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Swapnil
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In words, how would a path of an object moving in a straight line with a constant velocity differ from the path of an accelerating object moving in a straight line according to Einstein's picture of curved space-time?
Swapnil said:In words, how would a path of an object moving in a straight line with a constant velocity differ from the path of an accelerating object moving in a straight line according to Einstein's picture of curved space-time?
selfAdjoint said:no[t] literally straight lines in a curved geometry!
I see, but I don't "see." Is there a more visual way to see the difference between the paths of the two objects. Maybe by an analogy or something...selfAdjoint said:A unaccelerated body would fillow a geodesic (no literally straight lines in a curved geometry!) The path would look locally straight in three dimensions and it would also be linear in time.
An accelerated body's path would not be a geodesic; although it might look the same in three dimensions, it would bend in the time direction.
Swapnil said:I see, but I don't "see." Is there a more visual way to see the difference between the paths of the two objects. Maybe by an analogy or something...
In the theory of General Relativity (GR), acceleration refers to the change in the rate of motion of an object, while constant velocity refers to the movement of an object at a consistent speed and direction. In GR, acceleration is described by the curvature of spacetime, while constant velocity is described as motion along a straight line in curved spacetime.
In GR, the presence of mass and energy causes spacetime to curve, which in turn affects the path of an accelerating object. The object will follow a curved path in spacetime, which is influenced by the distribution of mass and energy in the surrounding space.
No, in GR, an object cannot maintain a constant velocity without experiencing some form of acceleration. This is because any motion in spacetime is affected by the curvature of spacetime, which results in an object experiencing some form of acceleration, even if it is moving at a constant speed and direction.
The Equivalence Principle is a fundamental concept in GR that states that the effects of gravity are indistinguishable from the effects of acceleration. This principle helps us understand that, in GR, the path of an object is influenced by the curvature of spacetime caused by the distribution of mass and energy, rather than a force acting upon it.
Yes, the paths of objects in GR can be predicted and calculated accurately using the field equations of GR, which describe the relationship between the curvature of spacetime and the distribution of mass and energy. However, the calculations can become complex when considering multiple objects and their interactions in spacetime.