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Saketh
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How are the Planck length, Planck time, and Planck mass "derived"?
I know their values, but I don't understand where we get them from.
I know their values, but I don't understand where we get them from.
Saketh said:I once saw a problem which asked to "derive" the Planck units. Your explanation makes sense -- that the units are just a standard -- but are the units a logical outgrowth of a previous scientific result? Or are they nothing more than a standard?
The Planck length is a fundamental constant in physics that represents the smallest possible length scale in the universe. It is derived from three other fundamental constants: the speed of light, the gravitational constant, and Planck's constant. The formula for the Planck length is given by LP = √(ħG/c3), where ħ is Planck's constant, G is the gravitational constant, and c is the speed of light.
The Planck time is another fundamental constant that represents the smallest possible unit of time. It is derived from the same three fundamental constants as the Planck length: the speed of light, the gravitational constant, and Planck's constant. The formula for the Planck time is given by tP = √(ħG/c5), where ħ is Planck's constant, G is the gravitational constant, and c is the speed of light.
The Planck length and time are significant because they represent the limits of our current understanding of the universe. They are the smallest possible units of length and time that can be measured, and they are associated with the fundamental forces of nature: gravity and electromagnetism. The Planck length and time are also used in theories such as string theory and loop quantum gravity to describe the structure of spacetime at a microscopic level.
Yes, there is a formula for the Planck mass, which is another fundamental constant derived from the same three fundamental constants as the Planck length and time. The formula for the Planck mass is given by mP = √(ħc/G), where ħ is Planck's constant, c is the speed of light, and G is the gravitational constant.
The Planck length, time, and mass are all derived from the same three fundamental constants and are all related to each other through the laws of physics. For example, the Planck mass can be calculated by multiplying the Planck length by the speed of light and dividing by the Planck time. Additionally, the Planck length and time are related through the speed of light, as seen in their respective formulas. These fundamental constants provide a way to understand the universe at a very small scale and can help us develop a more comprehensive theory of everything.