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| Extra dimensions | |
|---|---|
| Name | Extra dimensions |
| Field | Theoretical physics, Mathematics |
| Introduced | 19th century–20th century |
| Proponents | Theodor Kaluza, Oskar Klein, Kaluza–Klein proponents, Albert Einstein, Isaac Newton, Edward Witten, Juan Maldacena |
Extra dimensions Extra dimensions are hypothesized spatial or spacetime directions beyond the familiar three spatial and one temporal dimensions described in Isaac Newton's classical mechanics and Albert Einstein's General relativity. These proposals appear across research by Theodor Kaluza, Oskar Klein, Albert Einstein, Paul Dirac, Edward Witten, Juan Maldacena and institutions such as CERN, Princeton University, Institute for Advanced Study and California Institute of Technology. They motivate efforts in string theory, M-theory, Kaluza–Klein theory, brane cosmology and influence searches at experimental sites like Large Hadron Collider and observatories including Planck (spacecraft), LIGO.
The idea that physical reality may include additional spatial or temporal dimensions extends work by Bernhard Riemann on manifolds and by Hermann Minkowski on spacetime, and was formalized in proposals by Theodor Kaluza and Oskar Klein to unify James Clerk Maxwell's electromagnetism with Albert Einstein's gravitation. Modern formulations are central to frameworks developed at Princeton University, Harvard University, University of Cambridge and collaborative centers like Perimeter Institute. Research connects to major projects such as Large Hadron Collider, Wilkinson Microwave Anisotropy Probe, Planck (spacecraft) and theoretical programs led by figures including Edward Witten, Andrew Strominger, Joseph Polchinski and Cumrun Vafa.
Early mathematical groundwork for additional dimensions traces to Bernhard Riemann's 19th-century lectures and to attempts at unification in the 1920s by Theodor Kaluza and Oskar Klein, producing the Kaluza–Klein theory that linked James Clerk Maxwell's equations with gravity. Mid-20th-century interest intersected with work by Paul Dirac and advances at institutions like University of Göttingen and University of Cambridge. Renewed momentum arrived in the 1980s and 1990s with the emergence of string theory and later M-theory at research centers including Institute for Advanced Study, CERN, Caltech and SLAC National Accelerator Laboratory, driven by theorists such as Edward Witten, Michael Green, John Schwarz and Joseph Polchinski. Experimental impetus has been shaped by large collaborations at Large Hadron Collider, observational programs by Joint Institute for Nuclear Research and space missions like Planck (spacecraft).
Prominent frameworks include Kaluza–Klein theory, compactification models from string theory, warped extra dimensions in the Randall–Sundrum model developed at Princeton University and Stanford University, and braneworld scenarios inspired by Horava–Witten theory within M-theory. These approaches interact with mathematical programs at University of Oxford, Cambridge University and Institut des Hautes Études Scientifiques and inform conjectures by Juan Maldacena such as the AdS/CFT correspondence connecting anti-de Sitter space descriptions with Conformal field theory on lower-dimensional boundaries. Theoretical work also draws on contributions by Nathan Seiberg, Shinobu Hosono, Cumrun Vafa and groups at Max Planck Institute for Physics.
Mathematical descriptions use Riemannian and Lorentzian geometry developed from Bernhard Riemann and Hermann Minkowski, fiber bundle constructions from Elie Cartan and Hermann Weyl, and topology studied by Henri Poincaré and Élie Cartan. Compactification employs manifolds such as Calabi–Yau manifolds studied by Shing-Tung Yau and Phillip Candelas, orbifold techniques popularized in heterotic string work, and warped metrics from the Randall–Sundrum model. Field-theoretic treatments rely on methods advanced by Kenneth Wilson's renormalization group, path integral techniques from Richard Feynman, and supersymmetry formulations by Peter van Nieuwenhuizen and Sergio Ferrara. Mathematical consistency conditions include anomaly cancellation discussed by Michael Green and John Schwarz and dualities articulated by Edward Witten and Joseph Polchinski.
Searches for signatures of extra dimensions occur at Large Hadron Collider experiments such as ATLAS and CMS, in tabletop tests of Newtonian gravity at submillimeter scales conducted by groups linked to University of Washington and Institut Laue–Langevin, and through cosmological probes including Planck (spacecraft), Wilkinson Microwave Anisotropy Probe, Large Synoptic Survey Telescope and LIGO. Constraints derive from nonobservation of Kaluza–Klein resonances, limits on missing energy events at CERN, precision tests by collaborations at Brookhaven National Laboratory and Fermilab, and astrophysical bounds from Supernova 1987A observations analyzed by teams at European Southern Observatory and NASA. Null results have tightened parameter space relevant to models by Randall and Sundrum, Arkani-Hamed, Dimopoulos, Dvali and compactification schemes studied at CERN.
Extra-dimensional models offer mechanisms for addressing the hierarchy problem explored by Lisa Randall, Nima Arkani-Hamed and Savas Dimopoulos, provide dark sector candidates investigated by collaborations at Fermi Gamma-ray Space Telescope and Dark Energy Survey, and influence inflationary scenarios developed by Alan Guth, Andrei Linde and Paul Steinhardt. Connections to AdS/CFT correspondence spur reinterpretations of strongly coupled gauge theories studied at CERN and Institute for Advanced Study, while braneworld cosmologies interface with studies by Sean Carroll, Ruth Durrer and David Wands on cosmic microwave background anisotropies measured by Planck (spacecraft).
Critiques arise from the lack of definitive empirical evidence despite extensive searches at Large Hadron Collider and precision experiments at National Institute of Standards and Technology. Philosophical and methodological objections have been raised in forums at Perimeter Institute and Royal Society about testability, while alternative approaches include asymptotic safety advocated by Steven Weinberg, loop quantum gravity advanced at Pennsylvania State University and Rovelli's group, and emergent gravity scenarios explored by researchers at Princeton University and Cambridge University. Ongoing work by experimental collaborations at CERN, LIGO, Planck (spacecraft) and observatories worldwide continues to refine constraints and evaluate competing theories.