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So as far as I understand time dilation it means that time slows down as an object approaches lightspeed. This is an issue even with for example satellites around earth compared to people on earth (GPS).

Now I am wondering compared to what reference point is this speed measured? Is it absolute speed in comparison to the spacefabric (is that even possible to measure?)? If thats true then how come that the speed of the satelites around earth has an impact at all? I'd imagine it to be similar to me running back and forth on a plane. In the end my average speed will be the same (If I sit back down on my place) compared to me sitting down the whole time. Does that mean, that time dilation was the same?

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  • $\begingroup$ Is it absolute speed in comparison to the spacefabric (is that even possible to measure?)? No, absolute speed can't be defined in a sensible way. There are lots of questions here about that, eg physics.stackexchange.com/q/423597/123208 $\endgroup$
    – PM 2Ring
    Mar 27, 2022 at 13:36

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Now I am wondering compared to what reference point is this speed measured?

The reference “point” is a system of clocks, all of which are at rest in the chosen reference frame and synchronized. The time on the moving clock is compared to the time on the co-located stationary clock at each moment, and the time dilation is calculated from that.

I'd imagine it to be similar to me running back and forth on a plane. In the end my average speed will be the same (If I sit back down on my place) compared to me sitting down the whole time. Does that mean, that time dilation was the same?

This is a version of the twins paradox. The back and forth time dilation does not generally cancel out.

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You will get confused if you think that in Special Relativity time slows down in some absolute sense- it doesn't. In SR all motion is relative, and time dilation is relative. So, when you talk about an object moving at close to the speed of light, you have to answer the question 'relative to what?'. As you sit in your chair reading this, you are moving at close to the speed of light relative to a passing muon and your time is dilated, so that a second of your time is like a minute in the frame of the muon. Relative to a passing spaceship traveling at 0.5c, your time will be dilated by a different amount. So the degree of dilation is not absolute- it can take virtually any value depending on which reference frame you pick to measure it from.

Remember also that time dilation is entirely reciprocal, so if the interval of a second on your watch is equivalent to an interval of a minute in the frame of the muon, then an interval of a second in the life of the muon is equal to an interval of a minute in your frame.

If you wonder how time dilation can be reciprocal in that way, the answer is that time doesn't 'slow down' in the way you might think. A second on your watch is the same duration as a second on the watch of somebody moving at close to the speed of light relative to you. What causes the effect of time dilation is that the clocks in your frame are not synchronised with the clocks in the other frame. To see this, imagine you are walking down a corridor with clocks on the wall every 10 meters, and each of the clocks is running at exactly the same speed as your watch, but each is set to be a second ahead of the previous clock. As you walk down the corridor your watch will seem to start getting further and further behind the clocks on the wall, losing another second at each clock you pass, so it will appear that your watch is running slower than the clocks, but really what is happening is that your watch is running at the same speed as each individual clock, but in the frame of the clocks, where time advances by a second every ten metres, your watch time gets more and more behind (ie it seems dilated).

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If an object is moving relative to you, its time would be slower than your time.

But from the reference frame of the object, its time is faster than your time.

(This also plays into how the speed of light is measured using special relativity. To obtain $c$ as the answer, you must use a clock at rest with respect to you, and measure the distance traversed using a ruler or measuring tape that is at rest with respect to you. Otherwise, the answer may vary)

One thing that exists in general relativity is absolute acceleration, which has special physical significance. If the moving object accelerates to a frame of reference at rest with respect to you, its time elapsed will be shorter than your time elapsed. However, if you accelerate towards to the object to be at rest with it, then your time elapsed will be shorter than the object's time elapsed.

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Now I am wondering compared to what reference point is this speed measured?

There is no special reference point. Basically you can pick any inertial reference frame as the reference and do the calculations using the velocities of the clocks you want to compare relative to your chosen reference frame and everyone will agree on the proper time that elapses on the clocks you are observing, between chosen events. I will elaborate on this below.

Is it absolute speed in comparison to the spacefabric (is that even possible to measure?)?

There is no absolute speed. Only the speed you observe relative to your chosen reference frame. Rather than a spacefabric, we have spacetime, which is defined by a hypothetical or real grid of rulers and synchronised clocks that are all at rest in our chosen reference frame. Once a spacetime reference frame has been chosen, we can measure the path of a moving clock relative to the chosen reference frame. For example if the clock starts at (x1,t1) and ends at (x2,t2), where x is measured by rulers at rest in your chosen coordinate reference frame and t is measured by clocks at rest in your chosen reference frame, then its path length through spacetime is defined by $\sqrt{\Delta t^2 - \Delta x^2}$, where $\Delta x = (x2-x1)$ and $\Delta t = (t2-t1)$. This is sometimes known as the invariant or spacetime interval but it represents the proper time that actually elapses on the moving clock. The whole experiment can be repeated in another reference frame and they will get the same result.

I'd imagine it to be similar to me running back and forth on a plane. In the end my average speed will be the same (If I sit back down on my place) compared to me sitting down the whole time. Does that mean, that time dilation was the same?

In this case we could choose the reference frame of a passenger that remains seated on your aircraft. On his spacetime chart, he is stationary and his path is straight up because he is only advancing in time, while your path would be zigzag path on his chart, due to running back and forth relative to him. Now when you add up all the segments of your zigzag path using the spacetime interval formula it turns out your path (and elapsed proper time) is shorter than his. Initially it might seem odd that a zigzag path is somehow shorter than a straight path but this is because the formula has a minus in the square root unlike the addition we normally use to calculate distances using Pythagoras. Now a person on the ground will see the seated passenger moving at a great velocity relative to him, but the seated passenger will still be following a straight (but tilted) path in his spacetime and you will still be following a zigzag (but tilted) path through his spacetime and he will also calculate your proper time to be less than that of the seated passenger.

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