UglyEd said:I know that the faster something moves the slower relatively it experiences time. As in if i had a twin brother and at birth he was put into a spaceship traveling at half the speed of light, and I stayed on Earth moving a lot slower. When I reached 30yrs old. My brother would have only aged 15yrs? Right. If so is my brother really 30yrs old?
UglyEd said:This is totally hypothetical, but what if at the start of the universe there were 2 clocks. One clock was launched at and continued to move close to the speed of light. The other clock remained totally stationary.
Presumably you mean that both clocks are checked at the same moment? The problem with this is that different reference frames in relativity define simultaneity differently, meaning that two events that happen at the same time-coordinate in one frame happened at different time coordinates in another. So in one frame the event of clock A ticking 10 o'clock could happen "at the same time" as the event of clock B ticking 11 o'clock, meaning that in this frame clock A ticked slower, but in another frame the event of clock A ticking 10 o'clock could happen "at the same time" as the event of clock B ticking 9 o'clock, meaning that in this frame clock B ticked slower.UglyEd said:Then after a long period of time, the time on the 2 clocks were checked. Of course the clocked that had been moving would show less time had passed.
Yes, if the clocks are in the same location then all reference frames will agree on which one is behind. But if they were originally flying apart as UglyEd said, then for them to meet again at least one would have to accelerate in order to turn around (which involves changing velocity), so then you have another version of the twin paradox, where it will always be the clock that accelerated that's behind when they meet. You mention the geometry of the universe, and it's true that it is possible for two clocks to fly apart and meet again without either one accelerating if spacetime has an unusual geometry--in this case it'll depend on how their paths relate to the geometry of space, see this thread for a discussion of the issue.Giulio B. said:what about if the 2 clocks at the moment of measuring would be stiked together (maybe for a strange nonlinear geometry of the universe...that allowed them to meet after that time and that distance)
however in that case we could measure the 2 events like almost simoultaneous right?
-Job- said:The only thing that troubles me about the twin paradox is the question of why one twin would age faster than the other. I understand that only one twin is accelerated, but i thought acceleration, like velocity, was a relative concept. In this manner it seems that acceleration isn't relative but more like a property of matter, a hidden variable, so you can understand my confusion. Would a relative concept be responsible for a non-relative effect?
Just think of the fact that you experience G-forces when you accelerate, like how you're thrown forward when a car brakes, or pushed backwards into your seat when it speeds up (both are kinds of acceleration, since in physics 'acceleration' just means your velocity is changing, whether increasing or decreasing or just changing direction at constant speed). If you're in a capsule in space moving at constant velocity you'll be weightless, but if it accelerates, you'll feel these G-forces, you could measure them just by standing on a scale.-Job- said:I don't have a pendulum else i definitely would, in the meantime i'll take your word for it.
In any given inertial reference frame (inertial = not accelerating), the rate a clock is ticking depends only on the clock's speed at that moment in that frame. But since different frames see the same object having different frames, they also disagree about the rate a given clock is ticking. If you have two clocks A and B moving relative to one another, you can find one frame where A is moving faster and therefore ticking slower than B, and another frame where B is moving faster and ticking slower than A. Both frames are equally valid, there's no single truth about these things according to relativity.-Job- said:I have a question though. I'm assuming that time slows down for an object only while the object is accelerating and that whenever the object stops accelerating and reaches a constant velocity, time stays "slow"
You can certainly use your acceleration to figure out how much your velocity has changed in the frame you started out at rest in--for example, if your ship starts out docked to a space station and then accelerates away, you can figure out your speed relative to the space station by measuring your acceleration. But there's nothing that says you have to analyze the situation from the space station's frame, you could also analyze it from the point of view of a frame where the station and the docked ship were originally traveling at 0.8c, then the ship's acceleration caused it to come to rest while the station continued to move away at a constant velocity of 0.8c. In this frame, the ship's clock sped up during the acceleration, since its speed was decreasing, while the station's clock ticked at the same constant slowed-down rate.-Job- said:But this suggests I'm able to measure the acceleration that got me to my current velocity by examining the swing of my pendulum and determine the velocity that i am traveling at, and velocity is a relative concept so i don't believe it is determinable without a reference object, or no?
-Job- said:I don't have a pendulum else i definitely would, in the meantime i'll take your word for it. I have a question though. I'm assuming that time slows down for an object only while the object is accelerating and that whenever the object stops accelerating and reaches a constant velocity, time stays "slow", otherwise if it didn't stay "slow" and i were to survive an acceleration to c taking place in less than a minute, then no matter how long i might travel at c, i would age at the same rate as a stationary individual because time would go from "slow" to "normal" since my acceleration would now be 0.
But this suggests I'm able to measure the acceleration that got me to my current velocity by examining the swing of my pendulum and determine the velocity that i am traveling at, and velocity is a relative concept so i don't believe it is determinable without a reference object, or no?
Er... remain stationary to what?
UglyEd said:I mean as in. When ever the universe started. Say with th BB. One clock never moved. The other was launched out at near C. Like I said this is hypothetical.
Also is it true or do I have a misunderstanding? That if something moves at C time stops for it?
In any given inertial reference frame, the rate a clock slows down at any given moment depends only on its velocity. So, if you have a clock that moves at constant velocity for the outbound leg, then abruptly switches velocity and after that travels at constant velocity for the inbound leg, the total amount of time dilation between departing and returning could be calculated by (amount of time the outbound leg lasts in my frame)*(time dilation factor based on speed during outbound leg in my frame) + (amount of time the inbound leg lasts in my frame)*(time dilation factor based on speed during inbound leg in my frame). Even if this is calculated in different inertial frames with different opinions about how long each leg of the trip lasts and how fast the clock was moving during each leg, all the frames will get the same answer for the total amount of time elapsed on the clock between departing and returning. And if we assume this clock departed and returned from a clock that was moving inertially, all inertial frames will also agree on the amount of time ticked on the inertial clock between these two events--and the answer will always be that the clock that changed velocity has elapsed less time than the clock that didn't, no matter what frame you look at the problem in. So even though the amount of time dilation on the non-inertial clock is based on its velocity at different times, the fact that it changed velocity (accelerated) does explain why it elapsed less time.whizmd said:Most explanations of twin paradox invoke acceleration to explain time dilation. Although it is clear that accleration is not the cause of time dilation and the real cause is the velocity. Time dilation is calculated using velocity and not acceleration. The original time dialtion equation is totally independent of accleration and gives the precise amount of time dilation.
JesseM said:In any given inertial reference frame, the rate a clock slows down at any given moment depends only on its velocity. So, if you have a clock that moves at constant velocity for the outbound leg, then abruptly switches velocity and after that travels at constant velocity for the inbound leg, the total amount of time dilation between departing and returning could be calculated by (amount of time the outbound leg lasts in my frame)*(time dilation factor based on speed during outbound leg in my frame) + (amount of time the inbound leg lasts in my frame)*(time dilation factor based on speed during inbound leg in my frame). Even if this is calculated in different inertial frames with different opinions about how long each leg of the trip lasts and how fast the clock was moving during each leg, all the frames will get the same answer for the total amount of time elapsed on the clock between departing and returning. And if we assume this clock departed and returned from a clock that was moving inertially, all inertial frames will also agree on the amount of time ticked on the inertial clock between these two events--and the answer will always be that the clock that changed velocity has elapsed less time than the clock that didn't, no matter what frame you look at the problem in. So even though the amount of time dilation on the non-inertial clock is based on its velocity at different times, the fact that it changed velocity (accelerated) does explain why it elapsed less time.
You can think of this as a "geometric" property of spacetime--if you graph space on one axis and time on another, then the worldline of an inertial clock will always look like a straight line, while the worldline of a clock that moves away from the inertial clock, then instantly changes velocity and moves back towards it, will look like a bent line. The fact that the bent worldline between two events (the events of the two clocks departing from a single location and later reuniting at a single location) will always have less proper time (time as measured by a clock taking that path) than a straight worldline between the same two events is analogous to the fact that if you draw two points on a piece of paper, a straight line between them will always have a shorter length than a bent line between them.
whizmd said:.
Another way to eliminate the role of acceleration is to have the twins both start the journey together. Both twin A and B can accelerate to near speed of light say in one week. After one week of accleration twin B immediately decelerates at the same rate and acclerates back to return home and then decelerates to stop. Twin A continues for a journey of 10 years and then does the deceleration accleration deceleration routine to return home after another 10 years. In this way the accleration is taking only 4 weeks total for each twin (acclerate decelerate accelerate decclerate one week each = 4 weeks) However it is exactly symetrical for both the twins. Only difference is that Twin A differes from Twin B in that he travels for 20 years at uniform velocity. Now you expect Twin A to be younger due to effect of time dilation, don't you? We have succesfully removed the effect of accleration (it is same for both the twins). So what causes time dilation then? Motion through space? I have the answer to that But I would like to see yours?
Good luck
