# The Twin Paradox(again)

Recently I have been thinking about the twin paradox. For those of you who haven’t heard about it I got this from Wiki.

*"In physics, the twin paradox is a thought experiment in special relativity, in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth. This result appears puzzling because each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly. In fact, the result is not a paradox in the true sense, since it can be resolved within the standard framework of special relativity. The effect has been verified experimentally using measurements of precise clocks flown in airplanes[1] and satellites.*

*Starting with Paul Langevin in 1911, there have been numerous explanations of this paradox, many based upon there being no contradiction because there is no symmetry—only one twin has undergone acceleration and deceleration, thus differentiating the two cases."*

When I first learned about special relativity I considered the twin paradox. I couldn’t figure it out so I asked my teacher. My teacher told me that the paradox results from not taking General Relativity into account. One of the twins undergoes acceleration and to understand the effect of that acceleration requires General Relativity. I don’t understand General Relativity. The math is too complex for me. Still after talking to my teacher I felt satisfied that there was an answer, and that other people understood it. I didn’t think about it again for many years until this thread came up. Then I asked myself ‘why can’t they both accelerate’. This is a thought experiment you can do anything you want.

This is the revised twin paradox I can up with.

There are two identical spacecrafts, and two identical twins. The space crafts are controlled by computers which are both programmed the same way. The spacecraft will accelerate for a period of time. They will then do nothing for a period of time. They will then accelerate for a period of time. Then coast again. Then accelerate again until they both come back together into the same frame of reference. In this thought experiment you have perfect symmetry.

When observing each other I assume the Bob and Fred will see exactly the same thing. I assume this because there is perfect symmetry and so I can think up with no logical reason why they would see things any differently. Therefore I assume X=X’, and I will simple call this value X from now on. X can be any length, and according to special relativity the longer X is the more pronounced the effects of time dilation will be. In other words in this thought experiment the effects of time dilation can vary while the acceleration taking place stays the same. This leads me to wonder how the paradox can be solved with general relativity alone. I thought about this for a while, and came to the conclusion that the distance the two objects are away from each other must effect how they view each other. Based on this conclusion I came up with three possible solutions.

1) Time seems to go faster for things that are farther way. In the end I rejected this possibility because the two twins could stop their motion relative to each other and stay that way for any length of time. This creates a problem similar to the problem with X that I am trying to solve.

2) The General Relativity effects of acceleration are observed differently for things that are farther away. In this is the case the large X is the more pronounced the temporal effects the two twins will observe while the other ship is accelerating back towards them.

3) There is another force that pushes everything away from the observer based off of how far away it is. If this is the case it would be impossible to apply special relativity when large distances are involved. This one is the most bizarre because if it is true then every frame of reference will observe everything else accelerating away from it with the amount of acceleration increasing for things that are farther away.

I’ve reached the point were thinking about this on my own isn’t getting me anywhere. So I decided to post this here and see what other people think.

- Login to post comments

#1So, the problem is that the time dilation is dependent on X?

Isn't it just because time dilation is because of velocity, so the longer you have a high velocity, the longer the time dilation effects will increase, so there will be a bigger difference.

I have never done anything with relativity, so I am most likely just plain wrong, because I didn't understand it properly

#2Thunderios wrote:I don't know if what I've said makes any sense. I am just speculated based of my very limited understanding of special relativity. Still some people on this site seem to understand this better then I do so I wanted to see what they think.

The problems(if there really is a problem) is exactly what you said. The longer you have a high velocity the greater the effects of time dilation. It seems that you can have exact same acceleration with different values of X. The way I understand it General Relativity is the solution for the twin paradox, and General Relativity relies in some way on acceleration. If what I understand is correct then I can't understand how the same acceleration can counteract different amounts of time dilation.

It is possible I'm just missing, or failing to understand something. If so hopefully someone will explain were I have gone wrong.

#3RatDog wrote:About a month ago, I jumped into one of those discussions about general relativity, and it turned out I was wrong... I thought i had it figured out, and I had to get back to reading about it. As a layman, and from the video mentioned in the previous thread you posted, it again seems to make sense in principle. The clearest example was the graphical representation of TIME X SPACE, with the little car. I think it is in the third video.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#4Eh, I have some knowledge of relativity. I'm not sure if I understand what you're asking here though.

I assume that the two spaceships are traveling in opposite directions? When you say they come to 'rest,' you are referring to a third reference frame. If their motion is the same but in opposite directions, then they should observe the same period of time to have elapsed when they meet in this rest frame. What is the supposed paradox here? The farther they travel, the less time that will have elapsed in their reference frames relative to the rest frame because they will have traveled faster relative to the rest frame and/or for the longer period of time.

Our revels now are ended. These our actors, | As I foretold you, were all spirits, and | Are melted into air, into thin air; | And, like the baseless fabric of this vision, | The cloud-capped towers, the gorgeous palaces, | The solemn temples, the great globe itself, - Yea, all which it inherit, shall dissolve, | And, like this insubstantial pageant faded, | Leave not a rack behind. We are such stuff | As dreams are made on, and our little life | Is rounded with a sleep. - Shakespeare#5butterbattle wrote:I assume that if the two twins mirror each other exactly when they meet back up again neither twin will have aged more than the other. Based on this assumption I'm trying to understand what each of the twins will observe while watching the other. According to special relativity while both twin have motion in relation to each other and while both twin are in an inertial reference frames(I think this means no acceleration) they will both observe time moving more slowing for the other twin. When the twins meet up the same amount of time will have passed for both of them. Therefore I must assume that at some point the two twins will observe time moving faster for the other twin. I assume that the time when the twins observe time passing more quickly for the other twin must happen either while they are accelerating, or while they observe their fellow twin accelerating. Now consider two scenarios. In both scenarios the ships are programmed to accelerate the exact same amount, in one scenario X is 10 light years and in the other scenario X is a 100 light years. During the scenario were X is a 100 light years both twins will have observed a larger effect from time dilation. If there is a larger effect from time dilation then there must be a larger effect from the period/periods were the twins observe time flowing faster for their fellow twin. I’m trying to understand the larger effect from the period/periods were the twins observe time flowing faster for their fellow twin, and why it happens when the computers have been programmed to accelerate the same amount in both scenarios.

To me it looks like some sort of effect related to distance must take place. I suppose their is probably just something that I'm missing here although I'm not sure what.

#6The adjustment that resolves the 'paradox' occurs while they are undergoing acceleration/deceleration.

The apparent rate of time passing as seen from the other, when either or both are undergoing acceleration, and therefore described under General Relativity, gets much more complicated than for Special Relativity.

I haven't got time to chase this up in detail right now, but I looked into it a bit when this came up before, and it is all in the velocity changes, which prevents a paradox arising.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." -Sam HarrisThe path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#7I don't see any difference here, at all.

Unless I missed something...

The 'travel' (of the twins) is identical (albeit in different directions), therefore, there's no (relative) difference (to each other) than if they simply both stood still.

If they were triplets, and one triplet was on earth, the 2 triplets that were travelling closer to the speed of light would see that they aged less than the triplet who stayed on earth, once they returned to earth.

Same difference...

I keep asking myself " Are they just playin' stupid, or are they just plain stupid?..."

"To explain the unknown by the known is a logical procedure; to explain the known by the unknown is a form of theological lunacy" : David Brooks

" Only on the subject of God can smart people still imagine that they reap the fruits of human intelligence even as they plow them under." : Sam Harris

#8I think the 'problem' is reconciling the fact that each 'twin' will

the other aging much slower than themselves during the constant speed sections of the fight, as per SR, so how do they end up the same when they get back together?seeIt has to be in the acceleration stages that it all sorts out.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." -Sam HarrisThe path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#9That is a part of it that I still don't understand myself.

Suppose that two twins both began traveling at relativistic speeds relative to each other when they are 20 years old. Eventually, each might observe themselves to be 30 years old and observe the other one to be 25 years old. But then, if one of them suddenly goes into the others' reference frame, it seems that he would suddenly observe himself to be 25. I cannot wrap my brain around how this is possible.

Our revels now are ended. These our actors, | As I foretold you, were all spirits, and | Are melted into air, into thin air; | And, like the baseless fabric of this vision, | The cloud-capped towers, the gorgeous palaces, | The solemn temples, the great globe itself, - Yea, all which it inherit, shall dissolve, | And, like this insubstantial pageant faded, | Leave not a rack behind. We are such stuff | As dreams are made on, and our little life | Is rounded with a sleep. - Shakespeare#10BobSpence1 wrote:That's it exactly. Where does it sort out? It has to sort out somehow, and the most likely place is during the accelerations.

Trying to understand this better I've created two scenarios. In both scenarios the spacecraft are programed to accelerate for the same period of time. The difference between the two scenarios is how long the space craft are allowed to coast without accelerating. In scenario one the space craft is allowed to coast 10 light years. In scenario two the space craft is allowed to coast 100 light years(Scenario 1 x=10, scenario 2 x=100). The higher the value of X the greater the total effects from time dilation, and the more time that must be made up for during the acceleration parts.

The difference between X=10 and X=100 can't be sorted out by acceleration A1 because A1 is the same for both scenarios. I doubt it can be sorted out by acceleration A3 because I don't think that A3 is even really necessary for this thought experiment. That only leave acceleration A2. In scenario 1 and scenario 2 A1 and V1 are the same. The only difference between the two is X. This makes me wonder if distance has some affect on how we view the effects of acceleration.

In regards to acceleration the only other possibility that I can think of has to do with differences between when the two twins view that acceleration events as happening. Fred will not necessarily view Bob experience A2 while he is experiences A2. Just as Bob not necessarily view Fred experience A2 while he is experiencing A2. Perhaps the time difference can be made up through difference the two twins experience over exactly when the various events are happening. It hard for me to imagine that this could account for vary large values of X. I'll have to think about it more.

#11The two twins will experience the same time effects due to the acceleration, but while they are accelerating, the theory as to what they will see apparently happening with the other guy gets complicated.

And remember, to accelerate up to velocities where these dilation effects become significant takes quite a while, so there is time for quite a bit of time 'adjustment' to occur.

The bit that I still have a problem with is that if you arbitrarily extend the duration of the constant speed section, the cumulative time discrepancy must grow, but they still will only have to go through the same amount of deceleration/acceleration. So how can a greater perceived time discrepancy be made up in the same amount of accelerated motion?

I think it must have something to do with the greater distance between the two, if you travel longer at constant speed. That seems to me to be the only other variable. I tried to have a look at that in the earlier thread, but didn't have time to get my head around the math.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." -Sam HarrisThe path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#12RatDog wrote:I'm not sure what you guys are seeing, that I'm not.

Help me out here...

I'm modeling this now as if the 2 twins are both experiencing the same thing, in crafts that are right alongside each other. If they were to look out through a window at each other, while any of this accelerating/coasting etc, is going on, they wouldn't 'see' the other any differently than if they then glanced in the mirror at themselves.

IOW, 'relative' to space/time, they're the same, just as if they were sitting next to each other on a park bench (relative to space/time).

I keep asking myself " Are they just playin' stupid, or are they just plain stupid?..."

"To explain the unknown by the known is a logical procedure; to explain the known by the unknown is a form of theological lunacy" : David Brooks

" Only on the subject of God can smart people still imagine that they reap the fruits of human intelligence even as they plow them under." : Sam Harris

#13If they are 'right alongside each other', sure, there is no problem.

The problem is if they travel away from each other for some arbitrary period, then turn around and come back to meet up again.

During the period where each has been travelling at velocity V in opposite directions, relative to an observer in some inertial reference frame, they will have been travelling at V X 2 wrt to each other. So each will see the other travelling away from him at some velocity, that will appear less than V X 2, and less than the speed of light, but presumably fast enough to appear to be aging significantly slower than he is.

So we still have the 'paradox'.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

The path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#14redneF wrote:Imagine that Fred and Bob have clocks with them that start out at 0. When the trip ends both Fred and Bobs clocks will read 50 (of some arbitrary time unit). During the trip when his clock says 20 Fred observes Bob. What Fred sees is exactly the same thing as Bob would see if he observed Fred when his clock said 20. If Fred was able to read Bob's clock while observing him he wold likely see a number other then 20. Lets say that the number Fred saw was 30 (Even though I don't really know what it would be). If that was the case Bob would also see 30 while reading Fred clock.

Fred and Bob would see exactly the same things while observing each other, but they wouldn't see things happening to their twin at the same time they were happening to them. In other words if they could observe what was on their twins clock most of the time it would say something different from what was on their own clock.

#15RatDog wrote:I don't see a paradox here, so maybe I'm missing something lol. It is a very good possibility that my understanding is flawed, but what I think you are asking is that if the 'paradox' states that each twin will see the other's clock run slower (hence the time dilation), when/where does the reconciliation of clocks occur? I may be missing something here. As I understand this, the 'dilation' only occurs at constant acceleration and it is proportional to that acceleration. There is no actual time dilatation, it is just an effect of the constant speed of light. It just appears as though the clocks are running slower, so there is no moment of reconciliation per say... as the vectors reverse, you simply add the values together so time seems to speed up on the return trip, hence on arrival the gradual 'reconciliation'.

In the previous thread AIG had a perfect analogy about two people sitting in a stadium across from themselves, let's say that they start at the center of the field, as they walk to their seats, they seem to be getting smaller from their respective POV. As they come back to the center of the field they seem to be getting bigger... of course SR works differently, but that is a very good analogy. This part of the video from the previous thread depicts the perceived 'dilation' of time perfectly in my opinion.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#16OK, you have overcomplicated the matter and that is just adding to your confusion. Before I get to that, I want to state that any teacher who invokes general relativity to explain away any of the issues from special relativity probably does not understand either one and is just regurgitating a bad idea to cover their ignorance on the matter.

Time dilation happens for any velocity but for regular experience, the effect is too small to be worth taking into account. For example, a theoretical astronaut a hundred years from now may spend his whole career running around the solar system at 10% of c but after 30 years, he will return to earth only a day younger than his brother who never left earth.

Anyway, it would be much easier to just consider two brothers with one staying on the earth and the other taking off into space. If you add a third person into the mix, then you just have another entity to solve for. You can do that if you want to but it will not make the case for two entities clearer.

Here is one way to go about this:

Let's take two identical clocks and put one of them on the space ship. Both clocks should have radio gear so that they may be monitored one from the other. Here is the thing, for a distant clock, you have to calculate the time that it takes for the radio waves to travel to the other clock. So if one clock is on the moon, even though there is not enough relative motion to produce measurable time dilation, the moon clock will seem to be about two seconds late from the position of an observer on the earth and vice versa.

Here is where this starts to get interesting. If the clock is on a space ship heading away from the earth at a constant speed, then the distance the radio waves must travel and the travel time both are going to be increasing steadily. Because of this, the clock on the space ship will seem to be slower. However, from the pilot's POV, it is the clock back on the earth that seems to have slowed down.

If the space ship was traveling towards the earth, then the two brothers would experience the clocks as ticking faster than usual. One of the key factors that most people miss out on is that in any case, time is always proceeding forward. Just because the approaching clock seems to be faster than the receding one does not mean that you get back the time that was lost while heading on the outbound leg of the journey. The total number of times that the clock ticks are what you have to take into account more so than the rate at which they tick.

NoMoreCrazyPeople wrote:=

#17The rocket ship is a planet and the twins are a room outside it.

#18Answers in Gene Simmons wrote:I thought that's what I said... where was I wrong?

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#19Ktulu wrote:In the underline part I think you confused acceleration with velocity.

#20RatDog wrote:Yup, I stand correct it.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#21Answers in Gene Simmons wrote:I think the underline part is wrong. Time dilation occurs when relative motion exists between objects. It doesn't matter weather they are moving towards or away from each other.

Answers in Gene Simmons wrote:Actually I feel like I have simplified it. When both ships are exactly the same and doing the exact same thing you can make certain assumptions.

One assumption you can make is that the same amount of time will have passed for both twins.

Another thing you can assume is that the distance each twin views the other twin traveling during the over all journey is the same.

Also if Fred beams digital information that gives his current clock time to his twin Bob the information that Bob receives at any given time is the same as Fred would receive at that time if Bob was beaming the information. This is hard to visualizes so let me include Some tables.

Bob's Clock

Digital information received from Fred's clock

1

F1

2

F2

3

F3

4

F4

5

F5

6

F6

7

F7

8

F8

9

F9

10

F10

Fred's Clock

Digital information received from Bob's clock

1

B1

2

B2

3

B3

4

B4

5

B5

6

B6

7

B7

8

B8

9

B9

10

B10

F1=B1, F2=B2, F3=B3, F4=B4, F5=B5, F6=B6, F7=B7, F8=B8, F9=B9, F10=B10

#22RatDog wrote:Sorry for being dense here, but what is the paradox exactly? Are you asking about the reconciliation of clocks? or why one is slower than the other when they should be the same? I'm not clear on what's not clear.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#23Ktulu wrote:I doubt their actually is a paradox. The question is why isn't there a paradox. How do the clocks reconcile? If both twins do exactly the same thing then the same amount of time must pass for both of them. In this example the amount of time dilation can vary without effecting either the velocity or the acceleration. The question is how does the addition time dilation get reconciled when the velocities and accelerations haven't changed. Some how I think the answer must have something to do with distance, but I'm not exactly sure what the solution is.

Edit: By amount of time dilation I mean the total cumulative affects from the time dilation. Or in other words the total difference between what Fred sees on his clock, and the digital clock time he receives from Fred.

#24RatDog wrote:OK, you are going about this wrong. What are you measuring when you record the ticking of the clock?

Just for grins, let me say that the ticking is some form of information which happens to be sensitive to the changing distance between the two reference frames. As they close on each other, the ticking has to come in faster because of the decreasing distance.

Let's consider, instead of a ticking clock, a pure sine wave in the audio band. If the emitting object is approaching, then the frequency will be increased and as the object is receding, the frequency will be decreased. It is a simple Doppler shift here.

RatDog wrote:I see what you are trying to do. The only thing is that just because you can make assumptions does not mean that they are warranted.

One problem is that you have made the assumption of a central point which is a stationary reference. Well, there really is no such thing. Thought experiments may posit such but they may not hold true if you change one of the parameters. That can bork your assumptions to the point where the whole exercise breaks down.

In order to work the way that you are going, your model needs to have a third person who remains at the stationary reference. Then you reconcile the clocks of both astronauts to that third person. In that case, both of the astronauts show the same amount of time dilation in respect to the third person. However, by adding the second astronaut, you now have the additional complication of having to reconcile the clocks between the two of them.

Let me change one of your free parameters and perhaps you will see how this changes things. You have made the assumption that the two astronauts are moving on courses which are 180 degrees apart, basically, they are moving on the same line and in opposite directions. In my restatement, the two astronauts are not moving on the same line but in fact, the headings are 90 degrees apart. If that is not clear, then add in a third astronaut who is moving at right angles to the other two.

Assuming that the helm control is identical fr every astronaut, then the time dilation relative to the stationary observer must be the same for as many astronauts as you care to use. However, when you try to reconcile all of the clocks, what is going to come out? Remember that the astronaut moving at right angles is going to have a different relative velocity to each of the first two than they will have to each other.

NoMoreCrazyPeople wrote:=

#25Answers in Gene Simmons wrote:You are completely right. The way I have been looking at this is wrong. I didn't even consider the path the light took. I kept using the word observe without thinking about what it really meant. If I want to know what the other twin sees I have to consider the path that the light took to reach his ship. While I was looking into this issue I found a web page called ask a physicist. I did, and the physicist directed me to this. Some one had already asked this very same question.

http://www.askthephysicist.com/ask_phys_q&a_older.html#twin

Mystery solved. Thanks for you help everyone.