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Is it acceleration or speed that leads to time dilation or both?

For example, when a spaceship accelerated to (almost) the speed of light, then reversed course to come back towards earth, does this affect time dilation in the same way as if the the spaceship landed on a planet with very high gravity for a while?

I notice that in many videos they say that speed is the relevant factor that makes time slow down. But speed is relative, isn’t it? Both would travel with almost the speed of lost.

Is it therefore only the the acceleration that matters?

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marked as duplicate by WillO, Aaron Stevens, ZeroTheHero, John Rennie special-relativity Mar 20 at 6:04

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    $\begingroup$ There seems to be a lot of misconceptions, conflation of various relativity thought experiments, and unclear terminology here. Perhaps you could edit the question to be more focused on a single question while being more careful in your terminology? $\endgroup$ – Aaron Stevens Mar 20 at 0:09
  • $\begingroup$ If I am in motion in a given frame, then my clocks will run slow in that frame, by an amount that depends on my velocity. If I accelerate, then my velocity changes, and hence so does the tick-rate of my clocks. $\endgroup$ – WillO Mar 20 at 0:55
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Time dilation is due to speed, not acceleration. In essence time-dilation quantifies the tilt of the object's world-line relative to your temporal axis at any specific time. Acceleration quantifies the curvature of the world-line.

What follows is a more technical explanation, which I can expand further if you think it is helpful.

I prefer to think of it geometrically. Imagine that you plot in spacetime all the events that correspond to an object, i.e. the position of an object at time 0s, 1s, 2s, etc. The collection of such points will give you a world-line of the object (https://en.wikipedia.org/wiki/World_line).

To work with this world-line you need to parameterize it. A convenient way to do it is to say that the time and position of the object are given by $\left(time,\, position\right)=\left(ct\left(\tau\right), \mathbf{r}\left(\tau\right)\right)$, where $\tau$ is the proper time.

Next you could consider the tangent to the world-line $u^\mu = \frac{d}{d\tau}\left(ct\left(\tau\right), \mathbf{r}\left(\tau\right)\right)^\mu= (c\frac{dt}{d\tau}, \frac{d\mathbf{r}}{d\tau})^\mu$. This is known as four-velocity. What is the projection of this tangent onto your temporal axis? This is like a dot-product of the tangent vector with the unit-vector along your time-axis in your spacetime diagram. The projection is $(1, \mathbf{0}). (c\frac{dt}{d\tau}, \frac{d\mathbf{r}}{d\tau})=c\frac{dt}{d\tau}$. Now this projection is essentially the time-dilation. Usually we denote $\frac{dt}{d\tau}=\gamma$.

It is relatively easy to proove that $\gamma$, the Lorentz factor, that is directly related to time dilation, is a function of object velocity irrespective of acceleration, but I am not sure you are familiar with four-vector formalism necessary to show this.

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