A letter to Pauli
In 1927, working at Niels Bohr’s Institute of Theoretical Physics in Copenhagen, Werner Heisenberg formulated what became known as the uncertainty principle, first setting the idea out in a letter to the physicist Wolfgang Pauli on 23 February 1927 before publishing it formally. In his own paper he used the German word Ungenauigkeit, meaning imprecision, rather than the English term uncertainty that later became standard. The claim itself was specific: certain pairs of physical properties, most famously a particle’s position and its momentum, cannot both be known to arbitrary precision at the same time, and the more precisely one is pinned down, the less precisely the other can be.
Not a measurement problem
The principle is often misunderstood as a statement about the limits of measuring instruments, the idea that observing a particle inevitably disturbs it, but that is not what it actually describes. It reflects an intrinsic property of quantum systems themselves, independent of any particular measuring apparatus: position and momentum are represented mathematically as operators that do not commute with each other, meaning the order in which they are applied changes the result, and that non-commuting relationship alone guarantees no quantum state can simultaneously be an exact position state and an exact momentum state, regardless of how careful or non-invasive any hypothetical measurement might be.
Position and momentum, tied together
The relationship can be expressed as a lower bound: the product of the uncertainty in a particle’s position and the uncertainty in its momentum can never fall below a fixed value tied to the reduced Planck constant, roughly half of that constant. The same kind of relationship appears between other paired quantities, generally called complementary or canonically conjugate variables, including energy and time, and the different components of angular momentum, though position and momentum remain the version most commonly cited and taught, and the one Heisenberg himself originally worked through in his 1927 paper.
Refined by other physicists
Heisenberg’s original argument was refined mathematically by others rather than challenged. Earle Hesse Kennard derived the precise inequality relating the standard deviations of position and momentum that same year, 1927, and Hermann Weyl extended related formulations in 1928. Howard Percy Robertson generalised the relationship in 1929 to apply to any pair of quantities represented by Hermitian operators, not just position and momentum specifically, and Erwin Schrödinger refined that further in 1930 into what is now called the Robertson-Schrödinger relation, accounting for correlations the earlier version had not captured. None of these refinements overturned Heisenberg’s basic claim; they made it more general and mathematically precise.
A Nobel, then a wartime programme
The effect is meaningful only at quantum scales and becomes negligible for ordinary macroscopic objects, which is why nothing in everyday experience hints at it directly. Certain quantum states come as close as mathematically possible to the theoretical minimum uncertainty allowed, including the ground state of a quantum harmonic oscillator and so-called coherent states, while other states sit somewhat above that minimum. Heisenberg received the 1932 Nobel Prize in Physics for his broader creation of quantum mechanics, though the announcement was delayed until November 1933. He later joined Germany’s wartime nuclear research programme from September 1939 and was appointed director of the Kaiser Wilhelm Institute for Physics in 1942, and declassified recordings from his wartime detention, released only in 1992, indicated he had not worked out the critical mass needed for a bomb before learning of the Hiroshima attack.
Is it worth your time
This is worth an hour both for the physics itself, a genuinely fundamental limit rather than a shortcoming of instruments, refined into increasingly general mathematical form by several physicists across the following years rather than settled all at once, and for the more complicated later chapter of Heisenberg’s own life. The same mind that formalised the deepest limits of what can be known about a particle spent the Second World War inside a weapons programme whose actual progress historians are still working to understand fully, from records only released decades afterward.
