the twins paradox
It is true that the one that traveled is younger, is this a fact or it is a paradox
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.cire said:It is true that the one that traveled is younger, is this a fact or it is a paradox
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.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.
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.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.
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.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."
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, [...]
He has to stop when he gets there though.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."
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).russ_watters said:He has to stop when he gets there though.
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.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.
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.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.
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: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
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?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
I just told you, my name is spelled "Jesse", not "Jessie".yogi said:JESSIE
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:- 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.
There is no such thing as "proper distance", you just mean the distance in his own coordinate system.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
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: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.
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.
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.