Deriving Planck Length: Smallest Possible Length?

[Ed Quanta]

Ok so I understand how we derive Planck Length using the natural constants G,h, and c. However, how do we know this indeed represents the smallest possible length an object in the universe? Or does Planck length just represent the smallest possible length under which gravity is still influential?

 

[Andrew Mason]

Ok so I understand how we derive Planck Length using the natural constants G,h, and c. However, how do we know this indeed represents the smallest possible length an object in the universe? Or does Planck length just represent the smallest possible length under which gravity is still influential?

The Planck length is thought to be a fundamental unit of length below which length or distance has no meaning. It is said to be the smallest distance that can exist and still have meaning. How do we know that? We don't. It is just a theory and has never been tested. (Mind you, no one has found anything smaller, yet).

Planck invented the concept of natural units of mass, length and time. The idea was that you could avoid having to use these constants if you expressed mass, length and time in terms Planck units (for example, you would forget about G and express gravitational force in terms of Planck mass and length, as $$n\frac{m_p^2}{l_p^2}$$).

That these units could also have physical meaning seems to me to be somewhat of a stretch.

AM

 

[sir-pinski]

The Planck length is derived from the fundamental constants of nature, namely the gravitational constant (G), Planck's constant (h), and the speed of light (c). It is the scale at which quantum effects become significant and cannot be ignored. This means that at distances smaller than the Planck length, our current understanding of physics breaks down and we need a new theory to accurately describe the behavior of particles.

It is important to note that the Planck length is not the smallest possible length in the universe. It is simply the smallest length that our current understanding of physics can accurately describe. It is possible that there may be even smaller lengths that we are not yet aware of or cannot measure with our current technology.

Additionally, the Planck length does not necessarily represent the smallest length under which gravity is still influential. Gravity is a fundamental force that operates at all scales, and its effects can be observed even at the smallest scales. It is only when we try to combine gravity with quantum mechanics that the Planck length becomes significant.

In summary, the Planck length is a fundamental length scale that is derived from the fundamental constants of nature. It represents the smallest length that our current understanding of physics can accurately describe, but it is not necessarily the smallest length in the universe. It also does not necessarily signify the smallest scale at which gravity is influential.