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Complete re-edit. Trying to rephrase my question, based on some good comments. Made several questions in the hopes that they combined paint the picture and that atleast one of them is understood :)

Q1: For an object in free fall towards a mass, will time gradually slow down for the object as the object gains velocity towards the mass and as the object gets nearer the mass, relative to a stationary observer?

Q2: If we have two identical clocks, one stationary in flat spacetime and one in free fall towards a mass, will there by any difference in the passing of time between the two clocks, relative to a stationary observer? (I guess that GR tells us that both the gained velocity for the free falling clock as well as the lower gravitational potential both slows down time for the free falling clock, relative to a stationary observer - but my intuition tells me that experienced time for the two clocks will be identical . i.e. that the two clocks runs synchronous while one is stationary in flat spacetime and one is free falling, but only while its free falling.)

Q3: If the answer for Q2 is yes, then has this been experimentally verified - how was this done? How would it be done? We know that time passes more slowly at the surface of the earth than at the peek of a mountain and this has been experimentally verified. How do we measure the passing of time of a free falling clock relative to say a stationary observer on earth?

Q4: If we consider a single clock at rest relative to a large mass (carried in-air by a still butterfly), when the clock is released by its tender captivator and starts a free fall will its time slow down / be unchanged / speed up relative to the time of the same clock while it was at rest?

Q5: If we have two persons of the same measurable human age, one staying stationary in flat spacetime and the other could somehow be put in free fall toward some mass for a long time measured by the stationary human. Then the stationary human has a magic wand and creates a worm-hole which allows the human who has been free falling towards some mass (in a more and more curved spacetime, with greater and greater velocity toward that mass) to instantly step through the worm-hole and stand next to the stationary human again (a non-ageing worm-hole!). How would the free falling human have aged compared to the stationary human?

Tue Skeltved
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  • What exactly are you thinking about when you say "free fall in flat space-time"? – Jeanbaptiste Roux Aug 14 '21 at 16:05
  • Not affected by any other forced than gravity (free fall) and then in flat space-time, i e. As far away from gravity as possible. But the point is just to be relative to a identical clock which is not in free fall towards a large mass i guess. Does that make sense? (Struggling a bit to define the question properly) – Tue Skeltved Aug 14 '21 at 16:38
  • It quite confuses me because you say in the same sentence that there's a clock far away from the source of a gravitational field, that is in free fall but also in flat space-time. The point is that the source of the gravity curves the space-time so you are in free fall. But if you are infinitely far away from the unique source of gravity, then you are not in free fall and then precisely flat space-time. – Jeanbaptiste Roux Aug 14 '21 at 16:49
  • From wiki:" In general relativity, an object in free fall is subject to no force and is an inertial body moving along a geodesic. Far away from any sources of space-time curvature, where spacetime is flat, the Newtonian theory of free fall agrees with general relativity. " - so, free fall also applies to flat-space, unless wiki is wrong here? – Tue Skeltved Aug 14 '21 at 17:04
  • Wiki tells roughly speaking that general relativity agrees with Newtonian gravity in weak-field approximation. The curvature of space-time is the reason you are free-falling toward the massive body. – Jeanbaptiste Roux Aug 14 '21 at 17:25
  • Hello! Please only ask one question per post – otherwise it might get closed due to lack of focus. You can always [edit] your question or ask a new one. Thanks! – jng224 Aug 15 '21 at 12:25

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The best example is our GPS system. GPS satellites are at a different distance from the Earth than us, so their clocks tick at a different rate than clocks on Earth (they are closer to flat space time than us, because we are the ones who are deeper in the potential well). But simultaneously, they have a velocity relative to clocks on Earth.

So there is a special relativistic time dilation effect, and a general relativistic time dilation effect. And this is experimentally measured and our GPS systems compensate for these effects in order to prevent GPS measurement error.

This is explained quite well here:

https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Special_and_general_relativity

Special relativity makes the GPS satellite clocks tick slower from our perspective because they are moving.

General relativity makes our clocks tick slower because we are deeper.

For an object in free fall, you use its position in the spacetime metric to determine the general relativistic effect, and its velocity to determine the special relativistic effect.

Alwin
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