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delplace
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does anyone know something about the ratio of Planck length to Planck mass : signification, use in quantum relationships...
What is the Significance of the Planck Length-to-Mass Ratio in Quantum Physics?
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- Thread starter delplace
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- Length Mass Planck Planck length Ratio
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SUMMARY
The discussion centers on the significance of the Planck length-to-mass ratio in quantum physics, specifically highlighting the formulas for Planck length and Planck mass. The Planck length is defined as \(\ell_P = \sqrt{\frac{\hbar G}{c^3}}\) and the Planck mass as \(m_P = \sqrt{\frac{\hbar c}{G}}\). The ratio of Planck length to Planck mass simplifies to \(G/c^2\), indicating that \(\hbar\) does not factor into quantum relationships. The conversation also addresses a common misconception regarding the equations presented.
PREREQUISITES- Understanding of quantum mechanics concepts
- Familiarity with fundamental constants: \(\hbar\), \(G\), and \(c\)
- Basic knowledge of dimensional analysis in physics
- Ability to interpret mathematical equations in physics
- Research the implications of the Planck length in quantum gravity theories
- Explore the role of Planck units in theoretical physics
- Study the relationship between quantum mechanics and general relativity
- Investigate the significance of the Planck mass in particle physics
Physicists, students of quantum mechanics, and researchers interested in the foundational aspects of quantum theory and its relationship to gravity.
- #2
Vanadium 50
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The Planck length is: \sqrt{\frac{\hbar G}{c^3}}
and the Planck mass is: \sqrt{\frac{\hbar c}{G}}
The ratio is therefore G/c^{2}. Since there is no \hbar, it will not appear in "quantum relationships".
and the Planck mass is: \sqrt{\frac{\hbar c}{G}}
The ratio is therefore G/c^{2}. Since there is no \hbar, it will not appear in "quantum relationships".
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- #3
malawi_glenn
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Is this post also just for "testing us"? To see if we are worth your time?
- #4
Orion1
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Vanadium_50 said:
Negative, that equation is incorrect.
Planck length:
\ell_P = \sqrt\frac{\hbar G}{c^3}
[/Color]
Reference:
http://en.wikipedia.org/wiki/Planck_length"
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Vanadium 50
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Typo fixed. The point that hbar divides out, though, is unaffected.
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At least nobody is asking for Planck length divided by Planck time ...
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malawi_glenn
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Planck colour divided by Planck field then?
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