Quote:
Originally Posted by Jeffocal
I disagree with your conclusion that the clocks would tick slower on a surface of a collapsing star than the ones further out because the gravitational force and therefore the time dilation would be strongest at it' surface.
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The field strength is stronger on the surface than further out. A stronger field means more dilation (as in: slower clock). Clocks on the surface (where the field is stronger) are then slower than clocks further out (where the field is weaker).
Quote:
Originally Posted by Jeffocal
Both the clocks*at the center and at an infinite distance would slow to a complete stop relative to the surface of a mass as it collapsed through its event horizon because relativity tells us that the differential gravitational forces they would experience at those points in space would be infinite.
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Your previous quote disagreed that clocks on the surface are slower than clocks further out and your quote here says clocks on the surface do tick slower than clocks further out.
Some specific numbers are calculated by 2 different methods in this post:
Some numberic examples of gravitational time dilation in and arround Sol
And this one:
Re: Some numberic examples of gravitational time dilation in and arround Sol
You can also think of time dilation as the inverse of redshift (wavelength being the inverse of frequency where photons make great clocks). As a photon travels from the center of a collapsing mass to the surface it climbs out of a gravity well and is redshifted. This means the frequency of the photon is greater at the center and less at the surface... time ticks slower (as revealed by the photon) at the center vs. the surface.
Any time you climb uphill fighting the force of gravity your proper time gets larger relative to a clock which you leave behind. This is a fundamental aspect of general relativity by the equivalence principle. If you consider a rocket accelerating then clocks on the nose of the rocket tick faster than on the floor (by the engine). For the person on the floor of the rocket to reach the nose he must climb uphill against the force of acceleration.
To think of this graphically (and rather simply) you can plot the gravitational potential of a homogeneous ball:
-source
Points on the curve that have a steeper slope have clocks that run slower than points on the curve which have less slope. The "strength of the field" *is* the slope of the curve of potential. Edit:
Again, sorry, Time dilation is a function of potential not field strength! So, the further down on that plot the slower clocks run. The slope of the curve has nothing to do with it but rather how far up and down the curve it is. Sorry 
So, yes, clocks at the center of a mass where the field is strongest run slower than clocks on the surface where the field is weaker. EDIT: and, again, it's not the strength of the field but the value of gravitational potential. This is most easily shown mathematically with the equation for time dilation as a function of gravitational potential (U):
where U is:
-source
You might also notice the first sentence in the wiki for
gravitational time dilation:
Quote:
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Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential [where it is taken to be negative] (closer to the center of a massive object), the more slowly clocks run.
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I don't know what else to do to convince you of this. Do you have a link explaining or agreeing with what you're thinking?
~modest
