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Now, why do the objects falling towards the Earth move along the geodesic paths with no acceleration? A body in a free-fall moves with acceleration g, so, why is it written like that? To understand the passage, we must make two crucial observations. (1) To person at rest on the Earth's surface, a free-falling object is accelerating towards the ...

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user36790, please don't take this answer the wrong way. It is not meant to be disparaging. Per your user page, you are 17 years old. You have some misunderstandings. You're way ahead of your peers, many of whom will hold similar (or even stronger) misunderstandings throughout their lives. You have asked a number of related questions over the last few hours. ...

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Suppose you and I start on the equator, a kilometre apart, and we both head exactly due North in a straight line, so we head off in exactly parallel directions: Now we know that in Euclidean geometry parallel lines remain the same distance apart. But if you and I measure the distance, $d$, between us we find that $d$ starts off at 1km but decreases as we ...

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There are two answers to this. The simplest is that the curvature is small if you're far from any masses, so motion will be approximately in a straight line at a constant velocity. The second answer is far more important, but also far harder to explain. Basically it's that we define a straight line as the trajectory followed by a freely moving particle. So ...

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If you think of a right triangle, the base of the triangle is the mass, the height of the triangle is the momentum, and the energy or relativistic mass is the hypotenuse. A felt acceleration in the lab corresponds to a change in velocity ($\frac{momentum}{mass}$). This is the $tangent$ of the base angle of the triangle. It appears to the lab occupants like ...

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The acceleration you'd measure in a lab with an accelerometer would be the proper acceleration, which in relativity (unlike Newtonian physics) is distinct from the coordinate acceleration in some inertial frame (though at any given moment, the proper acceleration is equal to the coordinate acceleration in the inertial frame in which the object has an ...

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The interpretation of gravity as curvature of spacetime is model-dependent. You already mentioned the teleparallel equivalent of general relativity, modelling gravity by torsion. Another possibility are bi-metric theories, where the metric is a more ordinary field on a fixed background (this should be more in line with how string theorists tend to think of ...

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