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tanzanos
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Hypothetically: If a hollow sphere with a human inside were placed exactly at the centre of the Earth's core; then how would gravity affect the human (or any mass for that matter).
Maxwell's Demon said:Note also that the time dilation is at a maximum value at the center of gravity, because the gravitational potential continues to rise beneath the surface of the planet.
inflector said:If there is no acceleration then the gravitational potential is also zero by the equivalence principle
As Vanadium already noted, zero acceleration does not mean zero potential. It merely means that the potential is constant. What Vanadium left out is that gravitational time dilation is a consequence of gravitational potential not acceleration. Time is dilated inside the sphere.inflector said:That doesn't jive with the idea that there would be no acceleration combined with the equivalence principle. If there is no acceleration then the gravitational potential is also zero by the equivalence principle, therefore there should be no time dilation.
Assuming the Earth is of uniform density and arbitrarily setting the potential at infinity to zero, the gravitational potential at some distance r<R from the center of the Earth is given byThe gravitational potential does not continue to rise beneath the surface of the planet. As you get closer to the center it drops to zero.
Vanadium 50 said:No, force is the derivative of potential. No force means a constant potential, not zero potential.
D H said:As Vanadium already noted, zero acceleration does not mean zero potential. It merely means that the potential is constant. What Vanadium left out is that gravitational time dilation is a consequence of gravitational potential not acceleration. Time is dilated inside the sphere.
According to General Relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame.
The strong equivalence principle suggests that gravity is entirely geometrical by nature (that is, the metric alone determines the effect of gravity) and does not have any extra fields associated with it. If an observer measures a patch of space to be flat, then the strong equivalence principle suggests that it is absolutely equivalent to any other patch of flat space elsewhere in the universe.
Maxwell's Demon said:The point at the center of mass exhibits no vector force from the Earth's gravity, and within the volume of a spherical shell at the center of a massive body, there is no gravitational gradient at all - spacetime is 'flat' there.
D H said:You need to learn to walk before you can learn to run, inflector. Physics students really should learn about Newtonian mechanics in general and Newton's shell theorem in particular before delving into general relativity.
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General relativity must agree with Newtonian mechanics in the domain in which Newtonian mechanics has been well-tested.
D H said:Regarding the two wikipedia statements you cited regarding the equivalence principle: First off, it's wikipedia. No justification, no explanation, no math, just raw statements. Do learn to take things in wikipedia about controversial subjects or science beyond that taught to freshmen with a big grain of salt.
For objects at rest with respect to and outside of a non-rotating object with a spherical mass distribution, the Newtonian gravitational potential is Φ=-GM/r, where r is the distance to the center of the object. The gravitational time dilation factor derived from the Schwarzschild metric isinflector said:How can we address time dilation using Newtonian mechanics? Is there some sort of conversion factor like the Lorentz factor that allows one to go from a Newtonian gravitational potential to time dilation?
I said controversial or advanced. It certainly is advanced science. It is typically first taught at the college level as a senior year undergraduate or first year graduate course.I didn't think general relativity, the equivalence principle or time dilation was particularly controversial.
Indirectly, yes. Directly? Saying that will lead to misconceptions.In particular, anything that shows specifically how time dilation is not related to acceleration or space curvature.
Look at it in terms of energy. A photon climbing out of a gravity well will lose energy. Photons can't change in velocity; they lose energy by a decrease in their frequency. This is the gravitational redshift. This decrease in frequency also happens with electromagnetic signals such as a signal based on the ticking of a clock.I just don't yet understand how we can discuss this in terms of Newtonian gravitational potential since Newtonian mechanics doesn't allow for time dilation.
In addition to the above responses, it is important to correctly apply the equivalence principle. The equivalence principle applies only to a small region of spacetime, sufficiently small to ignore the spacetime curvature. If we are performing experiments comparing two clocks within the hollow in the center there is no gravitational acceleration and no relative time dilation and the equivalence principle holds nicely. If we are performing experiments comparing a clock within the hollow and a clock far above the surface then there is gravitational time dilation but the clocks are too far apart for the equivalence principle to hold.inflector said:That doesn't jive with the idea that there would be no acceleration combined with the equivalence principle. If there is no acceleration then the gravitational potential is also zero by the equivalence principle, therefore there should be no time dilation.
The "Gravity at Earth's Core: Human Impact Hypothesis" is a scientific theory that suggests human activity, such as mining and drilling, may have altered the Earth's gravity at its core. This hypothesis proposes that the removal of mass from the Earth's interior has caused a decrease in the planet's gravitational pull.
If the "Gravity at Earth's Core: Human Impact Hypothesis" is true, it could have significant implications for humans. Changes in gravity at the Earth's core could potentially impact the Earth's rotation and tilt, which could affect climate patterns and weather events. It could also have an impact on tectonic plate movement and the stability of the Earth's crust.
Currently, there is limited evidence to support this hypothesis. However, some studies have found that there has been a slight decrease in the Earth's overall mass over the past few decades, which could potentially be attributed to human activities like mining and drilling. Additionally, some researchers have found a correlation between the location of major mining sites and areas with a lower gravitational pull.
One major criticism of this hypothesis is the lack of concrete evidence to support it. While there have been some studies that suggest a decrease in the Earth's mass, it is difficult to definitively link this to human activity. Additionally, the Earth's core is incredibly dense and massive, so it is unlikely that human activities could significantly impact its gravitational pull.
If the "Gravity at Earth's Core: Human Impact Hypothesis" is proven to be true, it would challenge our current understanding of gravity and the Earth's core. It would suggest that human activities can have a significant impact on the Earth's gravitational pull, something that was previously thought to be impossible. It would also prompt further research and exploration into the effects of human activity on the planet's interior.