The Twin Paradox.

[TheGreatCoolEnergy]

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.

they are the same age clearly

If you drop someone 9 meter's and then lift him 9 meters he will in the end not have changed height if you understand what I'm saying

Ya but this is an argument of time, which is relative. You will still occupy the same amount of space in the universe no matter where you go, but time will change depending on speed(I think, I'm not a physics major)

 

[bobknowsall]

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

It's called time dilation. Time moves slower relative to you due to your speed. It's a complicated concept, but it makes sense after much thought.

 

[aiusepsi]

klakkat explained the right answer to the OPs question already.

The twin on Earth will be older, in a the literal sense that he will have lived for longer.

The way to come at relativity is the anchoring fact that light always moves at the same velocity for all observers, no matter how they're moving. This has consequences for how different observers perceive space and time.

A good example is muons generated by cosmic rays in the upper atmosphere. They rain down towards the Earth at a significant fraction of the speed of light. They appear to do something impossible - they reach the ground. Muons observed at rest in the lab decay very rapidly, and based on how fast the muons are going and how long they take to decay, they shouldn't make it to the Earth's surface.

What's happening is that because the muon is travelling quickly, it is time dilated. Time runs slower for the muon, so from our point of view on the Earth, the muon's decay time is longer.

From the point of view of the muon, the decay length is the same as it ever was, but to make up the discrepancy, the muon sees that the surface of the Earth is closer to the upper atmosphere.

Relativity has such a wealth of experimental support like this that it's beyond dispute. This is how the universe is.

The reason the Twin paradox appears strange is that you could say that it is the twin on the spaceship who is moving and the Earth is still, or you could say the spaceship is still and the Earth is moving, and there's no way that one could be older than the other because they're symmetrical descriptions of the same thing.

The resolution of the paradox is that it's not symmetrical. You can feel when you accelerate without reference to any outside object. For instance, if you close your eyes in a car, you can feel it getting faster or slower, or turning corners.

 

[Maze1125]

It might seem real strange but the fact of the matter is that time is the one true unchangable thing
unless proven otherwise

Which it has been.

 

[bradley348]

Pfft,

*jumps up and runs out in front of everyone*

Theres only one problem, Einsteins wrong.

*TRANSFROMERS REFERENCE!*

 

[Dusty Donuts]

I have an idea! I'm a twin, so i'll just ask my fellow Escapists to send me about a million bucks each and I can fund research into a rocket ship that can travel at 99.99999% of the speed of light and TEST it! Eh? EH?
OT: This looks like a few lines of indecipherable text to me having not done Physics and the Theory of Relativity, although having a few attempts of comprehending said Theory. They all...lets say, failed to succeed, and resulted in more than a few broken objects.

 

[Biosophilogical]

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.

But relative to the guy on the space ship the earth is the one that accelerates/decelerates so I don't think the paradox is solved so simply.

 

[MajoraPersona]

I still don't quite understand how the aging effect works. Unless the brother on the spaceship were to become accustomed to the speed and learn how to function as such. Then he'd likely age quite a bit more, at least mentally. His metabolizm may change radically to compensate for the speed anyway.

I was hoping to say something about the anti-christ, but you brought Einstein into the equation. Ah well, I'll say it anyway.

In the ancient Roman empire, when twins were born, they'd share a name. Except one of them would have Anti- before their common name. An example would be Loquax and Anti-Loquax. Anti comes from Latin, and refers to 'before', such as in the word Antechamber. Thus, I ask you, what came first, the Christ or the Anti-Christ?

Also, Schrodinger's Cat is a lie. It ignores a very basic princible of cats: they have multiple organs that are capable of failure.

 

[Deleric]

Hm. If the space twin (I'm just gonna call him Ender) has to travel 20 light years, and he's traveling at the speed of light, would that not take 20 years to accomplish, thus aging Ender accordingly? Then a trip back would add a simple 20 more years onto it?

At the same time, the Earth twin will not see his brother for 40 years, because it'll take 40 years for him to get back?

Don't you have to travel over the speed of light to have any slowdown of the aging process?

 

[Crystalgate]

But relative to the guy on the space ship the earth is the one that accelerates/decelerates so I don't think the paradox is solved so simply.

Nope, acceleration is not relative. You can always tell whether or not you're accelerating. Just because velocity is relative, it doesn't mean acceleration is.

 

[Godavari]

This brings up an intersting point. It makes you think of what perspective is really the correct one. Is there some kind of immovable grid of space-time that all things flow through? Or does it change to accomodate various objects?
Personally, I subscribe to the stance that quantum physics is bullshit way beyond human comprehension for the time being. Maybe when there's some actual evidence found for any of it, I'll start to take it seriously.

 

[oppp7]

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

It's called time dilation. Time moves slower relative to you due to your speed. It's a complicated concept, but it makes sense after much thought.

Ya, I understand that, but why would traveling in a fast ship cause your bodily functions/consciousness to increase? Plus, wouldn't you have aged since it seems longer for you?

 

[bobknowsall]

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

It's called time dilation. Time moves slower relative to you due to your speed. It's a complicated concept, but it makes sense after much thought.

Ya, I understand that, but why would traveling in a fast ship cause your bodily functions/consciousness to increase? Plus, wouldn't you have aged since it seems longer for you?

Dammit, oppp7, I'm an Escapist, not a theoretical physicist! (Good God, I just made a Star Trek reference. There's no hope for me now...)

Well, that's because travelling near the speed of light causes time to slow relative to you, meaning that the passage of years seems to go by far quicker than usual. If the human body is slowed down to that point, it means that you're effectively frozen in time while the ship's in motion. That probably doesn't make sense, but it's 3 a.m. here, and now is not a good time for theoretical physics analysis. *laughs*

 

[UsefulPlayer 1]

[small]On a side note, something people seem to note in the Halo series is that characters seem younger than they should be. Each Spartan is about 40 by the time of the original trilogy, yet look and sound like they're in their early twenties. Similarly, Commander Miranda Keyes in Halo 2/3 looks in her mid-twenties yet is actually in her early thirties (judging by timelines and references in the novels). Sgt. Johnson is in his late sixties by the end of Halo 3, as he was a Spartan-I (Operation TREBUCHET) and was born in the late 2400's, yet looks a healthy 45, or thereabouts. All of this is down to, you guessed it, the Twin Paradox, and the constant travel of these characters in Slipspace (i.e. near the speed of light). None of this is important, of course, but I thought that it would be interesting to mention the use of the paradox in gaming, while we were on the subject.[/small]

Dude, that's pretty cool.

I haven't even taken physics yet so I really know nothing substantial, but I still don't get why when you move at the speed of light affects time.

Like if you're flying at the speed of light for 20 years away from a clock on earth. Sure if you look back it's still the same time as you left, but the second you stop shouldn't your body have all the effects of living for another 20 years? Even if you travel faster then the speed of light making it look like you travel back in time, wouldn't in actuality it would still be the same time on earth regardless of what it looks like to what it actually is?

Wait, and if you fly away at the speed of light the clock look like it stops, but what would it look like if you were flying towards it?

 

[Biosophilogical]

But relative to the guy on the space ship the earth is the one that accelerates/decelerates so I don't think the paradox is solved so simply.

Nope, acceleration is not relative. You can always tell whether or not you're accelerating. Just because velocity is relative, it doesn't mean acceleration is.

But acceleration is the change in velocity over a given time. So relative to the spaceship, the Earth's velocity would change (accelerates/deceleration) and the spaceship would be stationary.

 

[Redingold]

Personally, I subscribe to the stance that quantum physics is bullshit way beyond human comprehension for the time being. Maybe when there's some actual evidence found for any of it, I'll start to take it seriously.

You don't seriously think that there isn't any evidence for it, do you? Go read Introducing Quantum Theory, or something. Scientists won't believe in something without evidence for it; at least, proper scientists won't. If there isn't any evidence, they'll go out and find some.

 

[Trivun]

Paradoxes are Paradoxes because they are unsolvable, Or never end

You are correct that true paradoxes are unsolvable, but a lot of apparent paradoxes aren't actually paradoxes at all, including the Twin Paradox. They are "unsolvable" only because we haven't yet developed the necessary methods to solve them, not because no solution exists. Another example is the oh-so-convincing but fundamentally flawed one (Zeno's, I think?) about one object never catching up with another despite it going much faster, because the distance between them is infinitely divided. It was eventually solved with Isaac Newton's invention of differential calculus, and the solution is that the division of the gap between the objects approaches a limit at infinity, at which it still tends towards zero distance in a finite amount of time, meaning that the pursuing (faster) object catches up with the fleeing (slower) one. Or something like that, anyway. I'd have to check the maths properly to be sure, and I'm too tired right now.

Although, knowing myself, I suspect that I might just stay up all night if I have to, otherwise this'll bug me. Not that I expect it to take too long to prove... but I may be wrong about that (NOT cocky, mind you) due to not thinking straight, due to being tired. Whatever. I'm babbling.

Bloody hell, I haven't seen you on here for ages. I'd have thought you'd be on the forums a bit more often, though given the amount of internet stuff you do it's a bit too much to expect, perhaps? Just mentioning, anyway.

Just thought I'd throw my oar in here again, but about some paradoxes being unsolvable, one of my housemates does Philosophy as part of his course (he's a joint honours student) so I can always talk to him about 'unsolvable' paradoxes. I'd agree with Sorceror's first point here though, that we simply haven't developed the understanding or knowledge necessary yet to solve them. Remember, just like Sorceror said, Zeno's Paradox wasn't solved until Newton came along. There are plenty of paradoxes that weren't solved until we had an understandable idea of the concept of infinity in mathematics. And there are still loads more still to be solved. It's just a matter of time and effort, really.

EDIT: Jacob, if you can read this then take a look at my new Youtube video, the Four Fantasies one. Let me know what you think, since it's part of a new series, kind of thing.