##### Gravity and Spacetime: Is Gravtiy a Force?

BLOG CREDITS Jatin Nitk

At the base of classical newtonion mechanics is the notion that a body’s motion can be described as a combination of inertial motion, and deviation from this inertial motion. Such deviations are caused by external forces acting on a body in accordance with Newton’s second law of motion.

The preferred inertial motions are related to the geometry of space and time: in the standard reference frames of classical mechanics, objects in free motion move along straight lines at constant speed. In modern parlance, their paths are geodesics, straight world lines in curved spacetime. According to general theory of relativity, gravity is not a force and there are no gravitational field. General theory of relativity describes gravity not as a force, but as a consequence of masses moving along straight line path in a curved spacetime caused by uneven distribution of mass. So what exactly is this spacetime? Spacetime is any mathematical model which fuses three dimensions of space and the one dimension of time into a single four dimensional manifold. Einstein described force of gravity, in his theory of general relativity, as a consequence of the curves in the fabric of spacetime. Matter like stars and planets creates distortions in spacetime that cause it to bend.

These curves, in turn, constrict the ways in which everything in universe moves, because objects have to follow paths, geodesics, along this warped curvature. Motion due to gravity is actually motion along the twists and turns of space time. However, for most application (about 30 orders of magnitude) gravity is well approximated by Newton’s law of universal gravitation, which describes gravity as a force. This can be understood easily using an analogy between a man falling off the roof of a house and an astronaut floating in a spaceship in deep space, not near any large masses. Under general theory of relativity these two scenarios are equivalent, not just similar, where both men aren’t under any gravitational field and are perfect example of an inertial frame of reference.

Man falling off a roof would be weightless and anything dropped on his way down will remain stationary relative to him or moving in uniform motion similar to the case of astronaut in deep space where he feels no weight and all objects relative to him are in rest. There is no observable distinction between inertial motion and motion under the influence of the gravitational force

. Under classical mechanics, man falling off a roof is in gravitational field of earth but under general relativity there is no such field and man is just following a straight line path, geodesics, but because spacetime is curved around matter, in this case earth, the man seems to be accelerating at 9.8 m/s2 toward earth. Both freely falling man and astronaut are in inertial frame of reference till their motion is stopped by some other objects such as earth. Similarly objects in a gravitational field behave equivalent to objects within an accelerating enclosure. For example, an observer will see a ball fall the same way in a rocket as it does on Earth, provided that the acceleration of the rocket is equal to 9.8 m/s2 (the acceleration due to gravity at the surface of the Earth).

This is called as the “Einstein equivalence principle” which states that “The outcome of any local non gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime” or simply the gravitational “force” as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference

. In conclusion, gravity is not the force of attraction that makes things fall straight down but consequence of curvature in spacetime due to matter.