In 1899, Max Planck suggested that there existed some fundamental natural units for length, mass, time and energy. He derived these using dimensional analysis, using only the Newton gravitational constant, the speed of light and the Planck constant - it was not yet called then.
Planck length, denoted ℓP, is a unit of length in the system of Planck units that was originally proposed by physicist Max Planck, equal to 1.616255(18)×10^−35 m.
The Planck length can be defined from three fundamental physical constants: the speed of light, the Planck constant, and the gravitational constant.
The Planck length is expected to be the shortest measurable distance, since any attempt to investigate the possible existence of shorter distances, by performing higher-energy collisions, would inevitably result in black hole production.
The Planck length is approximately the size of a black hole where quantum and gravitational effects are at the same scale: where its Compton wavelength and Schwarzschild radius are approximately the same
The Planck length is about 10^−20 times the diameter of a proton
The Planck length is the length at which quantum zero oscillations of the gravitational field completely distort Euclidean geometry. The gravitational field performs zero-point oscillations, and the geometry associated with it also oscillates.
Reference: Planck Unit - from Scholarly Community Encyclopedia
The ratio of the Planck length to the Planck time (ℓP/tP)
• Planck length = ℓP = L ≈ 1.61626 × 10^−35 m;
• Planck time = tP = T ≈ 5.391247 × 10^−44 s;
• ℓP/tP is the ratio of the Planck length to the Planck time;
Since, ℓP/tP = (1.61626 × 10^−35 m) / (5.391247 × 10^−44 s);
1. To divide two numbers in scientific notation, we subtract the exponents of the 10 and divide the coefficients:
2. Coefficient: (1.61626) / (5.391247) ≈ 0.299792458
3. Exponent: (10^(-35)) / (10^(-44)) = 10^(-35 - (-44)) = 10^9
4. So the simplified value is approximately:
5. 0.299792458 × 10^9 m/s
6. Now, we recognize that this is the speed of light in a vacuum, which is denoted by 'c':
7. c ≈ 2.99792458 × 10^8 m/s
8. So, the simplified expression is:
9. (1.61626 × 10^−35 m) / (5.391247 × 10^−44 s) ≈ 2.99792458 × 10^8 m/s;
The ratio of the Planck length to the Planck time (ℓP/tP) yields a value to the speed of light in a vacuum, c;
This is a fundamental constant in physics and is denoted by 'c'.
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