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HISTORY This unit was first developed by Max Planck who created a system of measurement based on natural units by using universal physical constants. The Planck length, Planck Time , and Planck Mass are units judiciously chosen so that ''c'', ''G'', and are all equal to 1 and thus disappear from equations of physical law that use those scaling factors. Although Quantum Mechanics and General Relativity were unknown at the time that the units were proposed, it later became clear that at distances of the Planck length, gravity would begin to display Quantum Mechanical effects, requiring a theory of Quantum Gravity to explain the effects. VALUE Ignoring a factor of , the Planck Mass is a mass whose Schwarzschild Radius and Compton Length are the same distance. This distance, called the Planck length, is equal to: : Metre where: : is The Reduced Planck Constant (or Dirac's Constant ) G c In common terms, the Planck length is equivalent to 10-33 centimeters. The estimated radius of the observable Universe (7.4 × 1026 M ) is 1.2 × 1062 Planck lengths. SIGNIFICANCE Ignoring a factor of , the Planck Mass is roughly the mass of a black hole whose Schwarzschild Radius equals its Compton Wavelength . The radius of such a black hole is roughly the Planck length. The meaning of this can be illustrated by a Thought Experiment . Assume the task is to measure an object's position by bouncing light off of it. To measure its position to high accuracy, photons of high energy and short wavelength are needed. If their energy is high enough to measure more precisely than a Planck length, they would in principle create a black hole when they collide with the object. The black hole would "swallow" the photon and make it impossible to obtain a measurement, and therefore defeat the experiment. A simple calculation using dimensional analysis suggests that this problem occurs when the object's position is measured at a length more precise than a Planck length. Note that this thought experiment involves both General Relativity and Quantum Mechanics (namely the Heisenberg Uncertainty Principle ). Together, these theories state it is impossible to measure positions more accurately than the Planck length. So, it suggests that in any theory of Quantum Gravity combining general relativity and quantum mechanics, traditional notions of space and time will break down at distances shorter than the Planck length or times shorter than the Planck Time . Therefore, the discovery that energy is quantized leads also to the fact that under the laws of physics as presently understood, space and time are also quantized (discrete, or "grainy" if you will) and not continuous. SEE ALSO EXTERNAL LINKS |
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