The twins paradox

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  • #1
cire
the twins paradox

It is true that the one that traveled is younger, is this a fact or it is a paradox
 

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  • #2
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Einstein's theory of time dilation has been somewhat proven.
The website: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html
says that:

In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation . They made airline flights around the world in both directions, each circuit taking about three days. They carried with them four cesium beam atomic clocks. When they returned and compared their clocks with the clock of the Observatory in Washington, D.C., they had gained about 0.15 microseconds compared to the ground based clock.
 
  • #3
Fredrik
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It's a fact, and not a paradox. If you'd like to know more, I suggest you use the search feature to find other threads about the twin paradox. There's about a gazillion of them.
 
  • #4
JesseM
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It depends what you mean by "the one who travelled". If both travel away from each other at constant velocity, so there's no acceleration involved, each one says the other is younger in his own reference frame, but unless one of them changes velocity they'll just get farther and farther apart, so they won't be able to get together to compare their ages in one spot. If one of them does change velocity so that they eventually meet up again, then the one that changed velocity will be the one who's younger when they meet.
 
  • #5
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cire said:
It is true that the one that traveled is younger, is this a fact or it is a paradox
The word "paradox" is kind of a hang-over from the days of classical physics. In purely classical terms it's a paradox because it was believe that time was absolute and therefore it would be a paradox to conclude that someone could pass through more or less time than someone else.

However, since that time we've come to realize via experiment that the conclusions of relativity are ontologically correct. In other words, it is possible for someone to pass through more or less time than someone else. This has been precisely verified in countless experiments. In literally billions of experiments actually if we count the experiments that take place in particle accelerators which we most certainly should include. The lifetime of sub-atomic particles is affected for the very same reason that the lifetime of the twins is affected in "The Twin Brothers Paradox" thought-experiment or "gedanken-experiment" as it's called in German.

The name of this thought-experiment was never changed from it's original name which includes the word paradox. But time dilation is no longer considered to be a paradox. It's now understood to be an actual property of nature. The old Newtonian concept of absolute time is now known to be ontologically incorrect.

So don't take the word paradox literally in this case. It's really not considered to be a paradox any longer. The word in this context is just a historical hangover.
 
  • #6
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christinono said:
In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation . They made airline flights around the world in both directions, each circuit taking about three days. They carried with them four cesium beam atomic clocks. When they returned and compared their clocks with the clock of the Observatory in Washington, D.C., they had gained about 0.15 microseconds compared to the ground based clock.
didn't they also put one on the space shuttle to test what the effects of gravity on time were? i think i remember hearing it somewhere.
 
  • #7
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Yep - a good example of both of these effects can be found in how GPS clocks are preset before launch - There is one correction to account for the velocity of the satellite clocks relative to the non-rotating earth centered reference, and there is a second correction to account for the altitude of the satellite(s) relative to the surface of the earth. The velocity correction is opposite to the height correction - and the latter is much larger. Once in orbit, they keep almost perfect time with the earth stations - small period corrections being required to adjust for the fact the orbits are not perfect.
 
  • #8
JesseM
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NeutronStar said:
The word "paradox" is kind of a hang-over from the days of classical physics. In purely classical terms it's a paradox because it was believe that time was absolute and therefore it would be a paradox to conclude that someone could pass through more or less time than someone else.
That isn't generally why people call it a "paradox". The reason people call it a paradox is because they mistakenly think that relativity says the laws of nature work the same in *all* reference frames, not just inertial ones, so they imagine that the situation is completely symmetrical, since from the travelling twin's point of view the earth moved away for a while and then turned around and moved back towards him. If the situation was indeed symmetrical, it would seem to be a paradox because each should predict the other ages slower, and both points of view would be equally valid. But since the principle of relativity only applies to inertial frames in SR, it isn't really symmetrical, so there's no paradox in the fact that one has objectively aged less when they meet up.
 
  • #9
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But JesseM - they guy who takes off from earth doesn't really have to turn around - he can go to a distant place that is 5 LY away as measured by earth equipment and send a message when he arrives saying: "I am here now and my clock only reads 3 years more than the day I left."
 
  • #10
JesseM
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yogi said:
But JesseM - they guy who takes off from earth doesn't really have to turn around - he can go to a distant place that is 5 LY away as measured by earth equipment and send a message when he arrives saying: "I am here now and my clock only reads 3 years more than the day I left."
Well, it will definitely take more than 10 years for the earth to get this message, as measured by earth-clocks. And if there was a satellite moving in such a way that it was at rest relative to the travelling twin, and 5 LY behind him according to his own measurements, then when this satellite passed by the earth, the earth could send a message saying "the satellite just passed by us and our clock reads only 3 years more than the day you left". Without either one changing velocities the situation must be symmetrical in this way.
 
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  • #11
jtbell
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christinono said:
In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation . They made airline flights around the world in both directions, [...]

For a more recent example of this sort of thing, comparing clocks in airplanes flying around in circles to clocks on the ground, see

"Timekeeping and Time Dissemination in a Distributed Space-Based Clock Ensemble" (from a conference in 2002)

http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf [Broken]

in particular the "Flight Tests" section.
 
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  • #12
cire
I don't understand this, I always thought it in this way:
there is one clock in S and another in S' if we measure the time from S to the clock at S' we get time contraction, but if we are sitting in S' and measure the time at the clock there there is not time contraction. Therefore I always thought that the twin that made the trip is equal biologically old to the one that stayed in earth because the aging occur in the the frame you are. Of course if you try to measure the time at S' from S there is time contraction.

thanks in advance :confused:
 
  • #13
russ_watters
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yogi said:
But JesseM - they guy who takes off from earth doesn't really have to turn around - he can go to a distant place that is 5 LY away as measured by earth equipment and send a message when he arrives saying: "I am here now and my clock only reads 3 years more than the day I left."
He has to stop when he gets there though.
 
  • #14
JesseM
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russ_watters said:
He has to stop when he gets there though.
That's not relevant, he could just send a message the moment he passes next to the planet (if you idealize both the planet and the traveller as point-sized, there can be a moment when his position exactly coincides with the planet).
 
  • #15
JesseM
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cire said:
I don't understand this, I always thought it in this way:
there is one clock in S and another in S' if we measure the time from S to the clock at S' we get time contraction, but if we are sitting in S' and measure the time at the clock there there is not time contraction.
S will see the clock at S' slowed down, but likewise S' will see the clock at S slowed down. The key thing to understand is that different frames define simultaneity differently, so S may say his clock read 10:00 "at the same time" that the clock at S' reads 8:00, while S' may say his clock reads 8:00 "at the same time" that the clock at S reads 5:00. And when the travelling twin switches from heading away from the earth to heading back towards it, his definition of simultaneity changes too, so he will go from thinking the earth clock is way behind his own to thinking it is way ahead of his own. As he returns to earth, he will still say the earth-clock is running slower than his own, but since it started out far ahead of his own when he turned around and began to return, it will still be ahead of his own when he reaches earth. So, even though the earth-clock was running slow from his point of view during both the outbound leg of the trip and the inbound leg, he will still agree with the earth-twin's prediction that his clock will be behind the earth-clock when he returns, because his plane of simultaneity swung around this way when he turned around.

This page has a diagram which may be helpful, with the verticle line representing the worldine of the earth-twin A, the bent line representing the outbound and inbound legs of the travelling twin B's worldline, and the red lines representing B's definition of simultaneity at different moments on his trip.
 
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  • #16
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Russ and Jessie - Quite right Jessie - the traveler doesn't have to slow down - he can send the message on the fly - and when it is received 5 years later by the stay at home on earth, he will be older of course by 5 years plus the time it took the traveler to make the journey as measured in the earth frame - but all that is irrelevant to the discussion - what is of consequence is that we can make a comparison of the time accumulated in the frame of the traveler with the time accumulated in the frame of the stay at home w/o having to postulate acceleration, or changing frames. It is a direct consequence of the invariance of the interval. It is the high speed particle experiment - the one why twin excursion - whatever you want to call it.
 
  • #17
JesseM
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yogi said:
what is of consequence is that we can make a comparison of the time accumulated in the frame of the traveler with the time accumulated in the frame of the stay at home w/o having to postulate acceleration, or changing frames.
Time accumulated between what two events? The two frames will disagree about simultaneity, so if neither changes frames, both will say the other twin aged less over a given time interval.
 
  • #18
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Jessie--There are two events - the starting point which is an event measured by twin 1 and twin 2 each in their own frame, and the ending point which is an event measured by twin 1 and twin 2 each in their own frame -- since each twin only measures time and distance in their own frame (the stay at home measures proper time and proper distance in the earth frame and the traveler measures proper time using the clock which accompanies him) - the spacetime interval according to SR must be the same (invariant). There is never any need for either twin to make any measurement in the other twins frame therefore there is no simultaneity confusion
 
  • #19
JesseM
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yogi said:
Jessie--There are two events - the starting point which is an event measured by twin 1 and twin 2 each in their own frame, and the ending point which is an event measured by twin 1 and twin 2 each in their own frame
Whose "ending point"? Each twin sees himself at rest and the other in motion, so it makes just as much sense to define the ending point as the moment the travelling twin passes a planet which is at rest relative to the earth as it does to define it as the moment the earth twin passes a satellite which is at rest relative to the travelling twin.
yogi said:
-- since each twin only measures time and distance in their own frame (the stay at home measures proper time and proper distance in the earth frame and the traveler measures proper time using the clock which accompanies him) - the spacetime interval according to SR must be the same (invariant). There is never any need for either twin to make any measurement in the other twins frame therefore there is no simultaneity confusion
Yes, of course it's true that if you just want to measure the spacetime interval/proper time between two events, there will be no disagreement between observers on this. But the travelling twin's proper time between departing the earth and passing the planet is the same as the earth twin's proper time between departing the travelling twin and passing the satellite (assuming, as I did before, that the distance to the planet in the earth's rest frame is equal to the distance to the satellite in the travelling twin's rest frame). And whichever twin you pick to measure the proper time between two points on his worldline, the other twin will say this time is less than his own coordinate time between those two points. So do you agree that if neither twin changes velocity, the situation is completely symmetrical in every way?
 
  • #20
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Jessie - It is true, that if you introduce a satellite that is spaced 5LY away in the traveling twins frame, there is symmetry by definition because neither frame can tell which is in motion - but what is of moment in the present proposition is the relationship between the proper time logged by two clocks in relative motion where one clock does not have a spatial component in its interval and the other one does - Let us simply say that at a time that both twins agree upon, the traveler takes off at 0.8c and heads toward a planet 5 LY away as measured in the earth frame. When the traveler arrives at the planet, he sends a message to his earth twin telling him how much time has passed on his pocket watch which he carried with him. What will he transmit?
 
  • #21
JesseM
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Yes, in this situation the travelling twin will see the distance as only 3 light years, and so if he's going at 0.8c he will see the time as 3/0.8 = 3.75 years. But in his frame, it is the earth clocks which are running slow, so at the moment he passes the planet even less then 3.75 years have passed on earth from his point of view--he would say that the earth clocks have only ticked forward 2.25 years at that moment. But since the earth-twin defines simultaneity differently in his own frame, he will say that at the moment the other twin passes the planet, his clocks have ticked forward by 6.25 years. Again, the "paradox" in the twin paradox really depends on the idea of the two twins meeting up again to compare clocks in the same location--only then does there have to be an objective truth about whose clock really elapsed less time.

(by the way, my name is spelled Jesse rather than Jessie--Jessie is short for Jessica)
 
  • #22
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JESSIE - stop with the first sentence - all the rest is based upon non-proper observations - not real measurements - and that is why relativity weasels out of the issue of time dilation in the one way traveler.

So we have the traveling twin reading 3.75 years on his watch. And we also know that the stay at home twin will have accumulated some time on his earthclock. The signal will take 5 years to be received, and the stay at home twin knows that the proper distance is 5LY which his brother traveled at 0.8c, so the proper time accumulated in the earth-planet frame is 5/0.8 = 6.25 years. Add this to the 5 years in transmission and the earth bound twin should receive a signal in 11.25 years - and since he knows the transmission transit time (5 years) he then can say - my brother's clock ran slower - since he took that long trip he has remained younger than me by 2.5 years.
 
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  • #23
JesseM
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yogi said:
JESSIE
I just told you, my name is spelled "Jesse", not "Jessie".
yogi said:
- stop with the first sentence - all the rest is based upon non-proper observations - not real measurements - and that is why relativity weasels out of the issue of time dilation in the one way traveler.
All of relativity is based on what you'd find if you performed a certain "real measurement". Simultaneity, for example, is based on the idea that each observer synchronizes spatially separated clocks by using the assumption that light travels at the same speed in all directions relative to themself. If the travelling twin is riding on the front end of a giant spaceship 3 lightyears long, and he synchronizes his clock with the clock at the ship's back end by sending a light-pulse out from the midpoint of the ship and making sure the clocks on both ends read the same time at the moment the light reaches them, then at the moment the back end passes the earth the clock on the back end will read 3.75 years (the same time his own clock reads when he passes the planet), but at that moment the earth-clock will only read 2.25 years. So when he says only 2.25 years have passed on earth at the time he passes the planet, this is based on perfectly real measurements. Likewise, if the planet is at rest relative to the earth, then the planet's clock and the earth's clock can also be synchronized by sending a light pulse from the midpoint of the line between them, and making sure that both the clock on earth and the clock on the planet read the same time when the light reaches them. In this case, when the travelling twin passes the planet, the clock on the planet will read 6.25 years.
yogi said:
So we have the traveling twin reading 3.75 years on his watch. And we also know that the stay at home twin will have accumulated some time on his earthclock. The signal will take 5 years to be received, and the stay at home twin knows that the proper distance is 5LY
There is no such thing as "proper distance", you just mean the distance in his own coordinate system.
yogi said:
which his brother traveled at 0.8c, so the proper time accumulated in the earth-planet frame is 5/0.8 = 6.25 years. Add this to the 5 years in transmission and the earth bound twin should receive a signal in 11.25 years - and since he knows the transmission transit time (5 years) he then can say - my brother's clock ran slower - since he took that long trip he has remained younger than me by 2.5 years.
Yes, but now suppose the earth sends a signal in the direction of the travelling twin when the earth-clock reads 2.25 years, at which point the earth will be a distance of 3 light years away in the twin's frame. With a few modifications, the exact same argument you made can be used to look at this from the travelling twin's perspective:
alternate-universe yogi said:
So we have the earth twin reading 2.25 years on his watch. And we also know that the travelling twin will have accumulated some time on his clock. The signal will take 3 years to be received, and the travelling twin knows that the distance in his coordinate system is 3LY which his brother traveled at 0.8c, so the proper time accumulated in the travelling twin frame is 3/0.8 = 3.75 years. Add this to the 3 years in transmission and the travelling twin should receive a signal in 6.75 years - and since he knows the transmission transit time (3 years) he then can say - my brother's clock ran slower - since he took that long trip he has remained younger than me by 1.5 years.
 
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  • #24
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ok Jessica - the earth clock will not read 2.25 years when the traveler (whether it be the front end reaching the planet or the back end reaching earth) completes the journey. The arrival event cannot take less than 5 years in the earth frame even if the traveler moves at c - and since he only moves at 0.8c the arrival event will correspond with an earth clock reading of 6.25 years. Your 2.25 years is a good example of jumping back and forth between what is measured in a frame by a comoving observer what how fast the clock appears to run when it is measured as it passes between two clocks in another frame.

Also - there is certainly a proper distance - the term is used by many authors when referring to a distance measured in the frame of the observer.

I would also disagree that all of relativity is based upon "real measurement" Maybe it should be - and if it were these differences in interpretation would not arise - take a look at Einstein's 1905 paper again ... three times he parenthetically emphasizes ... (as observed in the other frame). Then w/o justification he uses the apparent observations to arrive at real time dilation - As I have said many times on this board..only apparent observations as to how fast time passes in the other frame can be considered reciprocal - real time differences occur, but they cannot be reciprocal ..If between two spacetime events, a clock in a first frame accumulates more time than a clock in a second frame, then the clock in the second frame must accumlate less time than the clock in the first frame. Einstein was never able to explain this .. by 1912 he was certain the twin aging problem had nothing to do with acceleration .. but he still didn't address the problem with a positive explanation... only a negative comment that eliminated turn around acceleration as the culprit.

I know your name is Jesse - I am just twisting your tail.
 
  • #25
Hurkyl
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The arrival event cannot take less than 5 years in the earth frame even if the traveler moves at c - and since he only moves at 0.8c the arrival event will correspond with an earth clock reading of 6.25 years.

You're still falling prey to absolute simultaneity.
 

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