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It is defined1 as : where: : is the reduced Planck Constant : is the Gravitational Constant : is the Speed Of Light in a Vacuum : is in Second s. :The two digits between the Parentheses denote the Uncertainty in the last two digits of the value. SIGNIFICANCE According to the Big Bang Theory nothing is known about the Universe at time=0, though it is presumed that all Fundamental Forces coexisted and that all Matter , Energy , and Spacetime expanded outward from an extremely hot and dense Singularity . One Planck time after the event is the closest that Theoretical Physics can get to it, and at that time it appears that Gravity separated from the other fundamental forces. One second is about 1.855×1043 Planck times. The estimated Age Of The Universe in the Big Bang theory (4.3×1017 s) would be roughly 8×1060 Planck times. The average Life Expectancy of a human is approximately 3.9×1052 Planck times. As Of 2006 , the smallest unit of time that has been directly measured is on the Attosecond (10−18 s) timescale, or around 1026 Planck times. 23 DERIVATION Ignoring a factor of , the Planck Mass is roughly the mass of a Black Hole with a Schwarzschild Radius equal to its Compton Wavelength . The radius of such a black hole would be, roughly, the Planck Length . The following Thought Experiment illuminates this fact. The task is to measure an object's position by bouncing Electromagnetic Radiation , namely Photon s, off it. The shorter the Wavelength of the photons, and hence the higher their energy, the more accurate the measurement. If the photons are sufficiently energetic to make possible a measurement more precise than a Planck length, their collision with the object would, in principle, create a minuscule black hole. This black hole would "swallow" the photon and thereby make it impossible to obtain a measurement. A simple calculation using Dimensional Analysis suggests that this problem arises if we attempt to measure an object's position with a precision greater than one Planck length. This thought experiment draws on both General Relativity and the Heisenberg Uncertainty Principle of Quantum Mechanics . Combined, these two theories imply that it is impossible to measure position to a precision greater than the Planck length, or '''duration''' to a precision greater than the time a photon moving at ''c'' would take to travel a Planck length. Hence 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'''. SEE ALSO REFERENCES |
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