Copenhagen interpretation

Based on Wikipedia: Copenhagen interpretation

The Interpretation That Doesn't Exist

Here's a strange fact about one of the most influential ideas in physics: nobody actually wrote it down.

The Copenhagen interpretation—supposedly the standard way to understand quantum mechanics—has no founding document, no authoritative text, no definitive statement of what it actually claims. The two physicists most associated with it, Niels Bohr and Werner Heisenberg, disagreed with each other on key points. And the name itself? It was coined decades after the ideas it describes, by a physicist who later regretted inventing it.

This interpretation that isn't quite an interpretation has nevertheless dominated physics education for nearly a century. It shapes how generations of students first encounter the quantum world—a world so bizarre that even its discoverers struggled to explain what they had found.

When Physics Broke

To understand why physicists needed an "interpretation" at all, you have to understand the crisis that created quantum mechanics.

Starting around 1900, experiments began revealing that the physics of Isaac Newton and James Clerk Maxwell—the physics that had explained everything from planetary orbits to electromagnetic waves—simply didn't work at the atomic scale. Atoms didn't behave the way they should. Light didn't behave the way it should. The universe, at its smallest, operated by different rules.

For twenty-five years, physicists improvised. They patched classical physics with ad hoc corrections and heuristic tricks. Max Planck figured out how to calculate the spectrum of light emitted by a hot object, but only by assuming energy came in discrete chunks—an assumption that made no sense in classical physics. Albert Einstein explained why light could knock electrons out of metal, but only by treating light as if it were made of particles rather than waves. Niels Bohr created a model of the hydrogen atom that accurately predicted its spectrum of light emissions, but the model was built on arbitrary rules that violated classical physics and couldn't explain why they worked.

These weren't solutions. They were desperate patches.

By 1925, the patch-and-pray approach had hit a wall. The Bohr model couldn't be extended from hydrogen to helium, the next simplest atom. Physicists needed something fundamentally new.

The Revolution of 1925

That year, Werner Heisenberg—just twenty-three years old—proposed something radical. He suggested that physics should only discuss "observable" quantities: things you could actually measure, like the frequencies of light that atoms absorb and emit. Forget about trying to picture electrons orbiting a nucleus like tiny planets. Focus only on what experiments could detect.

Max Born, working with Heisenberg's ideas, realized that the mathematics needed to make this work involved matrices—rectangular arrays of numbers that can be multiplied together like ordinary numbers, with one crucial difference. When you multiply matrices, the order matters. Three times five equals five times three. But matrix A times matrix B does not necessarily equal matrix B times matrix A.

This might sound like a technical detail. It wasn't.

Born discovered that in this new mathematics, the position of a particle times its momentum gave a different answer than its momentum times its position. The difference was precisely related to Planck's constant—that mysterious number Planck had introduced in 1900. The fabric of reality, at the quantum level, was non-commutative.

Meanwhile, Erwin Schrödinger developed a different approach that treated electrons as waves. His famous equation described how these waves evolved over time. But what were these waves? Waves of what?

Born again provided the answer, though it was strange: the wave function gave you probabilities. Square the wave function at any point, and you get the probability of finding the particle there if you measured it.

Not a certainty. A probability.

The Problem of Probability

Probability was deeply troubling to many physicists, Einstein most famously among them.

In classical physics, probability appeared when you lacked information. You might say there's a fifty percent chance a coin lands heads, but that's just because you don't know exactly how it was flipped, how the air currents moved, how it hit the surface. In principle, if you knew everything about the initial conditions, you could predict the outcome with certainty. Classical probability reflects our ignorance, not reality's inherent randomness.

Quantum probability seemed different. Born's rule didn't describe what we don't know. It described what couldn't be known—fundamentally, in principle, no matter how much information you gathered. Before measurement, the particle genuinely didn't have a definite position. It existed in a "superposition" of possibilities.

This is where the Copenhagen interpretation enters—or rather, where various Copenhagen-like ideas attempt to make sense of this situation.

The Copenhagen Spirit

In 1929, Heisenberg published a textbook based on lectures he gave at the University of Chicago. In the preface, he wrote of the "Kopenhagener Geist der Quantentheorie"—the Copenhagen spirit of quantum theory—that had guided the field's development. Copenhagen, of course, was where Bohr's institute was located, where Heisenberg had worked as Bohr's assistant during the crucial years of the mid-1920s.

"Spirit" is an evocative word. It suggests not a doctrine but an attitude, an approach, a way of thinking. And that's fitting, because what came to be called the Copenhagen interpretation was never a tightly defined philosophical position. It was a loose collection of ideas, some of them held by Bohr, some by Heisenberg, some shared, some contradictory.

The term "Copenhagen interpretation" itself didn't appear until the 1950s, when Heisenberg used it in lectures criticizing alternative approaches—particularly the pilot-wave theory developed by David Bohm. By framing Copenhagen as "the" interpretation, Heisenberg positioned Bohm's ideas as deviant alternatives to an established orthodoxy. Before he published these lectures, Heisenberg privately expressed regret about the phrasing, worried it implied there were other legitimate interpretations—which he considered "nonsense."

Léon Rosenfeld, a close collaborator of Bohr's, called the term an "ambiguous expression" and suggested abandoning it. Nobody listened. The phrase stuck.

What Copenhagen Actually Claims

Despite its murky origins and lack of authoritative definition, there are ideas commonly associated with Copenhagen-type interpretations. Think of these not as a rigid doctrine but as a family of related views.

First: quantum mechanics is fundamentally probabilistic. The randomness isn't a result of ignorance that could be eliminated with better measurements or deeper theories. It's built into nature at the most basic level. When an atom decays, there is no hidden mechanism determining the exact moment—the universe genuinely doesn't decide until it happens.

Second: the principle of complementarity. Some properties of quantum systems cannot be simultaneously well-defined. The most famous example is position and momentum. You can measure where a particle is with arbitrary precision, or you can measure how fast it's moving with arbitrary precision, but you cannot do both at once. This isn't a limitation of your measuring devices. It's a feature of reality itself.

Third: measurement changes things. When you observe a quantum system, something irreversible happens. Before measurement, a particle might exist in a superposition of states. After measurement, it has a definite value. This transition—often called "wave function collapse"—is sudden, discontinuous, and (according to Copenhagen views) cannot be analyzed further in physical terms.

Fourth: the Born rule. The probability of getting a particular measurement result equals the square of the amplitude of the wave function for that result. This rule works spectacularly well—it's been tested in countless experiments—but Copenhagen interpretations don't explain why it works. It's taken as a fundamental postulate.

Fifth: there's a correspondence principle. As you move from the quantum realm to the everyday world, quantum predictions should smoothly approach classical predictions. The weird quantum effects don't suddenly turn off at some scale—they become statistically negligible as systems get larger and more complex.

The Measurement Problem

Here is where Copenhagen views get genuinely strange—and where critics have always focused their attacks.

According to the mathematics of quantum mechanics, systems evolve smoothly and continuously according to the Schrödinger equation. But according to Copenhagen interpretations, measurement causes a sudden, discontinuous "collapse" of the wave function. These two kinds of evolution are completely different.

So what counts as a measurement?

Bohr insisted that measuring devices must be described in classical, everyday language. He spoke of laboratory apparatus, of irreversible registrations, of macroscopic recording devices. But he never gave a precise criterion for where quantum description ends and classical description begins.

Heisenberg spoke of a "cut" between the quantum system being observed and the classical apparatus doing the observing. He suggested this cut could be moved—you could treat more or less of the experimental setup as quantum mechanical, as long as some part remained classical. The predictions wouldn't change.

But this creates a puzzle: if everything is made of atoms, and atoms are quantum, then measuring devices are quantum too. Why should they be described classically? Where exactly is this cut, and what makes it special?

This is the measurement problem, and Copenhagen interpretations don't really solve it so much as accept it as primitive, as part of how we must talk about quantum phenomena.

Bohr Versus Heisenberg

The two founding figures of Copenhagen thought genuinely disagreed on important points, which makes the idea of a unified "interpretation" somewhat misleading.

Take wave-particle duality. Light and matter sometimes behave like waves and sometimes like particles. But what determines which behavior you see?

Bohr argued that the experimental arrangement determines it. Set up a double-slit experiment, and you'll see wave-like interference patterns. Set up a which-path detector, and you'll see particle-like behavior. The two setups are complementary—they reveal different aspects of reality, and no single experiment can reveal both at once.

Heisenberg saw it differently. He thought the mathematical formalism itself could be interpreted either as describing waves or particles. It wasn't the experiment that determined which picture applied—it was how you chose to read the equations.

This might seem like philosophical hair-splitting, but it reflects a deeper disagreement about what quantum theory is telling us about reality.

Bohr distanced himself from what he saw as Heisenberg's more subjective approach. He didn't like language that made the observer's consciousness seem special or causally important. For Bohr, measurement was just a particular kind of physical interaction—one that happened to be irreversible in practice—and didn't require a conscious mind.

Is It Subjective?

Copenhagen interpretations are sometimes accused of making physics subjective—of putting the observer's mind at the center of physical reality. This accusation is mostly unfair.

It's true that Copenhagen views emphasize what happens when measurements are made, and measurements require apparatus, and apparatus require people to build and operate them. But the original Copenhagen physicists didn't think consciousness played any special physical role.

Wolfgang Pauli insisted that measurement results could be obtained and recorded by "objective registering apparatus." Heisenberg wrote explicitly that "the observer has only the function of registering decisions"—meaning physical events—and "it does not matter whether the observer is an apparatus or a human being."

The wave function, in Copenhagen views, is objective. It doesn't represent any individual physicist's beliefs or opinions. Different physicists with the same information should assign the same wave function. What's observer-dependent is which experiment gets performed, not what the results are once it's performed.

Still, there's something unsatisfying here. The quantum world seems to exist in a kind of potentiality until measurement actualizes specific outcomes. What determines when and how that transition happens? Copenhagen interpretations don't give a clear answer beyond saying it happens when we use measuring devices to extract information.

Counterfactual Definiteness

Here's a subtle but important feature of Copenhagen thinking: it denies "counterfactual definiteness."

That's a fancy term for the common-sense idea that physical quantities have definite values even when we don't measure them. Before you look at a coin, it's either heads or tails—looking at it just reveals which one it already was.

Copenhagen interpretations reject this for quantum systems. It's not that the electron has a definite position we don't know—it genuinely doesn't have a definite position until we measure it. Asking "what was the position before we measured?" is asking a meaningless question. There's no fact of the matter.

This sounds bizarre, but it's required by some experimental results. Certain experiments produce correlations between distant particles that can't be explained if we assume the particles had definite properties all along. The quantum formalism works precisely because it doesn't assign definite values to unmeasured quantities.

Shut Up and Calculate

The physicist N. David Mermin once coined the phrase "Shut up and calculate!" to characterize the Copenhagen attitude. The idea: stop asking metaphysical questions about what quantum mechanics "really means" and just use it to make predictions. The formalism works. Why worry about what reality is "actually like" underneath?

Mermin later regretted the phrase, finding it too dismissive. He acknowledged that Copenhagen came in many "versions, varieties, or flavors," and that different physicists meant different things by it.

The physicist Asher Peres observed that "very different, sometimes opposite, views are presented as 'the Copenhagen interpretation' by different authors." This isn't a failure of scholarship—it's a reflection of the fact that there never was a single Copenhagen interpretation.

The Opposition

From the beginning, Copenhagen ideas faced criticism from some of the greatest physicists of the twentieth century.

Einstein famously never accepted quantum mechanics as a complete description of reality. His quip that "God does not play dice" expressed his discomfort with fundamental randomness. He spent decades searching for hidden variables—underlying deterministic physics that would explain quantum probabilities the way molecular motions explain thermodynamic probabilities.

Einstein didn't doubt that quantum mechanics made accurate predictions. He doubted that its probabilistic description was the final word. Surely, he thought, there must be a deeper level of description where particles have definite positions and momenta, even if we can't measure them simultaneously.

In 1935, Einstein and two colleagues published what became known as the EPR paper (named for Einstein, Boris Podolsky, and Nathan Rosen). It described a thought experiment designed to show that quantum mechanics couldn't be a complete description of reality. The argument was subtle, involving entangled particles and correlations between distant measurements.

Bohr replied, essentially arguing that EPR had misunderstood what quantum mechanics was about. The debate continued for years without clear resolution.

Then, in 1952, David Bohm published a complete deterministic theory that reproduced all the predictions of quantum mechanics. His "pilot-wave" theory gave particles definite positions at all times, guided by a wave that was mathematically equivalent to the quantum wave function. Bohm's theory was exactly the kind of hidden-variable theory Einstein had hoped for.

This should have been a bombshell. It wasn't.

Most physicists ignored Bohm's work. The Copenhagen interpretation had become so entrenched that alternatives were barely considered legitimate. Some physicists dismissed Bohm's theory as inelegant or unphysical without engaging with its substance. Others didn't even know about it.

The Emperor's New Clothes?

In 1964, the physicist John Bell proved something remarkable. He showed that no hidden-variable theory could reproduce all the predictions of quantum mechanics unless it allowed faster-than-light influences between distant particles. This "nonlocality" was a genuine feature of quantum reality, not just a quirk of the Copenhagen interpretation.

Bell was famously critical of Copenhagen ideas. He wrote that the word "measurement" should be banned from quantum mechanics—it was too vague, too classical, too suggestive of minds and consciousness playing special roles.

Bell's theorem, and the experiments that confirmed it, didn't vindicate Copenhagen. If anything, they deepened the mystery. Quantum mechanics really was as strange as its founders had said. But the strangeness didn't require Copenhagen's philosophical framework. Other interpretations—Bohm's pilot-wave theory, the many-worlds interpretation, objective collapse theories—could handle the same phenomena with different philosophical commitments.

Why It Persists

Despite all the criticisms and alternatives, Copenhagen-type views remain the most commonly taught approach to quantum mechanics. Why?

Partly it's inertia. Generations of physics students learned Copenhagen ideas from their professors, who learned from their professors, in an unbroken chain back to Bohr and Heisenberg. Textbooks perpetuate the tradition.

Partly it's pragmatism. Copenhagen's vagueness is, paradoxically, a feature. Because it doesn't commit to a detailed picture of what's really happening during measurement, it doesn't generate predictions that differ from the bare quantum formalism. Alternative interpretations all make the same experimental predictions (at least for feasible experiments), so why prefer one over another?

Partly it's appropriate humility. Copenhagen interpretations take seriously the idea that quantum mechanics might be telling us something deep about the limits of physical description itself—that not all meaningful questions have answers, that some aspects of reality cannot be captured in classical terms. Maybe this is wisdom rather than evasion.

An Interpretation of Interpretations

What are we really arguing about when we argue about quantum interpretations?

The mathematics of quantum mechanics is not in dispute. Everyone agrees about how to calculate probabilities, how the wave function evolves, what experiments will show. The disagreement is about what the mathematics means—what kind of world could produce these mathematical regularities.

Some physicists think this is a meaningful question. Others think it's metaphysics, not physics—interesting philosophy, perhaps, but not something experiments can decide.

Copenhagen interpretations, in their various forms, tend toward the second view. They emphasize what we can measure and predict, and they're cautious about claims regarding what reality is like when we're not looking. This isn't necessarily anti-realism—Bohr certainly thought he was describing something objective—but it is a kind of epistemic humility.

Whether this humility is warranted or whether it's a failure of imagination remains one of the deep open questions in the foundations of physics.

The Quantum World

Here is what we can say with confidence: at the scale of atoms and electrons, the world behaves in ways that defy everyday intuition. Particles don't have definite positions and momenta simultaneously. Measurement changes what we measure. Randomness is fundamental, not just a reflection of ignorance. Distant particles can be correlated in ways that can't be explained by shared information in their past.

The Copenhagen interpretation doesn't explain why the world is like this. No interpretation does. They differ in what philosophical apparatus they use to describe it, what questions they declare meaningful, and what implications they draw for broader metaphysics.

Perhaps that's the deepest lesson of the Copenhagen perspective: in quantum mechanics, we have a theory that works—that predicts experimental outcomes with stunning precision—without anyone being able to tell a clear story about what's really happening. The formalism outruns our capacity for narrative. Maybe that's humbling. Maybe it's liberating.

Bohr reportedly kept a horseshoe above his door. When asked if he really believed it brought good luck, he replied: "No, but I am told it works whether you believe in it or not."

Quantum mechanics, too, works whether you understand it or not. The Copenhagen interpretation, in all its fuzzy, contradictory, historically contingent glory, is one way of making peace with that fact.