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By Dan Hooper, Ph.D., University of ChicagoA sketch of two-slit diffraction of light made by Thomas Young, which demonstrated the wave-particle duality. Young first presented this experiment at the Royal Society in 1803. (Image: Thomas Young/Public domain)All Matter Is a Particle and a Wave

In 1913, less than a decade after Einstein first proposed the concept of light quanta, Danish physicist Niels Bohr demonstrated that electrons also exhibit wave properties. Bohr built a model of the hydrogen atom, and the single electron in it exhibited both particle properties and wave properties.

It became more interesting and complicated a little over a decade later, in 1924, when French physicist Louis de Broglie claimed in his Ph.D. dissertation that everything is simultaneously both a particle and a wave. Prior to this, the scope of academic papers related to quantum physics was deliberately limited. Einsteins 1905 paper focused specifically on photons and Bohrs 1913 paper focused solely on electrons. De Broglie built upon and generalized the earlier works of both Einstein and Bohr.

But surely not everything is a wave, right? According to de Broglie, the wave-like features are there, but simply not visible to the naked human eye. The reason is that the extent of an objects waviness (or its quantum wavelength) is inversely proportional to its momentum.

For example, a baseball traveling at 100 miles per hour has a wavelength of 10-34 meters. When this is compared to the size of the baseball, it is clear that the wave-like nature of baseball is far too tiny to detect in any practical way. So a baseball might be a wave, but its wavelength is so small that its wave-like features are imperceptible.

The mathematical account presented by de Broglie illustrated that wave-like properties of matter are only detectable at the level of atomic and subatomic particles.

Learn more about the properties of light.

De Broglies paper was a bridge that connected and unified Einsteins idea of light quanta with Bohrs idea of electron waves. Initially, Einstein was impressed by de Broglies dissertation. In fact, he helped promote de Broglies ideas. More importantly, he convinced other scientists that it was absolutely imperative that these ideas be tested experimentally.

The first order of business was to determine whether electrons do or do not interfere with each other as waves do. This suggestion might seem fairly obvious, and it probably did to de Broglie and the other physicists working on quantum theory at the time as well. However, unlike de Broglie, Einstein was very famous, and his suggestions carried a lot of weight.

The necessary experiments were carried out and by 1927 it was demonstrated that electrons experience both constructive and destructive interference. Electrons are not only particles, but they also behave like waves.

From the mid-1920s to the late-1920s, a great deal of effort was directed toward developing a rigorous system of mathematics that could be used to describe and calculate how quantum particles-waves behave and interact.

For example, in 1925, Austrian-Irish physicist Erwin Schrdinger developed an equation that described the wave-like behavior of electrons. The Schrdinger equation, as its known, is still taught today, to nearly all undergraduate physics students. It makes accurate predictions, at least for electrons that are moving at speeds far below the speed of light.

Schrdinger was only one of several physicists working on this. Some of the others included Paul Dirac, Werner Heisenberg, and Max Born, each of whom made important contributions around the same time.

This new generation of quantum theorists was not content with the old quantum theory, developed by the likes of Einstein, Bohr and de Broglie. They were intent on building a more comprehensive and more mathematically robust system. This system would come to be known as quantum mechanics.

This is a transcript from the video series What Einstein Got Wrong. Watch it now, on The Great Courses Plus.

As the new generation made rapid progress in developing this system of quantum mechanics, Einstein became increasingly troubled by its implications. The concept of light quanta provided a notion of what it meant for light to be a wave. It had been long established that light consisted of oscillating or vibrating electric and magnetic fields. So, the peaks of a light wave would be those points in space where the electric and magnetic fields were strongest.

However, in the case of an electron-wave, it wasnt at all clear what the peaks of the wave really represented. The key question that was bothering Einstein was: what exactly is waving? A classical wave makes sense because it is made up of many objects. For example, a water wave is highest at one point because most water molecules are concentrated at that point. But the wave of a single electron cant be interpreted in terms of the collective behavior of many objects. After all, it is only one electron. Surely one object cant exhibit the kind of collective behavior that a water wave does.

Learn more about particle detectors.

In 1926, German physicist and mathematician Max Born proposed a radical answer to this essential question. Born argued that the shape of the electron-wave or any other quantum object, which is known as the wave function, should be interpreted to represent the probability of that object being found in a given location, when or if it were measured.

In other words, if you conduct an experiment to determine the location of a given electron, there is a high probability that you will find it somewhere where the absolute value of the wave function is very high. Whereas, there is a much lower probability that you will find it in a place where the absolute value of the wave function is low.

According to Born, there is no choice but to view the electron-wave in terms of the probability of it being found in a particular location, or in a particular configuration. This soon became the standard way for physicists to think about matter-waves in quantum mechanics.

The implications of studying electron-waves or matter-waves from the probabilistic point of view, and not the deterministic point of view that Einstein subscribed to, troubled him a lot. He could not find common ground among the new generation of quantum theorists. His bigger cause for concern was that the new interpretations were fast gaining acceptance in the scientific world of the time. Einstein set out to definitively disprove the new interpretations.

German physicist and mathematician Max Born was instrumental to the development of quantum mechanics. He was part of the new generation of quantum theorists who built upon the work of Albert Einstein and Niels Bohr. Born is also known for his contributions in the field of solid-state physics, as well as optics.

Max Born won the Physics Nobel Prize in 1954. He was awarded the Nobel Prize for his contributions toward the fundamental research in quantum mechanics, and particularly for his statistical interpretation of wave function.

French physicist Louis de Broglie is considered to be among the early contributors to the development of quantum theory, alongside Einstein and Bohr. His 1924 dissertation brought him to the attention of the scientific world at the time. In it, he posited that all matter exhibits wave properties.

The Schrdinger equation helps determine the optimal energy levels of a quantum mechanical system. It describes the wave function of the system, which in turn provides the probability of finding individual electrons or other quantum objects at particular locations within the system.

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