The Twin Paradox.

[Redingold]

I am very interested in advanced physics, and I consider myself to be fairly knowledgeable. However, I cannot figure out how to solve the Twin Paradox.

For those of you who don't know, the Twin Paradox stems from Einstein's work on relativity, and it goes something like this. As you get faster, time gets slower, or rather, it speeds up for everyone else. Space also contracts. This means that if you travel at extremely high speeds, you could reach distant objects in short amounts of time, that would appear to breach the speed of light (but because space has shrunk, you're going a shorter distance, so you're not actually breaking it).

Anyway, in the paradox, there are two twin brothers. One of them flies away to a distant star 20 light years away, at the speed of light. Now, because he is travelling at 99.9999% of the speed of light, time appears to have slowed massively for him, so he hasn't aged much when he gets there. However, his brother back on Earth has aged 20 years. This is difficult to understand, but perfectly acceptable under Einstein's laws.

Now, the brother at a distant star turns around, and comes back at 99.9999% of the speed of light. He gets back to Earth without ageing much, but his brother has aged another 20 years. So his twin brother is now 40 years older than him. A little confusing, but pretty simple once you understand the physics.

The problem occurs when you take in the whole relativity side of things. Under the principle of relativity, no motion is absolute, and must be measured with regards to something else. For instance, you are, quite probably, not moving now (sure, your arms and legs and so on might be, but that's not important). However, you are only stationary relative to the Earth. Relative to the Sun, you are moving at 90 miles a second (I think). Both viewpoints, that you are stationary, and that you are moving at 90 miles an hour, are correct.

So, back to the puzzle. From the point of view of the brother in his spaceship, it's the Earth that's gone whizzing off at 99.9999% of the speed of light. So when the Earth returns, after it's 40 light-year journey, the brother on it, because he was travelling at 99.9999% of the speed of light, hasn't aged much. The brother in his spaceship has aged 40 years. So we now have a situation where each brother is 40 years older than the other, depending on which viewpoint you take. This cannot be right.

So, my question is, how do you solve the Twin Paradox?

EDIT: Please tell me if my understanding or explanation of Special Relativity is flawed.

 

[TaborMallory]

Interesting.

Well, it wouldn't be called a Paradox if it could be solved, could it? I could be wrong though. I haven't spent much time on these sorts of things.

 

[Emphraim]

Well, that went right over my head completely. This is a stupid answer, but if both were going at near light speed, why wouldn't they both have aged 40 years, or nearly nothing?

 

[Proteus214]

In changing your point of reference to the near light speed ship, you change the relevance of time in the given context. The earth may appear to be spatially displacing itself from the ship, but in doing so from this reference, on the trip out to your destination it will appear as though the ship is not moving at all since the light still needs to "catch up" to the ship's rate of spatial displacement. On the way back, time will appear to move much faster than the ship, almost like a movie on fast-forward. So essentially, time is moving faster outside of the ship.

The factor that you are missing is actual spatial displacement relative to time.

 

[Redingold]

In changing your point of reference to the near light speed ship, you change the relevance of time in the given context. The earth may appear to be spatially displacing itself from the ship, but in doing so from this reference, on the trip out to your destination it will appear as though the ship is not moving at all since the light still needs to "catch up" to the ship's rate of spatial displacement. On the way back, time will appear to move much faster than the ship, almost like a movie on fast-forward.

The factor that you are missing is actual spatial displacement relative to time.

What do you mean by "The light needs to catch up"? Light always goes at light speed, regardless of who observes it.

Well, that went right over my head completely. This is a stupid answer, but if both were going at near light speed, why wouldn't they both have aged 40 years, or nearly nothing?

Yes, they should, but I can't figure out how.

 

[martin's a madman]

I would guess that the man on earth is older than the man in the spaceship because the Earth is moving in Relation to the sun but the Spaceship is moving in relation to the earth.

 

[Redingold]

I would guess that the man on earth is older than the man in the spaceship because the Earth is moving in Relation to the sun but the Spaceship is moving in relation to the earth.

I don't believe you understand the concept of relativity. The Earth moving around the Sun has nothing to do with this, because, from the Earth's viewpoint, it is not moving around the Sun. I'm not actually sure what point you're trying to make, but I assure you the Earth's movement around the Sun has nothing to do with this.

 

[oppp7]

I never understood the first part, no matter how many times I've heard it. Why would traveling fast make you age slower?

 

[klakkat]

The twin paradox is fairly simple, actually. You see, special relativity relies on inertial frames, that is, no acceleration. We can safely ignore the acceleration at the start of the journey when one twin is leaving earth; however, when the twin in the spaceship turns around at the end of the journey, he is no longer in the same inertial frame, resulting in different consequences than had the acceleration never occurred.

One way to think about this is by designating the stationary object. This is relative, of course, but since you have one twin that doesn't undergo acceleration (the one on earth) it is actually correct to only calculate the events from his point of view. Calculating events from the point of view of the twin in the spaceship is still correct, but much more difficult to do properly; it is often done wrong, resulting in the "paradox."

The key principle is inertial reference frames, inertial implying no acceleration. The earth is in a single reference frame (approximately; the accelerations it feels are negligible for relativistic effects), but the space ship is in two different inertial reference frames, one on each leg of the journey, which results in the misconception.

The other factor to keep in mind is Length Contraction. When moving near the speed of light, distances appear shorter. So the twin in the spaceship doesn't interpret that he traveled 20 light years; at 99.999% the speed of light, the twin in the spaceship would measure that he only traveled about 0.09 light years. The factor that is constant is velocity; time and distance are not.

I just realized I never actually stated the answer. The twin on earth is the older one.

 

[Redingold]

I never understood the first part, no matter how many times I've heard it. Why would traveling fast make you age slower?

Because. It's part of the nature of the Universe. If you want to know more, might I recommend buying a book called Why Does E=MC^2? And why should we care? By Brian Cox and Jeff Forshaw. It's a very well written book that helped me to understand this problem. Hell, the solution to the paradox is probably in there, but I can't find the book...

 

[martin's a madman]

I would guess that the man on earth is older than the man in the spaceship because the Earth is moving in Relation to the sun but the Spaceship is moving in relation to the earth.

I don't believe you understand the concept of relativity. The Earth moving around the Sun has nothing to do with this, because, from the Earth's viewpoint, it is not moving around the Sun. I'm not actually sure what point you're trying to make, but I assure you the Earth's movement around the Sun has nothing to do with this.

Well, it is paradoxical meaning it is contradictory which makes human logic not work. I don't think there would be a way to solve this with how humans understand things. But what you're saying is from the point of view of the person on Earth it is the spaceship that is moving, and from the point of view of the person in the spaceship it is the earth that is moving?

 

[Redingold]

The twin paradox is fairly simple, actually. You see, special relativity relies on inertial frames, that is, no acceleration. We can safely ignore the acceleration at the start of the journey when one twin is leaving earth; however, when the twin in the spaceship turns around at the end of the journey, he is no longer in the same inertial frame, resulting in different consequences than had the acceleration never occurred.

One way to think about this is by designating the stationary object. This is relative, of course, but since you have one twin that doesn't undergo acceleration (the one on earth) it is actually correct to only calculate the events from his point of view. Calculating events from the point of view of the twin in the spaceship is still correct, but much more difficult to do properly; it is often done wrong, resulting in the "paradox."

Oooooooooohhhhhhhh.............

So that's what it is. Thank you very much for your help.

EDIT: So what's the end result? Are both twins the same age, or is one older than the other?

 

[oppp7]

I never understood the first part, no matter how many times I've heard it. Why would traveling fast make you age slower?

Because. It's part of the nature of the Universe. If you want to know more, might I recommend buying a book called Why Does E=MC^2? And why should we care? By Brian Cox and Jeff Forshaw. It's a very well written book that helped me to understand this problem. Hell, the solution to the paradox is probably in there, but I can't find the book...

Thank you for answering. I might get that book.

 

[cleverlymadeup]

well part of this has been proven correct. they did a test a while ago where they got 2 atomic clocks, one "stationary" and one they put into a plane. they synced the clocks and the one in the airplane they flew around the world and once it landed they compared the clocks, the one in the air was behind the one on the ground

so yes the one twin would have aged less than the one on earth. although there wouldn't be a 40 year difference there would be the travel time for him to get there and back, ie the traveling twin might have aged 10-20 years instead of 40


EDIT: i could bug my friend the physics PHD/Professor but he's "not on facebook" this week and probly preparing for a world record of putting mouse traps on his tongue or some other bizarre stunt like that. and yes he really does those things among others

 

[Redingold]

well part of this has been proven correct. they did a test a while ago where they got 2 atomic clocks, one "stationary" and one they put into a plane. they synced the clocks and the one in the airplane they flew around the world and once it landed they compared the clocks, the one in the air was behind the one on the ground

so yes the one twin would have aged less than the one on earth. although there wouldn't be a 40 year difference there would be the travel time for him to get there and back, ie the traveling twin might have aged 10-20 years instead of 40

I knew of that experiment, but not the end result. That is very interesting. Thank you.

 

[martin's a madman]

well part of this has been proven correct. they did a test a while ago where they got 2 atomic clocks, one "stationary" and one they put into a plane. they synced the clocks and the one in the airplane they flew around the world and once it landed they compared the clocks, the one in the air was behind the one on the ground

so yes the one twin would have aged less than the one on earth. although there wouldn't be a 40 year difference there would be the travel time for him to get there and back, ie the traveling twin might have aged 10-20 years instead of 40

This answer seems to make sense. Is there footage or anything of the test?

 

[Katherine Kerensky]

This so easily makes sense to me, but not in a way I can explain.
I read too mach sci-fi, maybe.

 

[lozfoe444]

0_o
Um... wait, why do we care about this? We have other problems too!

 

[klakkat]

The twin paradox is fairly simple, actually. You see, special relativity relies on inertial frames, that is, no acceleration. We can safely ignore the acceleration at the start of the journey when one twin is leaving earth; however, when the twin in the spaceship turns around at the end of the journey, he is no longer in the same inertial frame, resulting in different consequences than had the acceleration never occurred.

One way to think about this is by designating the stationary object. This is relative, of course, but since you have one twin that doesn't undergo acceleration (the one on earth) it is actually correct to only calculate the events from his point of view. Calculating events from the point of view of the twin in the spaceship is still correct, but much more difficult to do properly; it is often done wrong, resulting in the "paradox."

Oooooooooohhhhhhhh.............

So that's what it is. Thank you very much for your help.

EDIT: So what's the end result? Are both twins the same age, or is one older than the other?

I edited my post. The correct answer is the twin on earth is the older one.

 

[cleverlymadeup]

well part of this has been proven correct. they did a test a while ago where they got 2 atomic clocks, one "stationary" and one they put into a plane. they synced the clocks and the one in the airplane they flew around the world and once it landed they compared the clocks, the one in the air was behind the one on the ground

so yes the one twin would have aged less than the one on earth. although there wouldn't be a 40 year difference there would be the travel time for him to get there and back, ie the traveling twin might have aged 10-20 years instead of 40

I knew of that experiment, but not the end result. That is very interesting. Thank you.

yeah it's a fairly old one, they got some info on it on wikipedia and i think there's something on it in "The Elegant Universe" by Briane Greene or a Michio Kaku book

as i added i would ask my friend the physics PHD/Professor but he's probly preparing for a trip out west to do his sideshow. tho he might not know the full answer as he does polymers rather than relativity and such. however he's great if you want someone stick a mouse trap on their tongue or sticking a fork in their nose or having a cinder block smashed with a sledgehammer over their crotch