Time Dilation Paradox: Exploring What Prevents it From Happening

[Vorde]

I was discussing the possibility of intergalactic travel with a friend and suddenly this occurred to me.

Classically, if someone speeds away at the speed of light (or near to it), he returns without having aged as much as everyone else.

But to him everything else sped away in the opposite direction at near to the speed of light and when returning everyone else should have aged much less.

What prevents this paradox from happening? Because from what I understand there is nothing science-fictiony to prevent this from happening in real life.

 

[VanOosten]

it has to do with the rocket frame not being an inertial observer, there is acceleration in his frame when he reverses direction.

 

[1MileCrash]

http://physics123.net/2009/02/the-twin-paradox-explained/

 

[jtbell]

This is the famous "twin paradox", about which much has been written, including (surprise! ) right here on PF:

http://www.google.com/search?q="twin+paradox"+site:physicsforums.com

 

[Altabeh]

I was discussing the possibility of intergalactic travel with a friend and suddenly this occurred to me.

Classically, if someone speeds away at the speed of light (or near to it), he returns without having aged as much as everyone else.

But to him everything else sped away in the opposite direction at near to the speed of light and when returning everyone else should have aged much less.

What prevents this paradox from happening? Because from what I understand there is nothing science-fictiony to prevent this from happening in real life.

If that is science, no: there are good evidences as to how this can be prevented. For instance, Grøn shows that this could be just a parodox within the pure realm of SR! If one also takes into account Principle of Equivalence in GR and defines a globally gravitational metric of some specific type to sweep away the problem of acceleration-deceleration when approaching and receding the turning point in the case that the traveling twin considers Earth and his brother moving rather than himself, it is quite easy to see that there is no paradox anymore. This paradox appears to exist because the calculations of the traveling twin, when considering Earth as moving, suffer the lack of gravitational effects of the star or whatever that he is approaching on his clock!

For a detailed discussion, see

http://iopscience.iop.org/0143-0807/27/4/019

AB

 

[bobc2]

It is interesting to resolve this apparent parodox using a space diagram. Is it possible to attach bmp or jpg pictures as part of a post?

 

[Drakkith]

I was discussing the possibility of intergalactic travel with a friend and suddenly this occurred to me.

Classically, if someone speeds away at the speed of light (or near to it), he returns without having aged as much as everyone else.

But to him everything else sped away in the opposite direction at near to the speed of light and when returning everyone else should have aged much less.

What prevents this paradox from happening? Because from what I understand there is nothing science-fictiony to prevent this from happening in real life.

The twin in the spacecraft gets accelerated. He feels the force of the acceleration while the other twin does not. It may "look" like the rest of the universe is accelerating instead of the spacecraft , but the universe doesn't experience the force.

 

[Vorde]

Thanks everyone, I understand it now, and ill remember to search the forum now.

 

[Fredrik]

It is interesting to resolve this apparent parodox using a space diagram. Is it possible to attach bmp or jpg pictures as part of a post?

Yes, but png is a better format. You can either upload the picture as an attachment, or upload it to another site and link to it (preferably using img tags).

 

[bobc2]

Thanks. I used to link to a site on the old Kaku forum but didn't know if it worked the same way here. But now that I'm in the reply window I'm noticing the tool list above. By the way, are there any of the old posters from the old Kaku forum around? Has Yuki been around (I think he had just finished his math PhD)?

 

[jtbell]

The image button at the top of the message-editing box is for linking to images that are hosted on other sites.

To upload an image or some other type of file to PF and attach it to your post, scroll down to the "Additional Options" section and click the "Manage Attachments" button.

 

[bobc2]

Got it. Thanks a lot. I notice a significantly increased level of knowledge of Special Relativity in the posts here as compared to the old Kaku forum. Interesting.

 

[ghwellsjr]

The twin in the spacecraft gets accelerated. He feels the force of the acceleration while the other twin does not. It may "look" like the rest of the universe is accelerating instead of the spacecraft , but the universe doesn't experience the force.

But there is a variation
of the Twin Paradox in which both twins undergo identical accelerations but one takes longer to return and he ends up younger. How do you account for that?

 

[Drakkith]

But there is a variation
of the Twin Paradox in which both twins undergo identical accelerations but one takes longer to return and he ends up younger. How do you account for that?

I'm not familiar with that example. Could you provide a link to it or something?

 

[PAllen]

I'm not familiar with that example. Could you provide a link to it or something?

Simple. Twin A travels a month, quicly accelarates to change direction back to inertial twin B; When twin A is almost back, twin B accelerates exactly inverse to twin A acceleration to meet twin B. So both have identical acceleration. However, when they meed twin A is younger. Many ways to look at it. One way is to note that when they meed, twin A deviation from geodesic is much greater, so younger. That is, twin A has deviated from an inertial path 'longer' than twin B.

 

[Fredrik]

I'm not familiar with that example. Could you provide a link to it or something?

DrGreg made this spacetime diagram for another thread where this was mentioned:

 

[ghwellsjr]

I was thinking of both twins starting off from Earth in separate spaceships accelerating to a final velocity side by side. As soon as they reach final velocity, Twin B turns around and returns to Earth but Twin A doesn't turn around until some time later. They both experience exactly the same accelerations, just at different times for the return trip. Twin A will be younger after they reunite.

 

[matheinste]

I was thinking of both twins starting off from Earth in separate spaceships accelerating to a final velocity side by side. As soon as they reach final velocity, Twin B turns around and returns to Earth but Twin A doesn't turn around until some time later. They both experience exactly the same accelerations, just at different times for the return trip. Twin A will be younger after they reunite.

That's odd because surely their spacetime "path lengths," and hence their proper times are equal.

Matheinste.

 

[Fredrik]

That's odd because surely their spacetime "path lengths," and hence their proper times are equal.

What he's describing is just DrGreg's diagram turned upside down (just the curves, not the axes), or equivalently, the smaller bulge moved down so that it touches the bigger one at the bottom instead of at the top. The proper times of these two curves are clearly not the same.

 

[DrGreg]

I was thinking of both twins starting off from Earth in separate spaceships accelerating to a final velocity side by side. As soon as they reach final velocity, Twin B turns around and returns to Earth but Twin A doesn't turn around until some time later. They both experience exactly the same accelerations, just at different times for the return trip. Twin A will be younger after they reunite.

Turn the diagram in post #16 upside down and shorten the blue (inertial) segments in B's worldline to zero.

(However, PAllen gave a different example in #15. Both examples are valid but I think ghwellsjr's is easier to understand.)

 

[matheinste]

What he's describing is just DrGreg's diagram turned upside down (just the curves, not the axes), or equivalently, the smaller bulge moved down so that it touches the bigger one at the bottom instead of at the top. The proper times of these two curves are clearly not the same.

My apologies to ghwellsjr, I badly misinterpreted what was clearly written.

Matheinste.

 

[flashprogram]

The twin in the spacecraft gets accelerated. He feels the force of the acceleration while the other twin does not. It may "look" like the rest of the universe is accelerating instead of the spacecraft , but the universe doesn't experience the force.

Suppose two genetically identical clone babies are born, one on Earth and one on the ship, this occurs at the exact moment the ship is at maximum velocity and not accelerating anymore. After a century passes on Earth time the Earth baby will probably have died of old age,experiencing a century of aging, but depending on the speed the baby on the spaceship might've only experienced a decade or two of aging, being maybe in his twenties, the ship remains at maximum velocity and there has been no acceleration nor deceleration.

 

[Drakkith]

Suppose two genetically identical clone babies are born, one on Earth and one on the ship, this occurs at the exact moment the ship is at maximum velocity and not accelerating anymore. After a century passes on Earth time the Earth baby will probably have died of old age,experiencing a century of aging, but depending on the speed the baby on the spaceship might've only experienced a decade or two of aging, being maybe in his twenties, the ship remains at maximum velocity and there has been no acceleration nor deceleration.

Everything that it took to make the baby, (food, water,parents, ETC) was accelerated with the ship.

 

[Fredrik]

Everything that it took to make the baby, (food, water,parents, ETC) was accelerated with the ship.

None of that is relevant in the scenario he's describing. He's just talking about time dilation, as seen from the Earth frame, when a ship is moving away and never accelerating.

 

[Drakkith]

None of that is relevant in the scenario he's describing. He's just talking about time dilation, as seen from the Earth frame, when a ship is moving away and never accelerating.

I don't see how all that isn't relavent, unless I've misunderstood his post. There isn't a paradox anymore.

 

[Fredrik]

My interpretation of his post is that he's just describing time dilation, in terms of the coordinates of one of the two inertial frames. That's why I'm saying acceleration isn't relevant.

I don't understand why he's describing time dilation in this thread, and I don't understand why he's quoting you at the same time. What he said seems to have nothing to do with what you said in the text he quoted.

 

[Passionflower]

Suppose two genetically identical clone babies are born, one on Earth and one on the ship, this occurs at the exact moment the ship is at maximum velocity and not accelerating anymore. After a century passes on Earth time the Earth baby will probably have died of old age,experiencing a century of aging, but depending on the speed the baby on the spaceship might've only experienced a decade or two of aging, being maybe in his twenties, the ship remains at maximum velocity and there has been no acceleration nor deceleration.

In this case you cannot tell who aged more than the other.

 

[Drakkith]

In this case you cannot tell who aged more than the other.

Why not? The ship accelerated to max speed, as it says, so the passengers would age less than the people on earth. I'm still not seeing a problem here.

 

[yuiop]

Why not? The ship accelerated to max speed, as it says, so the passengers would age less than the people on earth. I'm still not seeing a problem here.

If the twin that remained on Earth decided to accelerate at the ripe old age of 90 years, so that both twins are in the same rest frame, the occupants of that common reference frame would tell the Earth twin that his clone died at the age of 100 years, 50 years ago!

 

[bobc2]

It's not the accelerations, it's the comparative 4-D distances travelled. More precisely, it's the difference in the length of the world lines from the 4-D point of separation and the 4-D point of later intersection. Each one moves along his own world line at the same 4-D speed, i.e., the speed of light, c.

Upon a little reflection, one might ask, "What is actually moving? I mean, if the travelers are actually 4-D structures in a 4-D universe, then those 4-D structures (the travelers) are static, i.e., no motion at all as 4-D structures. So, who is doing the moving?"

 

[Drakkith]

The acceleration is necessary to understand who is actually traveling at the higher speed. Twin A takes off in a ship, and twin B doesnt. Twin A DOES know that he is traveling at X speed because he was the one that accelerated. Twin B knows that he is still stationary because he was never accelerated. Thus, both can reliably say that Twin A is the one that is actually traveling at velocity X.

If you take 2 ships, and only compare those 2 ships and their respective frames, there is no way to tell which one is actually traveling at what velocity because you have nothing to compare them against except each other. You would have to look back and see where each one came from and how much each accelerated to determine how fast each one is travelling.

Does all that sound about correct?

 

[DrGreg]

The acceleration is necessary to understand who is actually traveling at the higher speed. Twin A takes off in a ship, and twin B doesnt. Twin A DOES know that he is traveling at X speed because he was the one that accelerated. Twin B knows that he is still stationary because he was never accelerated. Thus, both can reliably say that Twin A is the one that is actually traveling at velocity X.

If you take 2 ships, and only compare those 2 ships and their respective frames, there is no way to tell which one is actually traveling at what velocity because you have nothing to compare them against except each other. You would have to look back and see where each one came from and how much each accelerated to determine how fast each one is travelling.

Does all that sound about correct?

No, because another way of looking at this is to assume that both twins were initially traveling at velocity −X and then twin A decelerated to become stationary, whilst twin B continues to move at velocity −X. That's an equally valid way to analyse the problem.

 

[Drakkith]

No, because another way of looking at this is to assume that both twins were initially traveling at velocity −X and then twin A decelerated to become stationary, whilst twin B continues to move at velocity −X. That's an equally valid way to analyse the problem.

Of course, which is why determing the initial frame is important. If you have it as earth, it's a pretty safe bet that we aren't traveling at .3c, and can say that most likely the spaceship is the one traveling at 0.3c and not us. Obviously, if this happened and it turned out that the ship was experiencing a faster rate of time, then it would be us on Earth that were traveling at 0.3c.

Hows that look?

 

[DrGreg]

Of course, which is why determing the initial frame is important. If you have it as earth, it's a pretty safe bet that we aren't traveling at .3c, and can say that most likely the spaceship is the one traveling at 0.3c and not us. Obviously, if this happened and it turned out that the ship was experiencing a faster rate of time, then it would be us on Earth that were traveling at 0.3c.

Hows that look?

No it's a fundamental principle of relativity that all velocities are relative. It's equally valid to consider the Earth stationary and a spaceship moving or to consider the spaceship stationary and the Earth moving, or to consider Alpha Centauri stationary and both Earth and the spaceship moving. That's the whole point of relativity, there's no such thing as "stationary" in any sense that everyone could agree.

 

[bobc2]

It seems like DrGreg's space-time diagram presents the situation in the most fundamental way. The world lines tell the story--the mathematical details and talk of accelerations just detracts from the fundamental simplicity of DrGreg's diagram.