Same old twin paradox

  1. Hai ,I am new to the forum.
    I have some basic questions regarding the same old twin paradox.
    Twin A stays at earth and Twin B is the traveller.
    from the A,s frame we all agree that Time is dilated for B because it is moving(relative to A) near to the speed of light.
    Now switch on to B,s frame.from B,s frame we have to agree that A is moving(relative to B-in opposite direction).So obviously,A,s time also should be dilated as per SR.
    Do this dilation cancell each other ,and they will be of same age when they meet again?.
    This is a thought experiment only.So i am expecting some logical answers (not mathematical)which can help me to get out of my ignorance.
     
  2. jcsd
  3. No only the twin who is actually moving will age slower, an easy way to imagine this is that the square of your velocity in space plus the square of your velocity in time will equal the square of the speed of light.

    I know you didn't want maths but this is very basic.

    Time velocity2 + Spatial velocity2 = C2

    Think of it a bit like a triangle where the sum of the hypotenuse is equal to the sum of the squares of the other two sides, each twin has a different shaped triangle, they still follow the same equation that rules the universe.
     
  4. I am really sorry.what did you mean by actually moving.Do you mean some energy should be involved(like the thrust of rocket) for time to be dilated?.or is it simply (as name of theory suggests-Special relativity),as i understand,only because of relative motion.
     
  5. I think they will both experience some time dilation, because they are both moving relative to space-time.

    when Tzemach said

    he was referring to the one that was moving the fasted relative to space-time.

    Im not cocmpletely sure, but thats how i understand it.


    - James
    - Loughborough Uni
     
  6. cristo

    cristo 8,394
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  7. Hey guys!

    For an object that is in MOTION, as it approaches the speed of light, it causes time to run slower for the object, compared to a stationary object. If the moving object were a person, they would age slower and their stationary identical twin would age faster.

    This can prove difficult, but you need to distinguish between A (from original post) moving RELATIVE to B, and Time Dilation of A relative to B due to the motion of B.

    Although B is actually in motion, From B's reference frame, you can say that A is moving relative to B. NewTonn appers to understand this adequately.

    Because of B's motion near the speed of light, time runs slower for B relative to A, where A is 'normal time'. This is taking A's refrence frame. For our twins, B ages slower and so twin A is older when twin B returns.

    Taking B's reference frame, now it has 'normal' time, and time can be considered to run faster for A. For our twins then, A ages faster, and so A is still older than B when twin B returns... nothing to cancel out.

    Gawsh I hope I didn't confuse you more.

    Cheers
     
  8. jambaugh

    jambaugh 1,799
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    Gold Member

    The key points to concentrate on when parsing the Twin paradox is that the "when" at which one is comparing their ages changes as you consider the two frames of motion. You compare their ages "at the same time" of course. But now in SR "at the same time" i.e. simultaneity changes as you change velocity frames.

    Each twin sees the other as younger because each twin's slices of "right now" through space-time is at an angle relative to the other's.

    Doe that help? Let me add that this is not "just a matter of perspective" but a physical effect in that if the traveling twin later comes to a stop relative to Earth he will in fact be younger. Contra-wise if the twin left on Earth later catches up with his brother's speed so that they are again at rest to each other then he will be the younger.

    Since space and time are unified now space travel implies time travel in a minor way. As I measure distance and duration the faster you travel through (my) space, the faster you also travel through (my) time (speeds here measured relative to your watch). Or as Stevie Miller put it:
    Time keeps on slippin', slippin', slippin', ... into the future!
     
    Last edited: Jun 24, 2007
  9. cristo

    cristo 8,394
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    Well, you managed to confuse me, and I'd like to think that I know what I'm talking about!!

    I like to try not to use phrases such as "speed causes time to run slower" as this is ambiguous, and could be taken to mean that a moving observer's proper time will change, which of course is not true.

    The correct way of phrasing such a point is that, if body B is travelling away from the earth, and A is "stationary" on earth then, in A's reference frame, the time taken for B to complete some outward journey is greater than the time as measured in B's reference frame, due to time dilation.

    I would point the OP to the discussion on baez's homepage that I linked to before, as well as standard relativity texts as given on the "relativity on the web" section of the homepage.
     
  10. That's what happens when you get a biological scientist attempting to translate the physics in his mind, into words that make sense... with actual high-class physicists watching... I'll keep trying, though.

    *shies and hides*:uhh:
     
  11. Janus

    Janus 2,367
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    The difference lies in the fact that B has to turn around to return to the Earth.

    Here's an analogy:

    Take two men, A & B. Have them start walking from the same point at the same pace, but in directions 45 degrees relative to the other. Each man measures progress as distance traveled in the direction that he himself is walking at that time.

    How does each man judge the progress of the other? From his point of view, the other man is always behind him. (From A's perpective, B has covered less distance in the direction that A is walking than A has, and vice versa for B.)

    This is the equivalent of our two twins seeing time dilated for each other. Each sees the other's progress through time as being less than his own.

    Now have man B make a 90 degree turn towards man B so that his path will intersect A's. This is the equivalent of Twin B turning around to return to Earth.

    This does not effect the Rate of B's progress as far as A is concerned because B is still walking at a 45 degree angle to A's path after the turn. So when B crosses A's path B will still be behind A.

    The same is true for B after the turn, but what about during the turn? Let's say that A, from B'd perpective was 70 meters behind and 100 meters to the right when he makes the 90 degree turn towards A. As he makes the turn, A will swing into a position 100 meters in front of him and 70 meters to the right. So from his position, A has suddenly jumped ahead of him.

    For twin B this is the same as saying that during the period when he slows down, and then starts his trip back to Earth, from his perspective time speeds up on the Earth.

    Now, man B continues walking in a straight line until his crosses A's path and then turns to start walking in the same direction as A. As he is walking, man A loses some of the head start he got when man B turned, but he never loses it all. B will cross A's path behind A. and when he turns to match A's direction he will stay behind A by a constant distance.

    For Twin B, this means that during his return trip, Earth undergoes time dilation and ages more slowly, but never loses all of the time it gained during the turn-around. When twin B reaches Earth, he brakes to a stop and both Twins continue to age at the same rate again, but with B younger than A from the prepective of both Twins.
     
  12. cristo

    cristo 8,394
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    Well, there are lots of high-class physicists here, but I'm not one of them! No, I just wanted to clear up any potential confusion that that phrase tends to cause.

    Still, your input is very welcome here!
     
  13. jtbell

    Staff: Mentor

    To make this more explicit, each man has to look backwards over his shoulder in order to see the other. This is obviously impossible if both men face in the same direction, but if they face in different directions, as in this example, it follows naturally from the geometry of the situation.

    By analogy, our traveling twins are "facing in different directions" in spacetime, including time as a dimension along with the three spatial dimensions. When the traveling twin turns around and begins his journey home, he also "turns" to "face in a new direction" in spacetime. This causes his "perspective" on the stay-at-home to change abruptly (including the age of the stay-at-home in the traveler's reference frame), even though the stay-at-home has done nothing himself, and notices nothing happening to him.
     
  14. JesseM

    JesseM 8,490
    Science Advisor

    The basic equations of special relativity such as the time dilation equation only apply in inertial reference frames--frames which are not accelerating, so an observer at rest in such a frame feels no G-forces. In the twin paradox, if the traveller moves away from the Earth for a while and then turns around to return so they can compare ages on Earth, then he must accelerate during the turnaround, so he doesn't have a single inertial frame of his own throughout the journey, and therefore he can't use the ordinary time dilation equation to predict how much the Earth twin will have aged.
     
  15. JesseM

    JesseM 8,490
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    In relativity there is no such thing as being "actually in motion", and there is no objective truth about which of two inertial observers is "actually" closer to the speed of light. Speed can only be defined relative to a particular frame, and the laws of physics work exactly the same in every inertial frame; so if two observers are moving apart at relativistic speeds, each one can consider themselves to be at rest and the other to be moving close to the speed of light, neither perspective is more correct than the other.

    If the velocity that two observers are moving apart is changing, though, there is an absolute truth about which one is accelerating--it'll be the one that experiences G-forces. Unlike velocity, acceleration is absolute in SR.
     
  16. Taking B,s reference frame,i couldn't understand,why time is running faster for A.in this frame,A is moving as faster as B(as viewed from A's frame) in space time,so his time should run slower as much as that of B (as viewed from A's frame).
     
  17. Time dilation is caused due to the relative motion(between two inertial frames) isn't it?.In this case One of the frame is accelerating.So the equation for time dilation is not apllicale to both frames.or if there is any equation of time dilation between one inertial frame and one accelerating frame,it is applicable to both in the same manner.
    So when traveller turns around and accelerate,whatever equation applicable for traveller,is true for the men at rest also.

    Finally both will give the same result of same ages for both twins.Am i correct?
     
  18. So you mean , acceleration is the cause for less ageing of B.
    Then i think either we have to re-define time dilation(including equations),or we have to admit that time dilation is not real and only a perspective.
    it is as in the case of ball dropped vertically from a moving train.
    For the man inside train will see the ball falling vertically.
    the man standing at platform will see the ball falling in a parabola.
    A man in sun will see the ball falling in a different path,with respect to the earths motion around sun.
    A man at centre of milky way will see the ball falling in a different path,incorporating both the movement of earth around sun and sun around galactic centre

    and so on....until the real and true path.Everybody is seeing the same event from their own perspectives.The event is one and same but the position of observer's in space are different.if we consider light is transmitted instantaneously,you will find that,the time and interval of event is same for all observers.The confusion comes when we introduce the time for light to reach the observer.
    Let us take the case of the duration of event.
    let the ball took 1 sec to reach the floor of train(as per nearest observer).
    consider an observer far away,and is moving at a speed of 150,000km / sec.
    let the image of dropping of ball from hand reach him after several years.The image of ball hitting the floor should reach him after 1 second.but at this time he is not in that position in the space(he is travelling at a speed of 150000 km/per hour).So the image has to travel again 150,000km to reach him.but when image reaches there (in half seconds).he is 75000 km ahead of the image. and so on...and finally when image reaches him it will take more than the actual duration of event.
    if we analys this properly, we can find out that the observer inside the train see a vertical path of ball because of his relative position in space with respect to ball.
    similarly the far away observer(Moving at 0.5c) ,see a more duration for the event because of his relative position in the space when he sees the begining of event and the end of event.
    in other words,there is an absolute path for an event and there is an absolute time for event.ONLY THE PERSPECTIVE MATTERS.
     
  19. pervect

    pervect 7,878
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    newTonn, have you read any of the FAQ's about this topic? For instance "The sci.physics.faq about the twin paradox"?

    This really has been covered before, and you don't seem to be grasping the idea that it's the relativity of simultaneity that is necessary and sufficient to resolve the "paradox".
     
  20. Janus

    Janus 2,367
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    Only from B's perspective, From A's perspective it was only B's relative motion that led to the age difference.
    The equations are perfectly fine as they are, Both A and B have to use them during the those periods when their relative motion is constant in order to get the correct age difference at the end. Besides, they have been verified by experiment.
    And if you want to say that time dilation is not "real", then you have to say that the age difference at the end of the trip is not "real" and that the results of said experiments are not "real".
    There is no "real and True path", you can only measure the path relative to some reference system, and no refernce system is "truer" than another.
    The effect that you mention is not what Relativity is based on but is instead called the Doppler effect. It is factored out when dealing with Relativistic effects. Time Dilation is what is left over after you account for light signal delay.

    If you try to hold on to the concept of absolute time, you will never grasp Relativity, as Relativity abandons that concept.
     
  21. JesseM

    JesseM 8,490
    Science Advisor

    The time dilation equation can be used for an inertial observer to calculate the elapsed time on any clock, accelerating or inertial (if the clock is accelerating you have to integrate the time dilation equation--see below). And if two observers are moving apart inertially, time dilation works the same way for both of them--each observer measures the other observer's clocks to be running slower than their own, according to their own set of rulers and clocks. If this seems impossible, check out my thread An illustration of relativity with rulers and clocks, where I show two systems of rulers and clocks moving alongside one another at relativistic speeds, and show how each one measures the other ruler to be shrunk and the other ruler's clocks to be slowed down and out of sync.
    The twin who accelerates cannot use the same equation--specifically, he can't assume that if his own clock has elapsed a time of T since leaving Earth, the Earth-twin's clock will have elapsed a time of [tex]T \sqrt{1 - v^2/c^2}[/tex], where v is his speed relative to the Earth. This equation will work for all inertial observers, though. If the travelling twin has the same speed v relative to the Earth both while he's travelling away from Earth and while he's returning to it (and the acceleration is treated as instantaneous), then if the Earth twin ages by an amount [tex](t_1 - t_0)[/tex] from the moment of departure [tex]t_0[/tex] to the moment they reunite [tex]t_1[/tex], the traveling twin will have aged by only [tex](t_1 - t_0) \sqrt{1 - v^2/c^2}[/tex]. If we don't want to treat the acceleration as instantaneous, and instead take into account the possibility that the traveling twin's speed v(t) relative to the Earth is changing throughout the journey, then the amount the traveling twin ages between departing and returning will be given by the integral [tex]\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt[/tex]. But again, these equations only work for calculating the amount of aging when the velocity and times are defined in terms of an inertial frame like the Earth-twin's rest frame.
    If they both use correct equations they'll both predict the same answer for their ages when they reunite at Earth, but the accelerating twin cannot use the standard SR equations like the time dilation equation to calculate the answer.
     
    Last edited: Jun 25, 2007
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