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Xeinstein
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Inside a spherical cavity centered at the Earth's center, is the space-time curvature is 0 or not 0? Would the clock run more slowly?
DaleSpam said:I am no GR expert, but my understanding is that there is 0 curvature. Light rays would not be deflected, nor would projectiles, and clocks at different points within the cavity would run at the same rate. These clocks would run slower than clocks on the surface because photons that went out from the cavity would be gravitationally redshifted as they climed.
Xeinstein said:Inside a spherical cavity centered at the Earth's center, is the space-time curvature is 0 or not 0?
Xeinstein said:Would the clock run more slowly?
nanobug said:Relative to what observer?
Xeinstein said:Is it possible that clocks run slower and curvature is zero?
In other words, wouldn't these two contradict each other?
No. My understanding is that there is no curvature within the cavity, so different clocks within the cavity will run at the same rate. Between the cavity and the surface is a region of curvature, and clocks within the cavity will run slower than clocks at the surface.Xeinstein said:Is it possible that clocks run slower and curvature is zero?
In other words, wouldn't these two contradict each other?
DaleSpam said:No. My understanding is that there is no curvature within the cavity, so different clocks within the cavity will run at the same rate. Between the cavity and the surface is a region of curvature, and clocks within the cavity will run slower than clocks at the surface.
My GR is not strong enough to really answer your question completely. But with the caveat that I am fairly ignorant here and may very well be wrong:Xeinstein said:Can you tell me if clock rate depend on "gravitational potential" or curvature?
DaleSpam said:I am no GR expert, but my understanding is that there is 0 curvature. Light rays would not be deflected, nor would projectiles, and clocks at different points within the cavity would run at the same rate. These clocks would run slower than clocks on the surface because photons that went out from the cavity would be gravitationally redshifted as they climed.
Because there is a region with spacetime-curvature between "away from any mass" and "inside the cavity". When you move a clock from "far away" trough that region, it's rate slows down (compared to a clock "far away"). When it reaches the cavity it is already going slower by a certain ratio, than the far-away-clock. But moving it around within the cavity doesn't change that ratio anymore.Xeinstein said:The curvature of outer space, away from any mass, is zero and inside the cavity is also zero. Is it true that the clock at outer space run faster than the clock inside the cavity, why it is so?
In simple terms: On the "gravitational potential". And curvature exists where the "gravitational potential" changes.Xeinstein said:Can you tell me if clock rate depend on "gravitational potential" or curvature?
The concept of curvature inside a cavity refers to the curvature of space or the shape of the inner surface of a cavity. This is often used in physics and engineering to study the effects of curved surfaces on the behavior of light, sound, or other waves.
The curvature inside a cavity is typically measured using mathematical equations such as the Gaussian curvature or the mean curvature. These equations take into account the shape and size of the cavity to determine the degree of curvature at a specific point.
The curvature inside a cavity can be affected by several factors, including the shape of the cavity, the material it is made of, and the presence of other objects or materials inside the cavity. Additionally, external forces such as gravity or pressure can also influence the curvature inside a cavity.
The curvature inside a cavity can significantly impact the behavior of waves. This is because curved surfaces can cause waves to reflect, refract, or diffract in different ways than they would on a flat surface. The amount and direction of curvature can determine the specific effects on the behavior of waves.
The study of curvature inside a cavity has many practical applications in various fields, including optics, acoustics, and electromagnetics. It is used to design and optimize devices such as mirrors, lenses, and antennas. It also has applications in medical imaging and industrial processes that involve the use of waves.