Expert: Kevin Johnson - 4/18/2005

Question
1.Is the planck's length defined as the sqrt. of Planck area or is the Planck area defined as the square of planck's length (which was defined or derived first)?

2.Are all lengths integral multiples of planck length ?

Answer
Hello Z,

1. Planck area is derived from Planck length (Planck length squared).

Max Planck wished to create a system of measurement based on natural units. These are all based on the Planck mass.

The Planck mass is a mass where its Schwarzschild radius and its Compton length are equal distances. This distance, called the Planck length, is equal to:

l = (h*G/(2*pi*c^3))^(1/2) = 1.616 * 10^(-35) m

with h: Planck's constant, G: gravitational constant and c: speed of light.

The Schwarzschild radius or gravitational radius is a characteristic radius associated with every mass. The term is used in physics and astronomy, especially in the theory of gravitation, general relativity. It was found in 1916 by Karl Schwarzschild and results from his discovery of an exact solution for the gravitational field outside a static, spherically symmetric star (which is a solution of the Einstein field equations). The Schwarzschild radius is proportional to the mass. The Sun has a Schwarzschild radius of approximately 3 km, the Earth's being approximately 9 mm.

An object smaller than its Schwarzschild radius is called a black hole. The surface at the Schwarzschild radius acts as an event horizon. Neither light nor particles can escape through this surface from the region inside, hence the name black hole.

The Compton wavelength of a particle is given by
l = h/(m*c),
where h is the Planck constant, m is the particle's mass and c is the speed of light. A particle generally behaves as quantum mechanically when observed at distances shorter than its Compton wavelength.

2. Only if space is quantized, as some theories suppose. This has not yet been generally agreed upon by physicists, let alone experimentally verified.

Peace,
Kevin.