In April's addition of New Scientist there is an article on page 10 by Jacob Aron. This article describes how Earth's core because of time dilations could be 2 1/2 years younger than it's surface. Or that the sun's core could be 40,000 years younger than its surface. Articles like these always get me thinking about the time differences between the emitted light and the absorbed light. It's very complicated to think about but imagine sitting at the center of the Earth and watching things happen up on the surface. In order for things to sync wouldn't everything you watch up there be slightly slowed down or red shifted? Also as you were looking up you would Watch things happening from even further away where the time difference would be even larger. Those moving images you see from there would need even more red shift in order to sync with your time. Wouldn't there need to be more and more red shift the further out you looked in order to sync with your time?
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asked May 14, 2016 at 18:17
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$\begingroup$ But you are not answering the question. From the center of the earth looking up at the surface wouldn't it be red shifted $\endgroup$– Bill AlseptMay 14, 2016 at 18:50
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$\begingroup$ Why do events on the surface have to be 'in sync' with events in the core? $\endgroup$– sammy gerbilMay 14, 2016 at 19:05
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$\begingroup$ That's kind of the question. How would you see things on the surface? Moving the same, moving slower, or moving faster? if you see it the same then that means it was slowed down for you to see it normal. $\endgroup$– Bill AlseptMay 14, 2016 at 19:11
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1$\begingroup$ One can show with a fairly simple gravity redshift/blueshift experiment using Moessbauer spectroscopy that this is, indeed, the case. Not sure why it's that surprising, though, if one accepts (as one has to) that the world is relativistic. $\endgroup$– CuriousOneMay 14, 2016 at 19:52
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$\begingroup$ @CuriousOne so you're agreeing it is red shifted? $\endgroup$– Bill AlseptMay 14, 2016 at 20:13
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1 Answer
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The surface has aged more : events move faster/happen quicker on the surface than in the core. So there would be a blue-shift in the light reaching the core. Light coming out of the core would be red-shifted. But in the case of the Earth (and even the Sun) the effect is incredibly small.
https://en.wikipedia.org/wiki/Blueshift#Gravitational_blueshift
answered May 14, 2016 at 19:48
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1$\begingroup$ Small, but sufficient that it has to be taken account of by the GPS. $\endgroup$– ProfRobMay 14, 2016 at 20:19
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$\begingroup$ I don't know I think you're looking at it backwards but this is the part I think is complicated. If you are looking up at the surface which is only 4000 miles away you see what it looks like 2 1/2 years ago. So what happened to those images during that 4000 mile trip. They would have to be slowing down. More importantly it seems we agree that the shift is caused by time dilation and not the expansion of space. $\endgroup$ May 14, 2016 at 20:23
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$\begingroup$ What I should have said, is that this effect is apparent in the relative clock rates in GPS vs the ground. $\endgroup$– ProfRobMay 14, 2016 at 20:31
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2$\begingroup$ @BillAlsept : You have misunderstood what the New Scientist article was saying. It does not take 2.5 years for light to travel unimpeded from the surface of the Earth to the core. It means that if identical synchronized clocks had been placed on the surface and in the core when the Earth was formed 4.5 billion years ago, they would now show a time difference of 2.5 years. The clock on the surface is running faster, but only by about 1 second in 6 years. $\endgroup$ May 14, 2016 at 21:06
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2$\begingroup$ @BillAlsept You might wonder why your accurate wristwatch and my accurate wristwatch disagree by 22,000 hours, if you didn't know about gravitational time dilation. But mostly you'd be surprised by our cool, breezy weather here on the surface. $\endgroup$– AsherMay 15, 2016 at 5:36