Follow the progression of the Planck Length to the Observable Universe in just 201+ notations within this horizontally-scrolled, working chart of the universe. We invite you to help us interpret what it means!
“In physics, the Planck length, denoted <span ℓP, is a unit of length, equal to 1.616199(97)×10−35 metres. It is a base unit in the system of Planck units, developed by physicist Max Planck. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, the Planck constant, and the gravitational constant.”
“The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the quantum of length, the smallest measurement of length with any meaning. And roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton.”
“All of the quantities that have “Planck” attached to their name can ultimately be understood from the concept of the “Planck mass.” The Planck mass, roughly speaking, is the mass a point particle would need to have for its classical Schwarzschild radius (the size of its event horizon, if you like) to be the same size as its quantum-mechanical Compton wavelength (or the spread of its wave-function, if you like). That mass is 1019 GeV/c2, or about 10-8 kilograms.”
“The significance of this mass is that it is the energy scale at which the quantum properties of the object (remember, this is a point particle!) are as important as the general relativity properties of the object. Therefore it is likely to be the mass scale at which quantum gravity effects start to matter. Turning this into a mass is as simple as using the formula for the Compton wavelength given in the above link and plugging in the Planck mass. Thus, the Planck length is the typical quantum size of a particle with a mass equal to the Planck mass. As you point out, the Planck time is then just the Planck length divided by the speed of light.”
“Since the Planck length has this special property of being the length scale where we can’t ignore quantum gravity effects, it is typically taken to be the size of a fundamental string, in string theory. Alternatively, if we consider more general theories of quantum gravity, one might speculate that it is the typical size of the “fuzziness” of spacetime. It’s a length scale (or energy scale) we are unlikely to probe in any future experiments so we tend to interpret it as the length scale at which classical general relativity (GR) “breaks down” — i.e. at which classical GR fails to provide an accurate description of nature. This is very similar to the way that the speed of light is considered the velocity scale at which Newtonian mechanics “breaks down” and special relativity is called for.”
Answered by: Brent Nelson, Ph.D., Research Fellow, University of Michigan
Follow the progression of the Planck Length to the Observable Universe in just 202 notations within this horizontally-scrolled, working chart of the universe.
Take three the constants: (1) Planck Constant (hbar relates to quantum mechanics), (2) the speed of light (creates to relativity), and (3) the universal gravitational constant G (of course, relates to gravity).
Combine the three in the only way to create a length: Planck Length equals the square root of hbar times G divided by c3 = 1.616229(38)×10−35 meters
Using dimensional analysis, a natural length scale emerges by quantizing gravitation with the curvature of space. It may also be true that another way to calculate it is within the entropy for black holes. A formula which is beyond our current comprehension is S = A / (4 L)2 where A is the area of the event horizon.