## Sonntag, 26. September 2010

### The Twin Paradox

As a physicist one of the most commom questions I get asked is: could you please explain the twin paradox?
Well it's not that complicated really! The twin paradox is a thought experiment meant to demonstrate Einstein's time diletation of travelling clocks (time progresses slower in traveling clocks).
Lets say we take two twins, Twin E (for Earthling) and Twin A (for Astronaut), keep E on Earth and send A into space. A would have to be in space for a very long time and travel at a high speed. On his return home, A would discover that his twin brother had aged much faster.
How does this work? In E's reference frame, the turning point is 3 light-years away and A travels at 60% of lightspeed (lightspeed c=299,792,458 meters per second) both ways. Thus, the trip takes 5 years each way and home arrival is 10 years after departure from E's point of view. The total travel time t=2L/v (t=time; v=velocity, 0.6c in our case; L=distance traveled away from earth=3 lightyears) = 10 years.
Because of the high speed involved we need to introduce ɣ=(1-v²/c²)^-1/2 (ɣ=gamma=Lorentz-factor) for A. From A's point of view the time he needs is t=2L/ɣv= 8 years!
As you can see the twin who stayed home is now two years older than his astronaut brother.

In the Drawing E (blue) is in the (ct,x)-system and A is in the (ct',x')-system. You can see that as time progresses, and A (red) gets further away from earth, events happen later in his system. This is how the twin paradox works graphically.
So what's so paradox about it? When Einstein postulated his work on relativity and Paul Langevin created this thought experiment, skeptics argued that the twin A could just as well have viewed himself as stationary, with the Earth and his twin brother speeding away from him and return to him later. In such a case, the Earth and twin E must be the younger ones, because they were in the 'moving frame of reference'. When compared to the original postulate, this is obviously paradoxical.
Of course this is not realistic, as twin A has to suffer g-forces to get up to speed, then again to turn around and head back and finally again to land on Earth. So the situation is not symmetrical.

Cheers

#### Kommentare:

1. Dieser Kommentar wurde vom Autor entfernt.

2. i took shit like this in school and i was like god damn school

3. Fascinating. Not only the Paradox, but the amount of effort you put into it.
There. I forgot a T in Effor. I'm anal about these things.

4. thanks pink freund ;)
@big hoss: well i probably was lucky i dint have much science in school so it wasnt ruind for me :)

5. These things are easy to explain. I couldn't do it better myself.

6. Whoah, impressive!

7. Very cool post bro !

8. Very interesting.

9. interesting thought

good blog

10. Good stuff looking forward to more.

11. Well explained, I have an interest in Physics since taking it in high school but my teacher was a bit of a bore, you should consider taking it up!

12. the chart is excellent- describes it well. you sir, have earned my follow.

13. looking forward to the next update...

14. Wow how long do you have to go to school to be a physicist? following you, this is pretty interesting stuff

15. Kind of shoots a hole in most time-travel theories. It means you'd age as you'd travel, but the travel time would seem shorter.

16. Error. Max buffer reached. My brain almost exploded. Awesome post though. I need to learn some more basics.

17. Will be taking adv physics next semester. So really interesting read this place is.

18. I cheated all the way through physics in college, it's great....Keep up the good work....Following you for sure.

19. Well done again, I love this kind of detail in explanation.

20. I remember a few years back trying to wrap my mind around relative time and time dialation, it feels great though now. this is a great post man

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21. I have to remember to always be awake when reading your blog :P

22. Cool man!
Nice post
supportin & follow you !!

23. this is a good post that makes me want to come back for more

24. wow, this is some confusing stuff

25. interesting blog dude!

26. Can you possibly do a writeup on string theory? I'd really like to know more about it. Thanks!

27. Well, now I know.

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29. young ass dude brother

30. Hey! I'm totally enjoying you blog!! This stuff is fun to look at! Keep it up! :)

31. Great post!

looking forward to reading the next one

32. I think you just blew my mind! Thanks for breaking that one down for me, very interesting now that I grasp the idea!

-NH

33. this stuff goes way over my head, interesting though!

34. Need more science! Can't wait til the next post.

35. Of Pericles, to rage the city turn, Following!