectively Distinct

A particle is an independent entity. When we say a particle exists we mean that it has a specific shape, size, and location. It also implies that when a particle is present at a location that space cannot be empty.

Waves are completely different from particles. Waves do not exist independently. A wave is essentially a disturbance in a field, which is a physical quantity with values for every point in space-time. It can’t exist without the field. In addition, the field must have a force that is constantly trying to restore it to equilibrium. It’s also worth noting that at the completion of a wave, that particular wave ceases to exist but the field is still right there.

Think of a Mexican wave in a packed stadium. If the crowd isn’t present, the Mexican wave can’t exist. The crowd is the field in this case. But when the Mexican wave is over, the crowd or fans are still present in the stadium.

Based on this evidence, it would seem that light can’t be both a particle and a wave. Claiming that it is sometimes a particle and sometimes a wave would be similar to claiming that light is sometimes a thing and at other times not a thing.

Learn more about Wave Nature and Particle Nature of Light.

### The Quantum Leap

Danish physicist Niels Bohr, who was awarded the Nobel Prize in Physics in 1922 (four years after Planck) for his contributions towards a better understanding of the atomic structure as well as quantum theory, was fascinated by Planck’s theory of light being emitted and absorbed as quanta. He decided to apply that concept to the atom.

He began with the hydrogen atom, which is the simplest form of an atom. It comprises a single proton, in its nucleus, and a single electron. His hypothesis was that the orbits of the electron were quantized. So, the electron could not orbit at any random distance from the nucleus. Instead it orbited on fixed tracks. The electron could jump from one track to the other, both towards and away from the nucleus. However, the electron never exists in the space between the tracks.

The electron managed to instantaneously absorb or emit the exact amount of energy required to move from one track to the next. This is what is known as the quantum leap. In popular parlance, this term is often mistakenly used to mean a major jump, when it actually denotes an instantaneous jump in lieu of a smooth transition.

Bohr’s hypothesis about electrons orbiting in quantized tracks made the atomic structure more stable than before, but it skewed what we knew about reality. The primary question was how could something go from point A to point B without ever having been in the middle?

### The Heisenberg Uncertainty Principle

Werner Heisenberg, a German theoretical physicist and another recipient of the Nobel Prize in Physics (in 1932), had worked with Bohr between September 1924 and May 1925. He later took up a position as a lecturer and an assistant to Bohr at the University of Copenhagen in 1926. A year later he came up with the mathematical account that explained quantum leap, which was based on infinite-dimensional matrices.

Picture a spreadsheet with data across both columns and rows. This is a two-dimensional matrix. If similar sheets are added both in front and behind this original sheet, it would form a three-dimensional matrix. The mathematical account Heisenberg had come up with required infinite-dimensional matrices.

Learn more about How Depiction of Math in Literature Collapses Certainty.

What really caught the attention of the scientific world was a peculiarity in Heisenberg’s mathematical theory. The theory provided pairs of observable properties, and the peculiarity was that when the value of one property was observed the value of the other property seemed to become uncertain. In fact, the more precise the measurement of one property, the more uncertain the measurement of the other became. This peculiarity came to be known as the Heisenberg uncertainty principle.

But surely this principle was wrong? Why would our act of measuring one property change the reality for another property?

This is a transcript from the video series Redefining Reality: The Intellectual Implications of Modern Science. Watch it now, on The Great Courses Plus.

### Schrödinger’s Superposed State

The Schrödinger equation, which is a linear partial differential equation and describes wave function, formulated by Austrian-Irish physicist Erwin Schrödinger significantly simplified Heisenberg’s mathematical account. Technically, the Schrödinger equation was simpler, but in practice, it added to the confusion.

Physical theories contain state variables or measurable quantities. The function of the theory is to determine how the state variables change over time. In the case of Schrödinger’s equation, the state variable is represented by psi (ψ), which is also known as the wave function. According to Schrödinger’s theory ψ represents every possible state the system could be in. Schrödinger termed this the superposed state.

This is where the confusion compounds because this doesn’t represent reality. We know that objects are not simultaneously in every place it could be. At any given point in time, objects can only be at one location or position. What’s even more interesting is, if we don’t observe the object or system it perfectly satisfies Schrödinger’s equation. However, the moment we do observe it, it collapses into any one of its states, but it’s impossible to predict what its value will be.

For example, a quantum coin continues to be both heads and tails until we don’t observe it. And, irrespective of any and all knowledge at our command right before our observation, we can’t predict with certainty whether it would be heads or tails. But as soon as we observe the quantum coin, it takes on just one value. This ties back to the question we began with. Is light a particle or a wave? It depends on how light is observed.

### Thomas Young’s Double-Slit Experiment

Imagine a light source that releases one quantum of light. This light is directed towards a wall with two slits in it and a screen on the other side of the wall. If the light is a wave, then it should pass through both slits at the same time and the waves emanating from the other side would be identical.

Since waves add and subtract, then the midway point on the screen between the two slits would be the brightest spot. This is so because both waves would be in phase, having traveled the same distance at the same speed. Hence, the resulting wave would be twice as big.

Move to either side of this midway point and one wave would reach earlier than the other. And at certain spots on the screen, the two waves would be completely out of phase, cancel each other out and result in a dark spot. So, if light is a wave, we would observe a series of alternating light and dark bands.

Now let’s suppose light is a particle, then the particles hitting the slits would pass through. The slits would act like shotguns, spewing light particles at random angles. There would be no light and dark bands, just random flashes on the screen.

If you carry out this test and check for the appearance of alternating light and dark bands or install a photo-detector to check if the photon passed through the left slit, right slit or both, you will find that light behaves both as a wave and a particle.

When the photo-detector is switched off, alternating light and dark bands will appear on the screen. When the photo-detector is switched on, the bands will disappear and random flashes will appear. The photo-detector will also inform you that the photon passed through one or the other slit, but never both. If the photo-detector is switched off again, the alternating bands would reappear.

As Schrödinger’s equation illustrates, light exists in a superposed state of both possible positions. When the photo-detector is off, we are not testing for the position. So, the bands appear. When the photo-detector is on, we are now observing the position and so the wave function collapses into one value to provide light a definite position. However, that value is random, not predictable. So, the Schrödinger equation is a description of reality when we’re not looking at it, but fails whenever we check.

### Common Questions About Light and Whether It’s a Wave or a Particle

**Q: Does Light Have Mass?**

Light is made up of photos, which do not have mass. Hence, on the face of it, light doesn’t have any mass and can’t be used to weigh anything. However, photons do contain energy. But Albert Einstein’s famous equation E=MC^{2}, which means energy equals mass times the speed of light squared, illustrated that energy and mass can be used interchangeably.

**Q: What Are the Implications of Heisenberg’s Uncertainty Principle?**

The impact of Heisenberg’s uncertainty principle on quantum mechanics forces us to choose between observing the wave nature of matter or the particle nature of matter. This is critical while observing light, because it exhibits the properties of both a wave and a particle.

**Q: What Is H in the Schrödinger Equation?**

The Schrödinger equation is represented as Hψ = Eψ. Here H denotes an operator, while E denotes the energy of the system. Psi (ψ) is the state variable.

**Q: What Does the Schrödinger Equation Calculate?**

Every quantum mechanical system, such as an atom, has a specific allowed energy level. The Schrödinger equation is used to measure this energy level. The state variable or wave function in the Schrödinger equation provides the probability of identifying the particle under observation in the system at a particular position.