anuttarasammyak said:
Better practice, although you are right in asking as some authors are sloppy in their typesetting, is to indicate the reduced Planck mass with diagonal line through the letters P or Pl in the subscript, just as one indicates the reduced Planck's constant with a diagonal link through the symbol "h" for Planck's constant.Alpha2021 said:
The Planck mass (M_{Pl}) is a fundamental physical constant derived from fundamental constants of nature: the speed of light (c), the gravitational constant (G), and the reduced Planck constant (ℏ). It is approximately 2.18 × 10^-8 kilograms.
The reduced Planck mass (often denoted as M_{Pl} or M_{Pl}^*) is the Planck mass divided by the square root of 8π. It is used in many areas of theoretical physics, particularly in contexts such as quantum field theory and general relativity. Its value is approximately 2.43 × 10^-8 kilograms.
The distinction arises because the reduced Planck mass simplifies equations in theoretical physics. By dividing the Planck mass by the square root of 8π, many equations, particularly those involving gravitational interactions, become more concise and easier to work with.
The Planck mass is often used in the context of dimensional analysis and to provide a scale for quantum gravity effects. The reduced Planck mass, on the other hand, is more commonly used in the formulation of physical theories such as string theory and quantum field theory, where it leads to simpler and more elegant equations.
The choice between using the Planck mass or the reduced Planck mass depends on the context of your work. If you are dealing with gravitational interactions or theoretical physics equations, the reduced Planck mass is usually preferred for its simplicity. For general purposes and dimensional analysis, the Planck mass is often used.
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