The Twin Paradox

Mephistopheles

Banned
Contributor
Can you resolve this problem.

If there are two twins on earth lets call them A and B, and B flies away and comes back at nearly the speed of light, then A has aged more than B. This occurs in A's frame of reference.

The paradox comes into play when you look at the exact same situation in B's frame of reference, in this case B sees A travel away at nearly the speed of light and come back, so therefore you would think that B would have aged more that A in B's reference frame.

Relativity states that all inertial reference frames of a given situation produce the same results, yet by switching frames of reference for the above problem we get two different results, A being older in one and B being older in the other.

There are some clever people on this forum so just for fun can you resolve the paradox?
 

LJKSet

Rookie
While, in the second scenario, B sees A travel away, it is, in fact, B who is doing the travelling. Therefore, using terrestrial time, it is his clock that starts to tick more slowly as he is the one travelling at near light speed, while A´s continues to tick at the terrestrial rate. So on B´s return, his clock would still be slower than A´s, meaning that A would have effectivley aged more than B.

Maybe.
 

canis

Race Winner
Valued Member
As all things in this type of theory are relative to what must be assumed to be a static point of reference it doesn't matter whose frame of reference is used as it is their positional vector to the static point of reference that will be used to work out their speed and therefore their potential time difference based upon the basic theories of Einstein and in extention the speed of the passage of time.

It desn't matter whose view point you use, the frame of reference in both examples must be made to the same assumed static point, so therefore the speed of travel will be the same for both no matter whose viewpoint is taken. It is not really possible to work out relativity calculations based upon differential distance between the two twins because neither of them is a truly static point, so not valid for use as a referential point :p

And for my next trick I will go on to prove black is white and white is black, possibly getting myself killed on the nearest zebra crossing :dizzy:
 

Mephistopheles

Banned
Contributor
Black is the absence of all colours and white is the sum of all colours but this depend on three things

The source

Pigmentation

Reflection

Using these three things you can prove that black is opposite to black just as white is opposite to black....
 

Mephistopheles

Banned
Contributor
Both of you are on the right lines.

The situation I described is true using the special theory of relativity to resolve it you have to use the general theory of relativity..

Keep going...
 

jez101

Bookies drive nice cars because of people like me
Contributor
I really struggle with the idea of time being relative. I honestly don't understand why a minute spent at light speed is any different from a minute spent stationary. Perhaps you could explain...?
 

Brogan

🦶 Leg end
Staff Member
Isn't it simply the case that time slows down the closer you approach light speed?

As A isn't travelling at light speed (although he is travelling as the Earth is moving, as is the galaxy and the universe ;)), time passes more quickly for A than B.
 

jez101

Bookies drive nice cars because of people like me
Contributor
Isn't it simply the case that time slows down the closer you approach light speed?

So what is a light-year then? I know it is a distance that light travels in a year, but if time slows down at light speed, how long is the "year" in a light-year..????? :dunno:

Isn't time slowing down, the same as you speeding up? say I am going at light speed (671m mph or thereabouts). If an hour is slower at light speed by say 50%, then I would have thought that I am going at 1,342m mph (earth time).

Is this why you can't go faster than the speed of light, because time stops and you are effectively travelling at an infinite speed?

I just don't get it!
 

jez101

Bookies drive nice cars because of people like me
Contributor
I just fried my brain trying to understand wikipedia's explanation. As for the twin paradox, I will let mephisto explain but it has something to do with acceleration and different frames of reference.

Anyway, that led me onto the Loretz equation and length contraction, the idea that the faster you are going, the shorter a distance appears to me (or is, I'm not quite sure :unsure: ).



where
L0 is the proper length (the length of the object in its rest frame),
L is the length observed by an observer in relative motion with respect to the object,
is the relative velocity between the observer and the moving object,
is the speed of light,
The bit I don't get, and the challenge back to you mephisto is to explain why I would arrive on a planet 4 light years away instantly if I travelled towards it at the speed of light (ie 4 x sqrt (1-1) = 0), when it has taken light, travelling at the same speed (light speed) 4 years to reach my starting point.

That sounds to me like a paradox, but because my brain is fried, I can no longer think and according to Descartes, that must mean I no longer exist :s
 

Bill Boddy

Professional layabout
Contributor
....
The bit I don't get, and the challenge back to you mephisto is to explain why I would arrive on a planet 4 light years away instantly if I travelled towards it at the speed of light (ie 4 x sqrt (1-1) = 0), when it has taken light, travelling at the same speed (light speed) 4 years to reach my starting point.

If you are on earth then the light takes 4 years to get to you. If you are moving at the speed of light then an observer on earth would see that it took you the four years, but since you are travelling at the speed of time to you it is instant.

That sounds to me like a paradox, but because my brain is fried, I can no longer think and according to Descartes, that must mean I no longer exist :s

Many years ago I came across a book "Mr. Tompkins in Wonderland" written by George Gamow. His hero goes to a series of lectures on scientific subjects, finding them confusing he falls asleep each time. In the first chapter it is a lecture on relativity, he wakes up in a universe where the speed of time is 15 mph. This leads him into a fairly simple way of understanding the theory, including foreshortening. The other chapters cover various other principles of physics in a similar way. Although some of George Gamow's work has now become outdated he was a genius in his way of making science understandable. Another book of his is "One, Two, Three.... Infinity" which is more complex and deals with many more issues.

Maybe you could say "I post, therefore I am".
 

jez101

Bookies drive nice cars because of people like me
Contributor
If you are on earth then the light takes 4 years to get to you. If you are moving at the speed of light then an observer on earth would see that it took you the four years, but since you are travelling at the speed of time to you it is instant.

That's the bit that puzzles me... How can I be taking 4 years and yet it feels instantaneous?
 

Bill Boddy

Professional layabout
Contributor
It's all relative. If you are traveling at the speed of light you are traveling at the speed of time. So the time is the same however far you travel. But you mass will be so immense that you will not be able to accelerate to the speed of light anyway, so it's all academic.
 

jez101

Bookies drive nice cars because of people like me
Contributor
It's all relative. If you are traveling at the speed of light you are traveling at the speed of time. So the time is the same however far you travel. But you mass will be so immense that you will not be able to accelerate to the speed of light anyway, so it's all academic.
I know that academically you are correct but that doesn't mean I understand it :(.

I guess its the bit about time travelling at the speed of light I didn't really understand. It just doesn't compute for my little brain that thinks of time as a constant. I guess it all feels a bit like creative accounting!
 
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