Planck length (Rev #4) in nLab
Context
Gravity
Formalism
Definition
Spacetime configurations
Properties
Spacetimes
| black hole spacetimes | vanishing angular momentum | positive angular momentum |
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| vanishing charge | Schwarzschild spacetime | Kerr spacetime |
| positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
Quantum theory
Physics
physics, mathematical physics, philosophy of physics
Surveys, textbooks and lecture notes
theory (physics), model (physics)
experiment, measurement, computable physics
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Axiomatizations
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Tools
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Structural phenomena
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Types of quantum field thories
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Contents
Idea
The fundamental physical unit of length.
Definition
Two important physical units of length induced by a mass mm are
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ℓ m≔2πℏmc \ell_m \coloneqq \frac{2 \pi \hbar}{m c}
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r m≔2mG/c 2 r_m \coloneqq 2 m G/c^2
where
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cc is the speed of light;
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ℏ\hbar is Planck's constant;
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GG is the gravitational constant;
Solving the equation
ℓ m = r m ⇔ 2πℏ/mc = 2mG/c 2 \array{ & \ell_m &=& r_m \\ \Leftrightarrow & 2\pi\hbar / m c &=& 2 m G / c^2 }
for mm yields the Planck mass
m P≔1πm ℓ=r=ℏcG. m_{P} \coloneqq \tfrac{1}{\sqrt{\pi}} m_{\ell = r} = \sqrt{\frac{\hbar c}{G}} \,.
The corresponding Compton wavelength ℓ m P\ell_{m_{P}} is given by the Planck length ℓ P\ell_P
ℓ P≔12πℓ m P=ℏGc 3 \ell_{P} \coloneqq \tfrac{1}{2\pi} \ell_{m_P} = \sqrt{ \frac{\hbar G}{c^3} } \,
References
- Wikipedia, Planck length
Revision on November 9, 2017 at 10:26:08 by Urs Schreiber See the history of this page for a list of all contributions to it.