page_title: Introduction to quantum mechanics
section_title: Copenhagen interpretation
hierarchical_section_title: Introduction to quantum mechanics / Copenhagen interpretation
caption_attribution_description: English: The Niels Bohr Institute at University of Copenhagen. Taken by me on 26-3-2005.
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: Bohr, Heisenberg, and others tried to explain what these experimental results and mathematical models really mean.  Their description, known as the Copenhagen interpretation of quantum mechanics, aimed to describe the nature of reality that was being probed by the measurements and described by the mathematical formulations of quantum mechanics.
  The main principles of the Copenhagen interpretation are:
  A system is completely described by a wave function, usually represented by the Greek letter  ("psi"). (Heisenberg)
  How  changes over time is given by the Schrödinger equation.
  The description of nature is essentially probabilistic. The probability of an event—for example, where on the screen a particle shows up in the double-slit experiment—is related to the square of the absolute value of the amplitude of its wave function. (Born rule, due to Max Born, which gives a physical meaning to the wave function in the Copenhagen interpretation: the probability amplitude)
  It is not possible to know the values of all of the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
  Matter, like energy, exhibits a wave–particle duality. An experiment can demonstrate the particle-like properties of matter, or its wave-like properties; but not both at the same time. (Complementarity principle due to Bohr)
  Measuring devices are essentially classical devices, and measure classical properties such as position and momentum.
  The quantum mechanical description of large systems should closely approximate the classical description. (Correspondence principle of Bohr and Heisenberg)
  Various consequences of these principles are discussed in more detail in the following subsections.
caption: The Niels Bohr Institute in Copenhagen, which was a focal point for researchers in quantum mechanics and related subjects in the 1920s and 1930s. Most of the world's best known theoretical physicists spent time there.
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