Planck Length

The Planck length is the fundamental unit of length in the system of Planck units. It has the value:

lP = 1.62 × 10-35m

In SI units, measurements of length are made in metres (usually given the symbol m). While the metre is convenient for everyday usage, such as measuring the height of people or buildings, it becomes less practical when we discuss the sizes of very small objects such as protons (radius close to 10-15 m).

A consequence of using metres to measure lengths is that the fundamental constants take on values that are not always convenient for including in equations:

Speed of light c = 299792458 m s-1
Gravitational constant G = 6.673(10) x 10-11 m3 kg-1s-2
Plank’s constant (reduced) $ \hbar $ = h/2π = 1.054571596(82) x 10-34 kg m2 s-1
Boltzmann constant k = 1.3806502(24) x 10-23kg m2 s-2K-1

The Planck length is derived dimensionally using combinations of these fundamental constants:

$ l_P = \sqrt{\frac{G\hbar}{c^3}} $

By redefining the base units for length, mass and time in terms of the Planck units, the fundamental constants have the values: c = G = $ \hbar $ = k = 1.

The Planck length, and associated Planck time, defines the scale at which the currently accepted theory of gravity fails. On this scale, the entire geometry of spacetime as predicted by general relativity breaks down. The main reason for this breakdown is that the Planck scale is smaller than the quantum wavelength of the Universe as a whole. Consequently, on such scales, an as yet undiscovered theory that combines general relativity and quantum mechanics is needed to describe the laws of physics. At this stage, scientists have not been able to determine what this theory is, even though they understand what some of its properties should be.

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