Theoretical Physics in COPENHAGEN: A Primer

COPENHAGEN is a human story with the mystery of quantum physics at its center. Here is a brief primer on major concepts.

An artist’s representation of the wave-particle duality (Source: Encyclopaedia Britannica)

Onstage at Lantern Theater Company January 11 through February 18, 2018, Copenhagen explores a pivotal moment in the relationship of Niels Bohr and Werner Heisenberg, two scientists at the cutting edge of the development of quantum physics. The play explores the notion of being on the forefront of incredible discovery — and what your responsibility is to the world and to your loved ones once those discoveries are unleashed.

Quantum physics is a branch of science that examines the workings of the smallest parts of our world: the atomic and subatomic elements of nature. By the turn of the 20th century, scientists suspected that the classical laws of nature might not apply at the atomic level, and quantum physics sprang from the desire to learn more about what might govern the building blocks of all matter.

Newtonian physics was the dominant belief for two centuries, and a major tenet for that system is causality. According to classical physics, knowing the initial conditions for an event means that one could theoretically predict every event that would follow, thanks to the laws of motion and conservation of energy. Quantum physics shakes that belief to its core, embracing instead the idea that deterministic causality may be impossible at the atomic level.

Participants in the 1927 Solvay Conference, where leading theoretical physicists gathered to discuss the new field of quantum physics. Participants pictured included Niels Bohr, Werner Heisenberg, Albert Einstein, and Erwin Schrödinger. (Source: Wikipedia)

According to the Copenhagen Interpretation of quantum physics, formulated primarily by Niels Bohr and Werner Heisenberg, uncertainty is at the heart of the discipline. In his Uncertainty Principle, Heisenberg posited that it is impossible to know with certainty both the position and the momentum of an atomic element, like an electron. The more precisely you measure one factor, the less precisely you can hope to measure the other.

This is largely because of the Complementarity Principle, contributed by Bohr. This states that matter has properties of both particles and waves — which would have been impossible in Newtonian physics — and that both are necessary for a complete understanding of atomic elements. By accepting that both states are true, we can begin to understand the seemingly contradictory behavior of atomic and subatomic elements.

Another main tenet of the Copenhagen Interpretation is that the act of measuring or observing essentially changes the thing being observed. For example, sending a beam of light to find a particle means that a photon will collide with an electron, which tells that electron’s position. However, that collision knocks the electron off its path, meaning that its momentum and velocity are now different than they were before the scientist went looking for it. For quantum physicists who adhere to the Copenhagen Interpretation, this means there is an essential unknowability at the core of the science.

This is why some major physicists of the time, including Einstein and Schrodinger, rejected the Copenhagen Interpretation; rather than seeing the lack of knowledge as its own kind of knowledge, they saw it as giving up on finding out. Bohr and Heisenberg were standing against hundreds of years of classical physics, and against some of the leading minds of their field.

“Quantum provides us with a striking illustration of the fact that though we can fully understand a connection … we can only speak of it in images and parables. We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections.” — Niels Bohr

World War II was ramping up as the theory of quantum physics made room for practical application, and theoretical physicists began exploring the possibility of nuclear energy, with Bohr and Heisenberg at the forefront.

A chain reaction in Uranium-235, the isotope Bohr and Heisenberg discuss in COPENHAGEN. (Source:

Nuclear fission is the splitting of an atom’s nucleus into two smaller pieces, as a result of either a reaction with free neutrons or radioactive decay. This releases tremendous energy, paving the way for both nuclear reactors that produce power and nuclear bombs that rain destruction. A chain reaction is necessary to sustain this energy release; each instance of fission releases neutrons, which can then go on to fission other nuclei in the material. The longer the chain, the more energy is released.

In order for the chain reaction to be self-sustaining, the fissile material must be at critical mass: the precise amount and shape needed to produce a self-sustaining chain reaction, which it can be controlled by density, mass, and other factors. This mass is determined in part by a diffusion calculation, which measures how the freed neutrons are distributed throughout the system. This equation helps discern how much of a particular isotope is required for the neutrons to fission in order to produce a self-sustaining chain reaction — and therefore how much would be necessary to build an atomic bomb.

In their visionary leap and embrace of uncertainty, Bohr and Heisenberg stood against hundreds of years of classical and deterministic physics, and some of the leading minds of their field. They also had a hand in fundamentally changing the direction of modern warfare, and the lives of hundreds of thousands of people.

Copenhagen is onstage at the Lantern January 11 through February 18, 2018. Visit our website for tickets and information.