Exploring the Twin Paradox of Special Relativity

In summary, the Special Theory of Relativity explains that the person who has accelerated away from the observer and accelerates again to join the observer is the person that grows older in the twin paradox. However, if both individuals accelerate in the same way, they will be the same age when they meet. Additionally, if one individual accelerates after a significant distance has built up between them, they will be the younger one when they reunite. This is due to the geometrical explanation of elapsed time being the distance between two events. Overall, acceleration does not cause time dilation, and the situation is not symmetric.
  • #1
Wannabeagenius
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Hi All,

I was recently trying to understand the Special Theory of Relativity and my understanding of the resolution of the twin paradox is that the person who has accelerated away from the observer and accelerates again to join the observer is the person that grows older. I understand the reasoning behind this.

However, what if I accelerated with respect to a stationary observer and then, after several years, the stationary observer accelerated to get back to me. Or vice-versa.

What is the explanation under those circumstances?

Thanks in advance.

Bob Guercio
 
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  • #2
If you accelerate the same way, you will be the same age when you meet, regardless of when you started the acceleration.
 
  • #3
Bob Guercio said:
However, what if I accelerated with respect to a stationary observer and then, after several years, the stationary observer accelerated to get back to me. Or vice-versa.

What is the explanation under those circumstances?
When do you accelerate? If you are initially at the same position and then you accelerate briefly to build up a velocity relative to the other observer, but after that you move inertially and it's the other observer who accelerates to return to you later, then your initial acceleration doesn't affect the results much (or at all, if your initial acceleration is treated as instantaneously brief)--it's the one who accelerates once a significant distance has built up between you that mainly determines which one will be younger when the two of you reunite.
 
  • #4
I understand the reasoning behind this.
No offence, but I doubt that you understand the reasoning, because there is none. The argument concerning acceleration is given merely to point out that the situation is not symmetric. Acceleration does not make clocks run slower.
However, what if I accelerated with respect to a stationary observer and then, after several years, the stationary observer accelerated to get back to me. Or vice-versa.

What is the explanation under those circumstances?
That's indeed the best counterexample to the widespread notion that acceleration somehow causes time dilation.
If you draw the example in a space-time-diagram, you see immediately that it is the usual twin paradox, but this time as seen in the frame where the outbound twin is at rest. The "stationary" observer is the "moving" one in this case, therefore he ages less.
The only explanation I know of is the geometrical one: The elapsed time is the distance between two events, calculated sqrt( (t2-t1)²-(x2-x1)²), where t and x are the coordinates of the events in an inertial frame.
 
  • #5
Bob Guercio said:
However, what if I accelerated with respect to a stationary observer and then, after several years, the stationary observer accelerated to get back to me. Or vice-versa.
Bob
The reason your are getting confusing answers is you have not detailed your question very well. I think I understand what you really mean.
First ignore the first “acceleration” as acceleration does not matter at all when working SR problems.
We just have YOU departing Earth at 0.5c

Now after some considerable period of time you want the on Earth to accelerate in pursuit to catch up with you.
This gives us a problem as we can hardly call your stationary if they are to be accelerated.
Therefore from now on let's call your “stationary observer” the OBSERVER.

We will ignore the acceleration as well by bring it up to speed in a time interval insignificantly small compared the travel times being used. (even GR gravitational time affects are zero where high accelerations are in effect instant due to short time of application no matter how high the "Equivalent Gravity")
Also, the OBSERVER cannot catch up to YOU by following at the same speed so 0.5c relative to Earth won’t do. We send the OBSERVER at twice the speed or 0.8c.
(Note: If you do not already know that 0.5c plus 0.5c = 0.8c spend some time in a chapter or site on relativistic speed addition. If you cannot do relativistic speed addition you cannot do SR twin examples).
The OBSERVER and YOU had seen the separation speed as 0.5c and now both of you will see the closing speed as 0.5c (do the math).

So just how did YOU get back together with the OBSERVER? Certainly not by changing speed WRT earth, meaning YOU are the one that is stationary not the OBSERVER in your new version of this problem.
So the answers is as the one that remained in the stationary reference frame YOU will have aged much more upon reconnecting with the much younger OBSERVER.
 
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  • #6
This thread needs space-time diagrams. Too bad I'm too lazy to draw one. :smile:

It also needs more input from the OP. Bob, do you feel that your question has been answered?
 

FAQ: Exploring the Twin Paradox of Special Relativity

1. What is the Twin Paradox of Special Relativity?

The Twin Paradox is a thought experiment that explores the concept of time dilation in Special Relativity. It involves two twins, one of whom travels at high speeds through space while the other stays on Earth. When the traveling twin returns, they will have aged less than the stationary twin due to time dilation.

2. How does time dilation work in the Twin Paradox?

Time dilation is a phenomenon in Special Relativity where time appears to pass slower for objects in motion. This is due to the fact that as an object's speed increases, its relative velocity through space increases, causing time to slow down for that object.

3. Is the Twin Paradox a real paradox?

No, the Twin Paradox is not a true paradox. It may seem counterintuitive at first, but it can be explained and understood through the principles of Special Relativity.

4. Can the Twin Paradox be observed in real life?

While the Twin Paradox is a thought experiment, its principles have been observed and confirmed through experiments with high-speed particles and atomic clocks. However, in order to observe the effects on a human scale, one twin would have to travel at speeds close to the speed of light, which is currently not possible with our technology.

5. What implications does the Twin Paradox have for space travel?

The Twin Paradox is important in understanding the effects of time dilation on space travel. It shows that as an object approaches the speed of light, time will pass slower for that object, making long-distance space travel more feasible. It also highlights the need for precise timekeeping in space missions.

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