Understanding Time Dilation: Exploring the Twin Paradox in Special Relativity

[AYYYLAMOOOO]

I have a question regarding time dilation within the frame work of special relativity. I'm sorry as I know that this forum is constantly receiving questions like this however I just cannot seem to find my answer. Anyways, the question is concerning the twin paradox.

We know that the twin aboard the spaceship would experience time slower and therefore age in a less rapid manner than the twin who is on the Earth. I've also been told that both twins would view the other one's time slower than their own, and this is where I have difficulty understanding it.

Let's call the twin on the spaceship Alice and the one on the Earth Bob to avoid confusion.

If Alice was constantly viewing Bob, always seeing that Bob's time is passing slower and aging less, then how does it work that Alice would return home to find that Bob had actually aged faster?

I'm only in high school and so I would greatly appreciate it if you could conceptually explain it rather than with mathematics. Thanks!

 

[PeterDonis]

Please read the Usenet Physics FAQ article on the twin paradox:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

Pay particular attention to the Doppler Shift analysis; it explains what Alice and Bob (the article calls them Stella and Terence) actually see, and makes clear that they do not actually see each other's time always passing slower.

If you have questions after reading the article, feel free to ask; but reading the article will give you a much better basis for discussion.

 

[bcrowell]

If Alice was constantly viewing Bob, always seeing that Bob's time is passing slower and aging less, then how does it work that Alice would return home to find that Bob had actually aged faster?!

"Viewing" is not instantaneous. When Alice looks at Bob, she is receiving optical signals from Bob that travel at the speed of light.

 

[Yash1993]

In this case, you consider two frames; Earth on which bob resides and other Star-ship in which Alice is used to travel nearer to c. As per your statement that Alice viewing to the Earth since she herself moves with near to c with respect to earth. So, Alice finds that Earth is moving apart from her with speed nearer to -c.But Earth itself moves with regular speed by free fall due to sun's gravitational speed and therefore clocks placed on the Earth moving faster compared to Star-ship where Alice travels!

 

[Nugatory]

In this case, you consider two frames; Earth on which bob resides and other Star-ship in which Alice is used to travel nearer to c. As per your statement that Alice viewing to the Earth since she herself moves with near to c with respect to earth. So, Alice finds that Earth is moving apart from her with speed nearer to -c.But Earth itself moves with regular speed by free fall due to sun's gravitational speed and therefore clocks placed on the Earth moving faster compared to Star-ship where Alice travels!

This is not correct. The FAQ that PeterDonis linked in post #2 provides a correct explanation.

 

[Mister T]

In this case, you consider two frames; Earth on which bob resides and other Star-ship in which Alice is used to travel nearer to c.

It's meaningless to claim Alice's speed relative to Bob is "nearer to c" because by definition "relative to Bob" means treat Bob as though he's at rest. You could just as well say that Bob's speed relative to Alice is "nearer to c".

 

[jtbell]

If Alice was constantly viewing Bob, always seeing that Bob's time is passing slower and aging less, then how does it work that Alice would return home to find that Bob had actually aged faster?

See this old post which describes a very similar situation:

https://www.physicsforums.com/threads/time-difference-cameras.69214/#post-510214

 

[Jonathan Scott]

There's a simple analogy which doesn't involve relativity but makes it easy to understand the concepts.

Imagine two people walking away from a starting point at the same speed, the first going north and the second going north-east, at 45 degrees to the first one. They both see the other one making progress more slowly than themselves in their own direction. Then the second one turns through a right-angle and heads north-west. They both still see the other one making less progress than themselves in their own direction, but the second one now sees the first as having jumped ahead, as a result of turning.

The twins paradox works rather like this. The direction in this space-space analogy corresponds to the velocity in space-time, and the distance traveled corresponds to the time elapsed, which depends on the path. It's obviously a bit more complicated in space-time (mainly because it involves some minus signs), but the principles are very similar.

 

[AYYYLAMOOO]

Hey thanks for the explanations guys.

Pay particular attention to the Doppler Shift analysis; it explains what Alice and Bob (the article calls them Stella and Terence) actually see, and makes clear that they do not actually see each other's time always passing slower.

Alright, then let's say that the spaceship is always next to us, just traveling around in a circular motion.
Through my intuition this would eliminate the Doppler Shift effect, and so how would this affect the twins' perspectives of viewing one another?

 

[Janus]

Hey thanks for the explanations guys.
Alright, then let's say that the spaceship is always next to us, just traveling around in a circular motion.
Through my intuition this would eliminate the Doppler Shift effect, and so how would this affect the twins' perspectives of viewing one another?

Now you are dealing with accelerated (circular) motion, and now the circling ship is in an accelerated frame where the simple time dilation relationship doesn't hold.
So basically, the central observer can just apply SR time dilation to the circling ship and will see it age slowly just due to its speed relative to him.
The observer in the circling ship, viewing things from his accelerated frame will see the central ship age faster.

 

[AYYYLAMOOO]

The observer in the circling ship, viewing things from his accelerated frame will see the central ship age faster.

Oh.

So within the framework of an accelerated perspective the stationary things are indeed transpiring at quicker speeds?

 

[jartsa]

Hey thanks for the explanations guys.
Alright, then let's say that the spaceship is always next to us, just traveling around in a circular motion.
Through my intuition this would eliminate the Doppler Shift effect, and so how would this affect the twins' perspectives of viewing one another?

Still the same old Doppler shift effect occurs.

"My twin is approaching and is Doppler shifted", says the circling twin.

 

[Janus]

Oh.

So within the framework of an accelerated perspective the stationary things are indeed transpiring at quicker speeds?

Not quite. As I said, the rules in an accelerated frame differs from an inertial. Whether a clock runs faster or slower than yours and by how much depends on a number of factors:
It's relative speed with respect to you,
The magnitude of the acceleration
Its direction with respect to the acceleration.
Its distance from you as measured along the line of acceleration.

The first factor is just SR time dilation.

The second factor determines works with the third and fourth to determine the time difference factor.

With the third factor, if you are accelerating towards the clock (like you are if you are circling it) then it runs faster. If you are accelerating away, it will run slower. the greater your acceleration, the larger the difference.

With the fourth factor, The further apart you and clock are, the greater the difference.

Thus if you are at rest with respect to a clock and then start accelerating directly away from it on a straight line, the following happens according to you:
The clock runs slow due to its increasing relative speed with respect to you.
The clock runs slow by an additional factor caused by its direction from you, its distance at any given moment(which increases with time) and the magnitude of your acceleration.

If you are rest with respect to a clock and then start accelerating toward it
The clock runs slow due to its increasing speed with respect to you.
The clock runs fast by a factor caused by its direction and distance at any given moment and the magnitude of your acceleration.
The net rate at which the clock runs( fast or slow) depends on which of the above effects is stronger at the moment in question.

One thing that should be noted is that factor 1 can be zero and you still have to take the other factors into account.
In other words, If you have two clocks that remain stationary with respect to each other ( as measured by the clocks), and both are accelerating along the line separating the clocks, the "Leading" clock will run fast compared to the "Trailing clock". An observer at the leading clock sees the trailing clock run slow, and an observer at the trailing clock sees the leading clock run fast.

As you can see, acceleration adds a whole new set of factors to deal with that likely best left until you are really comfortable with dealing with SR in strictly inertial frames.