What happens during acceleration in twin paradox?

[vraeleragon]

Hi, I just recently studying special relativity in my class. It's fun and I kind of understand what's going on. But the professor skips the acceleration/deceleration part because it's for advance level. So what happens during the acceleration and deceleration (assuming the object won't get crushed during the acceleration/deceleration)? Can anybody explain in the language of first year introductory physics in college? Thanks!

 

[ghwellsjr]

In the classic Twin Paradox, both twins start out at the same age at rest at the same location. One of them instantly accelerates to a high speed and then coasts for a long time. Eventually, he instantly decelerates to a stop and then accelerates backwards to the same high speed but in the opposite direction. He coasts at this high speed for the same length of time as before and then decelerates to a stop and once more is at rest with his twin.

I don't think your professor is really skipping the acceleration/deceleration but rather he is making them instantaneous like I just did so that they will have no effect on the analysis of the scenario which allows you to focus only on the speed of the traveling twin. There are other versions of the Twin Paradox where the traveling twin accelerates and decelerates at some moderate rate such as 1 g for the entire trip. That makes the analysis much more complicated and doesn't provide any more insight into explaining the scenario.

Both versions of the Twin Paradox are absolutely unrealistic and can never be performed due to the exceedingly high energy requirements, not to mention the long travel times, so it doesn't matter which version you use to understand it. Be glad your professor is making it easier on you.

 

[rude man]

I recommend Hermann Bondi's "Relativity and Common Sense" (inexpensive Dover book). You don't need any math beyond first-year high school algebra to understand!
The bases for time-shifts is the constancy of the speed of light in any reference frame, plus acceleration between observers.

 

[bobc2]

Hi, I just recently studying special relativity in my class. It's fun and I kind of understand what's going on. But the professor skips the acceleration/deceleration part because it's for advance level. So what happens during the acceleration and deceleration (assuming the object won't get crushed during the acceleration/deceleration)? Can anybody explain in the language of first year introductory physics in college? Thanks!

vraeleragon, it's really not very complicated conceptually. I've prepared a set of sketches to help you visualize what is going on in the 4-dimensional universe with the twins. As the traveling twin changes velocity, his X1 axis continuously rotates such that the photon world line always bisects the angle between his blue X4 and blue X1 axes. These are what we refer to as a continuous sequence of boosts. The Lorentz transformations describe the boosts mathematicially. If you need a little more background on the space-time sketches and the 4-dimensional universe concept, you can go to this earlier post that outlines the concept, beginning with post #19 (be sure you understand relativity of simultaneity--if not ask questions):

https://www.physicsforums.com/showthread.php?p=4138802#post4138802

 

[tom.stoer]

In special relativity the equation for the relation of proper time τ and coordinate time t is

\tau = \int_0^t dt \, \sqrt{1-\vec{v}^2}

(c=1)

Now one can use the coordinate t as proper time of the non-moving twin (defining an inertial frame).

The interesting fact is that the proper time can be calculates simply by integrating \sqrt{1-\vec{v}^2} w/o ever referring to acceleration. One can e.g. use a circular path with constant v² which starts and ends at the location of the non-moving twin.

 

[bobc2]

In special relativity the equation for the relation of proper time τ and coordinate time t is

\tau = \int_0^t dt \, \sqrt{1-\vec{v}^2}

(c=1)

Now one can use the coordinate t as proper time of the non-moving twin (defining an inertial frame).

The interesting fact is that the proper time can be calculates simply by integrating \sqrt{1-\vec{v}^2} w/o ever referring to acceleration. One can e.g. use a circular path with constant v² which starts and ends at the location of the non-moving twin.

Very nice observation. And it is clear that it is the difference between the paths taken through the 4-D universe that accounts for the difference in ages when the twins meet.

 

[tom.stoer]

have a look at this thread https://www.physicsforums.com/showthread.php?t=646318

 

[bobc2]

have a look at this thread https://www.physicsforums.com/showthread.php?t=646318

Good posts. Thanks.

 

[Vandam]

vraeleragon, it's really not very complicated conceptually. I've prepared a set of sketches to help you visualize what is going on in the 4-dimensional universe with the twins. As the traveling twin changes velocity, his X1 axis continuously rotates such that the photon world line always bisects the angle between his blue X4 and blue X1 axes. These are what we refer to as a continuous sequence of boosts. The Lorentz transformations describe the boosts mathematicially. If you need a little more background on the space-time sketches and the 4-dimensional universe concept, you can go to this earlier post that outlines the concept, beginning with post #19 (be sure you understand relativity of simultaneity--if not ask questions):

https://www.physicsforums.com/showthread.php?p=4138802#post4138802

(edit: image deleted)

Spot on, Bob!

I Remember posting a diagram with this 'rotating' 3D worlds at accelleration when I started on this forum. Didn't have any response though...
(second part of post: https://www.physicsforums.com/showpost.php?p=4005255&postcount=8)

Bob, you will love this one:

It's a bit off-topic here but there's some interesting feature happening with this 3Dworld rotation;
Add a third 'observer' (let's make him red) in your sketch with a world line parallell to the black one. Right of where the blue turns around.
For blue, in the successive blue worlds, red's clock runs... backwards! And then -once inertial again - forward again (again over the red clock events his 3D spaces went over already!)

But blue observer will not literally SEE this. When you draw the lightbeams from the red clock events you will notice that blue observer will never litterally SEE the red clock going backwards.

The interesting question is whether the clock 'really' runs backwards. Of course it does in the successive 3D worlds, but the question and answer only make sense if we agree on the ontological definition of a 3D world, i.e. space-like simultaneous events. This is a dicy topic on this forum, where most members prefer to stick to the mathematics. But I always keep Richard Feynman's words in mind, and will keep on repeating it: <<... Physics is not mathematics, and mathematics is not physics. One helps the other. But you have to have some understanding of the connection of the words with the real world. ...>>
(minute 45:43 in http://www.youtube.com/watch?feature=pl ... d0xTfdt6qw)
The 'real world' is nothing else than Special Relativity's Minkoswki 4D manifold as one physical block entity. We then know that the ticking of the clock -'backward' or 'forward'- is nothing else than reading 'observer independent' timeless clock events that are located in 4D block Spacetime.

 

[Dale]

It's a bit off-topic here but there's some interesting feature happening with this 3Dworld rotation;
Add a third 'observer' (let's make him red) in your sketch with a world line parallell to the black one. Right of where the blue turns around.
For blue, in the successive blue worlds, red's clock runs... backwards! And then -once inertial again - forward again (again over the red clock events his 3D spaces went over already!)

This is indeed quite interesting. It is interesting in the same way as the sudden onset of chest pain and shortness of breath would be interesting, i.e. it is an indication of a severe underlying pathology.

In this case, the pathology is that the same event is mapped to multiple coordinates. This makes the mapping no longer 1 to 1, which is a requirement for coordinate systems. So this coordinate system will be DOA unless some emergency surgery is performed. Specifically, it needs an immediate "back in time"-ectomy and some careful suturing along the cut.

There is no question about whether or not the back-in-time part is good physics, it isn't even good math. Dolby and Gull present an alternative treatment.
http://arxiv.org/abs/gr-qc/0104077

 

[Vandam]

This is indeed quite interesting. It is interesting in the same way as the sudden onset of chest pain and shortness of breath would be interesting, i.e. it is an indication of a severe underlying pathology.

In this case, the pathology is that the same event is mapped to multiple coordinates. This makes the mapping no longer 1 to 1, which is a requirement for coordinate systems. So this coordinate system will be DOA unless some emergency surgery is performed. Specifically, it needs an immediate "back in time"-ectomy and some careful suturing along the cut.

There is no question about whether or not the back-in-time part is good physics, it isn't even good math. Dolby and Gull present an alternative treatment.
http://arxiv.org/abs/gr-qc/0104077

Thanks for that cure-link, Dale.

 

[bobc2]

That was a great reference, DaleSpam. Vandam, here's a rendition about what you were suggesting. I've added in a Red guy as you suggested. He is at rest along with the black guy. As the Blue guy does his turn-around, the sequence of Black clock readings (as presented in the sequence of Blue's 3-D world cross-sections of the 4-D universe) progress into the future whereas the Red clock readings proceed into the past. As Blue enters the turn-around, the Black clock begins with event "black E" and at the end of the turn-around the last Black clock reading corresponds to event "black h." But, although Red's clocks begin with event "red E" (same simultaneous plane as "Black E") and end with event "red h", we see the sequence of Red clock readings going into the past along Red's X4 axis world line. The E, a, b, c, ... h designations identify the discrete hyperplanes (planes of simultaneity) in the movement through 4-D Space-Time of Blue as he progresses along his world line.