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The twin paradox

  1. Jun 30, 2003 #1
    Can anybody PLEASE explain the twin paradox to me? I just don't get it!
  2. jcsd
  3. Jun 30, 2003 #2


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    The formulae of Special Relativity generally only hold in inertial reference frames.

    A frame with any acceleration involved is not an inertial frame.

    Therefore, the formulae of Special Relativity generally are not valid for accelerating reference frames.

    Thus, applying the formulae of Special Relativity to an accelerating reference frame will typically produce paradoxical results.

    The twin paradox is (typically) the above sequence of events. Fred stays on earth, George goes off into space on a rocketship, turns around, and comes back. The formulae of Special Relativity (when applied to Fred's reference frame) says that Fred will be much older than George. However, if you apply them to George's reference frame, Fred will be much younger. Contradiction!!! However, George must accelerate (i.e. turning around), so you cannot apply the formulae of Special Relativity to George's reference frame.
  4. Jun 30, 2003 #3


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    Think of it this way one twin must accelrate into the others frame of referencene which breaks the symetry. General relativity deals with accelrated frames of references.
  5. Jun 30, 2003 #4
    **ready to jump off a cliff**


    I still don't understand...

    WHY does movement make one's time flow slower?
  6. Jun 30, 2003 #5

    It is not an intuitive concept. Do a google search on special relativity. Einstein used the hypothesis that the speed of light is fixed for all observers in intertial rest frames to derive certain properties - one of which is as stated.
  7. Jun 30, 2003 #6


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    Tail, you (the person/twin on the space craft) will not feel time slowing down at all it will feel no different than time feels to you now. It is the twin on earth that 'percieves' your time slowing in that he would have aged significantly more than you and the wrinkles on his face and the lack of wrinkles on yours is what is percieved(as well as the fact you can pick up a newspaper in the far future etc.).

    This is one of the postulates involved, roughly stated you cannot distinguish anything differently on a space ship travelling the near speed of light (w/o a reference) any more than you can in the reference frame you're in right now.

    This is all based on the fact that the speed of light is constant not time.

    Last edited: Jun 30, 2003
  8. Jun 30, 2003 #7
    It has been one of the favorite flaps since Einstein published his theory. It was still being debated as late as the 1960s. Physics Today magazine devoted an extensive part of one issue to wrangling pro and con over whether the conclusion was real or not. The consensus of relativists is that it is a real difference. Remember a few things as you puzzle it out.

    1. Light travels through space at a fixed rate of speed independent of the relative motion of source or motion of an observer. That is a postulate of relativity. You can't figure this out if you don't really accept that. Many people, including scientists, have had trouble accepting this lightspeed invariance principle.

    2. Time measurement is properly done by using stationary clocks, both near and far. These can be set up and synchronized using the lightspeed invariance principle. Each observer, both the stay-at-home A and the space-traveler B, ought to use the own clock setups. This is called PROPER TIME measurement. The alternative is to use clocks that are whizzing about at high speeds in space relative to that observer. This is IMPROPER TIME measurement. The theory of relativity assumes that the two types of time may not run in sync. In fact, relativity deduces that there is a rate difference.

    3. Time runs neither fast nor slow. That is because fast and slow are always measurements of something against some reference time. What runs fast or slow are clocks, when they are compared to one another. The clocks that are stationary for an observer tend to run faster than clocks that are whizzing about. Consequently, the PROPER TIME tends to run ahead of IMPROPER TIME when the two are compared for a given experience by one observer.

    4. Clocks in different places that are exactly synchronized for one observer will not necessarily still be synchronized for another observer. This is called relativity of simultaneity. Forgetting it is a common mistake made by people determined to disprove the time effects of relativity. Don't make that mistake.

    5. For cases of accelerating observers (for example observer B in an accelerating spaceship) an appeal to something called the general clock principle is used. It is a small but significant first step toward Einstein's general theory of relativity. This principle says that a system of tangent unaccelerated observer measurements can be used for accumulating time intervals in place of a single truly accelerating system. Each temporary frame is comoving with the actual observer at one instance of time. The computations using the clock principle end up as differential equations obeying the lightspeed invariance principle.

    A book entitled "Time and the Space Traveler" by Marder (unfortunately out of print) sets up and solves the particular case of a spaceship accelerating constantly at 1G away from home station for the first half of a trip, then decelerating at 1G for the next two quarters (which brings the ship speed down to zero and accelerates the first half of the trip back home) and finally accelerating 1G like the first part (which brings the spaceship to rest at home base). Note that the onboard observer experiences only 1G acceleration and no jerks. Marder solves the diffEQ for this and sets it up so that different trip distances can be used (distances to certain stars and galaxies) parametrically. One can also use different experiential acceleration values instead of 1G.

    One last tip: the most rewarding approach to analyzing the twin{1} paradox is Herman Bondi's radar method. In this presentation of the problem, both observers A and B send radar signals toward each other throughout the complete journey. Add up the time intervals for each observer and it produces the right answer beautifully.


    {1} the observers don't really have to be twins. Rather, they need to use identical types of reliable reference clocks, one at rest with A and one at rest with B. What is wanted is the final elasped times of the trip according to each clock.
    Last edited: Jun 30, 2003
  9. Jun 30, 2003 #8


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    First off, you start with the fact that the speed of light(in a vacuum) is a constant for all observers. This comes fromt he fact that the speed of light is dependant on properties of of the vacuum which do not change with movement.

    Thus if you have two observers watching the same light beam, each will come up with the same answer for the light beam's speed with respect to themselves, even if they are moving with respect to each other.

    Now let's assume observer B has a device which sends a pulse of light to a mirror and back. He uses this as a type of "light clock".

    The light would take a path something like this:


    And the time it would take for the light to go to the mirror and back would be one time period.

    Now let's assume that he is moving with repect to observer A in a direction at a right angle to the light pulse. He would still see the light travel from source to mirror and back in one light period.(nothing has changed as far as he is concerned.

    A, however, would see something like this in B's light clock.


    this is because the source and the mirror move while the pulse is crossing the distance between them. Note that the path that A sees the light travel is longer than the path that B sees it travel.

    Since A must measure the speed of light as the same value as B does, this means that, For A, the time it takes for the the pulse to bounce back and forth will be longer. For instance, the same time period that B measures as 1 sec, could be 1.2 sec as measured by A.

    All events that happen for B that are sychronized with his Light clock, must also be synchronized as seen by A. Thus all events for B seem to take longer when measured from A. From A's perspective time has slowed down for B.
  10. Jun 30, 2003 #9
    Yes, I know that the time only is relatively slower. But let's say the time as it is on the Earth (the twin who is here) flows 'normally', and for anyone else it flows faster/slower. So, if time flows 'slower' for the second twin, why? How can moving change the speed of time (from another person's view)?

    I don't think I'll ever understand it...
  11. Jun 30, 2003 #10
    I have some questions related to relativity.
    He experiences acceleration so no longer can he be thought of as the inertial frame of reference (the non changing frame of reference) so if must be concluded that time was progressing slower for twin B (and he will be younger).
    (1)I missed the logic behind this. Why must we come to this conclusion? As Twin B accelerates away from Twin A, Twin A finds increasingly dilated time compared with Twin B. As Twin B turns around, Twin A finds increasingly less dilated time compared with Twin B. When Twin B is at rest with respect to Twin A, time is the same according to both. When Twin B starts accelerating towards Twin A, Twin A finds increasingly more dilated time compared to Twin B. So for the entire trip, according to Twin A, Twin B’s clock ran slow. How’s that?

    (2) What is the ether medium? Would the ether medium constitute absolute space?
    (3) Only masses objects may travel at the speed of light? Does light (a photon) have mass or not? I’ve heard it can be considered to consist of matter with mass. Say light bounces off a mirror. Does this happen instantly? Can light go from v=c to v= -c in an instant? That would be an infinite acceleration, and if light has mass, that would imply an infinite force. But if light has no mass, then there is no force to effect an infinite acceleration.
    (4) Say a friend of mine was traveling at the speed of light with reference to me. Would any instant of time according to him be equivalent to an infinite amount of time according to me?
  12. Jun 30, 2003 #11


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    1) beacsue Twin B was travelling from the unaccelrated reference point of Twin A

    2)Aether is an old concept that became redunant at the turn of the 19th century and was thought to be the medium that light waves travelled through and yes it would constitue absolute space.

    3)No, nothing may be accelrated to the speed of light, photons don't accelrate to the speed of light so they may travel at that speed is one way of looking at it. Photons have no rest mass which is the common defintion of mass though they do havce relativistic mass (though the idea of relativistic mass is barely talked about these days).

    4) What your describing is an impossibilty, but using the Lorentz trabnsformation for time you would find that he would not experince any change of time compared to you while he is travelling at c.
  13. Jun 30, 2003 #12


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    A lot of good stuff here. I'll post this one thought since I'm not feeling that hot today.

    The postulates of special relativity:

    (1) The laws of physics are the same in all inertial frames of referance
    (2) The speed of light is independant of the source.

    The second one, of course, means that no matter what inertial frame you're in you'll always measure (from an inertial frame in flat spacetime) the speed of light to have one and only one value - c = 2.998x10^8 m/s

    With that you can prove that a moving clocks run slower compared to a stationary clock (a stationary clock is defined as an ideal clock which is at rest in the observers frame of referance).

    As for the proof - I wrote this one up since it's a nice one to use - simplicity itself.


  14. Jul 1, 2003 #13
    Ok, that's it. You've been very kind, but I give up. I obviously need to study general relativity first!

    Well, thanks anyway! :smile:
  15. Jul 1, 2003 #14


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    No, general relativity relies on special relativity you need to know SR before you can study GR. GR is alot more complex than SR.
  16. Jul 1, 2003 #15
    Wait, I've an idea...

    A question: does travelling warp time?
  17. Jul 2, 2003 #16


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    Your always travelling at the speed of light. The thing is you travel at the speed of light through both space and time.

    Think of space and time as the two trays on a balancing scale, w/ one one tray representing space and the other tray representing time. When you are standing completely still in space (doubt this is possible but for simplicity sakes) you are travelling only in time and not space, which would be like putting say 100 lbs on the 'time tray' and nothing on the 'space tray.'

    However, when you are moving spatially you are not travelling completely in time. Your time component is reduced the faster you move. The faster you move the more weight gets thrown on the 'space tray'AT THE EXPENCE OF THE WEIGHT ON THE 'TIME TRAY.' As you increase your speed (adding more and more weight to your 'time tray' from your 'space tray') your travelling less through time and more through space. So you see travelling through space at the speed of light would be like putting the 100 pound weight entirely on the 'space tray' and nothing on the 'time tray.'

    The 100 lbs. is really 300 000 km/s (the speed of light). When you are spatially moving near the speed of light you significantly change the amount of time travel through according to previous posts, does that answer your question enough?
  18. Jul 2, 2003 #17


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    I should quickly mention that the scale model is false in the sense that it would imply that space and time are equally proportional to one another and they're not. Simply put going half the speed of light does not mean you reduce time by a half. You have to travel pretty close to the speed of light to start yielding significant time change but the exact numbers I'm not quite sure of.
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