Stationary observers in gravitational-force fields calculate the same local object motions that stationary observers calculate for local accelerating objects. Accelerating observers feel the same effects as if they were stationary in gravitational-force field. Local accelerations and gravitational-field effects curve space the same. Uniform-velocity observers cannot distinguish whether object motions are due to gravitational force or acceleration {equivalence principle}| {principle of equivalence} {background independence, acceleration}.
To observers, accelerations caused by gravitation and accelerations caused by mechanical forces are equivalent. Observers cannot distinguish between gravity-caused accelerations and rocket, elevator, or collision accelerations. For example, people inside an elevator cannot distinguish if elevator has accelerated upward or gravitational field is greater, because locally they feel the same stress on their feet.
non-local
Except for high gravity and/or acceleration, space-time points approximate reference frames with linear coordinate transformations. Observers apply special relativity.
Over space-time regions, gravitational fields vary with distance and accelerations vary, so reference frames have non-linear coordinate transformations. Over space-time regions, because space-time curvature differs over space-time points, observers can distinguish object motions due to accelerations or to gravitational-force fields. Observers apply general relativity.
inertial and gravitational mass
Mass has two properties. Mass (gravitational mass) causes gravity. Mass {inertial mass} resists acceleration. Because space-time unifies space and time, gravitational mass is the same as inertial mass, because they both curve space-time the same amount. For example, in gravitational fields, all objects, no matter what their mass, accelerate (free fall) at same rate. Same-diameter lead balls fall at same rate as cloth balls. Object acceleration depends only on gravitational-field strength, not on object mass. This is because, gravity from object and object resistance to motion are equal. Objects in free fall feel no force. Observers in free fall observing objects in free fall see no relative motion. Space-time curvature is not an outside force but sets the field of motion.
Physical Sciences>Physics>Relativity>General Relativity>Principles
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Date Modified: 2022.0224