There is probably no area of science more bizarre and confusing than trying to understand the behavior of matter and energy at the smallest scales. In the early part of the twentieth century, physicists such as Max Planck, Albert Einstein, Niels Bohr, and many others laid the foundation for understanding this bizarre realm of nature: quantum physics.

The equations and methods of quantum physics have been refined over the last century, making astounding predictions that have been confirmed more precisely than any other scientific theory in the history of the world.

Quantum mechanics works by performing an analysis on the quantum wavefunction (defined by an equation called the Schroedinger equation).

The problem is that the rule about how the quantum wavefunction work seem to drastically conflict with the intuitions we have developed to understand our day-to-day macroscopic world. Trying to understand the underlying meaning of quantum physics has proven to be much more difficult than understanding the behaviors themselves. The most commonly-taught interpretation is known as the Copenhagen interpretation of quantum mechanics ... but what is it really?

### The Pioneers

The central ideas of the Copenhagen interpretation were developed by a core group of quantum physics pioneers centered around Niels Bohr's Copenhagen Institute through the 1920's, driving an interpretation of the quantum wavefunction that has become the default conception taught in quantum physics courses.

One of the key elements of this interpretation is that the Schroedinger equation represents the probability of observing a particular outcome when an experiment is performed. In his book *The Hidden Reality*, physicist Brian Greene explains it as follows:

"The standard approach to quantum mechanics, developed by Bohr and his group, and called the

Copenhagen interpretationin their honor, envisions that whenever you try to see a probability wave, the very act of observation thwarts your attempt."

The problem is that we only ever observe any physical phenomena at the macroscopic level, so the actual quantum behavior at the microscopic level is not directly available to us. As described in *Quantum Enigma*:

"There is no 'official' Copenhagen interpretation. But every version grabs the bull by the horns and asserts that

an observation produces the property observed. The tricky word here is 'observation.'..."The Copenhagen interpretation considers two realms: there is the macroscopic, classical realm of our measuring instruments governed by Newton's laws; and there is the microscopic, quantum realm of atoms and other small things governed by the Schroedinger equation. It argues that we never deal

directlywith the quantum objects of the microscopic realm. We therefore need not worry about their physical reality, or their lack of it. An 'existence' that allows the calculation of their effects on our macroscopic instruments is enough for us to consider."

The lack of an official Copenhagen interpretation is problematic, making the exact details of the interpretation difficult to nail down. As explained by John G. Cramer in an article entitled "The Transactional Interpretation of Quantum Mechanics":

"Despite an extensive literature which refers to, discusses, and criticizes the Copenhagen interpretation of quantum mechanics, nowhere does there seem to be any concise statement which defines the full Copenhagen interpretation."

Cramer goes on to try to define some of the central ideas that are consistently applied when speaking of the Copenhagen interpretation, arriving at the following list:

**The uncertainty principle**- Developed by Werner Heisenberg in 1927, this indicates that there exist pairs of conjugate variables which cannot both be measured to an arbitrary level of accuracy. In other words, there is an absolute cap imposed by quantum physics on how accurately certain pairs of measurements can be made, most commonly the measurements of position and momentum at the same time.**The statistical interpretation**- Developed by Max Born in 1926, this interprets the Schroedinger wave function as yielding the probability of an outcome in any given state. The mathematical process for doing this is known as the Born rule.

**The complementarity concept**- Developed by Niels Bohr in 1928, this includes the idea of wave-particle duality and that the wave function collapse is linked to the act of making a measurement.**Identification of the state vector with "knowledge of the system"**- The Schroedinger equation contains a series of state vectors, and these vectors change over time and with observations to represent the knowledge of a system at any given time.**The positivism of Heisenberg**- This represents an emphasis on discussing solely the observable outcomes of the experiments, rather than on the "meaning" or underlying "reality". This is an implicit (and sometimes explicit) acceptance of the philosophical concept of instrumentalism.

This seems like a pretty comprehensive list of the key points behind the Copenhagen interpretation, but the interpretation is not without some fairly serious problems and has sparked many criticisms ... which are worth addressing on their own individually.

### Origin of the Phrase "Copenhagen Interpretation"

As mentioned above, the exact nature of the Copenhagen interpretation has always been a bit nebulous. One of the earliest references to the idea of this was in Werner Heisenberg's 1930 book *The Physical Principles of the Quantum Theory*, wherein he referenced "the Copenhagen spirit of quantum theory." But at that time - and for several years after - it was also really the *only* interpretation of quantum mechanics (even though there were some differences between its adherents), so there was no need to distinguish it with its own name.

It only began to be referred to as "the Copenhagen interpretation" when alternative approaches, such as David Bohm's hidden-variables approach and Hugh Everett's Many Worlds Interpretation, arose to challenge the established interpretation. The term "Copenhagen interpretation" is generally attributed to Werner Heisenberg when he was speaking in the 1950's against these alternative interpretations. Lectures using the phrase "Copenhagen Interpretation" appeared in Heisenberg's 1958 collection of essays, *Physics and Philosophy*.