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:
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:
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 traveling 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:
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 traveling 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:
christinono said:
He has to stop when he gets there though.yogi said:
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:
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 traveling 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:
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:
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 traveling 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 traveling twin.yogi said:
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 traveling 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 traveling 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 traveling 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:
I just told you, my name is spelled "Jesse", not "Jessie".yogi said:
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 traveling 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 traveling twin passes the planet, the clock on the planet will read 6.25 years.yogi said:
There is no such thing as "proper distance", you just mean the distance in his own coordinate system.yogi said:
Yes, but now suppose the Earth sends a signal in the direction of the traveling 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 traveling twin's perspective:yogi said:
alternate-universe yogi said:
This is why these conversations annoy me: it started with the twins paradox and morphed into various other scenarios. By constantly changing the scenario, you can confuse an otherwise relatively simple question. In the twins paradox, the accelerations are what tell you which twin is moving. In Jesse's first post he saidyogi said:
Well, that's not the twins paradox anymore. Then you proposed a third scenario:
which involves an acceleration at the beginning (taking off from earth), but then not at the end. I was wrong to say he needed to stop - he doesn't, you already know he's the one moving because he "took off". In Jesse's scenario, which sounds like two ships, you need some way to figure out which one is moving. If it really is just two ships from distant planets who have never met but cross paths, the situation really is symmetrical - until you start defining "stationary" things like planets to reference their movement from.
Well, if you're asking what the Earth clock reads "at the same time" that the traveling twin reaches the planet, then the answer will be different depending on your reference frame. So let's just focus on the reading on the clock at the back of the ship at the moment it passes the earth. Remember, the traveling twin "synchronized" the clock at the front with the clock at the back based on the assumption that light travels at c in all directions relative to himself. So, he just sent out a light pulse from the midpoint of the ship, and made sure that both clocks read the same time at the moment the light hit them. But from the point of view of the earth, this procedure will not result in the two clocks being synchronized. From the Earth's point of view, light travels at c in all directions relative to the earth, so since the back end of the ship was moving towards the point where the light pulse was emitted, and the front end was moving away from the point where it was emitted, this means the light will hit the back end before the front end, and thus the traveling twin's "synchronization" procedure will result in the clock at the back end being ahead of the clock at the front end, from the Earth's point of view. In this case, if the ship appears 1.8 light-years long in the Earth's frame (so that it is 3 light-years long in the ship's own rest frame, and thus in the ship's frame the back end passes the Earth at the same moment the front end passes the distant planet), then the clock at the back end will always appear 2.4 years ahead of the clock at the front end. The back end will take 1.8/0.8=2.25 years to reach the Earth's position in the earth-frame, and it will have ticked forward by 2.25*0.6=1.35 years in that time, so the total time it will read at the moment it passes the Earth is 1.35+2.4=3.75 years, which of course is the same time that the clock at the front end reads at the moment it passes the planet. So by the ship's definition of "same moment", the front end passed the planet at the "same moment" that the back end passed the earth, and both frames agree that when the back end passed the earth, the clock on the back end read 3.75 years while the clock on Earth read 2.25 years.yogi said:
Of course that's true, the key words being "in the Earth frame".yogi said:
Yes, all correct. But the thing to note is that in the Earth's frame, the event of the back end passing the Earth happens well before the event of the front end passing the planet. But because the traveling twin considers the clocks on both ends to be synchronized, then in his frame both these events happened at the same time. And the situation is symmetrical, because the way the earth-observer decides what reading on his own clock corresponds to the time the distant front end of the ship reached the planet is to have another clock sitting on the planet, which he "synchronizes" with his clock on Earth using exactly the same light-pulse method that the traveling twin used, except that he assumes light travels at the same speed in both directions relative to himself (which means from the traveling twin's point of view, the clock on the planet is ahead of the clock on Earth by 4 years). This is what I meant by saying all of relativity is based on "real measurements", it's all based on noting the times on clocks next to each event.yogi said:
I've never heard this term, but I googled it and you're right that some people use it. It seems like confusing terminology, because "proper time" is a time interval as measured by an observer, even an accelerating one, whereas this definition of "proper distance" just means length as measured in an inertial observer's reference frame, so it doesn't really seem analogous to proper time.yogi said:
Well, see above. 2.25 years is the time the earth-clock reads when the back end of the ship passes the earth, and at that moment the clock on the back end reads 3.75 years, just as the clock on the front end reads 3.75 years as it passes the planet. And these two clocks were synchronized by the traveller based on the assumption that light travels at speed c in all directions in his own frame, so if you send a light pulse from the midpoint of the ship, both clocks should read the same time at the moment the light hits them.yogi said:
You are not taking into account the physical procedure Einstein gave for how each observer should "synchronize" clocks at different locations which are at rest in his own frame. Once you do this, you get the relativity of simultaneity, and you understand how each observer can measure the other observer's clocks to be running slower than his own. The question of whose clock is "really" running slower is not physically meaningful unless you can think up a physical procedure to decide whose clocks are "really" synchronized, but all the evidence points to the fact that no experiment will pick out a preferred reference frame.yogi said:
This simply isn't true. It is the calculated consequence of time dilation, and that's what explains why it is real. By saying that its not real, you're implying a Universal Reference frame centered around the stationary (Stationary) observer. In actuality, this observer's distance measurement is no more valid than the "moving" observer's distance measurement. In fact, if we use the time in the "moving" frame and the distance in the "stationary" frame, as you suggest, we'll get nonsensical results from our calculations: things like greater than C speed.yogi said:
If he only has one clock, how should he assign time-coordinates to distant events? Einstein based the notion of a relativistic reference frame on the idea that each observer uses a large network of clocks which are all at rest relative to himself, and which have been synchronized using the assumption that light travels at the same speed in all directions relative to himself. Of course, he can also assign time-coordinates by noting the distance something was according to his own rulers and calculating (time he observed light from distant event, according to his own clock) - (distance of event from him, according to his own ruler)/(speed of light)...this will give exactly the same result as if he assigned coordinates using a network of synchronized clocks. For example, as I mentioned before, at t=6.75 years according to the traveling twin's clock he will see the earth-clock as reading t=2.25 years, and he will see the Earth next to the 3-light-year mark on a ruler at rest relative to himself, so if he calculates (6.75) - (3)/(1) he finds that this event should be assigned a time-coordinate of 3.75 years in his own system, just like if he had used a synchronized clock 3 light years away from him.yogi said:
Again, what physical procedure should the earth-twin use to assign a time-coordinate to the even of the traveling twin reaching the planet? Obviously he can't just use the time he sees the traveling twin reach the planet, since light doesn't travel instantaneously. So it seems he has two options--either look at the local reading on a clock sitting on the planet which was synchronized with the Earth's clock using light signals, or do the calculation (time he observed light from distant event, according to his own clock) - (distance of event from him, according to his own ruler)/(speed of light). Either way, the point is that if the traveling twin uses precisely the same procedure to assign a time-coordinate to the event of the earth-clock reading 2.25 years, he will find that it happened when his own clock read 3.75 years, i.e. the moment he was passing the planet. Are you suggesting that the traveling twin should not use the same physical procedure as the earth-twin to assign time-coordinates to distant events? If not, why not? Even if you believe there is an absolute truth about simultaneity, if you have no physical procedure to determine whose definition of simultaneity is the correct one, then you have no reason to prefer the earth-twin's definition over the traveling twin's definition (after all, even if you believe in ether, it is possible that the Earth has a velocity of 0.8c relative to the ether, and that the traveling twin is the one who is at rest relative to the ether).yogi said:
Uh, why in the hell do you think the earth-twin's distance reading is correct while the traveling twin's distance reading is mistaken? Even if there is an ether frame and only measurements made in the ether frame are "really" correct, if there is no experiment you can do to determine which frame this is, then you have absolutely no reason to believe the Earth is any more likely than the traveling twin to be at rest in the ether frame.yogi said:
What page? I am quite sure that Resnick does not say one frame's measurements are objectively true while the others are mistaken.yogi said:
Uh, why can the Earth frame have two clocks but the traveling twin can have only one? That's just silly and arbitrary. Especially since I was secretly told by Zeus that it is actually the traveling twin who is at rest relative to the ether, while the Earth is moving at 0.8c relative to the ether, so if people in the earth-frame try to synchronize their clocks by assuming light travels at the same speed in all directions relative to them, their clocks will be objectively out-of-sync.yogi said:
Can the Earth also send a radio signal to the traveling twin when his clock reads 2.25 years, so if the twin assumes the signal traveled at velocity c relative to himself, he will conclude that this signal was sent at the same moment he was passing the planet?yogi said:
How exactly does the Earth assign a time-coordinate to the distant event of the muon decaying? Can an observer traveling alongside the muon use the same method to figure out what the Earth clock read at the same time-coordinate (in his frame) that the muon decayed?yogi said:
Yes, from the point of view of an observer moving alongside the muon, the clock in the earth-frame runs slower.yogi said:
Yes, the two twins age at different rates. In the muon's frame, the earth-twin ages slower, and in the Earth's frame, the muon-twin ages slower. But since Zeus let me in on the secret that it's actually the muon that's at rest relative to the ether, I know that it's really the earth-twin that aged less. But since there's no experiment you can do to actually determine the rest frame of the ether, and since you aren't tight with the Z-man like me, I'm afraid you'll just have to take my word for it.yogi said:
You do need to do a "simultaneity procedure" if you want to compare J's reading on Earth with Q's reading once he reaches point P. All frames will agree on what Q reads at the moment he reaches P (this is just Q's proper time), but since different frames define simultaneity differently, they will disagree about what J's clock reads "at the same moment".yogi said:
Yes, but you acted as if one frame's definition of simultaneity should be preferred over another's. Without choosing a definition of simultaneity, there is no answer to the question of what J's clock read "at the same time" that Q's clock read when he reached P, so there's no way to decide whose was running faster or slower.yogi said:
No, again you seem to be assuming some notion of absolute velocity. But if you believe in absolute velocity, it is quite possible to believe that the absolute velocity of the Earth was initially 0.8c, and that when Q changed velocity, his absolute velocity dropped to zero, so it is the Earth that is moving while he is at rest. Of course, if you don't believe in absolute velocity, the phrase "he is moving toward P rather than the earth-Planet system moving in the opposite direction" is meaningless (unless you forgot to add the words "in the earth-Planet's frame", but in that case the issue of who accelerated and who didn't would be irrelevant to the question of who is moving and who isn't in this frame).yogi said:
From the standpoint of Q's rest frame, it is completely irrelevant who accelerated and who didn't, either way Q is at rest in this frame and P is moving.yogi said:
No, in Q's rest frame the distance is 3 light years.yogi said:
Again, I don't see how acceleration is relevant.yogi said:
"with reference to the proper frame of the other"? Are you implying that each one's "proper frame" is the frame in which he was initially at rest? That's a nonstandard definition, and it doesn't really make any sense, since both P and Q probably had to be accelerated earlier when they were put in place to be launched by the spring--do you have to consider an object's entire history back to its creation to determine its "proper frame"?yogi said:
What if, two hours before P and Q were launched, P was accelerated but Q wasn't? Would this break the symmetry somehow? Or if you're allowed to pick an arbitrary starting time for each object, with each one's "proper frame" being the object's rest frame at this starting time, then what if we pick a starting time after both were launched?yogi said:
You need to explain the details of your "the one who didn't accelerate is the one whose frame we must use" theory. For example, what about the fact that the Earth is constantly accelerating in its orbit, does that make a difference? What if two objects have been traveling at constant velocity for a million years, but the first one accelerated 1,000,001 years ago while the second acccelerated 1,000,002 years ago, does that somehow obligate us to look at things from the second object's frame?yogi said: