Question about space twins return

[asprung]

It is said that a spaceman traveling at high velocity, when viewed from earth’s time frame, will age slower then his twin on earth. (The earth twin when viewed from the space twin’s time frame should age slower than the space twin).

Assuming that when he ages to 50 in his time frame a blast takes the space twins hand off.

Assuming again that when he returns to earth the space twin has only aged to 25. What has happened to his lost hand?

[insane_alien]

it remains gone.

 

you are mixing frames here. even though the space twin is 50 from the perspective of the earth twin it doesn't mean that he is 50 fromhis own perspective. when the blast occured he was younger than 25 in his frame of reference.

[D H]

Assuming that when he ages to 50 in his time frame a blast takes the space twins hand off.

Assuming again that when he returns to earth the space twin has only aged to 25. What has happened to his lost hand?

What lost hand? That won't happen for another 25 years, in some future trip taken by the space twin.

[swansont]

It is said that a spaceman traveling at high velocity, when viewed from earth’s time frame, will age slower then his twin on earth. (The earth twin when viewed from the space twin’s time frame should age slower than the space twin).

Assuming that when he ages to 50 in his time frame a blast takes the space twins hand off.

Assuming again that when he returns to earth the space twin has only aged to 25. What has happened to his lost hand?

 

Just in case you miss the point of D H's post, you have the space twin losing his hand at 50 but returning to earth at 25. I don't think you have laid out a scenario that has anything to do with relativity.

[asprung]

Im assuming he is 50 in his own time frame. That would make him younger when viewed from earths time frame. I thought that when he entered earths time frame he would be the age he was viewed as being from that time frame.

[D H]

Now why would you assume that? He is 25 in his own frame.

[Moontanman]

Ok why is only the time frame of the moving astronaut real? From his perspective time should slow down on the earth, but only the moving twin's apparent time dilation is real when he returns to a relative stop to the earth.

[swansont]

Im assuming he is 50 in his own time frame. That would make him younger when viewed from earths time frame. I thought that when he entered earths time frame he would be the age he was viewed as being from that time frame.

 

If he aged 50 years in his own time frame, then his body has aged 50 years. He won't magically look younger (or older) to someone else, even though their clocks don't agree.

[D H]

All frames are equally valid, and they all yield the same answer.

 

Here is a situation that yields the numbers that asprung hinted at in the original post. Suppose the traveling twin has a magical spacecraft that can instantaneous accelerate to any speed less than the speed of light and not have the occupants turn into a blob of protoplasm at the rear end of the spacecraft. At age 20, the traveling twin sets off for a star 14.79 light years away at a 98.6% of the speed of light. (The actual numbers: The star is [math]5\sqrt{35}/2[/math] light years distant, and the space craft velocity is [math]\sqrt{35}/6\, c[/math]). To the traveling twin, that 14.79 light year distance to the star contracts by a factor of 6. The spacecraft clock indicates that the outbound journey takes 2.5 years. This is exactly how much the traveling twin ages during the outbound journey. The same thing happens on the return trip. Total elapsed time for the trip from the perspective of the traveling twin is 5 years. As far as the traveling twin is concerned, she is 25 years old when she returns -- and she has a clock and a youthful smile to prove it.

 

From the perspective of the Earthbound twin, the outbound trip takes 15 years, and so does the return trip. As far as the Earthbound twin is concerned, he is 50 years old when his twin returns -- and he has a clock and some gray hairs to prove it. Both are right, and both agree that the other is also right.

 

Suppose during this trip the two twins remain in constant communication with one another, with a timing signal embedded in the communication stream. This timing signal is in the form of a counter that increments once per second, with seconds measured in the frame of the transmitter.

 

During the outbound trip, both twins will see the same thing. The signal sent by the other twin is incrementing slower than once per second: once every [math]6+\sqrt{35} \approx 11.92[/math] seconds. Each twin sees the other as aging slower than they themselves are aging.

 

Both twins will see the same thing just before the traveling twin finally returns. In this case, each twin sees the other as aging faster than they themselves are aging. The factor is the inverse of the slowing on the outbound trip. The timing signal from the other twin increments 11.92 times every second.

 

So, if both twins see the same thing, how can the traveling twin come home having aged only 5 years while her twin has aged 30 years? This is the crux of the twin paradox. The answer is that the point in time at which the signal transitions from slow to fast is not the same for the two twins. In the case of the traveling twin, this occurs when the traveling twin turns around. In the case of the Earthbound twin, this occurs shortly before the traveling twin returns.

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I had stuff to do in real life, so I left that last post a bit unfinished. To finish it off, what does each of the twins see on their own clock and in the signal sent by the other twin?

 

From the traveling twin's perspective, it takes here 2.5 years to travel to the other star. When she arrives, the signal from her twin will show that the Earthbound twin has aged by all of 76.63 days ([math]2.5\,\text{years}/(6+\surd 35)[/math]). After she turns around, the relativistic Doppler works exactly the other way. The time counter from her Earthbound twin advances 11.92 times per seconds. Her Earthbound twin appears to age 29.79 years during the 2.5 year return trip. On her return, the count sent from Earth will show that thirty years have passed on the Earth.

 

The Earthbound twin calculates that it will take the traveling twin fifteen years to reach the star. However, that is not when the Earthbound twin sees the traveling twins signal switch from slow to fast. It takes an additional 14.79 years for the turnaround signal to reach Earth. In terms of signals, the Earthbound twin sees the traveling twin aging slowly (1 second per 11.92 seconds) for 29.79 years. The traveling twin appears to have aged only 2.5 years during this 29.79 year interval During the next 76.63 days the Earthbound twin will "see" the traveling twin as aging 11.92 times faster than he is aging. 76.63 day * 11.92 = 2.5 years. Total trip time from the perspective of the Earthbound twin is 30 years. Total aging of the traveling twin is five years.

 

Bottom line: Both the traveling twin and Earthbound twin arrive at the same answers for the how much each of the twins aged during the trip. The traveling twin ages five years, and the Earthbound twin ages thirty years.

Edited October 11, 2009 by D H
Consecutive posts merged.

[Moontanman]

Ok, let me tell you the way i have been told it works and you tell me where I'm wrong and maybe I'll understand better. This happens in a universe containing only the two observers.

 

From the stand point of both observers both are traveling at close to the speed of light. The twin who is traveling sees the stationary twin as moving. The staionary twin sees the other as moving. Reletively speaking both see the other as moving. But only the one who is actually moving feels time dilation. Since both points of view are valid what decides which one's time dilation is real. Or maybe how do they tell wich one is moving so that only one experinces time dilation?

 

I am sorry if this is stupid way of looking at it but it's the best I can do.

[Janus]

Ok, let me tell you the way i have been told it works and you tell me where I'm wrong and maybe I'll understand better. This happens in a universe containing only the two observers.

 

From the stand point of both observers both are traveling at close to the speed of light. The twin who is traveling sees the stationary twin as moving. The staionary twin sees the other as moving. Reletively speaking both see the other as moving. But only the one who is actually moving feels time dilation.

Nobody feels time dilation. It is something that you measure as happening to someone else. You can never say which twin is "really" moving.

 

Since both points of view are valid what decides which one's time dilation is real. Or maybe how do they tell wich one is moving so that only one experinces time dilation?

 

One twin stays in the same inertial frame, the other changes inertial frames.

This is important.

 

One of the effects of Relativity is the "Relativity of Simultaneity"

 

Imagine two clocks, one with the "stationary twin" and one at the point where the "traveling twin" turns around to make the return trip.

 

According to the Stationary twin, these tow clocks read the same time.

 

However, according to the traveling twin on the outbound trip, the clock at the end point reads a later time than the stationary twin's clock( for example if the stationary twin's clock reads 2009, the end point clock would read sometime in 2010. Both clocks run slow according to him.

 

When he reaches the endpoint, he stops ans heads back toward his brother. At this point he has changed inertial frames, and in his new inertial frame, it is the stationary twin's clock that reads later than the end point. So if for instance the endpoint clock read 2011 and the stationary twin's clock read 2010 when he first reached the end point, the endpoint clock will read 2011 and the stationary clock will read 2012 after he turns around. by his reckoning, the stationary twin;s clock jumps forward 2 yrs as he himself changes frames.

 

If you add up the time that elapses on the Stationary twin's clock; running slow on the outbound trip, jumping forward on turnaround, running slow on the return trip, more total time elapses on the stationary twin's clock than on his when they meet up again.

 

The stationary twin, who never changes inertial frame, just sees his brother as aging slower during the entire round trip.

 

 

I am sorry if this is stupid way of looking at it but it's the best I can do.

[D H]

Nobody feels time dilation. It is something that you measure as happening to someone else.

This is a very important point. Understanding it is crucial to understanding relativity in general. BTW, the same goes for length contraction. It too is something you measure as happening to someone else.

 

The stationary twin, who never changes inertial frame, just sees his brother as aging slower during the entire round trip.

Not true. See post #9.

 

Here's a space-time diagram of a trip to and from a point 3 light years away at 3/5 c. Source: http://www.csupomona.edu/~ajm/materials/twinparadox.html

 

 

In this case, the Earthbound twin sees his brother aging slower for the first eight years of the trip and then aging faster for the final two years.

[Moontanman]

I wish i could understand

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it's the why that stumps me I guess

[D H]

I wish i could understand

I tried to give a detailed explanation in post #9, Janus added some more info in post #11. Space-time diagrams (see post #12) help a lot.

 

I think the problem is that you have some misconceptions about relativity. A couple common ones that get in the way of understanding:

• There is no absolute reference frame. There is no way to tell who is moving and who isn't.
  
• Time dilation and length contraction don't happen to you. Suppose you are traveling at a relativistic speed with respect to someone else. Time dilation and length contraction are something you see happening elsewhere. That other party will appear to you to be subject to time dilation and length contraction.

 

it's the why that stumps me I guess

The why is because, as Janus mentioned, the traveling twin accelerated to turn around. While velocity is relative, acceleration is not. Acceleration remains absolute in both special and general relativity.

[Iggy]

The stationary twin, who never changes inertial frame, just sees his brother as aging slower during the entire round trip.

 

Not true. See post #9.

 

Compensating for doppler shift the stationary twin calculates that his brother ages slower the entire trip. Is that correct?

 

Acceleration remains absolute in both special and general relativity.

 

The 'accelerating' twin can't consider himself at rest while the rest of the universe relatively accelerates in general relativity? You sure?

[swansont]

The 'accelerating' twin can't consider himself at rest while the rest of the universe relatively accelerates in general relativity? You sure?

 

Freefall in a uniform gravitational field is an inertial frame in GR. If you accelerate, it's like standing in a gravitational field — you feel a force, and if you can feel/measure it, you know you aren't in an inertial frame.

[asprung]

I understand that the accepted view is that the space twin is younger than his earth twin when he returns to earth. That means he must have aged slower viewed from earths time frame than in his own time frame. Accordingly he must at some point be older in his time than viewed from earths. My question was - if he lost his hand at this point what would happen to it when he returns to earth and enters earths time frame .

[D H]

I understand that the accepted view is that the space twin is younger than his earth twin when he returns to earth. That means he must have aged slower viewed from earths time frame than in his own time frame. Accordingly he must at some point be older in his time than viewed from earths. My question was - if he lost his hand at this point what would happen to it when he returns to earth and enters earths time frame .

This doesn't make a bit of sense. Please elaborate.

[asprung]

I am trying to say that at some point the space twin must be older when viewed in his time frame than he would be when viewed from earths time frame. He loses his hand in his time frame but is the age he is viewed as being from earths time frame ,when he returns to earth. It would thus seem he is younger when he returns to earth then when he lost his hand - is it still gone.

I am sorry I dont make sense.

[D H]

You are still not making sense. You appear to be thinking that the traveling twin suddenly gets younger upon returning to Earth. That simply does not happen. If the traveling twin loses his hand at some time during the trip, the hand will still be missing when the trip ends.

 

It appears you think there is some God's eye frame in which one can absolutely compare events in two frames separated by some non-zero distance and moving with respect to one another. Such a frame doesn't exist. Simultaneity is relative.

[asprung]

I was led to understand that the space twin would age at the rate that he started the trip with in his own time frame, and that time dilution would only occur when viewed from a diffrent time frame.

[D H]

The simplest explanation of the twin paradox is that when the traveling twin gets up to speed the distance to the target star shrinks due to length contraction. In terms of the example in post #9, the 14.79 light year distance to the target star contracts to a mere 2.465 light years. At a velocity of 0.986 c, it takes the traveling twin 2.5 years as measured by the traveling twin to reach the star. The same thing happens on the return trip. Total time for the trip as measured by the traveling twin: five years. The Earth-bound twin sees something quite different. He calculates the time taken to go to the star and come back as thirty years, total. His twin does indeed return thirty years later from the perspective of the Earth-bound twin. This is the simple explanation. Everything else you will read about the twin paradox is an explanation of why this is not a true paradox.

 

Imagine you are driving along a freeway at 60 miles per hour toward a city 60 miles away. Your velocity with respect to the frame defined by the car you are driving is identically zero. From the perspective of that frame, the car is not moving. The target city is moving toward you at 60 miles per hour. It is still 60 miles away, however.

 

Now imagine that the speed of light is a mere 100 mph rather than 670 million mph. As you get up to 60 mph, the passing countryside is going to look a bit weird. One oddity is that the distance between you and the city shrinks from 60 miles to 48. You make it to the target city in 48 minutes as measured on your wristwatch. The police officer who you just zoomed past sees things quite differently. He sees you as traveling at 60 mph (posted limit = 60, so you are OK). To him, the distance to the target city is still 60 miles. The one oddity he sees is that your wristwatch is going a bit slow.

 

Time dilation and length contraction are not something that happen to you. They are things that appear to be happening to the world outside you. They are not just appearances, however. It does take you only 48 minutes to reach the target city.

[asprung]

I had questioned in another post why length contraction would not distort the space twin.I was told that he did not experence it his own time frame only when viewed from another time frame.I had understood that time dilution and length contraction went hand in hand. My question is meaningless if the space twin does experince time dilution in his own time frame. I have the unaccepted view that time dilution only slows the clock but not what is being measured by it. This would put the situation in a different light.

[Sisyphus]

I have the unaccepted view that time dilution only slows the clock but not what is being measured by it.

 

I think you have to ask yourself what the difference is.

[swansont]

I had questioned in another post why length contraction would not distort the space twin.I was told that he did not experence it his own time frame only when viewed from another time frame.I had understood that time dilution and length contraction went hand in hand. My question is meaningless if the space twin does experince time dilution in his own time frame. I have the unaccepted view that time dilution only slows the clock but not what is being measured by it. This would put the situation in a different light.

 

Length contraction and time dilation affect the dimensions of space and time. For time dilation, time itself runs slow for a moving frame, and by extension, all items in that frame experience the slowed time. It is not mechanical in nature — you cannot have something in that frame immune to the effects.

 

Your view is "unaccepted" because it has been demonstrated that nature doesn't work that way.

 

 

(BTW, it's dilation, not dilution)