# Variable light speed from gravity time dilation

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At 186,000 miles per second it takes 500 seconds for light to reach us from the sun. Due to time dilation from gravity, clocks on Earth, the Sun and in 0-G in space would run at different times. (1) Which clock would show 500 seconds? It seems that light would travel at a constant speed but only relative to its current location considering gravity. Also, (2) would an observer in space see the speed of the light beam change as gravity changed? To prove general relativity we observed light being bent around the Sun. (3) Is space actually warped from gravity or is time dilation from gravity causing the bend?

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At 186,000 miles per second it takes 500 seconds for light to reach us from the sun. Due to time dilation from gravity, clocks on Earth, the Sun and in 0-G in space would run at different times. (1) Which clock would show 500 seconds? It seems that light would travel at a constant speed but only relative to its current location considering gravity. Also, (2) would an observer in space see the speed of the light beam change as gravity changed? To prove general relativity we observed light being bent around the Sun. (3) Is space actually warped from gravity or is time dilation from gravity causing the bend?

Standard GR disclaimer: My depth of knowledge in GR is limited

As with Special Relativity, what different observers see can be explained by different effects, e.g. in SR the stationary observer sees time dilation while the moving one sees length contraction, but they can agree on why their clock reads what it does when the trip is over. In GR, the effect of moving into different frames is also important. If I'm in a gravity-free area, I measure lightspeed to be c. If I'm in a gravitational potential I also measures lightspeed to be c, if I confine the measurement to be made in a locally flat region of spacetime.

In case 1 you move between frames, so no clock is going to measure the trip to be 500 seconds.

In case 2, an observer might measure light speed to be something other than c, if they were to assume everything is in the same frame of reference. From what I understand of the Shapiro delay (time delay of light passing near a massive object), you can view it either as a time dilation or as due to the extra length of travel due to the curvature of space. However, if one were to be unaware of these effects, it would seem like the light had slowed down. Bending and time delay have both been measured as confirmations of GR.

3. The construct of GR is that it is the geometrical effect, in which mass warps spacetime and gives rise to time dilation. Gravity is a perception of moving or being in that warped spacetime — things fall the way they do because of the curvature. Gravity and curvature are the same thing, rather than one causing the other.

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Great! I had actually at least considered most of what you said.

Question 4 should have been: Would the light trip from the Sun to the Earth take longer the from the Earth to the Sun? Intuition says yes but it would be going along the same curvature and that says it would be equal.

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At 186,000 miles per second it takes 500 seconds for light to reach us from the sun. Due to time dilation from gravity, clocks on Earth, the Sun and in 0-G in space would run at different times. (1) Which clock would show 500 seconds?

I'm assuming that the 500 seconds you stated above is an approximation to the actual travel time. Typically one has to state with respect to what frame of reference one is measuring time so that 500 s is with respect to a particular frame of reference. The precise travel time is only a very small difference from that in the absense of gravitational effects. This means that approximately its 500 seconds from all frames of reference which are moving slowing with respect to the sun. The 186,000 miles per second is the speed of light in flat spacetime as measured from an inertial frame of reference. The speed of light is a function of the gravitational potential and thus varies with position.

Also, (2) would an observer in space see the speed of the light beam change as gravity changed?

Yes.

To prove general relativity we observed light being bent around the Sun.

To be precise that does not prove GR. It merely comnfirms a prediction made by GR.

(3) Is space actually warped from gravity or is time dilation from gravity causing the bend?

Space can be curved by gravity. the presence of time dilation does not gaurentee spatial curvature.

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I'm assuming that the 500 seconds you stated above is an approximation to the actual travel time...

Space can be curved by gravity. the presence of time dilation does not gaurentee spatial curvature.

Yes, the 500 seconds was an approximation and just a # to work from. The impact of gravity on light speed observed from different frames was important.

I still have a little trouble accepting gravity bending a metric without an ether but time will tell the real story.

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Great! I had actually at least considered most of what you said.

Question 4 should have been: Would the light trip from the Sun to the Earth take longer the from the Earth to the Sun? Intuition says yes but it would be going along the same curvature and that says it would be equal.

For the same observer, it should be the same.

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