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Twin Paradox revisited 
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#19
May1211, 06:03 PM

P: 103

Is the rate of seperation mentioned (.5c) and proper velocity as mentioned by your link? 


#20
May1211, 06:12 PM

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P: 16,947

Look, this isn't complicated. Pick any reference frame you like (inertial or not) and evaluate the integral I provided in post 8. If you don't have enough information to evaluate the integral (as in this case) then your problem is incompletely specified. 


#21
May1211, 07:01 PM

P: 103




#22
May1211, 07:26 PM

P: 1,280

You can define your speed/direction to be X. You can define your acceleration to be a net change in speed of 1 unit. This net change can be negative or positive. We will say that you accelerate in direction "A." All reference frames will observe that change of speed of 1 unit, regardless of the relative speed of and direction of X. However, all reference frames will not agree on whether or not you slowed down, sped up, start moving, or stopped moving, or changed direction, because the motion is still relative. For example, a frame which measures X as 50 mph going in direction "A" will observe you speed up to 51 mph. A frame which measures X as 50 mph going in direction "B" will observe you slow down to 49 mph. A frame which measures X as 0 mph will observe you to start moving in direction A at 1 mph. A frame which measures X as 1 mph in direction B will observe you stop moving. As you can see, that initial speed of X can be whatever we want, but the net change in speed will always be 1 MPH and is therefore absolute. Acceleration is a change in speed, what the speed started and ended at is relative, but the difference between the two is absolute. The (named) paradox lies in the fact that if they are brought within the same reference frame, they can't perceive one another as being younger, and this is true. However, that can never happen. Bring them back together by accelerating them at equal amounts will render them agreeing on their age (how much time has passed.) An unequal amount of acceleration will make them agree that one is absolutely younger than the other. When they are in the same reference frame, they must observe the same thing, and they will agree on everything. This is because for them to be in the same reference frame after speeding away from one another, one or both must accelerate. If they both accelerate at equal amounts, they agree that they are the same age. If A accelerates more than B, they will both agree that A is the younger twin. If B accelerates more than A, they will both agree that B is the younger twin. Does that make sense? 


#23
May1211, 08:15 PM

P: 1,011

The twin on the rocket is affected by the thrust of propellant, while the twin on the Earth is not. Dynamical effects occur on the first twin which do not occur on the second. The motion of the twin on the Earth is not changing as rapidly as the motion of the twin in the rocket ship. The paradox is solved by GR. Devices have been developed to measure the effects of acceleration. Simply measuring a force is sufficient for such a task, which is what accelerometers do. Distance itself doesn't need to be measured. Proper acceleration is NOT relative to an observer, but coordinate acceleration is. The proper acceleration is what you should consider as relevant to the Twin Paradox. Basically, it is the acceleration received by physical, nonfictitious forces. Such forces involve the transfer of kinetic energy to or from a given body. Such forces are defined by direct interaction on the body. This is what causes the difference between the twin on the Earth and the twin on the relativisticallyfast rocket. The rocketing twin has gained much more kinetic energy in the process, and is therefore mechanically subject to a literal slowdown of its clocks. This effect persists even after acceleration has stopped. For example, the time dilation of relativisticallyfast mumesons from outer space persists in such a manner that even after they have accelerated, their clocks have slowed down to the effect they do not decay until the particles collide with the Earth's atmosphere. This is a physical effect not attributed to the their coordinate motions relative to some arbitrary observer. The acceleration requires a literal build up of inertial mass. So the rocket twin somehow gains inertial mass. The mass is derived by the energy released by the reaction causing the rocket to gain momentum. The Earth twin has no such contribution to its inertial mass. 


#24
May1211, 08:58 PM

P: 1,011

If you do not take GR into account, what you tend to end up with is a misleading notion of symmetry, where the distance between the twins is understood to be the same for both, and that the rate change of this distance is the same for both, and that the rate of change of the rate change of this distance is the same for both. This is where most people get it wrong. The truth is that proper acceleration is what matters in this situation. That is to say the acceleration which can be measured with the body being accelerated. It is the consequence of physical forces acting on the body in question. SR simply doesn't deal with proper acceleration. That's one the reasons why GR is relevant here. When you say this: "In A's reference frame B is aging slower. In B's reference frame A is aging slower. They don't agree, because they are in different reference frames. Bring them back together in the same reference frame, and they must agree (read on.)" The first three sentences relate to a SpecialRelativistic effect (connected to relative velocity), while the last one is the result of a GeneralRelativistic effect (connected to accumulated time delay that results from an increased inertial mass due to accumulated proper acceleration). Another note I would like to make is on this use of the word "agree" that we see so often when comparing observers. The person on the Earth saying that he/she aged 10 microseconds more than the person on the rocket, who in turn says that he/she aged 10 microseconds more than the person on the Earth is not agreement between the observers, but nor is either claim in agreement with the reality. What is 10 microsecond "less aged" in this case is the image received by other observer. It makes no sense to say that other person aged 10 microseconds less just because his/her image took 10 extra microseconds to get to the observer. This SpecialRelativistic effect, which is misattributed to a "reduced aging rate" of the "other" twin, is simply due to the fact that the light, just like any other wave, is subject to the Doppler effect. To claim that there is a difference in aging occurring with relative velocity alone is just as errant as saying that the aberration of light means that the observed object is physically distorted in a way depending the reference frame. They are only time delays (http://www.youtube.com/watch?v=wteiuxyqtoM) and optical distortions (http://www.youtube.com/watch?v=JQnHTKZBTI4) of the image received. Observing the image of the object the moment it is received is not evidence of a simultaneous event any more than the sound of thunder or the image of lighting is evidence of a simultaneous event. 


#25
May1211, 09:28 PM

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#26
May1311, 06:47 AM

P: 3,181

A careful reading of the first paper on this topic may be useful to avoid this kind of misunderstandings. You can find a translation here: http://en.wikisource.org/wiki/The_Ev...Space_and_Time (in particular p.46  53) Cheers, Harald 


#27
Feb912, 11:43 AM

P: 103

An accelerometer is a device that measures proper acceleration, also called the fouracceleration. For example, an accelerometer on a rocket accelerating through space will measure the rate of change of the velocity of the rocket relative to any inertial frame of reference. Thus it uses and extenal FOR to determine acceleration so how can acceleration be deemed "absolute" when time and velocity are not deemed so? (just to clear things up, i do believe that absolute acceleration is properly defined and can be attained, my argument is that the componenets that make up acceleration should also be as well based on this logic) 


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