Visualizing Time Dilation: Exploring the Effects of Relativity on Twin's Journey

In summary, the gamma factor describes how much the time between ticks of the traveling twin's clock are elongated (dilated) in the Earth twin's frame. For example, if the traveling twin is moving at 0.866c in the Earth's frame, then it takes 2 seconds of time in this frame for the traveling twin's clock to tick forward by 1 second. You can also take the inverse of these numbers to see how much less the traveling twin will have aged in total between leaving Earth and returning, assuming he travels at uniform speed; for example if the traveling twin travels away and back at 0.866c, then if the Earth twin has aged N years during that time, the traveling twin has only aged N/
  • #1
gonegahgah
376
0
Are there any graphs that depict the amount of time dilation that occurs by the fraction of the speed of light for the traveling twin?
 
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  • #2
You mean, time dilation factor on one axis and velocity on the other? If so just enter "time dilation graph" into a google image search, you'll various examples such as this one.
 
  • #3
Thanks for that Jesse.
 
  • #4
I'm not sure what the graph results mean.
The formula give the results of:
0.866c -> 2
0.9428c -> 3
0.9682c -> 4
0.9798c -> 5
etc
Does this mean that the traveling twin will appear to the home twin to take twice as long to travel to and back from their destination when they travel at 0.866c, three times as long when they travel at 0.9428c, four times as long at 0.9682c, etc.?
Can someone please clarify if this is what is meant or something else?
 
  • #5
gonegahgah said:
I'm not sure what the graph results mean.
The formula give the results of:
0.866c -> 2
0.9428c -> 3
0.9682c -> 4
0.9798c -> 5
etc
Does this mean that the traveling twin will appear to the home twin to take twice as long to travel to and back from their destination when they travel at 0.866c, three times as long when they travel at 0.9428c, four times as long at 0.9682c, etc.?
Can someone please clarify if this is what is meant or something else?
No, the formula doesn't refer to travel time, it refers to how much the time between ticks of the traveling twin's clock are elongated (dilated) in the Earth twin's frame. For example, if the traveling twin is moving at 0.866c in the Earth's frame, then it takes 2 seconds of time in this frame for the traveling twin's clock to tick forward by 1 second. You can also take the inverse of these numbers to see how much less the traveling twin will have aged in total between leaving Earth and returning, assuming he travels at uniform speed; for example if the traveling twin travels away and back at 0.866c, then if the Earth twin has aged N years during that time, the traveling twin has only aged N/2 years upon return.

The actual travel time in the Earth's frame depends only on the velocity in the Earth's frame, for example if the traveling twin goes to a destination 5 light-years away and returns to Earth, traveling at 0.866c the whole time, the time of this journey in the Earth's frame is (5+5)/0.866 = 11.547 years (which means upon return, the Earth twin will be 11.547 years older while the traveling twin is only 5.7735 years older).
 
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  • #6
Just in case you were asking for the relative age of the traveling twin compared to the stay-at-home twin, here is a graph that depicts that:
AgeVSspeed.PNG

If you complare this graph to the one that JesseM pointed you to, you will see that it is simply the reciprocal of the Y axis. You can also see that the shape of the graph is a simply quarter of a circle.
 
  • #7
gonegahgah said:
Does this mean that the traveling twin will appear to the home twin to take twice as long to travel to and back from their destination when they travel at 0.866c, three times as long when they travel at 0.9428c, four times as long at 0.9682c, etc.?

gonegahgah,

The gamma factor at 0.866c is 2. This means that the traveling twin ages 1/gamma = 1/2 as much as the inertial twin over the very same interval. As JesseM pointed out, this is the same as saying that the traveling twin experiences a dilated (stretched) duration by a factor of gamma = 2, wrt the traveling twin's aging as the reference.

I recommend you forget the classic twins scenario, and instead focus on all-inertial scenarios first. In the case of the classic twins scenario, one twin (B) undergoes a proper acceleration, and the analysis of the scenario is much more complex. Master the easier all-inertial scenarios first, then go into the more complicated ones. It will save you a great amount of time in the end. Food for thought.

GrayGhost
 
  • #8
It increases exponentially as the object travels closer to the speed of light. Most text that teach the theory should show it...
 
  • #9
Thank you for that information. That explains it to me a lot better.
 

1. What is the "Graph of Twin's Time Dilation"?

The "Graph of Twin's Time Dilation" is a visual representation of the time dilation effect predicted by Einstein's theory of relativity. It shows the difference in time experienced by two twins, one who stays on Earth and the other who travels at high speeds to a distant location and back.

2. How does the graph demonstrate time dilation?

The graph shows that as the traveling twin's speed increases, the difference in time experienced by the two twins also increases. This is due to the fact that time, according to relativity, is not absolute and can be affected by the relative motion of objects.

3. What causes time dilation in the graph?

The time dilation effect seen in the graph is caused by the difference in velocity between the two twins. The traveling twin experiences time passing slower due to their high speed, while the stationary twin experiences time at a normal rate.

4. How does the graph support Einstein's theory of relativity?

The graph of Twin's Time Dilation provides visual evidence for the predictions made by Einstein's theory of relativity. It shows that time is not absolute and can be affected by the relative motion of objects, which is a key concept in the theory.

5. What are the real-life implications of the graph of Twin's Time Dilation?

The graph demonstrates the concept of time dilation, which has been confirmed through experiments and is essential in many modern technologies such as GPS systems. It also helps us understand the effects of extreme speeds on time and the nature of our universe.

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