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A twist on the twin paradox, help me figure this out!

  1. Sep 8, 2003 #1
    [SOLVED] A twist on the twin paradox, help me figure this out!

    Relativity question:

    A twist on the twin paradox (that again??) Yes, that again.

    First, it took me a while to accept that the acceleration breaks the symmetry of special relativity and accounts for the difference in aging of the twins when one returns to the other. But finally, I am able to see that their frames of reference are in fact different due to this acceleration, and grudgingly accept it, because it is still hard for me to understand. I don’t know any relativity math, but I’m sure ole Einstein came up with a formula that explains this perfectly. Now let me propose a thought experiment that I still don’t understand.

    Two people living on two ‘planets’, surrounded by a vacuum. Both planets have equal net negative charges, so that they can be equally acted upon by a magnetic force. Starting with both planets at rest and their perfect wrist watches are in sync. They are in the same frame of reference with respect to motion.

    Now, let’s turn on a large negative magnetic field that is directly in between the two planets, and acts to uniformly accelerate the two planets directly away from each other. Both people feel equal forces, of course. Continue this until they are almost at the speed of light and then turn the field off and let them coast. (Note: the magnetic field stuff has nothing to do with the physics question here, I am just using a plausible method of doing my experiment to avoid confusion.)

    Questions:
    1. When accelerating, what are their clocks doing relative to each other. My logic tells me that they must still be in sync, because if you were to immediately reverse the field and bring them back together they would have both taken the exact same journey, acceleration and all, and so one can’t have aged more than the other. If one were to be older, which one would it be?

    2. Now we’re coasting, so each person can argue they are at rest and the other is moving. Now, each person could look at the others watch with an amazing telescope (oh yeah, their planet is equipped with one of those too!), and see the other’s watch going slower than their own. This is basic special relativity, is it not? Is this correct?

    If so, then the next part of the experiment really baffles me. If not, then please explain, but let me finish the experiment.

    According to what I understand of SR, now that they’ve coasted a bit, their watches will no longer be in sync. Now, let’s reverse the magnetic field (which is quite strong and can reach the planets without any problem at all, just a wee bit bigger than a typical refrigerator magnet… ). Now the planets are accelerating, or decelerating relative to each other and come to a relative halt and then accelerate toward each other. All the same concepts apply, we let them coast back together (further increasing the difference in their watches, not resolving it, because time dilation has nothing do do with the direction of the motion, just the motion itself) and then stop them again where they started. All logic tells me that their watches must, must, MUST be the same, but what I know of SR, during both coasting periods, their watches weren’t in sync. In fact, each would have measured the others as going slower than their own, equally. Both can’t be right, because for all practical purposes they are equal. How would you distinguish which would go faster or slower?

    I think my logic is correct, and their watches will be the same, however I don’t understand why under the laws of relativity. Will someone please explain this in layman’s terms, as I don’t know the math formulas, nor do I care to!

    Thanks!
     
  2. jcsd
  3. Sep 8, 2003 #2

    chroot

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    Your misunderstanding is in this statement. There is no way to say two clocks are "in sync" unless they are in the same inertial reference frame. The concept of "in sync" has no place when used across two different frames of reference. Just because each observer sees the other's clock going slower does not mean the clocks are getting "out of sync."

    In your problem, the two clocks will experience the same proper time along their journeys, and will agree with each other when reunited.
    Why do you not care to? It's no harder than basic algebra. Point of fact, you'll never really understand anything about relativity in the absence of any mathematical skill.

    - Warren
     
  4. Sep 8, 2003 #3

    Chi Meson

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    There is no difference and it does not matter that one planet is accelerating from the other, or both are accelerating away from one common central point. THe observed effects one sees the other go through are a function of the relative velocity between them. So you are correct with that statement: it's basic relativity.

    BTW. THere is no magnetic "charge." a magnet will not attract or repel a charged object. It COULD cause it to go in a spiral though. Other topic though.

    As the two planets moved away, they would see each others clocks go slow. As Chroot pointed out, this means nothing as far as being "in synch" or not. The whole idea of "in synch" is now meaningless.

    One way to think of why this is not paradoxical: When you see an airplane in the sky, it's small right? But when you're in an airplane looking down, the people on the ground are small. Isn't this a contradiction? No it's a matter of perspective. When travelling at relativistic speeds, there is a "perspective" effect on the time that you observe others are experiencing.
     
  5. Sep 9, 2003 #4

    Janus

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    Both will measure the other's clock as moving at a slower rate whil ethey are accelerating apart.

    okay,
    But time dilation has a lot to do with th e direction of acceleration and the the distance between the accelerating objects. During the part when the planet's are decelerating and accelerating twoard each other they will see the other's clock as moving much faster. How much faster depends on the magnitude of the acceleration and the distance btween them. In this instance, this faster rate period will completely counter the period when thay saw each other's clocks run slow.
    As I pointed out, during part of the time each will see the other's clock run fast , just enough so that when they come back together, both will agree that their clocks show the same time, even though for the rest of the time they saw each other's clocks run slow.



    Edit: Closed a quote, Integral
     
    Last edited by a moderator: Sep 9, 2003
  6. Sep 9, 2003 #5
    Thanks Janus! You're actually answering my question without passive aggressive digs at my intelligence.

    So this is the first time I've heard anything of seeing anothers clock moving 'faster'. I'm having a tough time grasping that one. Also, how is direction involved? Apparently this is a part of relativity that I've missed.

    Thanks again

    As far as not being interested in math, it's because I think better in words rather than variables.

    As far as things not being in sync, you guys are arguing semantics. Let's change the experiment. At the point where both planets are halted, if you were to accelerate one only and leave the other put, when they were brought back together the times would be different. This is what I meant by out of sync. If you want to call it something else, just let me know.
     
  7. Sep 9, 2003 #6

    chroot

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    The issue of "in sync" is not semantic at all - in fact, it strikes right to the heart of relativity theory.

    It is critical that you recognize what is known as the "failure of simultaneity." Let me explain. In the pre-relativity view of the world, it was believed that space and time were independent -- essentially, that the entire universe shared one time coordinate. Watches in London and watches in New York ticked at the same rate, and measured the same, common, time coordinate.

    If you imagine a simple two dimensional spacetime, with one dimension of space and one dimension of time, it made sense in pre-relativity physics draw a "surface of simultaneity," as follows:

    Code (Text):


             time
               ^
               |
               |
               |  New York  London
       5 pm UT | ----x--------x----- <-- surface of
               |                        simultaneity
               |
               |  New York  London
       4 pm UT | ----x--------x----- <-- another one
               |
               |
               |
               +---------------------------> space

     
    In other words, every point in the universe experienced the instant "4 pm UT" in synchronism.

    With this pre-relativity notion of simultaneity, it was possible to compare the reading on a local clock with the reading on a distant one, since it was believed time was experienced identically everywhere.

    Then, there came relativity, and disabused this idea of universal simultaneity. Two separated clocks do not necessarily experience time in the same way -- they don't need to agree upon what is "4 pm UT" and, further, they don't need to tick at the same rate.

    In other words, in relativity theory, time is a distinctly personal experience. The only clock in the universe that is an accurate time-keeping device for you is your own wristwatch, since it goes everywhere you go, accelerates when you accelerate, and so on. No other clock in the universe is necessarily "in sync" with you. Some people would call the wristwatch a "comoving clock." The term comoving means, in more technical jargon, to be in the same frame of reference.

    Oddly enough, it DOES matter that the wristwatch is strapped directly to your wrist. If you sychronized your wristwatch and a clock on your desk a few meters behind your captain's seat while coasting freely through space, then went on a fantastic journey with large accelerations, your wristwatch would no longer agree with your desk clock! The only way to keep your wristwatch and desk clock in sync is to keep them in the same inertial reference frame -- which means no accelerations whatsoever.

    So there you go. It makes no sense to compare the times on two clocks that are distant from each other -- at least not unless you can gaurantee they're in the same inertial reference frame. The only way to compare the times on two clocks is to bring them together into the same inertial reference frame.

    - Warren

    edit: code tags fixing
     
    Last edited by a moderator: Sep 9, 2003
  8. Sep 9, 2003 #7
    - when does 'proper time' click in?
    - how is 'same inertial reference frame' defined? for eg, are two strictly inertial objects 1M lightyears apart but with 0 relative velocity in same reference frame?
     
  9. Sep 9, 2003 #8

    Chi Meson

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    "proper time" is the proper term for the time on the wristwatch attached to the person you are observing. In a typical example a question would be: "If Chroot experienced 25 days during his voyage, how much time passed in your reference frame?" The 25 days is the proper time which then is plugged into the Lorentz transformation formula to find the "dilated" time.

    An inertial frame is a frame of reference that is not accelerating. With general relativity, this also means "not close to massive objects." This also means NOT a frame of reference that is going in circles (such as in a hypothetical space station that is spinning to simulate gravitational effects).

    "Same inertial reference frames" must be traveling with exactly the same velocity (same speed, same direction) thereby having a relative speed of zero.

    This does indeed mean that all of us on the surface of the earth are NOT in exactly the same frame of reference, since we are all going in different tangential directions at any one time, but since the maximum relative speed is only about 2000 mph (Equador vs. Singapore) relativistic effects are not noticed.
     
  10. Sep 9, 2003 #9
    Chroot

    Definition-Semantic: relating to meaning in language

    Ok, in my post I think it's pretty clear that I understand the basic thing to me that you are for some unknown reason explaining over and over regarding time. It's basic SR, as basic as SR gets.

    My quote:
    "when they were brought back together the times would be different. This is what I meant by out of sync."

    Go back and read my post, that is exactly what I said. Keywords: brought back together.

    Your answer Chroot:
    So there you go. It makes no sense to compare the times on two clocks that are distant from each other -- at least not unless you can gaurantee they're in the same inertial reference frame. The only way to compare the times on two clocks is to bring them together into the same inertial reference frame.

    Keywords: bring them together.

    If you can't figure out that that is semantics, you might consider getting on some English language forums for a while.

    Seriously man, your posts are all condescending and rude. Please stop replying to mine if you are going to post just to make yourself feel smart and not bother to actually answer people's questions. It's wasting everybody's time. Go back and look at my original question and show me one thing you have written that actually answers it.

    The key to my thought experiment is this. In the twin paradox, which isn't a paradox at all, two people are separated, one of them traveling away at large speed, and returns to find the other one aged comparatively. Their clocks are out of sync once they are brought back together. In my experiment two people are again separated and travel at high speed, but when they are brought back together, neither has aged relative to the other. I am trying to answer why.

    Janus has already answered the question by stating that the clocks will run faster relative to each other when the two people are accelerating toward each other, offsetting the time dilation effects during the coast period, so this answers the question. Now I'd just like to know more about this effect. This is no longer SR, but GR, and I haven't heard about clocks moving faster before, or the direction of acceleration having an effect.
     
    Last edited by a moderator: Sep 10, 2003
  11. Sep 10, 2003 #10

    Chi Meson

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    What you stated here is the "paradox" of the twin paradox. "How do you tell which one ages if the two have equal velocities [edit: "speeds" not "vlocities"] relative to each other?" THe answer is in determining who's coffee sloshes. The person who stays on earth has a full cup of coffee. The twin on the space ship also has a cup of coffee. WHen the ship takes off, who's coffee sloshes? THe one on the ship. He's the one accelerating; time dilation is on him.


    If, in your situation, both worlds accelerate, both twins coffees slosh the same amount; time dilation happens in equal amounts to both. (Coffee sloshing image thanks to the ubiquitous Richard Feynman).

    PS; in fairness to Chroot, notice your use of "in synch" in your first question.
     
    Last edited: Sep 11, 2003
  12. Sep 10, 2003 #11

    chroot

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    My first reply answered it.
    No, it's still very, very much SR.

    - Warren
     
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