Explaining Plank Length & Its Dependence on Constants

[Ed Quanta]

The question I am trying to answer is:
'Explain why you would expect the Plank length to depend on the three fundamental constants G, c and h, ie assume that there is some function with f(lp,G,c,h)=0'

So..., what is the answer?

 

[selfAdjoint]

The Planck length is DEFINED to be a certain function of those constants, such that all their other dimensions cancel out, and one is left with only the dimension of length. Similar definitions with different formulas give Planck time and Planck mass.

 

[R0man]

The Plank length is a concept in physics that represents the smallest possible length that can exist in our universe. It is named after the physicist Max Planck, who first proposed its existence. The Plank length is defined as the square root of the product of three fundamental constants: the gravitational constant (G), the speed of light (c), and Planck's constant (h). This means that any change in these three constants will result in a corresponding change in the Plank length.

To understand why we would expect the Plank length to depend on these three constants, we need to look at the role each of these constants plays in defining the properties of our universe.

First, let's consider the gravitational constant (G). This constant is responsible for determining the strength of the gravitational force between two objects. In other words, it determines how much two masses will attract each other. The strength of gravity is a fundamental property of our universe and plays a crucial role in the structure and behavior of objects on both a macroscopic and microscopic scale.

Next, we have the speed of light (c), which is the maximum speed at which any object can travel in our universe. This constant is a fundamental property of space and time and is the basis for Einstein's theory of relativity. It also plays a crucial role in determining the behavior of particles at the quantum level.

Finally, we have Planck's constant (h), which is a fundamental constant in quantum mechanics. It relates the energy of a photon to its frequency and is used to describe the behavior of subatomic particles. Planck's constant also plays a crucial role in determining the size and properties of atoms and molecules.

Given the significance of these three constants in defining the structure and behavior of our universe, it is not surprising that they would also play a role in determining the smallest possible length that can exist. Any change in these constants would result in a corresponding change in the Plank length, as it is derived from their product.

In summary, the Plank length is dependent on the three fundamental constants G, c, and h because they are essential in defining the properties of our universe. Any change in these constants would result in a change in the smallest possible length that can exist.