So my understanding is that if someone moves faster, they age slower relatively to someone who stands still. A common example is if a spaceship accelerates away from earth and does a loop around a black hole. The people on the starship will age slower compared to the people on earth. But this is because of acceleration right? When the spaceship comes back and accelerates in the opposite way (decelerates) to slow down and land on Earth, doesn’t the time dilation get undone? And both the spaceship people and the Earth people are the same age again?
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deceleration is still acceleration. it just causes more time dilation.
time dilation doesn’t get “undone”
Its not the acceleration, its a function of how fast you’re going. If you imagine going fast puts you on fast forward, then you slow down again – you’re not rewinding, you’re returning to normal speed.
> the spaceship people and the Earth people are the same age again?
No, once it happens it happens. We actually have done this experiment with atomic clocks and yes, one is younger than the other.
The acceleration is not what cause changes to how fast time flows. It’s the relative speeds.
So accelerating by itself will not cause you to age slower or faster. And decelerating will not reverse it either.
Time dialation is real, and its impact is needed to be calculated for GPS. The satellites are moving fast enough where if dialation is not accounted for, your car would tell you to drive into the ocean pretty quickly.
> But this is because of acceleration right?
Nope! It’s because of the speed they get to. Time behaves differently at different top speeds. (Also, in the example with the black hole, just being close to a black hole causes time to behave differently too, because they’re crazy like that.)
Everyone is acting like this is obvious but it’s a question about relativity that is raised enough that it has a name and a Wikipedia page:
https://en.wikipedia.org/wiki/Twin_paradox
Your thought process wrongly assumes that time dilation is related to acceleration, which it is not, and even if – simply changing the direction of your acceleration does not “undo” anything related to that movement. You can’t turn back time just by driving your car in reverse.
It is related to your velocity however and how much time you spend at that velocity – again it doesn’t matter in which direction you are going with that velocity though.
In your thought experiment, the spaceship wouldn’t even need to fly towards a black hole and return.
It could simply fly circles around Earth’s orbit. As long as it does that with a velocity that is non-negligibly high compared to the speed of light, anyone on that spaceship would age more slowly than anyone on Earth.
You could basically fly circles around Earth near light speed. If you do that for one year, then you will be one year older while several hundred years will have passed on Earth (numbers are only estimates for the sake of the argument).
Deceleration is just acceleration in the opposite direction, that’s the simple answer. Its impossible to “undo” time dilation, time passed differently relative to each other, undoing that would require Marvel levels of time manipulation.
You’re thinking of acceleration as increasing speed. Think of it as current speed instead.
Now imagine you have two scales, speed and time. Speed can be from 0 (no movement) to 100 (moving at the speed of light). Time can be from 0 (time doesn’t pass) to 100 (time passes normally).
These two scales have to add to 100. So if you have no movement (0), then time passes normally (100). If you are moving at the speed of light (100), then time doesn’t pass (0). If you’re moving at half the speed of light (50), then time passes half as fast (50).
We have experimentally proven time dilation, both gravitational and speed-based.
In fact, correction for both are necessary for the correct functioning of GPS (GPS satellites are moving fast -> slower time, but at the same time experience less gravity because the are further from Earth -> faster time. Those differences do not cancel out evenly and the clocks end up running slightly fast by an amount precisely predicted by special and general relativity.)
Due to time dilation, your head is younger than your feet
An easier way to think about things might be to imagine that EVERYTHING is moving the same amount – but some of that is movement in time and some is movement in space. The more you move in space, the less you have left of that set amount of movement to move in time. So when you accelerate in a gravity field, the fact that the field distorts space so that you have to actually move less in time as a result means slower time. The direction you’re accelerating (moving toward a black hole vs away) doesn’t change the amount of change in movement.
I think there’s two possible misunderstandings you have. Neither are trivial, and neither are obviously incorrect.
The first is the idea that “but everything goes back to normal, right?” which I’m sorry to say is completely wrong. Satellites circling the earth are actually moving fast enough that time dilation has to be accounted for, and they never slow down. The effect just keeps adding up. Now, they’re moving fast enough that we’re only talking about microseconds, but that matters when you travel so fast! Otherwise you won’t know where you’re supposed to be! So no, this effect is permanent.
The other thing is, as u/frenchtoaster pointed out, the twins paradox. The idea that since everything is relative, then from the traveling spaceships point of view, it’s earth that moved away quickly, not the spaceship, so their time should be dilated.
But that’s not true either. The act of accelerating, changing your relative speed, causes the change of frame of reference. Slowing down again changes it back, but the dilated time experienced is still experienced. Turning around and going home just does it again.
You talk about directions “go there” / “come back” / “opposite way”. Time dilation doesn’t care about direction, not even about acceleration, only about speed. So it doesn’t matter where it goes, time dilation applies all the time.
The GPS system has to ba calibrated for time dilation, and would go out of sync in a few hours if it didn’t.