Time Dilation, who is aging slower?

[ajward]

So finally I can understand the time dilation principle. Correct me if I am wrong but here is how I understand it:

If 2 twins on Earth conducted an experiment of time dilation, twin 2 hops into a rocket ship and flies around the Earth at a high rate of speed for years. When they meet up again the twin 2 appears younger than twin 1 on earth, because of the time dilation. So during this time twin 2 is flying, twin 1 can watch his brother age slower. All his activities on board are slower but to twin 2 everything is normal. What if you took twin 2's perspective... Twin 2 feels normal and he looks back to Earth to see his brother. To twin 2 his brother (twin 1) is moving at a high rate of speed because relative to twin 2, in the ship, he is not moving. So, would twin 2 see his brother twin 1 age slower because of time dilation relative to twin 2 in the ship? This is why I get stumped. If twin 2 and twin 1 meet up and supposedly twin 2 is younger than twin 1, then twin 2 must be seeing his brother twin 1 age faster even though relative to twin 2 his brother should experience the time dilation.

Maybe an even deeper question is where is the absolute perspective that decides who will age slower. because if you are on another planet, the rocket ship may actually appear to be going slower than the Earth which would say that twin 1 should be younger than twin 2.

edit: I read a little bit of similar posts, sorry for the repost but i did read that the guy twin who is accelerating back to Earth will age less because of that acceleration. but my question is again...only to the observer the guy is accelerating to him, whether he is on Earth or in the ship, who decides who will age?

 

[ajward]

I think I understand it now:

During constant velocity both view each other aging slower which is not true to the 3rd observer. The 3rd observer sees both age the same. It is the acceleration of the guy in the rocket that slows his relative time down and during the acceleration and deceleration of the rocket, his twin brother on Earth ages quicker than him. The guy on Earth does not have an acceleration acting on him which is why his age doesn't slow like the twin in the rocket. Please correct me if i am wrong here.

 

[jason12345]

I think I understand it now:

During constant velocity both view each other aging slower which is not true to the 3rd observer. The 3rd observer sees both age the same. It is the acceleration of the guy in the rocket that slows his relative time down and during the acceleration and deceleration of the rocket, his twin brother on Earth ages quicker than him. The guy on Earth does not have an acceleration acting on him which is why his age doesn't slow like the twin in the rocket. Please correct me if i am wrong here.

This is correct. As it turns out, the ageing of the accelerated twin depends upon the magnitude of the acceleration and so they can appear youger when the acceleration is below a certain value.

 

[JesseM]

This is correct. As it turns out, the ageing of the accelerated twin depends upon the magnitude of the acceleration and so they can appear youger when the acceleration is below a certain value.

It's not really correct that the aging depends on the magnitude of the acceleration, although it is true that if one twin moves inertially (constant speed and direction, unlike the circular orbit ajward mentioned where the direction is always changing) while the other moves away from the twin then accelerates at some point and later the two twins reunite, then the twin that accelerated will always have aged less. However, you would calculate the aging of each twin using only their velocity as a function of time (relative to some inertial reference frame), not their acceleration.

It's pretty closely analogous to how if you draw two points on a 2D plane, and then create two paths going from the first point to the other, and one is a totally straight path while the other has a bend in it somewhere, then the bent path will always have a greater total length; however, it's not as if the bent path accumulated all that extra length during the bent section, it's more a question of the overall geometry of the paths and the fact that in a 2D plane a straight line is always the shortest distance between points.

 

[Hurkyl]

So during this time twin 2 is flying, twin 1 can watch his brother age slower.

Yes, and no. As twin 1 looks through a telescope, he sees his brother's aging vary a lot due to the doppler effect, ranging between aging very slowly and aging very quickly. However, if he attempts to plot his observations according to an Earth centered inertial frame, the plotted results will have twin 2 aging slower than coordinate time throughout.

(If Earth was a point particle, though, then twin 1's observations would be uniform)

Twin 2 feels normal and he looks back to Earth to see his brother.

(except, of course, for the high rate of lateral acceleration)

To twin 2 his brother (twin 1) is moving at a high rate of speed because relative to twin 2

Not as much as you'd think, because twin 2 is orbiting the Earth. If we're treating the Earth as a point particle, then twin 1 looks immobile!

So, would twin 2 see his brother twin 1 age slower because of time dilation relative to twin 2 in the ship?

Switching back to a realistic Earth, twin 2 looking through his telescope would see twin 1's rate of aging varying from slow to fast. However, how would twin 2 plot his observations? There isn't a rocket centered inertial frame! There are lots of schemes he could use -- and each different scheme has its own pecularities as to how time dilation looks. The one I'm most familiar has the following behavior:
* If you are accelerating towards something, its clocks speed up relative to coordinate time.
* If you are accelerating away from something, its clocks slow down, or even start running backwards relative to coordinate time.

If twin 2 uses this method to plot his observations, then the plot will show twin 1 was aging faster than coordinate time throughout.

 

[Austin0]

* If you are accelerating towards something, its clocks speed up relative to coordinate time.
* If you are accelerating away from something, its clocks slow down, or even start running backwards relative to coordinate time.

Could you explain what you mean by "running backwards relative to coordinate time "

Do you mean simply an increasing interval of retardation relative to coordinate time?

I guess I am confused in understanding the difference between slowing down [which is obvious due to the doppler effect] and running backwards which, to me at least , is not obvious.
Thanks

 

[Hurkyl]

Could you explain what you mean by "running backwards relative to coordinate time "

Do you mean simply an increasing interval of retardation relative to coordinate time?

No, I actually mean running backwards -- you have two distinct coordinate tuples for which the change in coordinate time is positive, but the proper time difference is negative. The same event in space-time does not have a unique label -- it has several different coordinate labels. (Some events might get no labels at all, which would mean part of the universe doesn't even appear in this coordinate chart)

The particular coordinate system I'm describing is easiest described geometrically -- but I imagine you haven't yet learned the Minkowski geometry needed to talk about the geometry of space-time... However, I'll assume you know what a "line of simultaneity" is. Roughly speaking, the coordinate system I'm talking about is constructed by your observer looking at the time on his watch, and then declaring all points on his current line of simultaneity have that time as their coordinate time.

When you're talking about an inertial observer, all of his lines of simultaneity have the same orientation -- they're parallel -- and so every event gets a unique coordinate time. However, for an accelerating observer, his lines of simultaneity have different orientations, and so they will intersect someplace, leading to the same event receiving multiple different coordinate-times.

In such a circumstance, if you follow the coordinates continuously, you will see that as coordinate time increases, the reading on a clock can slow down, stop, and run in reverse. (And maybe stop and go back to running forwards again, depending on how our remote clock and our observer is travelling)


And just to emphasize this point in case it's missed -- this is a coordinate effect: like most other coordinate systems (inertial frames included, as well as standard coordinates for Euclidean geometry), it has very little direct correlation with what the observer actually sees through his telescope.

 

[Petkovsky]

Well this is how I understand it. You have the guy traveling in a rocket, and the one on the earth. The rocket guy's time is greater, he has traveled more into the future, hence the guy on the Earth in his frame of reference has aged more. The Earth guy's time is slower, and in his frame of reference the guy in the rocket has aged less.

 

[Austin0]

No, I actually mean running backwards

--

The particular coordinate system I'm describing is easiest described geometrically -- but I imagine you haven't yet learned the Minkowski geometry needed to talk about the geometry of space-time...

Without knowing exactly what geometry you mean I would still say it was a safe assumption of yours.

However, I'll assume you know what a "line of simultaneity" is.

AH, that seems to be the question here.

Roughly speaking, the coordinate system I'm talking about is constructed by your observer looking at the time on his watch, and then declaring all points on his current line of simultaneity have that time as their coordinate time.

If this means that hypothetical [or real] observers comoving along this axis with synchronized watches would consider all proximate events at this time reading to be simultaneous and so by extension simultaneous with the watch observation of the original observer, then that is my understanding.

In this context, are you saying that that some possible sequence of observers in the accelerating frame could successively pass the Earth clock and see the same reading on it while their clocks positively incremented? Or that some other series of observers could pass that clock and perceive actual retrograde readings?

When you're talking about an inertial observer, all of his lines of simultaneity have the same orientation -- they're parallel -- and so every event gets a unique coordinate time. However, for an accelerating observer, his lines of simultaneity have different orientations, and so they will intersect someplace, leading to the same event receiving multiple different coordinate-times.

Both the logic and the geometry of this description are quite clear. If the distance was such that they converged before reaching the other world line then they would intersect that line with reversed ordering. While I don't question the geometry I have no idea what meaning to attach to this.
Are you suggesting that the accelerating observer could observe this occurence of retrograde chronolgy after sufficient passage of time for light to reach him from these tuples of events?

My understanding is that one of the fundamental observations of SR is that, the very term simultaneous can only be applied with any actuallity with colocated events.
In this case all observers agree irrespective of their relative motion.
Beyond this it is problematic. The synchronized clock solution within a sigle inertial frame as good as it gets.
SO if the geometric interpretation of these graphed lines seems to describe a reality that has no observational reality within that frame I don't know what to think.
In the following sentence you say

In such a circumstance, if you follow the coordinates continuously, you will see that as coordinate time increases, the reading on a clock can slow down, stop, and run in reverse. (And maybe stop and go back to running forwards again, depending on how our remote clock and our observer is travelling)

But in the sense you are talking about arent these lines just hypothetical graphs of a possible future relationship that will only occur if their current states of motion are preserved without change long enough .
So I see how the lines of simultaneity are relevant within the Minkowski system as graphically representing clock desynchronization but don't get how they could lead to temporal order reversal. But there is a lot I don't get. Thanks for your input.

And just to emphasize this point in case it's missed -- this is a coordinate effect: like most other coordinate systems (inertial frames included, as well as standard coordinates for Euclidean geometry), it has very little direct correlation with what the observer actually sees through his telescope.

 

[shadowofra]

I think the concept of apparent time distortion at near-c is intuitive. Not so the idea that clocks and time itself for the "moving" party actually do slow down or speed up. I have never heard a physical explanation for this - nor did Einsteins original thought experiments ever illustrate this.

Furthermore the common classroom example of twin 1 moving at near-c in a rocket and twin2 remaining still is absurd. Motion is relative. If twin1 moves fast then twin2 moves just as fast relative to twin1. They will be the same age when reunited regardless of the apparent time distortion during the intervening period. There are plenty of very blue and very red shifted objects in the cosmos. And to them I'm sure we and our sun are red & blue shifted too.

Does this mean our clocks are all messed up because of it? Whose clock? Theirs? Ours? No matter I'm sure modern math will just invent infinite universes branching off with different time - one extra for each blue/red shifted object. Who needs meaning when you can have complexity.

 

[JesseM]

I think the concept of apparent time distortion at near-c is intuitive. Not so the idea that clocks and time itself for the "moving" party actually do slow down or speed up. I have never heard a physical explanation for this - nor did Einsteins original thought experiments ever illustrate this.

It's an automatic consequence of the idea that all laws of physics should work the same way in the different inertial frames of SR which are related by the Lorentz transform. Another way of putting it is that if the two fundamental postulates of relativity are correct--the first postulate saying the laws of physics work the same way in all inertial frames, the second saying that the speed of light is the same in all inertial frames--then you can show that it's a logical consequence of this that each inertial frame must measure moving clocks to slow down.

Furthermore the common classroom example of twin 1 moving at near-c in a rocket and twin2 remaining still is absurd. Motion is relative. If twin1 moves fast then twin2 moves just as fast relative to twin1.

Inertial motion is relative, so as long as twin1 and twin2 move apart at constant velocity without accelerating, then it's true that in twin1's frame twin2 is moving and has a slowed-down clock, whereas in twin2's frame twin1 is moving and has a slowed down clock. This has to do with the fact that different frames in relativity disagree about which events are "simultaneous", so for example twin1 might say that the event of his clock reading 10 years is simultaneous with the event of twin2's clock reading 8 years, but twin2 might say that the event of his clock reading 8 years is simultaneous with the event of twin1's clock reading 6.4 years. The only way they can avoid problems of simultaneity is by reuniting at a single location to compare clocks there--all frames agree about local events that happen at the same position and time, so all frames will agree about what each clock reads at the moment they reunite. However, in order for them to reunite after they have been moving apart for some time, one of the twins has to accelerate so that they are then moving towards each other (otherwise they'll just move apart forever and never reunite), and acceleration is not relative in relativity--the one who accelerates will feel G-forces as they accelerate (as measured by an accelerometer), so there is no doubt about which one it was. And the time dilation law which says moving clocks slow down only applies in inertial frames of reference, so the twin that accelerated at the midpoint of the journey cannot say that the other twin's clock was running slow the whole time. Whichever twin accelerates, that twin's clock will actually show less time elapsed (meaning that twin has aged less) when the two twins reunite.

Does this mean our clocks are all messed up because of it? Whose clock? Theirs? Ours? No matter I'm sure modern math will just invent infinite universes branching off with different time - one extra for each blue/red shifted object. Who needs meaning when you can have complexity.

No, there is no need for multiple universes, different inertial frames are nothing more than different coordinate systems which assign time and space coordinates differently, but they all agree on all physical predictions about local events such as what two clocks read at the moment they unite at a single position in space.