page_title: Introduction to quantum mechanics
section_title: Uncertainty principle
hierarchical_section_title: Introduction to quantum mechanics / Copenhagen interpretation / Uncertainty principle
caption_attribution_description: Werner Karl Heisenberg (1901 - 1976)
context_page_description: Quantum mechanics is the science of the very small. It explains the behavior of matter and its interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large and the small worlds that classical physics could not explain. The desire to resolve inconsistencies between observed phenomena and classical theory led to two major revolutions in physics that created a shift in the original scientific paradigm: the theory of relativity and the development of quantum mechanics. It describes these concepts in roughly the order in which they were first discovered.
  Light behaves in some aspects like particles and in other aspects like waves. Matter—the "stuff" of the universe consisting of particles such as electrons and atoms—exhibits wavelike behavior too.
context_section_description: Suppose it is desired to measure the position and speed of an object—for example a car going through a radar speed trap.  It can be assumed that the car has a definite position and speed at a particular moment in time. How accurately these values can be measured depends on the quality of the measuring equipment. If the precision of the measuring equipment is improved, it provides a result closer to the true value.  It might be assumed that the speed of the car and its position could be operationally defined and measured simultaneously, as precisely as might be desired.
  In 1927, Heisenberg proved that this last assumption is not correct. Quantum mechanics shows that certain pairs of physical properties, for example position and speed, cannot be simultaneously measured, nor defined in operational terms, to arbitrary precision: the more precisely one property is measured, or defined in operational terms, the less precisely can the other. This statement is known as the uncertainty principle. The uncertainty principle is not only a statement about the accuracy of our measuring equipment, but, more deeply, is about the conceptual nature of the measured quantities—the assumption that the car had simultaneously defined position and speed does not work in quantum mechanics. On a scale of cars and people, these uncertainties are negligible, but when dealing with atoms and electrons they become critical.
  Heisenberg gave, as an illustration, the measurement of the position and momentum of an electron using a photon of light. In measuring the electron's position, the higher the frequency of the photon, the more accurate is the measurement of the position of the impact of the photon with the electron, but the greater is the disturbance of the electron. This is because from the impact with the photon, the electron absorbs a random amount of energy, rendering the measurement obtained of its momentum increasingly uncertain (momentum is velocity multiplied by mass), for one is necessarily measuring its post-impact disturbed momentum from the collision products and not its original momentum. With a photon of lower frequency, the disturbance (and hence uncertainty) in the momentum is less, but so is the accuracy of the measurement of the position of the impact.
  At the heart of the uncertainty principle is not a mystery, but the simple fact that for any mathematical analysis in the position and velocity domains (Fourier analysis), achieving a sharper (more precise) curve in the position domain can only be done at the expense of a more gradual (less precise) curve in the speed domain, and vice versa. More sharpness in the position domain requires contributions from more frequencies in the speed domain to create the narrower curve, and vice versa. It is a fundamental tradeoff inherent in any such related or complementary measurements, but is only really noticeable at the smallest (Planck) scale, near the size of elementary particles.
  The uncertainty principle shows mathematically that the product of the uncertainty in the position and momentum of a particle (momentum is velocity multiplied by mass) could never be less than a certain value, and that this value is related to Planck's constant.
caption: Werner Heisenberg at the age of 26. Heisenberg won the Nobel Prize in Physics in 1932 for the work he did at around this time.[40]
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