# Is a photon going through a center of mass affected by time dilation more then another going around?

Please don't mark as duplicate. My specific question was not answered in other posts. And this question here Which Photon would win the race?

is also about neutrinos, electrons.

My question now is only about photons, and the shapiro delay.

then if you try to make analogy to the shapiro delay, then comes my question:

1. according to the shapiro delay, a photon going around the mass arrives later then it should.
2. there is no experiment where they would somehow shoot a photon also through the center of mass (maybe between two close stars or an artificial mass with a whole through it, or something else)
3. so shapiro delay only talks about the photon going around, and that photon needed more time to arrive from point A to B, but it's speed had to stay c, so the distance it traveled had to be longer (which it really is in 3D)
4. so a photon going through a tunnel through the center of mass (or between the two SUNs here) has to travel at speed c too, but its distance is shorter in 3D so it's time need to be shorter too. So that photon has to arrive from A to B faster.
5. Imagine this set: 1. We shoot two photons, one around one of the stars, and one inbetween two stars.
2. We shoot the one going around in an angle that it will cross point B too.

Question:

1. so was there any experiment like this?
2. Am I right that time dilation would affect the photon going between two stars more and it would arrive first?
• I could be completely off but wouldn't it be strictly based on the distance traveled since the speed photons travel at isn't affected by time dilation? – Yogi DMT Oct 27 '16 at 20:29
• You are correct. Though that is 3D distance. Since the observer has to see both photons' speed at c. And from the observer's view, they go different length paths. That is why time1=(straight or short path)/c<(bent or longer path)/c=time2. So obviously the photon going straight would arrive sooner. But time dilation does not affect it. – Árpád Szendrei Oct 27 '16 at 20:32
• They have to see the photons travelling at c through 3D space, the observers don't get to choose the structure of space however. For example if we shot a beam of light from point A at a mirror very far away and the mirror altered it's trajectory ever so slightly such that it comes back such that point B is only a few inches from A, it would still take light 2D/c time to reach B, not A-B/c time. – Yogi DMT Oct 27 '16 at 20:53
• I dont understand this. If the mirror is D, then it will take (A-D)/c+(B-D)/c time no? But my point is, time dilation does not affect the photons, right? – Árpád Szendrei Oct 27 '16 at 20:58
• My point was that the actual distance light travels has nothing to do with the viewing angle (ie. from above, or horizontally to AB). – Yogi DMT Oct 27 '16 at 21:00

## 1 Answer

You would think that a particle moving in the centre of mass experiences the same time as moving through space wthout any mass in it. In both cases no gravity is felt, so you would think time proceeds at it's fastest rate. The pace of time is nevertheless dependent on the gravitational potential, which is different in both cases, so time is moving at different paces for the two photons (coordinate time, because for the photon itself the pace of time is zero). So if you compensate for the differences, the two photons don't arrive at the same time.

• This is time dilation. But if that is true for a photon, then its speed would be different for the two photons (from an observer's view). That is impossible. Since the observer has to see both photons' speed at c. And from the observer's view, they go different length paths. That is why time1=(straight or short path)/c<(bent or longer path)/c=time2. So obviously the photon going straight would arrive sooner. But time dilation does not affect it. – Árpád Szendrei Oct 27 '16 at 20:30
• So where you say "so time is moving at different paces for the two photons (coordinate time, because for the photon itself the pace of time is zero)" I must disagree. For the photons, time seizes to exist, for both of them. Time dilation cannot change that. – Árpád Szendrei Oct 27 '16 at 20:30
• OK I figured it out I think. there are two effects: #1 to us observers, the local clocks appear to tick slower closer to the gravitational center. That slows down the photon (from our view) going between the two suns more that the one going around. #2 space is not flat there, so the diameter is bigger then it would be in flat space, so the photons have to travel extra distance. So it will come down to how much slower the photon seems to be traveling between the two suns and how much more extra distance they have to travel. I guess it would need the GR calculation. But there are no SR effects. – Árpád Szendrei Oct 28 '16 at 19:04
• Can you please explain this part " The pace of time is nevertheless dependent on the gravitational potential"? – Árpád Szendrei Dec 13 '16 at 18:18