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I seem to recall reading a post a long time ago (that I cannot find) that gravity in the Newtonian limit (eg the Solar system) can be completely explained in terms of time dilation alone. Is that true and if so, how does that work?

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- Thread starter yuiop
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In summary, Kev says that in order to use GR without a curved spacetime, you have to alter the constants used by GR. He suggests using euclidian flat space still using G as a constant.

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I seem to recall reading a post a long time ago (that I cannot find) that gravity in the Newtonian limit (eg the Solar system) can be completely explained in terms of time dilation alone. Is that true and if so, how does that work?

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In the weak field limit, when GR goes to Newtonian gravity, a function of g_00 acts like the potential, and g_00 is the time dilation factor ( or it's square root).

In fact,

[tex]-g_{00} = 1 + \frac{2\phi}{c^2}[/tex]

Is this what you mean ?

In fact,

[tex]-g_{00} = 1 + \frac{2\phi}{c^2}[/tex]

Is this what you mean ?

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Mentz114 said:

In fact,

[tex]-g_{00} = 1 + \frac{2\phi}{c^2}[/tex]

Is this what you mean ?

Not sure. Assuming [tex]\phi = GM/R[/tex]

and [tex]-g_{00} = 1 + \frac{2GM}{Rc^2}[/tex]

is obtained from the binomial aproximation of [tex] \frac{1}{\sqrt{1-2GM/Rc^2}}[/tex]

How is the Newtonian of gravitational potential of -2GM/R obtained from that?

Where do the +1 and c^2 go and how is the inverse square law of gravity recovered?

Also, as I understand it. GR does not have gravitational forces acting on a free falling body, but there still are gravitational forces acting on a stationary body. Does GR alter the force felt by a stationary body or is it the usual GM/R^2?

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Kev,

it takes four pages to demonstrate properly, but if you start with the EFE with a simple source, and let most of the gradients involved disappear, then solve the equations of motion you get an inverse square force law, with a function of g_00 playing the part of the potential. Newtonian gravity is recovered in full. Quite a triumph, in fact.

In my earlier post, phi is not the Newtonian potential, but a function of it.

Here's a good explanatory article.

http://www.mth.uct.ac.za/omei/gr/chap7/node3.html [Broken]

it takes four pages to demonstrate properly, but if you start with the EFE with a simple source, and let most of the gradients involved disappear, then solve the equations of motion you get an inverse square force law, with a function of g_00 playing the part of the potential. Newtonian gravity is recovered in full. Quite a triumph, in fact.

In my earlier post, phi is not the Newtonian potential, but a function of it.

Here's a good explanatory article.

http://www.mth.uct.ac.za/omei/gr/chap7/node3.html [Broken]

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mojocujo said:

Sounds dodgy to me. GR does not have a length scale. Care to elucidate ?

Time dilation is a phenomenon predicted by Einstein's theory of relativity, which states that time appears to move slower in the presence of a strong gravitational field. This means that clocks ticking at different altitudes will measure time differently, with the clock closer to the source of gravity ticking slower. Therefore, the curvature of space and time caused by massive objects, such as planets and stars, creates a gravitational force that we experience as gravity.

One of the most famous examples of time dilation is the observation of the gravitational redshift, where light emitted from a source in a strong gravitational field will appear redshifted to an outside observer. Additionally, experiments with atomic clocks have also shown that time runs slower in a stronger gravitational field. The phenomenon of gravitational lensing, where light from distant objects is bent by the curvature of space and time, is also evidence of the effects of gravity on time and space.

Time dilation only becomes noticeable in extreme conditions, such as near black holes or at extremely high speeds. In our daily lives, the effects of time dilation are too small to be perceived. However, GPS satellites, which are in orbit around the Earth and experience weaker gravity than us on the surface, have to account for time dilation in order to maintain accurate time measurements.

No, time dilation is not the same as time travel. Time dilation refers to the difference in the passage of time between two points in space due to gravity or high speeds. Time travel, on the other hand, refers to the concept of moving to a different point in time, which is currently not possible according to our current understanding of physics.

As mentioned before, the effects of time dilation are only noticeable in extreme conditions. However, there are some instances where time dilation can be observed in a laboratory setting, such as with atomic clocks. In addition, astronauts in orbit around the Earth experience a slight time dilation compared to those on the surface, but this effect is too small to be noticeable in their daily lives.

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