page_title: Heisenberg's uncertainty principle
section_title: The idea of indeterminacy
hierarchical_section_title: Heisenberg's uncertainty principle / The idea of indeterminacy
context_page_description: Heisenberg's uncertainty principle is one of the most important results of twentieth century physics. It relates to measurements of sub-atomic particles. Certain pairs of measurements such as where a particle is and where it is going cannot be precisely pinned down.ᵖ⁹⁶
  Albert Einstein thought that such a quantum theory could give us only a partial description of nature.ᵖ⁹⁹ He thought that Heisenberg's discovery showed that human knowledge is limited, but he also thought that nature is absolute. That is, he thought that there is no "uncertainty" in nature, and that the uncertainty exists only in our knowledge about it. However, many other scientists disagree with Einstein.
  Heisenberg's idea is that if something like an electron were shot into a big box with a certain speed and in a certain direction, then it would be possible to calculate a fairly accurate idea of what its path would be like in the future. However, if the box were made smaller then we would have a more certain idea of where it was located, and because of that we would have to have a less certain idea of how it was traveling.
context_section_description: The uncertainty principle came from Werner Heisenberg's matrix mechanics. Max Planck  already knew that the energy of a unit of light is proportional to the frequency of that unit of light (), and that its amount of energy can be expressed in familiar terms such as the joule by using a proportionality constant. The constant he gave the world is now called the Planck constant and is represented by the letter h.  When matrices are used to express quantum mechanics, frequently two matrices have to be multiplied to get a third matrix that gives the answer the physicist is trying to find. But multiplying a matrix such as P (for momentum) by a matrix such as X (for position) gives a different answer matrix from the one you get when you multiply X by P. The result of multiplying P by X and X by P and then comparing them always involves the Planck constant as a factor. The number used to write the Planck constant will always depend on the system of measurement in use. (With a certain system of measurement, its numerical value is one.) The slope of the line in the diagram to the right that shows the ratio of frequency to energy will also depend on the system of measurement chosen.
  The following diagrams show what happens when we try to measure both location and momentum.
  The practical result of this mathematical discovery is that when a physicist makes position more clear then momentum becomes less clear, and that when the physicist makes momentum more clear then position becomes less clear. Heisenberg said that things are "indeterminate," and other people liked to say that they were "uncertain." But the mathematics shows that it is the things in the world that are indeterminate or "fuzzy," and not that it is just that humans are uncertain about what is going on.
caption: E
          ∝
          ν
        
      
      {\displaystyle E\propto \nu }
    
  ,
   i.e., Energy is proportional to frequency