Twin Paradox

[MolotovCocktail]

How many of you here are familiar with the twin paradox. For those of you who don't know, the twin paradox basically is when you have one set of twins, put one sibling on a rocket and accelerated to near light speeds. Of course, if you travel at near light speeds, the time relative to the person going that fast is a lot slower than for the sibling still on Earth according to the theory of relativity. This therefore leads to twins that are not the same age when he/she returns from the trip. For example, if you were on a rocket ship going at near light speeds for, say, 10 years, several decades may have passed for the observer on Earth.

 

I am quite fascinated with this phenomenon, and I think Kip Thorne even theorized that this may make some sort of time travel possible if you were to attach a wormhole with one end on the rocket ship.

[Klaynos]

This has been discussed many many many times on these forums before,

 

The paradox is flawed because it is a SR paradox. But as one of the twins has to accelerate 3 times (once to leave, once to turn around, ones to stop when they get back) you cannot use SR you have to use GR and when you churn through the maths it all works out OK and they are the same age.

[timo]

How ´bout a WiSci article about the topic. Anyone interested in writing it?

[Klaynos]

How ´bout a WiSci article about the topic. Anyone interested in writing it?

 

If there are no other takers I'll make a start on it but my knowledge is not great on GR at all!

[swansont]

This has been discussed many many many times on these forums before,

 

The paradox is flawed because it is a SR paradox. But as one of the twins has to accelerate 3 times (once to leave, once to turn around, ones to stop when they get back) you cannot use SR you have to use GR and when you churn through the maths it all works out OK and they are the same age.

 

 

No, they aren't the same age when the twins are reunited. The apparent paradox is how they can both see the other's clock running slow, and the answer, as you correctly point out, is that there is a change from one inertial frame to another (an acceleration, in this case). That's where all of the breaking of the symmetry takes place. But the returning twin would indeed be younger.

[foodchain]

No, they aren't the same age when the twins are reunited. The apparent paradox is how they can both see the other's clock running slow, and the answer, as you correctly point out, is that there is a change from one inertial frame to another (an acceleration, in this case). That's where all of the breaking of the symmetry takes place. But the returning twin would indeed be younger.

 

So does that mean time is relative or time is not a constant? I mean we can judge how far light will travel, so it does exist in time right? I am greatly confused now:D I mean a lot can happen in the passing of a second, but one that that did occur was the second past right? Independent of whatever occurred.

[swansont]

So does that mean time is relative or time is not a constant? I mean we can judge how far light will travel, so it does exist in time right? I am greatly confused now:D I mean a lot can happen in the passing of a second, but one that that did occur was the second past right? Independent of whatever occurred.

 

Time is relative. Its rate depends on your coordinate system, and things that you think are simultaneous will not be seen as such in other frames.

[MolotovCocktail]

In Steven Hawking's book "The Universe in a Nutshell", he wrote of an experiment that involved 2 jet airliners, one going east the other going west. They put an atomic clock on each plane and flew them in opposite directions. When they landed, they found that the plane that was going east(?) was a few billionths of a second younger than the plane going west. Of course, he noted that you have to fly an airplane 400 billion times if you wanted to gain 1 second in your life (which will be more than canceled by any airline meals that you eat )

[CPL.Luke]

swansont if the twin in the space ship was accelerated uniformly so that there was no way that they could tell they are the one accelerating, wouldn't they see the earth as accelerating and thus see its clocks run at the same rate at which earth see's the rockets clocks moving, and thus there still would be a paradox?

 

or does GR have some remody for this?

[foodchain]

In Steven Hawking's book "The Universe in a Nutshell", he wrote of an experiment that involved 2 jet airliners, one going east the other going west. They put an atomic clock on each plane and flew them in opposite directions. When they landed, they found that the plane that was going east(?) was a few billionths of a second younger than the plane going west. Of course, he noted that you have to fly an airplane 400 billion times if you wanted to gain 1 second in your life (which will be more than canceled by any airline meals that you eat )

 

Could that at all be attributed to instrumentation used? I know the variety of things used to gauge time can vary greatly is all and well I have had to replace more then one such device already in my lifetime.

[Cap'n Refsmmat]

Atomic clocks are incredibly accurate, so I doubt it.

 

The experiment has been replicated, I believe.

[MolotovCocktail]

Also remember, foodchain, that your clocks are run on mechanical gears, uses vibration of a quartz crystal (which can grow out of sync after a period of time) to maintain accuracy, and depend on your clumsy fingers to set it.

 

Atomic clocks, on the other hand, uses the resonance frequency of atoms, usually cesium atoms, to maintain their accuracy. So yes, they are extremely accurate.

 

How ´bout a WiSci article about the topic. Anyone interested in writing it?

I'm interested in writing it, but I need a professional to back me up with it because I am no expert, but I do feel that I am quite familiar with it to be able to explain the basics.

[swansont]

swansont if the twin in the space ship was accelerated uniformly so that there was no way that they could tell they are the one accelerating, wouldn't they see the earth as accelerating and thus see its clocks run at the same rate at which earth see's the rockets clocks moving, and thus there still would be a paradox?

 

or does GR have some remody for this?

 

You can always tell who is in an accelerating frame. That's not relative.

[Sisyphus]

swansont if the twin in the space ship was accelerated uniformly so that there was no way that they could tell they are the one accelerating, wouldn't they see the earth as accelerating and thus see its clocks run at the same rate at which earth see's the rockets clocks moving, and thus there still would be a paradox?

 

or does GR have some remody for this?

 

You can always tell if you're accelerating and by how much by looking at the rest of the universe. If you're accelerating but assume you're stationary, the laws of motion no longer work. Specifically, you'll see the entire rest of the universe accelerating in the same direction with no forces accounting for any of it. Rotation is even worse, since you'll see everything "making circles around you" going far, far faster than the speed of light.

 

Acceleration is not relative that way, only velocity.

[swansont]

Could that at all be attributed to instrumentation used? I know the variety of things used to gauge time can vary greatly is all and well I have had to replace more then one such device already in my lifetime.

 

You'd still have to explain why all of the clocks (they used four for each trip) that went one direction behaved differently when they went in the other. The vibrations, etc. would look the same, independent of the direction of travel.

 

And it's not like it was just this one experiment. Any satellite with clocks on board, including GPS, demonstrate this behavior. GPS wouldn't come anywhere close to working if the corrections made for relativity were wrong.

[Mowgli]

Would the twins age equally if they depart from each other symmetrically and come back to each other using the same acceleration and decelaration? Each twin is in motion relative to the other throughout the journey, but still no time dilation?

[swansont]

Would the twins age equally if they depart from each other symmetrically and come back to each other using the same acceleration and decelaration? Each twin is in motion relative to the other throughout the journey, but still no time dilation?

 

They would see dilation, as they are in different inertial frames during the travel, but their clocks would agree when they returned. If there was a third observer at the origin of the trip, he would see a different dilation, and his clock would not agree.

[Farsight]

How many of you here are familiar with the twin paradox. For those of you who don't know, the twin paradox basically is when you have one set of twins, put one sibling on a rocket and accelerated to near light speeds. Of course, if you travel at near light speeds, the time relative to the person going that fast is a lot slower than for the sibling still on Earth according to the theory of relativity. This therefore leads to twins that are not the same age when he/she returns from the trip. For example, if you were on a rocket ship going at near light speeds for, say, 10 years, several decades may have passed for the observer on Earth.

 

I'm familiar with this. The paradox is that each twin considers the time for the other twin to be going slower than his own. It sounds counterintuitive, but it's isn't really a paradox. If you and I are separated by distance, our sizes look smaller to one another. We don't have a problem with that. The thing is, if we're separated by velocity, our times look smaller to one another. When the travelling twin turns round, he "skips some simultaneity", so when he comes back he has aged less than the one who stayed on earth. Look up "bricks and ticks" for an analogy that might explain it to your satisfaction.

 

I am quite fascinated with this phenomenon, and I think Kip Thorne even theorized that this may make some sort of time travel possible if you were to attach a wormhole with one end on the rocket ship.

 

I'm afraid this is speculation. Personally I'd go so far as to say it's wild speculation, or worse.

[Mowgli]

They would see dilation, as they are in different inertial frames during the travel, but their clocks would agree when they returned.

 

So, at any instant during the journey, one twin will see the other's clock dilated? And at the instant when the are at rest together, the dilation will disappear?

[timo]

If there are no other takers I'll make a start on it but my knowledge is not great on GR at all!

 

I'm interested in writing it, but I need a professional to back me up with it because I am no expert, but I do feel that I am quite familiar with it to be able to explain the basics.

 

Finding someone to proof-read will probably not be a problem. For questions that arise during writing, you can ask in the forum. If you´re still interested, the two of you should contact each other via PM to discuss the details. Considering style, I was thinking about something like the redshift-article (http://www.wisci.org/wiki/Redshift), i.e. neither hollow words nor a pure calculation without any explanations.

[swansont]

So, at any instant during the journey, one twin will see the other's clock dilated? And at the instant when the are at rest together, the dilation will disappear?

 

Right. Clocks will generally only agree when they are in the same frame.

[Mowgli]

Right. Clocks will generally only agree when they are in the same frame.

 

So, one twin will see the other's clock running slower (showing a smaller value) throughout the journey. But the moment the twins get back together, the clocks will be synchronized. Does the synchronization happen in the end of the journey (in an instant) or sometime before, in a gradual fashion?

[Edtharan]

The twins "paradox" only occurs if only one of the twins undergoes acceleration.

 

Think of the twins starting off floating in space. At this point neither twin is experiencing any force.

 

One of the twins ignites their rocket and begins to move off. This is acceleration.

 

This twin, feels a force. To speed up the rocket expels fuel, and this pushes the rocket. However, the Twin (Lets Call him Adam) does not fell the fuel pushing on him. So he is not accelerated by the rocket fuel. Adam has to be accelerated by the rocket pushing on him (not the fuel directly).

 

So, Adam feels a force and sees the other twin (Lets Call her Betty) is still floating.

 

So both twins see the other moving away at a faster and faster rate, but only one of them experiences a force associated with this "Acceleration". It is this force that can be used to distinguish between the frames of reference of the two twins. It is this force that makes the final experiences of the twins different from each other.

 

As Adam is experiencing a force and Betty is not, this creates differing inertial frames of reference.

 

The other ting is that Adam makes a round trip. First he accelerates away, then he begins to accelerate back towards Betty and finally decelerates (in this case deceleration is the same as an acceleration in the opposite direction until Adam's velocity is the same as Betty's velocity).

 

So we have 3 different phases of acceleration that Adam experiences and we can work out the effects on Adam.

 

Phase 1: Acceleration away

Under this movement both Twins will see the other's clocks running slow.

 

Phase 2: Acceleration towards

Under this movement Adam will see Betty's clocks running fast and Betty will see Adams clocks running slow.

 

Phase 3: Deceleration

Under this movement both Twins will see the other's clocks running fast.

 

You will notice that in Phase 2 acceleration Adam's clock is different to Betty's clock. It is this phase of the journey that causes the difference in the clocks. And this phase that causes the difference in their ages.

 

This effect does not occur under constant motion (but turning around is not constant motion).

 

But the moment the twins get back together, the clocks will be synchronized.

No, the clocks are not synchronised. They will be different.

 

What was meant was if the clocks are only in the same frame of reference they will agree, but once you change the frame of reference, they won't agree.

 

So if two clocks start in the same frame of reference and are left in that same frame of reference, then they will be the same.

 

If you accelerate one (change it's frame of reference) then they won't agree.

[MolotovCocktail]

Finding someone to proof-read will probably not be a problem. For questions that arise during writing, you can ask in the forum. If you´re still interested, the two of you should contact each other via PM to discuss the details. Considering style, I was thinking about something like the redshift-article (http://www.wisci.org/wiki/Redshift), i.e. neither hollow words nor a pure calculation without any explanations.

 

Alrighty then. I will write the article on the subject as soon as possible. Thanks for the offer .

 

Just a couple of questions on writing on WiSci:

 

1) Do I need to register before I can contribute?

2) If I do need to, how do I log in?

[Klaynos]

Alrighty then. I will write the article on the subject as soon as possible. Thanks for the offer .

 

Just a couple of questions on writing on WiSci:

 

1) Do I need to register before I can contribute?

2) If I do need to, how do I log in?

 

No you don't.

 

But in the top right there is: Log in / create account