Time Dilation Questions

[u/MultiMillionMiler]

So I've read alot of the other posts on this topic and they did answer alot of the more basic questions I had, thanks! But there's one thing I'm still confused about. The supposed solution to the twin paradox where both clocks would "appear slower" from the others POV, is that one accelerated to get up to speed, and that is absolute, not relative, since it's experiencing a force (which is equivalent to gravity), but if this is the case, how come the dilation effect doesn't just apply to the accelerating/deceleration portion of the trip? For example the Voyager 1 probe has experienced something like a good 2 full seconds of time dilation compared to Earth since it's launch, due to all that time traveling despite the speed itself being small compared to c. But if acceleration is the absolute factor that causes the dilation for one object and not the other, why would all those years at a constant speed then add up to those couple seconds? I feel like I'm missing something obvious here but can't figure it out lol.

2nd question, since acceleration/speed, gravity, and even rotation all add a time dilating effect on an object, what happens if you combine all 3? Say you send a probe at near the speed of light in an extremely close orbit near the event horizon of a black hole, and then somehow have it spin as fast as a pulsar or something. So that you nearly max out all 3 gravity effects at once (acceleration/speed, high gravitational field, and rotation), would these add up to something more than c, or would it not be possible to max out all 3 forces like that in the first place due to the combined vectors exceeding the equivalent of c? Thanks!

[u/joeyneilsen]

Time dilation is about relative speed, so it applies whether you're accelerating or not. And it's not really acceleration up to speed that resolves the twin paradox, it's the turning around to go from heading away to heading home. The traveling twin isn't in an inertial frame. They're in two inertial frames: one outbound and one inbound. That's why it's not really a paradox. Treating it like "my frame and their frame are equivalent because of relativity" is really just a misstatement of what's actually happening.

[u/MyNameIsNardo]

Things that are relative with inertial motion: * The time separation between events (time dilation) * The spatial separation between events (length contraction) * Which events happen at the same time (simultaneity)

Things that are absolute between inertial reference frames: * The speed of light relative to you * The combined separation between events in space and time (spacetime interval) * Which events could possibly influence other events (causality and lightcones)

In the twin paradox, time dilation is in some sense experienced by both observers. This is what makes it counterintuitive in the first place. Both observers, even after accounting for light travel time, will conclude that the other observer's clock is slower. If neither twin accelerates (including changing direction), then the situation is perfectly symmetrical forever. This is possible because the way time dilation and length contraction work in the first place is by "pivoting" the time and space axes for each observer. When separated by some distance, the twins will not agree on which things happen at the same place at different times or the same time in different places. If one (or both) of them turn around to reunite, the resulting acceleration will pivot the axes such that by the time they're in the same place at the same time again they will agree on who experienced the most time and who traveled the furthest distance. They will always have agreed on their individual measurements of the speed of light, their calculation of the spacetime interval between any two events, and any cause-and-effect relationships.

In your example, Voyager's time dilation due to velocity is the same as our time dilation from Voyager's perspective. As far as Voyager is concerned, we only think its clock is two seconds behind because we're perceiving Voyager's past as the present (again, even after accounting for the travel time of light). Voyager also sees us as thinking it's shorter than it is and that it has travelled a further distance than it has. What we perceive as its current moment some distance away is "actually" its past a bit closer up. However, from our perspective, Voyager is the one making these same weird conclusions about us. If a third observer between us is moving a bit slower to stay exactly in the middle, it'll make similar conclusions about both us and Voyager in space and time.

Time dilation due to gravity is (by definition) the same as time dilation due to an equivalent acceleration. No matter what combination of things you do, no observer would ever see you moving faster than light, which is in some sense equivalent to saying that no observer will ever see your clock slow down to complete stop compared to theirs.

[u/LazyLie4895]

I'll answer question 1 since I'm much more familiar with Special Relativity.

Most of the common paradoxes arise from not taking the relativity of simultaneity into consideration. Basically, different observers disagree on what's "now" at locations far away from themselves.

In the twin paradox, the two planets are stationary. They will agree on what's "now". However, an observer moving from the Earth to the distant planet does not agree with the observer on Earth about what's "now" at the distant planet. They will consider the distant planet as being in the future compared to an observer on Earth.

Roughly speaking, an observer moving toward something far away will see the something as being in the future compared to a stationary observer at the same location. Conversely, they consider something far away that they're moving away from as being in the past compared to a stationary observer in the same location. Acceleration doesn't have to come into play other than causing you to change from one frame of reference to another.

So when travelling toward the distant planet, the observer will consider the destination to be in the future. They will observe the destination's clock ticking slower due to time dilation. If you factor in all effects (destination's starting clock, time dilation, and length contraction), you'll calculate that they arrive exactly at the time that you on Earth expect them to arrive. When they turn around, they shift frames again, and now they consider Earth to be far in the future. If you calculate all the relevant effects again, you'll find that they will also arrive on Earth exactly as expected.

There are variations of this paradox that don't involve acceleration at all (using multiple observers that have always been travelling in inertial frames that just happen to meet up at specific times and locations). The resolution is that they all consider what's "now" to be different at locations far away from them.

[u/nicuramar]

What happens when accelerating is that the “plane of simultaneity” shifts. See the illustrations and explanation here: https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime_tachyon/index.html#Twin

[u/Underhill42]

This is a nice slow explanation that breaks down all the interacting aspects of Relativity that combine to create the twin paradox: https://www.youtube.com/watch?v=GsMqCHCV5Xc

Basically, both twins see the other aging slower the whole time, the "secret sauce" is in the turnaround. You can even ignore the acceleration, as they do in the video, and just say they teleport from a ship departing to another returning.

In the moment of teleportation they move from a reference frame in which the Earth is currently (lets say) five years older than when they left, to a reference frame in which the Earth is currently 35 years older.

That's the Relativity of Simultaneity. The less talked about "third twin" to time dilation and length contraction:

There is no universal timeline or "now" in the universe. Whether two unrelated events A and B happen simultaneously, A then B, or B then A, depends entirely on the reference frame of the observer.

The light speed limit means that, if light could travel from A to B, so that there's a potential causal connection between them, then all observers will still agree on the sequence of events, though not the amount of time (or space) between them. But if A and B happened completely outside each other's light cones, then it's impossible to say which happened first. It's just not a meaningful question in a universe that operates like ours.

[u/MultiMillionMiler → u/Underhill42]

I get more of that idea now, but was just curious what the direct physical cause of it is in the first place. Some force of the motion distorting spacetime for the dilating effect to occur? There has to be some physical process for it to occur regardless of how we might perceive it from different reference frames right? I understand that spacetime is one entity but what exactly is it that gravity does to time for example that makes it squeeze/stretch, instead of, I don't know, twist or spiral or loop or whatever.

[u/Underhill42 → u/MultiMillionMiler]

I like the geometric interpretation of acceleration rotating your reference frame in 4D spacetime. I'll eliminate one dimension of space to make it easier to visualize.

Picture a 2D + time universe, like a movie with all the frames stacked one atop the other so that from our 3D god's-eye view the entire movie exists simultaneously as one 3D spacetime "movie cube" - a block universe.

As a 2D observer passing through 3D spacetime, in your reference frame you're always at rest in space, and moving through time. Watching the universe pass by one 2D movie frame at a time.

There's also light speed delay so you can't actually see the much of the frame you're currently in until the light reaches you many frames from now... but you can prove that things must have happened "now" for you to see them "then". But we're not going to worry about that, when I say "now", I'm talking about what you can eventually prove must have happened in this moment.

Then a relativistic traveler passes you by. From their perspective they're also motionless while the universe passes them by in the direction they call time.

But importantly, the direction they call time is NOT the same direction you call time - they might be passing through the "movie cube" left-to-right, instead of front to back. So their time axis is your x axis, while your time axis is their x axis. And their "now" movie frames reflect that. Their frames are perpendicular to their path, so they're slicing "now" frames out of the movie cube at an entirely different angle than yours.

The speed of light limit means no two observers can pass through the movie at right angles to each other - that would be exactly light speed. Instead there will always be a little overlap in their time axes.

That visualization works for the basic concept, but breaks breaks down if you try to dig into the details too much. Mostly because the "rotation" between space and time is hyperbolic rather than circular, which intuition isn't so good at.

But it gives the basic idea of what you're dealing with. Space and time are fundamentally the same thing, and no two relativistic observers will agree on which direction through 4D spacetime is actually time.

[u/MultiMillionMiler → u/Underhill42]

I read a theory about "multiple time dimensions", is that just a mathematical representation of like time axis for each of the 3 space dimensions (like time axis or something), or does it literally mean something like intersecting timelines in higher dimensions?

[u/Underhill42 → u/MultiMillionMiler]

No idea, I mostly avoid the wildly speculative stuff. The tested-and-verified stuff is weird and counterintuitive enough, and I don't understand it nearly well enough to confuse the issue by loading a bunch of almost-certainly-false nonsense into my head too.

(In science there's only two kinds of knowledge - the verified accurate, and the speculative. And the speculative covers so much territory that 99.99999% of it MUST be wrong. Even the stuff that looks convincing at first pass.)

[u/joepierson123]

For example the Voyager 1 probe has experienced something like a good 2 full seconds of time dilation compared to Earth since it's launch

Yes and from Voyager's perspective our clocks are running 2 seconds slower due to time dilation

There's no twin paradox here because Voyager is not coming back. 

[u/MultiMillionMiler → u/joepierson123]

Let's pretend Voyager 1 did a very long sweeping curve on a return trajectory toward Earth, at a constant speed, then what?

[u/joepierson123 → u/MultiMillionMiler]

If Voyager maintained the same speed during the u-turn from Earth's perspective nothing, it would still observe voyager's clock slowing down.

From voyager's perspective, it would observe Earth's time speeding up until it made the entire u-turn then it would observe Earth's time slowing down again during the entire return trip. 

[u/Optimal_Mixture_7327]

Time dilation has nothing to do with the twin paradox, which is an example of the clock effect.

But whatever, the clocks "appear" to run slower on the outbound journey and faster on the inbound journey (red shift and blue shift).

Both clocks run slow in accordance with time dilation, meaning, each twin defines an arbitrary pair of spatial hypersurfaces between which their own world-line distance is longer than that of other twin.

Acceleration is NOT gravity. Acceleration is any motion relative to the local gravitational field and gravity is the presence of geodesic deviation. They are not the same.

Acceleration is irrelevant to the clock effect as could have a 1g acceleration on both twins and the traveling twin still comes back younger.

[u/Aggressive-Share-363]

Time dilation does apply based on speed. You need thr acceleration to account for the difference when you bring them back to the same location. Them disagreeing while being aeperatrnisnt a problem, thats just relativity.