The Twin Paradox.

[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?

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

Ah. Thank you.

 

[Trivun]

I did Physics A-Level (got a C too, but that's beside the point). We covered this in passing when learning about Einstein's Theory of Relativity and comparing it to classical Newtonian physics. I can't recall what was said about the paradox, but I think that it would only be that the brother on Earth has aged 40 years, though I'm not certain. It all boils down to perspective though, that is the crux of any argument on relativity. Everything is different in different perspectives, according to the theory, so paradoxes like this are bound to arise.

[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 (Project ORION) 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]

 

[Lenny Magic]

Which twin was born first? That is really the thing missing here...

 

[Jedamethis]

My brain just exploded.
I hate it because whenever I start thinking about these kind of things, my mind is just going 'Who gives a fuck! Shut up and go to sleep!'

Although I do think it's very interesting, I could never even understand these things, let alone come close to solving one...

 

[Dahni]

I'm not exactly an expert in physics however I thought I'd throw this in.

i did see somewhere that a physicist said that when you are close to a large object, time will speed up for you. On a very very basic level, this would mean that time goes slower for a taller person on earth than it would for a shorter person. Yes, the difference would probably be tiny but it'd be there. If the twin on the spaceship is moving out away from large objects, into open space, there would be no planets or stars nearby that could possibly bend time & therefore make it faster. If he travelled for 40 lightyears in total, it wouldn't actually take him 40 years to do so. He'd travel at the same speed, as explained by Newton's first law, but time would affect him less because no planets are speeding up time and it would take him 40 lightyears to reach his destination but to him, it would probably end up taking less time, the further he got from planets. The twin on Earth would be affected by the bend Earth makes on time in what we understand to be the "normal" way and his twin would still be gone for 40 years.

I'm not sure if that made sense.
& I might have mixed some parts up.

As I said, I'm no physics expert.

 

[Unit Alpha]

Time is relative. So I'd say that the idea that the one traveling at the speed of light shouldn't have aged 40 years less than the one on earth. It's like saying that if I drive around in a car at 60 miles an hour, I'll somehow age slightly slower.

For you to age slower, you would have to being going at FTL speeds, not sub-light speeds. Of course this makes it impossible because FTL travel is impossible without wormholes, etc.

 

[obliterate]

I have a better idea...what about if we travel at the speed of light and held a mirror in front of our faces...light has to reflect of your face so you can see it but if you are traveling at the speed of light what will happen ?

 

[Unit Alpha]

actually near the speed of light slows time down, faster makes you go backwards in time. to quote Hawking from the universe in a nutshell (at least I think that was the book an author it was my mom's book on tape)

"There once was a lady in white
who could travel much faster then light
she departed one day
in a relative way
and arrived early the previous night"

I think it's awesome and it sums up the effects of faster then light travel, thank you Hawkins

Time is relative. So I'd say that the idea that the one traveling at the speed of light shouldn't have aged 40 years less than the one on earth. It's like saying that if I drive around in a car at 60 miles an hour, I'll somehow age slightly slower.

For you to age slower, you would have to being going at FTL speeds, not sub-light speeds. Of course this makes it impossible because FTL travel is impossible without wormholes, etc.

I'm assuming that it is a gradual slow down and not something like at 97.765% time starts to slow down. Besides the point that all of this, however well researched and thought out, is just a theory until it has been proved in a real life application. For all we know, traveling at FTL speeds would cause us to vanish into an alternate universe.

 

[saxist01]

I think the brother on earth only APPEARS to be traveling at the speed of light from the space-brothers perspective. However, space-time wouldn't contract and time slow down for things APPEARING to be traveling the speed of light. You have to ACTUALLY be traveling the speed of light. Therefore - even though the space brother thinks the twin, and earth are traveling at the speed of light, they aren't. He is, therefore he ages less due to his speed rather than the brother on earth.

 

[GM.Casper]

'Speed' can be determined only in relation to other objects and thus is relative, acceleration is detectable by itself. Since the Earth stands still (relatively) while the space ship accelerates and decelerates, ship is the one affected by time dilation.

And a new question: FTL breaks causality (allowing time travel). But if your space ship moves at a low speed and takes a shortcut trough a wormhole or something, would it still break causality? (Assuming the other end of the wormhole is not displaced in time).

 

[Glademaster_v1legacy]

I am fairly sure I saw a movie where this nearly exact thing happened ages ago but I cannot for the life of me remember what it is called but on topic I have no idea but it is interesting stuff give me two years to catch up on and then I'll give it a crack.

 

[Sorceror Nobody]

Physics geek here. Most of this has already been said above, but my way of wording it may be more useful for some people, I don't know. Either way, this is for the benefit of those people who persist in asking the question long after it has already been answered...

Time slows down (relative to an observer in a different frame of reference) at any relative speed, and it stops completely at light speed (again, from the POV of the observer - the traveller sees no slowing of time for themself, but sees the other person slow down/stop). So the first point is that the twin that went on the journey aged more slowly from the perspective of the "left behind" twin, and thus returned 40 years younger.

However, since it's entirely relative: from the POV of the travelling twin, the left-behind twin was the one that was moving, thus the age gap should be the exact opposite way around. How can they both be 40 years younger than the other? This is the apparent paradox.

The resolution of the paradox is that in order to return from the journey, the travelling twin has to turn around and come back, which is an acceleration. Special Relativity cannot cope with accelerations (it only deals with UNIFORM relative velocities), so the paradox isn't so much resolved as negated. In order to correctly describe the actual outcome of the scenario, General Relativity has to be used instead.

Oh, and in response to Unit Alpha...

...all of this, however well researched and thought out, is just a theory until it has been proved in a real life application.

The three main effects of motion at any velocity (though only apparent at massive speeds) according to Special Relativity, i.e. length contraction, time dilation and mass increase, have ALL been proven by real-life experiments, including the one mentioned in a post above with the atomic clocks on the planes. Gravity's effect on time (because gravity bends light's path, which slows down time) is also taken into account. In fact, if you want a real-life application, how about this? GPS satellites have to allow for the difference between the rate at which time passes in their orbit (where the earth's gravity is weaker) and the rate on the earth's surface (where the gravity is stronger).

 

[Ultracake]

Paradoxes are Paradoxes because they are unsolvable, Or never end

For example, I walk into a door. At that exact point in spacetime there was an anomalous spike in spacetime causing me to suddenly age 50 years Cause galactacus farted or something


Actually that was a terrible example.. wasnt even a paradox at all

 

[Snowalker]

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 heard this test aswell, same results, except there was one difference.

I was told one of the clocks was sent into orbit, the reason I was told of this was A.) The whole Twin Paradox was being debated among my friends and B.) My friend did not believe the 4th dimension to be time, and that time and space were related. So one guy looked this test up to prove me right on both accounts.. Yeah, I don't have a lot of friends anymore.

 

[Sorceror Nobody]

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.

 

[TheGreatCoolEnergy]

Hmm don't know overly much about physics but I think the brother on earth would be older because only the brother on the ship was moving at the speed of light, the earth was moving at its regualr pace, it just appeared to be moving faster to the brother who is in the ship. It could be compared to a moving car. When you are on the ground the car appears to be moving fast, yet when your in the car you appear to be not be moving at all, but rather the earth around you is moving.

Another paradox-The Hangman:

There is a exicutioner on a hill blocking a road. He has one simple rule: Everytime someone crosses his path, he shall ask "where are you going?". If the person asks honnestly, he is allowed through, and the exicutioner can not hang him. However, if the person tells a lie, the exicutioner must hang him. Then one day, a man convicted of murder walks to the exicutioner. He asks "where are you going?" and the man says "To you to get hanged." This is the honnest answer. What should the exicutioner do? He can not hang the man as he gave an honnest answer, yet the man came there to be hanged.

 

[wrecker77]

*Head exploads*

I have no idea what to say.

For example, I walk into a door. At that exact point in spacetime there was an anomalous spike in spacetime causing me to suddenly age 50 years Cause galactacus farted or something

I see.... so The man who gave you the box...Is You!

Sorry if you dont get it. Around here, thats a well known parodox riddle thing.