at the center of a planet/star/etc
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Wikipedia wrote:In the physics of general relativity, the equivalence principle refers to several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
Xaihe wrote:Thanks everyone. So does this mean that the equivalence principle can't be applied to the center of a gravitational well?Wikipedia wrote:In the physics of general relativity, the equivalence principle refers to several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
http://en.wikipedia.org/wiki/Equivalence_principle
twistor59 wrote:Xaihe wrote:Thanks everyone. So does this mean that the equivalence principle can't be applied to the center of a gravitational well?Wikipedia wrote:In the physics of general relativity, the equivalence principle refers to several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
http://en.wikipedia.org/wiki/Equivalence_principle
I'm not quite with you. Why do you say that it doesn't apply there ?
Xaihe wrote:I know what you're trying to explain, but I don't think you understand my point exactly. What I'm questioning is whether there is an assumption here and whether that assumption is valid.
First, my own assumption is that mass curves spacetime and that this accounts for gravity and time dilation. Then, the assumption necessary for the picture you laid out is that spacetime at a particular point can be curved in multiple (possibly opposing) directions at once. And this opposite curvature would then account for the apparent decreased acceleration and increased time dilation. I'm just having some trouble wrapping my head around this idea (which is no argument).
If my interpretation is wrong, please let me know where (and if you would, why).
Xaihe wrote:I know what you're trying to explain, but I don't think you understand my point exactly. What I'm questioning is whether there is an assumption here and whether that assumption is valid.
First, my own assumption is that mass curves spacetime and that this accounts for gravity and time dilation. Then, the assumption necessary for the picture you laid out is that spacetime at a particular point can be curved in multiple (possibly opposing) directions at once. And this opposite curvature would then account for the apparent decreased acceleration and increased time dilation. I'm just having some trouble wrapping my head around this idea (which is no argument).
If my interpretation is wrong, please let me know where (and if you would, why).
hackenslash wrote:There is some truth to that, but the equivalence principle tells us that time dilation also occurs when immersed in a gravitational field, meaning that there is indeed a GR solution for time dilation. Twistor's above calculation gives the solution employing the Schwarzschild interior metric, and it is indeed referred to as gravitational time dilation.
Google scholar results for 'gravitational time dilation.
Xaihe wrote:I know what you're trying to explain, but I don't think you understand my point exactly. What I'm questioning is whether there is an assumption here and whether that assumption is valid.
First, my own assumption is that mass curves spacetime and that this accounts for gravity and time dilation. Then, the assumption necessary for the picture you laid out is that spacetime at a particular point can be curved in multiple (possibly opposing) directions at once. And this opposite curvature would then account for the apparent decreased acceleration and increased time dilation. I'm just having some trouble wrapping my head around this idea (which is no argument).
If my interpretation is wrong, please let me know where (and if you would, why).
CdesignProponentsist wrote:Man! He looks happy to be in the center of Jupiter...
CdesignProponentsist wrote:I think it may be better to think of it this way. The distortion of spacetime increases as you approach the surface, but as you approach the center of mass the spacetime distortion increases at a lesser and lesser rate. The distortion is still there and at maximum at the center of mass, but never gets any less until you pass it.
CdesignProponentsist wrote:
So in effect that would mean that the acceleration that you feel (how many Gs) is the rate of change in spacetime distortion and not the overall distortion relative to an outside inertial frame.
Is that correct?
iamthereforeithink wrote:Interesting stuff here. To make sure I understand the explanations offered, I had a simple follow up question:
Let's say there is a hole running from one end of the earth to the other through the center of the earth. As we know, an object dropped into such a hole (ignoring the effects of rotation), will execute simple harmonic motion with a period of 84 minutes and 23 seconds. However (per my understanding), this period for the SHM is from the reference frame of an observer on the earth's surface. Now, if the object dropped into the hole is me, and I'm wearing a watch, how will my watch record the period of the oscillation?
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