Planck length — LLMpedia

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Planck length The Planck length is a fundamental physical scale proposed in the context of Max Planck's work and later developments by Albert Einstein, Paul Dirac, Werner Heisenberg, Erwin Schrödinger, and researchers in general relativity and quantum mechanics. It appears in discussions involving the Planck constant, the gravitational constant, the speed of light in vacuum, and the combination of constants used in Planck units. The scale is often cited in proposals by proponents of quantum gravity such as scholars around John Archibald Wheeler, Roger Penrose, Stephen Hawking, Abhay Ashtekar, and researchers at institutions like CERN, Perimeter Institute for Theoretical Physics, and Institute for Advanced Study. Debates about its role intersect with work by groups associated with Loop Quantum Gravity, String Theory, M-theory, Asymptotic Safety, and alternatives advanced by Carlo Rovelli, Edward Witten, Juan Maldacena, and Lee Smolin.

Definition and value

The Planck length is defined using combinations of the universal constants introduced by Max Planck and later used by Albert Einstein in general relativity: specifically the reduced Planck constant (ħ), the gravitational constant (G), and the speed of light c widely employed in special relativity. Its conventional numeric value is approximately 1.616255×10^−35 metres, a quantity reported in data compilations by organizations such as the International Bureau of Weights and Measures, and used in theoretical work by researchers at NASA, European Space Agency, and academic groups at Cambridge University, Princeton University, and Harvard University. This length scale is central to discussions in texts like those by Stephen Hawking, Roger Penrose, Kip Thorne, Brian Greene, and Leonard Susskind.

The idea of natural units based on fundamental constants originates with Max Planck in the early 20th century, influenced by exchanges with contemporaries such as Albert Einstein, Hendrik Lorentz, Wilhelm Wien, and Planck's contemporaries at the Kaiser Wilhelm Institute. Later attention to the Planck length emerged in the context of reconciling general relativity with quantum mechanics through work by John Archibald Wheeler on geometrodynamics, by Paul Dirac on large number hypotheses, and by Oskar Klein in compactification ideas pursued by Theodor Kaluza and Kaluza–Klein theory. Debates during the mid-20th century involved figures like Richard Feynman, Julian Schwinger, Freeman Dyson, and were later shaped by conceptual frameworks developed at research centers such as Los Alamos National Laboratory and the Institute for Advanced Study.

The Planck length can be obtained by dimensional analysis combining ħ, G, and c in the expression l_P = sqrt(ħ G / c^3). This procedure uses constants first emphasized by Max Planck and employed in quantum field theory by Paul Dirac and Richard Feynman, making the scale relevant to phenomena studied by the CERN community and theorists such as Edward Witten and Juan Maldacena. The derivation is similar in spirit to constructions of other Planck units discussed by Max Planck and later compiled by national metrology institutes like the National Institute of Standards and Technology and the International Bureau of Weights and Measures.

Physically, the Planck length is interpreted by many researchers as the scale at which classical notions of spacetime from Albert Einstein's general relativity may cease to apply and quantum effects emphasized by Niels Bohr, Werner Heisenberg, and Erwin Schrödinger become dominant. Authors such as Stephen Hawking, Roger Penrose, Carlo Rovelli, Lee Smolin, and Abhay Ashtekar discuss scenarios where spacetime might be discrete or exhibit foam-like structure described in proposals by John Wheeler (spacetime foam) or by string-theoretic frameworks advanced by Michael Green and John Schwarz. Interpretations also appear in cosmological contexts treated by Alan Guth, Andrei Linde, Max Tegmark, and researchers at Kavli Institute for Theoretical Physics.

The Planck length functions as a reference scale in competing approaches to quantum gravity developed by Loop Quantum Gravity proponents such as Carlo Rovelli and Abhay Ashtekar and in String Theory and M-theory programs led by Edward Witten, Juan Maldacena, and Michael Green. It features in semiclassical analyses by Stephen Hawking of black hole thermodynamics and in conjectures like the holographic principle associated with Gerard 't Hooft and Leonard Susskind, and in the AdS/CFT correspondence elaborated by Juan Maldacena. Alternative approaches including Asymptotic Safety advocated by Steven Weinberg and causal set theory discussed by Rafael Sorkin also reference Planck-scale effects in their formulations.

Direct measurement of Planck-scale structure remains beyond current experimental reach according to teams at CERN, LHC, LIGO Scientific Collaboration, Virgo, and observatories like Fermi Gamma-ray Space Telescope and Event Horizon Telescope. Empirical bounds are set indirectly via high-energy astrophysical observations considered by researchers such as Sheperd Doeleman, Vera Rubin Observatory collaborators, and particle-physics experiments involving groups at SLAC National Accelerator Laboratory and Brookhaven National Laboratory. Proposed probes include studies of gamma-ray bursts examined by Neil Gehrels's teams, precision tests of Lorentz symmetry pursued by Alan Kostelecký, and tabletop experiments inspired by concepts from John Preskill and Frank Wilczek, but none have produced conclusive evidence of discrete spacetime at the Planck length.