Like Frogs in a Well

Published by Arun Isaac on

Tags: musing, physics

Simple visualizations (such as the one shown in the figure) of this curvature, typically appeal to a 2D fabric of space curved into a third dimension by the presence of a mass such as the earth. This curvature creates a three dimensional "well" into which other masses fall, thus resulting in what we perceive as gravity.

Spacetime fabric curved by the presence of a mass

Figure 1: Spacetime fabric curved by the presence of a mass

Gravity is a curvature of space, Einstein explained.

Masses distort or curve the space around them, thus creating a "well" into which other masses fall.

Simple visualizations (such as the one shown in the figure) of this curvature, typically appeal to a 2D fabric of space curved into a third dimension by the presence of a mass such as the earth. This curvature creates a three dimensional "well" into which other masses fall, thus resulting in what we perceive as gravity.

However, our world is not a 2D world curved into a 3^rd dimension, but rather a 3D world curved into a 4^th dimension. Thus, every mass creates a four dimensional "well" around it, the depth of this well depending on the magnitude of the mass. How such a 4D well can be readily visualized, I do not know. But, mathematically speaking, it makes sense.

Going by this picture of our universe, we all live out our lives in the "gravity well" of our planet earth. Essentially, we are like frogs living their lives out in a well!

It is said that frogs living in a well think that the sky is as wide as a lid. There is an old saying in my mother tongue, Tamil, "கிணற்றுத் தவளை போல", meaning "like frogs in a well", which refers to this. I suppose, we are not very much different either. We, denizens of a lonely planet, a tiny speck lost in the vastness of the cosmos, once thought that the earth was the centre of the universe. We, the humans of this time and era, know better, but our essential anthropocentrism has not changed much.

Check out "Pale Blue Dot" by Carl Sagan on YouTube at https://www.youtube.com/watch?v=wupToqz1e2g

Image Credits

Spacetime fabric curved by the presence of a mass -- by Johnstone, released under the Creative Commons Attribution-ShareAlike 3.0 Unported license