The Copenhagen Interpretation and Competing Interpretations of Quantum Mechanics

Christian Schirm - via Wikimedia Commons.

Physics has always been that horrible and confusing class through which high school teenagers fight to survive, which explains why many I know absolutely hate it. Some take the class for the credit it provides, but they often come to regret taking it. Many fail their physics classes, whether an AP class or a normal class. 

It is also evident, however, that many find value in physics after they take it; the class takes you on a rollercoaster – everything moves so fast that you do not have the chance to appreciate it. As with a rollercoaster, the appreciation does not culminate until later, long after the event is over.

Many consider Newtonian physics – in itself a complicated science – as the epitome of difficulty. They unfortunately (or fortunately) are not aware of two other principal concepts of physics – relativistic physics and quantum mechanics. Quantum mechanics makes classical mechanics look like child’s play.

Let us now consider adult’s play: the main interpretation of quantum mechanics, the Copenhagen Interpretation. Brace yourselves as we attempt to understand one of the only sciences that is inherently indeterministic, a concept that fundamentally rejects natural patterns.

The basics of Copenhagen

The interpretation accords to the correspondence principle, a Bohrean* rule that there must be agreement between the physics of the large bodies – classical mechanics – and the physics of the small bodies – quantum mechanics. The correspondence principle argues that new theories should be able – and are required – to reproduce the results of older, more well-established theories, like quantum and classical mechanics.. Ernest Rutherford, experimenter and advocate of the Rutherford model of the atom, discovered that the atom was a small, positively charged core surrounded by a negatively charged cloud of particles. The problem with this was that, based on classical mechanics and electrodynamics, the electrons constituting the negatively charged cloud should continuously emit radiation until the positively charged nucleus swallows the electrons up. This was the first of many contradictions between classical understanding and new theories of physics. The Copenhagen Interpretation also accords to indeterminism, a Bohrean principle arguing that events can occur without cause, that no prediction is certain and is based entirely on probability. 

A history

In the late 19th century, as a result of discoveries related to the atom and subatomic particles, physicists were forced to revise classical mechanics. For twenty-five years, scientists and physicists struggled to create a cohesive and not immediately disprovable theory of quantum mechanics; quantum mechanics was a mess: then, the principal interpretation was old quantum theory, a set of corrections made to classical mechanics that were eventually realized to be incohesive. 

The foundation of new quantum theory, from which Copenhagen was created, began in 1925, when Werner Heisenberg, in a landmark paper, discovered the uncertain nature of electrons and other elementary particles, and Max Born, used matrices – a rectangular array of numbers that is not commutable in matrix multiplication – to represent the behavior of electrons. Later, Erwin Schrodinger devised the wave function and the wave equation and Max Born discovered that the wave function, ψ, is a tool for calculating probability of quantum events.

And such was the birth of quantum theory. The Copenhagen interpretation was later conceptualized to describe abstract phenomena in quantum mechanics.

Copenhagen

The Copenhagen interpretation is an umbrella term: to this day, there is no consensus on what it actually is. Although contested, Copenhagen is the most widely accepted interpretation of quantum mechanics.

There are four essential concepts of the Copenhagen Interpretation; two physicists, Hans Primas and Roland Omnes, argue that there are six more essential concepts in addition to those that are widely accepted. 

Four accepted postulates

• Quantum mechanics is indeterministic – phenomena occur randomly and happen without cause.

• Quantum mechanics follows the correspondence principle; there must be some phenomenon – whether known or unknown – that connects classical and quantum mechanics to one another.

• Quantum mechanics adheres to the Born rule: the probability of finding a particle in a particular position is proportional to the square of the magnitude of that point’s wave function when observed.

• Complementarity: quantum systems have pairs of complementary properties in which neither property can be observed or measured simultaneously with the other. The complementarity principle is evident in the wave-particle duality of photons and electron spin.** 

Six additional postulates proposed by physicists Hans Primas and Roland Omnes

• Quantum mechanics can apply specifically to individual objects: the wave function will yield similar probability densities regardless of the sample size. 

• Any measurements made on a quantum system result in waveform collapse; this leads to quantum decoherence, leading the particle to adhere to classical mechanics. As a result, the outcome of the system must be explained as a classical system.

• Devices used to conduct measurements and experimentation on quantum systems must be explained in classical mechanical terms, whereas the measured quantum system must in quantum mechanical terms.

• During observation, the quantum system must interact with the measurement system. When the waveform collapses, the particle enters an eigenstate – one particular state or position. A conscious observer would, therefore, measure only one state of the quantum system. After the measurement is made, the quantum system can never return to superposition, and if it is entangled to another quantum system, the entanglement, too, is lost.

• Statements made about measurements that did not occur do not exist: an experimenter could not assume that a particle will be located known as a Mach-Zehnder interferometer unless interferometer were built to be able to observe and measure the path of the photon in that specific area of the interferometer.

• Wave functions are logical equations – there is no room for bias, essentially.

Alternatives to Copenhagen

Recently, new interpretations of quantum mechanics have been proposed as challenges – some implausible, some plausible – to Copenhagen. While the Copenhagen interpretation maintains the current scientific consensus, it is still widely disputed. 

Many-worlds

The first of the alternatives is the many-worlds interpretation, perhaps the most popular opposing interpretation to Copenhagen.

The many-worlds interpretation was first proposed by American physicist Hugh Everett to counter Copenhagen, having the consensus even then, in 1957. Although many-worlds is quite similar to Copenhagen – it also argues for superposition and waveform collapse – it seeks to describe measurement and what happens to the other eigenstates after waveform collapse. 

A quantum system is in superposition until it is measured, but what exactly defines a measurement? Once the measurement or observation is made, the waveform collapses, and the Copenhagen interpretation defines that the wave function determines what the observer observes. Say a photon is in superposition, or wave-particle duality: when a measurement or observation is made, the waveform collapses and we see the photon as a wave. 

But what happens to the particle eigenstate? Why does measurement cause decoherence? In the many-worlds interpretation, the waveform collapse of the photon leads to quantum decoherence, and as a result is two separate universes, one in which the photon observed is a particle and the other in which it is a wave. This applies to every quantum system with multiple eigenstates – proton or electron charges, however, as they have only one eigenstate, would not create new universes when observed. Many-worlds also follows the wave equation, so it is often regarded as a secondary theory to Copenhagen; but as new experiments are formulated that can make many-worlds falsifiable, the interpretation could become more plausible than Copenhagen.

Consistent histories

In the consistent histories interpretation, waveform collapse does not exist, a significant difference from Copenhagen and many-worlds. Consistent histories claims that quantum systems follow a classical consistency criterion that allows probabilities of certain histories to be applied to various quantum systems; if it were to become the predominant theory in quantum mechanics, researchers could learn the entire history of quantum particles from the origin of the universe to the present through probabilities in classical mechanics. Consistent histories also postulates that the current understanding of quantum mechanics is consistent with classical mechanics, another significant dissimilarity to Copenhagen and many-worlds.

Oddities: quantum Darwinism

Unsurprisingly, there are many more theories than just these three, so I have attached a link to all of them down in the description. Definitely look into them if you want to hear some of the wackier, lesser known interpretations. Now, let us consider quantum Darwinism.

If you know evolution by natural selection, this is essentially self explanatory. Quantum Darwinism attempts to explain that classical mechanics comes from the quantum world – quantum systems underwent natural selection and evolved to classical ones. While this theory does follow universal Darwinism*** and does attempt to answer the quantum measurement problem, it is much more an assumption than a strong theory. It applies Darwinism to fields other than biology, as if Darwinism applies to the entire universe itself. 

Other interpretations

Some other interpretations of quantum mechanics include the ensemble interpretation, the transactional interpretation, stochastic mechanics, objective collapse, conscious observer waveform collapse (which is extremely anthropocentric), De Broglie-Bohm theory, quantum Bayesianism, quantum information theory and relational quantum mechanics.

Wrapping it up

        The Copenhagen interpretation is obviously one of the most compelling and least understood theories in all of science. Although it is still the most widely accepted by the entire scientific community, Copenhagen is evidence for the fact that quantum mechanics is the wild west of all science. There will be many more entries in the future surrounding this field and particle physics, so stay tuned. As always, take care and stay curious, everyone.

* After Niels Bohr, the Danish physicist known for his contributions to atomic structure and quantum theory.

** No two electrons occupying the same orbital can have the same spin (see “Pauli Exclusion Principle” in References).

*** A train of thought that extends the approaches of Darwinism in biology to other phenomena in nature (see “Universal Darwinism” in References).

If you have any questions, comments, or corrections, please comment on this post or email learningbywilliam@gmail.com with your concerns. Thank you.

References

(n.d.). Retrieved from https://math.ucr.edu/home/baez/spin/node3.html

Alex Voinescu, MoonKnight, John Rennie, Anixx, Peter Krauss, User31182, CalmariusCalmarius 7. Why does observation collapse the wave function? Retrieved from https://physics.stackexchange.com/questions/35328/why-does-observation-collapse-the-wave-function

Complementarity (physics). (2022, August 13). Retrieved from https://en.wikipedia.org/wiki/Complementarity_(physics)

Contributor, T. (2021, October 14). Superposition - Definition from WhatIs.com. Retrieved from https://whatis.techtarget.com/definition/superposition

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Dawkins, R. (n.d.). Universal Darwinism (Chapter 29) - The Nature of Life. Retrieved from https://www.cambridge.org/core/books/nature-of-life/universal-darwinism/0939B49903C60A59B57DC5C007415ECF

Faye, J. (2019, December 06). Copenhagen Interpretation of Quantum Mechanics. Retrieved from https://plato.stanford.edu/entries/qm-copenhagen/

Indeterminism. (2022, May 24). Retrieved from https://en.wikipedia.org/wiki/Indeterminism

Interpretations of quantum mechanics. (2022, August 22). Retrieved from https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

Pauli exclusion principle. (2022, August 17). Retrieved from https://en.wikipedia.org/wiki/Pauli_exclusion_principle

Uncertainty principle. (2022, August 31). Retrieved from https://en.wikipedia.org/wiki/Uncertainty_principle

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