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  2. Five-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Five-dimensional_space

    According to Klein's definition, "a geometry is the study of the invariant properties of a spacetime, under transformations within itself." Therefore, the geometry of the 5th dimension studies the invariant properties of such space-time, as we move within it, expressed in formal equations. [11]

  3. Kaluza–Klein theory - Wikipedia

    en.wikipedia.org/wiki/Kaluza–Klein_theory

    In modern geometry, the extra fifth dimension can be understood to be the circle group U(1), as electromagnetism can essentially be formulated as a gauge theory on a fiber bundle, the circle bundle, with gauge group U(1). In Kaluza–Klein theory this group suggests that gauge symmetry is the symmetry of circular compact dimensions.

  4. Multiple time dimensions - Wikipedia

    en.wikipedia.org/wiki/Multiple_time_dimensions

    Multiple independent timeframes, in which time passes at different rates, have long been a feature of stories. [15] Fantasy writers such as J. R. R. Tolkien and C. S. Lewis have made use of these and other multiple time dimensions, such as those proposed by Dunne, in some of their most well-known stories. [15]

  5. Quantum geometry - Wikipedia

    en.wikipedia.org/wiki/Quantum_geometry

    Each theory of quantum gravity uses the term "quantum geometry" in a slightly different fashion. String theory, a leading candidate for a quantum theory of gravity, uses it to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions [clarification needed], minimal possible distance scale, and other effects that challenge intuition.

  6. Quantum spacetime - Wikipedia

    en.wikipedia.org/wiki/Quantum_spacetime

    Quantum spacetimes are often described mathematically using the noncommutative geometry of Connes, quantum geometry, or quantum groups. Any noncommutative algebra with at least four generators could be interpreted as a quantum spacetime, but the following desiderata have been suggested:

  7. Quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/Quantum_mechanics

    Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.

  8. Quintessence (physics) - Wikipedia

    en.wikipedia.org/wiki/Quintessence_(physics)

    [clarification needed] Similarly, modern quintessence would be the fifth known "dynamical, time-dependent, and spatially inhomogeneous" contribution to the overall mass–energy content of the universe. Of course, the other four components are not the ancient Greek classical elements, but rather "baryons, neutrinos, dark matter, [and] radiation."

  9. Degenerate energy levels - Wikipedia

    en.wikipedia.org/wiki/Degenerate_energy_levels

    For an N-particle system in three dimensions, a single energy level may correspond to several different wave functions or energy states. These degenerate states at the same level all have an equal probability of being filled. The number of such states gives the degeneracy of a particular energy level. Degenerate states in a quantum system