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My thought process, where have I gone wrong?

Question 1: There is no gravitational force at the center of the earth is there still gravitational time dilation. Answer: Yes, there is a potential difference between the center of the earth and the surface, so according to general relativity the center will be slightly slower than the surface.

Question 2: Does all the mass in the observable universe have an effect on local gravitational potential and thus cause noticeable local time dilation? Answer: Yes and No. Think about the observable universe as a very large low density sphere. As you move outward in this sphere, the area thus mass increases in proportion to r^3. This overpowers the inverse square law of gravity, so time is significantly slowed. However, everywhere has its own sphere so the universe affects everywhere equally, as a result, there is no noticeable local change.

Question 3: Is the local time dilation currently changing? Answer: Yes. The universe is expanding, thus the mass of universe is moving further away, this overcomes the observable universe expanding. This means time is currently speeding up.

Question 4: If time is speeding up does this mean when we look at distant objects we are looking into the past thus when time is slower? Answer: Yes. Distant objects will be slower and red shifted. This will make it look like the universe is expanding at an accelerating rate.

Question 5: Does this mean the theory of dark energy is incorrect? Answer: ??? I must have made a mistake somewhere. Ask the internet.

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  • $\begingroup$ "Think about the observable universe as a very large low density sphere. As you move outward in this sphere, the area thus mass increases in proportion to r^3. " You can't move outward in this sphere. Your observable universe always has you at its center. $\endgroup$ – D. Halsey Aug 13 '18 at 19:56
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Does all the mass in the observable universe have an effect on local gravitational potential and thus cause noticeable local time dilation?

This is where you went off track. Only a static spacetime can be described completely in terms of a single gravitational potential. Cosmological spacetimes are not static.

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You are confusing physical models of the same thing. As soon as you mention time dilation, you have moved out of the realm of Newtonian physics and are now in the realm of Einsteinian gravity. You should go read an intro to relativity book, I recommend d'Inverno's textbook since he answers all of your questions thoroughly.

  1. There is no such thing as a gravitational force in general relativity (Einstein's view of gravity). So your first question is nonsense, since you are mixing time dilation and gravitational forces. Yes, the closer you are to a massive object the more the effects of time dilation will be pronounced, so one can say that a clock near the Earth's core will tick more slowly than compared to a clock at the surface.

  2. This is essentially the question of whether or not general relativity is "fully Machian." This is debatable, but the consensus seems to be that it is not fully machian. Take as a counter example the Minkowski (everywhere flat, geodesically complete) spacetime. There is no mass in this spacetime, yet its geometrical structure is completely determined by the metric (which encapsulates the effect of gravity). So, the easy answer is NO. Also, the universe is likely not shaped like a sphere.... see the cosmology section in d'Inverno's book.

  3. Not sure what you mean by "local time dilation." I assume you're talking about gravitational time dilation, rather than special relativistic time dilation. So yeah it's always "changing" in the sense that my position in the slightly non-spherical gravitational potential field of the earth is changing. But your next statement, "This means time is speeding up" is nonsense.... The time on my wrist watch is not being effected by the expansion of space, see here for instance.

  4. The premise of this is nonsense.

  5. The premise of this is nonsense.

Just a bit of advice: before you try tearing apart the best theories we currently have, you should educate yourself in the current literature, otherwise you risk sounding like a crackpot, which if you want to then more power to you.

d'Inverno's book is truly great! Give it a chance.

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Your question is not nonsense, but until we know whether or not gravity is affected by time dilatation in a feedback loop over long distances, it is actually impossible to accurately answer.

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