Oooo. I wonder if this affects all the calculations based on Earth core radioactive decay. Then again, 2.5 years out a billions probably isn't enough to matter.

I like it when papers get published with calculations anyone could have done with decent high school education.

RetiredAg said:

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So the center of the earth is 5,997.5 years old?

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You b astard!

Just simply being on the second story of a house makes you lose a portion of you life.

Quote:

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moving about 10 feet to the top of the stairs, you would age quicker by 900 billionths of a second.

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http://www.telegraph.co.uk/news/science/science-news/8020988/Einsteins-theory-of-relativity-works-on-a-human-scale-the-higher-you-are-the-faster-you-age.html

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This effect causes time to run slower where the gravitational potential is lower.

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Just curious, do these calculations eliminate the possibility that the devices measuring time are being effected by different gravitational pulls? The only way I can picture time changing in respect to gravity would be using a measuring device for time that's effected by gravity such as an old clock with moving parts and gears. I'm not sure how much a digital clock would be effected by differing pulls over time.

Yes, this effect isn't due to effects on the mechanical parts of the clocks. This can be measured on atomic clocks, or any other clock you choose.

Thanks for clarifying

dargscisyhp said:

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Or the center of the Earth, at least. Relatively speaking, anyway. According to the calculation done in this paper, the center of the Earth is 2.5 years younger than the surface. This is due to an effect called gravitational time dilation. This effect causes time to run slower where the gravitational potential is lower. You can find the equation for gravitational potential in equations (1) and (2) of the paper, and equations (3) and (4) describe the time dilation. It's one of those calculations that made me go, "Neat!," so I thought I would share it here.

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I am not an expert physicist, but I did watch "Interstellar"

My understanding is that time slows down the more gravitational force that you are subject to, correct?

My understanding is that "gravitational potential" is the measure of work that you have to do in order to fight gravitational pull.

So, the core of the earth will experience more gravitational potential, and time will run slower there correct? Or maybe I don't understand the concept right.

Great question!

Your line of thinking is essentially correct. Gravitational potential is essentially how much work you'd have to do (per unit mass) to escape the gravitational pull of a massive body. Be careful, though, not to equate gravitational potential with the magnitude of gravitational force at a given point. Remember that at the center of the Earth you will experience no gravitational force at all.

Let me answer your question with a question: would you have to do more work from the center of the Earth to escape its gravitational pull, or from the surface of the Earth?

Yes, defined analogously to electrostatic potential (U=qV).

dargscisyhp said:

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Great question!

Your line of thinking is essentially correct. Gravitational potential is essentially how much work you'd have to do (per unit mass) to escape the gravitational pull of a massive body. Be careful, though, not to equate gravitational potential with the magnitude of gravitational force at a given point. Remember that at the center of the Earth you will experience no gravitational force at all.

Let me answer your question with a question: would you have to do more work from the center of the Earth to escape its gravitational pull, or from the surface of the Earth?

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You would have to do more work to escape the center of mass. You need to get to the surface, and then escape the gravitational pull once in orbit.

But in that case, is your sentence that I bolded a typo? I thought that time runs slower where gravitational potential is higher, not lower. That is where I am confused.

The potential has to be set with respect to some reference point. By convention, that reference point is set at infinity with a potential of zero. The reference point is not particularly important because what matters physically is the potential difference between two points, and that is independent of your reference point, however the conventional reference point makes the math easier in a lot of cases which is why it's typically used. Anyway, this convention causes all potentials to get a negative sign, and the more negative the potential the more work you have to do against it to escape it (get to infinity) since the magnitude of the potential difference between any point x and infinity is larger the more negative the potential at x is.

You could choose any other reference point, though and all this would still apply. Let's say you chose your potential to be 0 at the center of the earth. Then it would be a (which is positive) at the surface of the Earth and b at some arbitrarily high point (let's say halfway between here and alpha centauri). b - a < b - 0 and therefore the potential difference to escape will still be higher from the position with the lowest potential.

Another, more physical and less mathematical way to think of this is that an object wants to rest where its potential is minimized. Being at the lowest possible potential means that it's as deep as it can go into the potential well, and will have to do more work to get out of it.

dargscisyhp said:

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Another, more physical and less mathematical way to think of this is that an object wants to rest where its potential is minimized. Being at the lowest possible potential means that it's as deep as it can go into the potential well, and will have to do more work to get out of it.

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Thanks.

This makes sense. A lower potential means more work needed to escape, less potential energy.

I helped my wife prepare lessons on potential gravitational energy for her high school physics class earlier this year, I just didn't realize that this was the same concept.

To a high schooler, all you have to do is think about dropping a penny from a building. All of the potential acceleration from falling is energy. Once the penny is brought to the top of the building, that energy is stored there until you drop the penny out the window.

This is the same concept. I just had a pack of dumb pills for breakfast, and was unable to mash this concept together with Kerbal Space Program and relativity. Thanks for your patience.