# On the fact whether gravitational time dilation's additiveness or neutralization (and direction dependness) is true?

I have read all other similar questions about photon acceleration/deceleration, speed changes, etc., and they are all about bent photon paths. My question is specifically for a path that is not bent in 3D.

I have read this question, and Anna V's answer:

Gravitational lensing has been observed which means that the photons bend. An acceleration can be defined in its change of direction, angular acceleration in radians/second^2, so the answer is positive, yes, light can be accelerated, but its speed will still be c locally.

See the following setup:

1. let's make the setup so that the two masses (Suns) have the same gravitational effects, and are same shape and the photon travels just halfway between them. the photon's path will still be straight in 3D. So no bending will take effect this way, since the photon is equally affected by both suns gravity. We shoot a photon from point A, and it will arrive at point B.
2. So you can see that the GR effect where mass bends spacetime, will have a seemingly neutral affect on the photon's direction. (the two bending effects will seemingly neutralize each other)
3. I understand that locally the speed of the photon is still c.

4. according to GR, the gravitational effects of the suns still need to affect the photon, and from a far away observer's view they should (according to shapiro effect) slow down the photon.

5. So here the other GR effect, that slows down local clocks (to a far away observer) will either be neutral (so the two masses time dilation effect will neutralize each other - so it is dependent on the direction/position of the central masses), or it will add up, and the local clocks will slow seemingly down at a double rate (and so the time dilation effect is additive independently from the direction/position of the center of masses). PLEASE note that my MAIN questions is basically this, whether the gravitational time dilation is additive or neutralizing (question 2.).

### Questions:

1st QUESTION: 1. It is obvious to see that the photon will travel on a straight path in 3D, because the gravitational spacetime bending effect of the two suns' will equalize each other in their common gravitational area (and that is where the photon will pass between them) right?

MAIN QUESTION: We know as per GR that normally the sun's gravitational effects will make the clocks tick slower near the sun (from a far away observer's view) and that will cause the photon to to seem to travel slower than speed c(from a far away observer's view).

1. The MAIN question is, will the gravitational time dilation effects of the two suns equalize each other, so that the clocks near the two suns (in their common gravitational area, so between the two suns, where the photon passes) will tick slower (so time will pass slower) from a far away observer's view, so will gravitational time dilation be additive (independent of the center of masses direction/position) or neutralizing(depending on the center of masses direction/position)? (This is what as per GR would in part cause the photon seem to travel slower then speed c)

ANOTHER QUESTIONS: 3. in this setup the Shapiro effect is still valid? So from a far away observer's view the photon will arrive slower then it should (so it's speed will be calculated less then c)? 4. if yes, slower then c, will this still be because of two affects (like Shapiro) first - the gravitational effect will slow down local clocks(for a far away observer), so the photon will move with less then c. and another effect - the gravitational affect of spacetime curvature will cause extra distance (for a far away observer) and that will slow down the photon too?

PLEASE note that my MAIN question is question 2.

• it would be better if you do not start with something like "please do not close this as duplicate", as that immediately makes one think that it probably should. Instead you could add a small section at the bottom of the post linking the related questions and explaining why they are however different enough from yours – glS Oct 31 '16 at 17:39
• Thank you for your edits, I edited the part where I explain why my question is specific and different. On the photon, I could use EM waves, but the photon is also individual (or measurable individually), so I wasn't sure if EM waves' acceleration/deceleration would make sense. – Árpád Szendrei Oct 31 '16 at 17:45