Exploring the Twin Paradox: General Relativity & Time Travel

[MotolovCocktail]

How many of you over here are familiar with the twin paradox?

I am personally quite fascinated with this phenomenon predicted by General Relativity. In a nut shell, since your relative time slows down at speeds close to the speed of light, it implies that if, say, your twin brother were to go into such a space craft, go away for 40 or so years, he would have only aged by about 10 years or so upon return because time would have slowed down greatly for him. You, on the other hand, would have aged 40 or more years. This would then make twins who were born on the same date that aren't the same age, hence the twin paradox.

There are many speculations as to what one could do with such a thing, and I've read somewhere that Kip Thorne even proposed this as a solution to time travel (putting one end of the wormhole on a separate spaceship and accelerate it to near light speeds). Likewise, it would make a vacation to some distant part of the galaxy impractical, since thousands of years would have gone by upon return.

So, what are your speculations, interests, or thoughts on the matter?

 

[yogi]

Its inception was consequent to the interpretation Einstein gave to the Special Relativity transforms in Part IV of his 1905 paper. The so called paradox is not really a paradox - it does not mean that the traveling twin enjoys greater longevity - The traveler simply gets to see more of the universe in the short amount of time that transpires on his clock while he is in motion

 

[jeesusfreek]

actually.

how would the second twin (who is traveling at 0.99c or thereabouts) not enjoy a greater longevity? in an Earth reference frame (we have to use this reference frame. the twin on the spaceship was accelerating when he turned around at the end of his journey as well as at the beginning and the end, thereby making his/her reference frame unusable) the twin on the spaceship only aged, say, 4.5 years, and the twin on Earth aged 100 years - and those numbers actually fit within the formula for time dilation. Can one not conclude that the twin who has aged only 4.5 years actually will enjoy a longer life (considering the average life for a human being in the U.S. is only 70-something years.)

According to time dilation, all life processes actually slow down for the twin on the spaceship, hence, in the 100 years that have passed, only 4.5 have transpired and taken their toll upon his/her body (again, in an Earth reference frame, since it is the only valid one in this situation)

 

[MeJennifer]

Can one not conclude that the twin who has aged only 4.5 years actually will enjoy a longer life (considering the average life for a human being in the U.S. is only 70-something years.)

Assuming the average life for a human being is 70, it would be 70 years on his local clock. So it would not be any different for the twin.

 

[MeJennifer]

The traveler simply gets to see more of the universe in the short amount of time that transpires on his clock while he is in motion

It depends a bit on what you mean by "seeing more".

Both the spatial and the temporal trip length is measured much shorter by the traveler than by an observer on earth.
Only the combined spatio-temporal trip length is measured exactly the same for both the traveler and the observer.

 

[yogi]

To clarify - the traveler still lives 70 years - just like his brother on Earth - but in the 70 years he can see a bigger part of the universe as it passes by. The traveler still croaks when he is 70 - he has eaten the same number of meals, sleeps the same number of nights, watches the same on board movies - the stay at home also lives to 70 - and kicks off. But the traveler is still going strong - outbound on his spaceship taking in the universe - he has not reached 70 years in his own time frame until long after the stay at home twin has reached his 70 years on earth.

 

[daniel_i_l]

Proper time is always constant. No matter how fast somebody moves between two events the amount of time that he measures on his clock will be the same.

 

[MeJennifer]

Proper time is always constant. No matter how fast somebody moves between two events the amount of time that he measures on his clock will be the same.

The accumulated proper times between two events for different particles completely depend on their relative pathlengts in space-time.

 

[jeesusfreek]

Assuming the average life for a human being is 70, it would be 70 years on his local clock. So it would not be any different for the twin.

It would be different though. Using Earth as the reference frame (as I stated above, only the Earth reference frame can be used in the twin paradox - the twin who states that he who was in the spaceship aged less than the twin on Earth is the only one who is correct - he is in a non-accelerating reference frame, and so can be the only one considered out of 2 possibilities) the twin who aged 4.5 years aged exactly that - had 4.5 [Earth] years of meals, sleep, etc. The twin on the Earth aged 100 years, and experienced 100 [again, Earth] years of meals, sleep, and so on and so forth.
What you are talking about is the reference frame, and according to Einstein, the only reference frames that are valid in special relativity are non-accelerating ones.

Since the spaceship accelerated when first leaving and finally returning, as well as at the turning point in it's journey (assuming a collinear journey), would be points where acceleration or deceleration was required.

I may be misunderstanding you - if what you are saying is that the twin on the spaceship does not experience some paranormal life span, then you are incorrect. Normal in the ship's reference frame, perhaps, but that is not a valid one in special relativity for the above stated reasons. Paranormal, yes, in Earth's reference frame. When 200 years go by on Earth and someone returns from near light speed travel and they have only aged 9 years? Not exactly normal.

 

[MeJennifer]

I may be misunderstanding you - if what you are saying is that the twin on the spaceship does not experience some paranormal life span, then you are incorrect.

None of the twins experience some kind of paranormal lifespan.
Both the twin's lifespan is simply their accumulated proper time which is, if we assume an average of 70, about 70 years for each twin.

Proper time by the way is frame invariant.

Paranormal, yes, in Earth's reference frame. When 200 years go by on Earth and someone returns from near light speed travel and they have only aged 9 years? Not exactly normal.

There is nothing paranormal going on here jeesusfreek.
It is due to the fact that different objects do not have to accumulate the same amount of time between two events.

 

[yogi]

Look at it this way - both twins croak at age 70 - but the 70th year for the twin on Earth arrives in 70 years of Earth time - the 70th year for the traveler arrives in 70 years of spaceship time which corresponds to a longer Earth time. The situation is obviously asymmetrical - different authors have different ideas about what causes the difference - but they all (almost all) agree about the amount of age difference and that the traveler doesn't realize longevity in the sense of a longer life. It is a way to get a peek into the future of the Earth if your willing to give up some of the present.

 

[MeJennifer]

It is a way to get a peek into the future of the Earth if your willing to give up some of the present.

Interesting way of putting it!

 

[daniel_i_l]

The accumulated proper times between two events for different particles completely depend on their relative pathlengts in space-time.

Your right. I was talking about the case where the two events happen to the the person traveling. For example, if we take two events - the birth and death of person A, the the amount of time that A measures between these two events will be the same no matter how fast he goes.