Planck length and the speed of light

[helenk]

How can the Planck length and the speed of light both be universal constants? Will the Planck length change depending on your frame of reference?

:)

 

[rhenretta]

Planck length is based on 3 constants, none of which change due to speed

$$\ell_{p}=\sqrt{\frac{\hbar G}{c^3}$$

Since $$\hbar$$ , G, and c are all constants, Planck length also remains constant

 

[Entropia]

The Planck length and the speed of light are two of the most fundamental constants in physics. The Planck length is the smallest possible length in the universe, while the speed of light is the maximum speed at which anything can travel. These two constants are universal in the sense that they are the same for all observers, regardless of their frame of reference.

The Planck length is often described as the scale at which the effects of quantum mechanics and gravity become significant. It is a product of the fundamental constants of nature, including the speed of light, Planck's constant, and the gravitational constant. This means that any change in the value of the speed of light or any of these other constants would also result in a change in the value of the Planck length.

However, the speed of light and the other fundamental constants are believed to be truly universal and unchanging. This is supported by numerous experiments and observations, including the famous Michelson-Morley experiment and the measurements of the cosmic microwave background radiation. Therefore, it is highly unlikely that the Planck length would change depending on one's frame of reference.

In summary, the Planck length and the speed of light are both universal constants that are intimately connected. While the Planck length may vary depending on the values of other fundamental constants, its value is believed to be constant in all frames of reference. This reinforces the idea that these constants are truly fundamental and play a crucial role in our understanding of the universe.