Gravity

 

Defying Gravity

It's time to try defying gravity
I think I'll try defying gravity
And you can't pull me down

Gravity follows spacetime. Is spacetime Euclidean ? Or is spacetime Non- Euclidean and  hyperbolic?

“According to Albert Einstein's general theory of relativity, gravity is no longer a force that acts on massive bodies, as viewed by Isaac Newton's universal gravitation. Instead, general relativity links gravity to the geometry of spacetime itself, and particularly to its curvature.

In classical physics, time proceeds constantly and independently for all objects. In relativity, spacetime is a four-dimensional continuum combining the familiar three dimensions of space with the dimension of time.

To account for gravity in relativity, the structure of this four-dimensional spacetime must be extended beyond the rules of classical geometry, where parallel lines never meet and the sum of a triangle’s angles is 180°. In general relativity, spacetime is not 'flat' but is curved by the presence of massive bodies."
  https://sci.esa.int/web/lisa-pathfinder/-/56434-spacetime-curvature

This is a bit of an exaggeration. Gravity IS a force, but it is an apparent, fictitious, or pseudo force. These fictitious forces  are familiar forces. Water in a bucket spinning overhead on a rope, appears to defy Gravity because of Centrifugal force. If a Centrifugal force were not acting on the water, it would slosh out of that spinning bucket. A motorcyclist in a Globe of Death seems to defy Gravity and rise on the walls because of Centrifugal force. Water in a drain spins in a clockwise direction in the Northern Hemisphere, but in a counterclockwise direction in the Southern Hemisphere, because of the Coriolis force.

Saying that Gravity is not a force, but is a fictitious force means that there is, with apologies to Paul Harvey, a Rest of The Story. Gravity is like a trick in stage magic. Understanding how it works can better understand how you were tricked. Like Humpty Dumpty told in Alice in Through the Looking Glass, understanding  Gravity means “which is to be master — that’s all.”  If you wish to master and  defy Gravity you have to understand Gravity.

Gravity is the observation that particles will follow the shortest geodesic in spacetime.  When spacetime is curved, as it is required to be by General Relativity, then what appears to the path of a particle may be because spacetime is curved.  In Euclidean , what is called classical geometry in the quote above,  this apparent deviation from a straight line is attributed to Gravity.  If spacetime is curved, Non-Euclidean, and hyperbolic where the angles in triangles sum to less than 180 degrees, then Gravity can be a fictitious force.

If Gravity is a fictitious force, then efforts to include Gravity in a Unified Field Theory may be misplaced.  If Gravity is a fictitious force then efforts to develop a theory of Quantum Gravity may be as silly as trying to develop a theory of Quantum Centrifugal Force.