How to Use Hilbert space in a Sentence

Hilbert space

noun
  • Any space with these two features, no matter its size or origin, was a Hilbert space.
    — Quanta Magazine, 26 Aug. 2026
  • Our three-color traffic light has a three-dimensional Hilbert space.
    — Quanta Magazine, 26 Aug. 2026
  • As the world influences the object, changing its state, the arrow turns smoothly through Hilbert space.
    — Quanta Magazine, 26 Aug. 2026
  • The more dimensions there are, the more information these Hilbert spaces can encode.
    — Matt Von Hippel, Quanta Magazine, 19 Nov. 2025
  • The state of any object, from an electron to a galaxy, can be captured by such a vector, pointing in some direction through such a Hilbert space.
    — Quanta Magazine, 26 Aug. 2026
  • That’s all well and good, but our Universe isn’t well-described as a physical Hilbert space, so that isn’t a compelling argument.
    — Ethan Siegel, Big Think, 8 Aug. 2025
  • This arrow points in some direction through a space capturing all the possible futures of any quantum object — a Hilbert space.
    — Quanta Magazine, 26 Aug. 2026
  • Shaghoulian observed that this split was analogous to the kind that enlarges the Hilbert spaces of topological field theories.
    — Matt Von Hippel, Quanta Magazine, 19 Nov. 2025
  • In this case, the number of possible states is unlimited, and so its Hilbert space is infinite-dimensional.
    — Matt Von Hippel, Quanta Magazine, 19 Nov. 2025
  • Its arrow exists in a three-dimensional Hilbert space, where the three axes represent the three possible future colors.
    — Quanta Magazine, 26 Aug. 2026
  • One of his lines of research seeks to distill our familiar world from the disorienting Hilbert space that encapsulates all the ways the universe could possibly be.
    — Quanta Magazine, 26 Aug. 2026
  • Its Hilbert space spans all possible measurements — energy, position, momentum, etc.
    — Quanta Magazine, 26 Aug. 2026
  • Topological field theories can also have one-dimensional Hilbert spaces.
    — Matt Von Hippel, Quanta Magazine, 19 Nov. 2025
  • Von Neumann himself helped develop it as a potential remedy for some logical inconsistencies with Hilbert space that troubled him.
    — Quanta Magazine, 26 Aug. 2026
  • Hilbert spaces, named for the early-20th-century mathematician David Hilbert, account for different quantum states by adding new mathematical dimensions.
    — Matt Von Hippel, Quanta Magazine, 19 Nov. 2025
  • Jonathan Sorce, a physicist at Princeton University, says that Hilbert space is a handy mathematical construction that is remarkably useful for describing many quantum systems — but not all of them.
    — Quanta Magazine, 26 Aug. 2026

Some of these examples are programmatically compiled from various online sources to illustrate current usage of the word 'Hilbert space.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

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