# Time dilation

## Main Question or Discussion Point

The twin paradox is very confusing, and even after reading the explanation, I still get questions. The only explanation of the paradox is when an object is first moving away from earth, and then moving towards the earth. They make it very complicated.

How about just moving one direction, and then stop.

Let's say that an object moves one lightyear from earth in the rest frame in a straight line for an average speed that makes the dialation for the object 0.5 in the rest-frame. The object will see the earth move away from it, and assume it is dialated by 0.5 as well. When both observe this, what will be true when the object stops? Will the object be "older" or will the earth be?

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JesseM
Because of the relativity of simultaneity, different frames disagree on the age difference between two twins at different locations at any given "instant" (since the relativity of simultaneity means that different frames disagree about whether two events at different locations happened at the 'same instant' or at different times). In your example, suppose there is a third observer who is traveling alongside the twin moving away from the Earth at 0.5c, but when this twin changes speed to come to rest relative to the Earth, this third observer continues to move inertially. In the frame of this third observer, the Earth-twin will continue to be younger than the traveling twin after they come to rest relative to one another, although from then on they will age at the same rate. On the other hand, in the frame of the Earth-twin, it's the traveling twin who is younger, although after the traveling twin comes to rest they age at the same rate.

The twin paradox is very confusing, and even after reading the explanation, I still get questions. The only explanation of the paradox is when an object is first moving away from earth, and then moving towards the earth. They make it very complicated.

How about just moving one direction, and then stop.
Look here. If you stop your calculations after "phase 3", you get the answer to your question. The "stay at home" twin will be older.

JesseM
Look here. If you stop your calculations after "phase 3", you get the answer to your question. The "stay at home" twin will be older.
Only in the rest frame of the stay-at-home twin! If you repeat the calculation in another frame, you can find that the stay-at-home twin is younger when the traveling twin stops, as I noted above.

Why time is light and time dosnt age just are perception of it dose.

(will and object be older) no it wouldnt your perception of it would due to the fact that you would be thinking and the object is an object that cannot think or see light and create it into time that we feel every second of every day...(will the earth be) no it wouldnt mainly for the same reason, yet the start location would be the the orgin of the light and the first stop would be the reflection off the earth then the third stop would be at the asorbtion of the object or the reflection off that object so the answer is no&no but the answer is yes&yes in another way which is the light would be "older" the object and the earths light would be older to, the age differ from each refection from point B to C and back to B, and yes "they" do make it complicated. An observer eyes would be tricked by the light and would have a miss perception of it. so math would say how old the light is from each reflection from the start A to B to C and back to B for us to see :D so each question is true and false in some way its true and in some ways its false but math says that there both wrong and the observers sight would be tricked by the light. truely a paradox :D but it only is if you think it is, or make it what it is. only a paradox if your lack of understanding makes it one :D

Only in the rest frame of the stay-at-home twin! If you repeat the calculation in another frame, you can find that the stay-at-home twin is younger when the traveling twin stops, as I noted above.
I don't believe this is correct. The situation is not symmetric, since one twin stays in an inertial frame the entire time (the stay-at-home), but the other accelerates to speed and the decelerates back to rest at the end. It's these periods of non-inertial motion that causes the actual elapsed time in the moving frame to be less than the elapsed time in the stationary frame.

pervect
Staff Emeritus
I don't believe this is correct. The situation is not symmetric, since one twin stays in an inertial frame the entire time (the stay-at-home), but the other accelerates to speed and the decelerates back to rest at the end. It's these periods of non-inertial motion that causes the actual elapsed time in the moving frame to be less than the elapsed time in the stationary frame.
There are many different ways of explaining the twin paradox - Jesse's explanation is correct, though some people explain it differently.

JesseM
I don't believe this is correct. The situation is not symmetric, since one twin stays in an inertial frame the entire time (the stay-at-home), but the other accelerates to speed and the decelerates back to rest at the end. It's these periods of non-inertial motion that causes the actual elapsed time in the moving frame to be less than the elapsed time in the stationary frame.
But consider the perspective of the third observer who moves along with the traveling twin initially, but does not accelerate when the traveling twin does, and just continues on inertially. In her (inertial) frame, the traveling twin is initially at rest before accelerating, and the stay-at-home twin is moving, so the stay-at-home twin ages slower during this period. The when the traveling twin accelerates, he moves to the same speed as the stay-at-home twin in her frame, and from then on both age at the same rate in the observer's frame, but with the the stay-at-home twin younger than the traveling twin by a constant amount due to their different rates of aging before the acceleration.

But consider the perspective of the third observer who moves along with the traveling twin initially, but does not accelerate when the traveling twin does, and just continues on inertially. In her (inertial) frame, the traveling twin is initially at rest before accelerating, and the stay-at-home twin is moving, so the stay-at-home twin ages slower during this period. The when the traveling twin accelerates, he moves to the same speed as the stay-at-home twin in her frame, and from then on both age at the same rate in the observer's frame, but with the the stay-at-home twin younger than the traveling twin by a constant amount due to their different rates of aging before the acceleration.
The problem is what happens during that period of acceleration. This is the difficulty of the twin paradox problem, which is often swept under the rug and is the reason why I wish it wouldn't be inflicted upon first-year relativity students. If you really calculate the elapsed proper time, taking into account the proper acceleration, then the reference frame of the observer doesn't matter.

The link posted earlier by 1effect shows the relevant calculations.

JesseM
The problem is what happens during that period of acceleration. This is the difficulty of the twin paradox problem, which is often swept under the rug and is the reason why I wish it wouldn't be inflicted upon first-year relativity students.
Dramatic things only happen during the period of acceleration if you try to take the perspective of the twin who accelerates. As seen in any inertial frame, if the acceleration is very brief, there will be a very small difference between each twin's respective age immediately before the acceleration and their respective ages immediately after (and if the acceleration is instantaneous, there is no difference).
belliott4488 said:
If you really calculate the elapsed proper time, taking into account the proper acceleration, then the reference frame of the observer doesn't matter.
Sure it does, if the twins are at different spatial locations. Only in the case where the two twins reunite at a single location do all frames agree on their relative ages. Remember the relativity of simultaneity!

If both twins are exactly 30 when the traveling twin departs the stay-at-home twin, and in the stay-at-home twin's frame, the traveling twin moves away for 10 years at 0.6c before instantaneously accelerating to come to rest relative to the stay-at-home twin, then in this frame the stay-at-home twin turning 40 will happen simultaneously with the traveling twin accelerating while turning 38. But in the frame of an inertial observer who sees the traveling twin at rest until accelerating, the stay-at-home twin is moving away at 0.6c for 8 years before the traveling twin accelerates (again at age 38) to match speeds with him, and at the moment of acceleration the stay-at-home twin is 36.4 years old. This is just an example of the relativity of simultaneity. Both frames agree the traveling twin is turning 38 at the moment of acceleration, but in the first frame this event is simultaneous with the stay-at-home twin turning 40, while in the second frame this event is simultaneous with the stay-at-home twin turning 36.4.

Do you disagree with these numbers? I can demonstrate that they work using the full Lorentz transformation if you wish.