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What is the Heisenberg Uncertainty Principle? - Chad Orzel


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The Heisenberg Uncertainty Principle states that you can never simultaneously know the exact position and the exact speed of an object. Why not? Because everything in the universe behaves like both a particle and a wave at the same time. Chad Orzel navigates this complex concept of quantum physics.

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Minute Physics offers a shorter version of the Uncertainty Principle argument with cartoon sheep! Check it out!

The Uncertainty Principle was introduced by Werner Heisenberg in 1927, as part of a long-running project to develop a complete theory of quantum physics. Heisenberg had developed a quantum theory in 1926 built around the idea that only directly measurable quantities should be considered. The uncertainty principle of 1927 was a further elaboration of these ideas; this became one of the pillars of the “Copenhagen Interpretation” of quantum physics, along with Niels Bohr’s Principle of Complementarity. Uncertainty relations show up between many pairs of quantities in quantum physics. The American Institute of Physics has a very good online exhibit about Heisenberg’s life and physics. It includes some audio clips of Heisenberg reflecting on the development of the theory. Michael Frayn’s play “Copenhagen” draws on this history, exploring ideas of uncertainty through an imagined conversation between Heisenberg, Bohr, and Bohr’s wife, Margrethe about the famously mysterious falling-out between Heisenberg and Bohr during WWII.

Heisenberg’s quantum theory was expressed in terms of matrix algebra, a branch of mathematics that was not commonly used in physics at the time (in fact, Heisenberg laboriously re-invented a good deal of mathematics before his mentor Max Born recognized that he was working with matrices), and was initially very coolly received. The Austrian physicist Erwin Schrodinger developed a wave equation at about the same time that produced the same results, by more familiar means, and the Schrodinger equations was more rapidly embraced. The two formulations are mathematically equivalent, though, and modern physicists learn both and switch between them readily, using whichever picture is most convenient for a given problem. Heisenberg won the 1932 Nobel Prize in Physics. Schrodinger shared the 1933 Nobel Prize in Physics with Paul Dirac, who managed to incorporate Einstein’s special relativity into quantum mechanics in 1930.

While the Uncertainty Principle limits what we can know about the position and momentum of an object simultaneously, in many cases, we only care about one of the two properties, and can improve our knowledge of that quantity at the cost of losing information about the other. In optics, many experiments make use of “squeezed states” of light, which sacrifice information about the number of photons in a laser pulse to gain better information about the phase of the field. Here is a blog post “What is Squeezing” describing this! Squeezed light is used to boost the sensitivity of the Laser Interferometer Gravity-wave Observatory (LIGO), and the LIGO magazine devoted a special issue to squeezed light. Squeezed states can also be made with atoms as described in these two posts: Post One and Post Two .

The Uncertainty Principle limits the information that can be known from a single realization of an experiment, but in recent years, physicists have been exploring the use of “weak measurements” to reconstruct the average position and momentum of quantum objects through many repetitions of a given experiment. One of these experiments traced the path of photons going through a double-slit experiment. This was deemed the top breakthrough of 2011 by Physics World magazine!

Finally, it should be noted that the interpretation presented in the video, while fairly widely accepted, is not the only formulation of quantum mechanics. In the 1950’s, David Bohm showed that the Schrodinger equation governing the wavefunction of a quantum object can be re-formulated in such a way that the object in fact has a definite position and momentum at all times, but is “guided” by a field that depends on the usual quantum wavefunction. While “Bohmian mechanics” recovers some of the well-defined properties of classical physics, the guiding field must have some mathematical properties that raise a different set of philosophical issues relating to the phenomenon of entanglement. So, it doesn’t “fix” all the weirdness of quantum physics.

The Bohmian approach has a small but passionate community of advocates actively researching its implications. As yet, it does not produce any predictions that are experimentally distinguishable from the more orthodox interpretations, but comparing the approaches provides valuable insights into the philosophical foundations of quantum physics. A blog post offers a brief non-mathematical description. A more technical description can be found at the Stanford Encyclopedia of Philosophy and Bohmian-Mechanics offers a number of resources on the theory that you may find interesting!

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