constant

planck mass

Planck mass, the fundamental mass scale in quantum gravity
Value
\(m_{P} = 2.176434 \times 10^{-8}\)kilogram
24 related articles · 1 formulas

Description

The Planck mass is a fundamental scale in physics where quantum effects and gravitational effects become equally important. It is defined as the mass of a particle whose reduced Compton wavelength equals its Schwarzschild radius, making it the natural unit of mass in quantum gravity. Its value is about 2.18×10^-8 kg, which is roughly the mass of a grain of dust, but it corresponds to an enormous energy of about 10^19 GeV.

History

The concept was introduced by Max Planck in 1899, who proposed natural units based on these constants, though he did not explicitly discuss its role in quantum gravity. The modern interpretation as the scale of quantum gravity developed in the mid-20th century.

How it works

The Planck mass emerges from combining three fundamental constants: the speed of light (c), the reduced Planck constant (ħ), and Newton's gravitational constant (G). It is given by m_P = sqrt(ħc/G). At this mass scale, the gravitational attraction between two such particles would be so strong that quantum fluctuations of spacetime itself become significant, requiring a full theory of quantum gravity to describe.

In practice

It is not directly used in everyday technology, but it sets the energy scale for hypothetical particles like the graviton and for theories of quantum gravity, such as string theory and loop quantum gravity.

Fun fact

The Planck mass is about 2.18×10^-8 kg, which is roughly the mass of a flea egg, yet it packs the energy of a large lightning bolt into a single particle.

Concept graph →

Formulas

$$G\mu = \frac{\mu}{m_{\text{Pl}}^2}$$
Dimensionless measure of cosmic string energy density.
What is in the formula
μvariablemass per unit length of cosmic string — linear mass density kilogram per metre
GconstantNewton's constant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
m_PlconstantPlanck mass, the fundamental mass scale in quantum gravity — planck mass = 2.176434e-8 kilogram

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