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A very simple question about general relativity

  1. Mar 24, 2005 #1
    Been asking this since 1994.



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    50,000 years have passed since Colony spaceship A and Colony spaceship B launched from Earth. Like in a star trek episode, they all reverted to barbarism, and then regrew a new technological society. Forgot where they came from, and what theyre doing. Theyre big colony ships.

    Colony ship A gets on the radio and finds out that they are 1 light-year away from Colony ship B. They start commmunicating with eachother, and discover they are also at rest with eachother. They decide to join forces, but Colony ship B's propulsion system is broke. So Colony Ship A then accelerates REAL FAST at 99.99999999999999% the speed of light in 1 minute to dock with Colony ship B, 1 year later Colony Ship A decelerates and then docks with the other colony ship.

    So according to relativity colony ship A only aged a few hours, while Colony Ship B aged an entire year.

    WRONG!



    ------B ----------A

    C

    Some guy on Planet C thats monitoring the entire situation, notices that Colony ship A and B are wizzing by at 99.9999999999999999999999% the speed of light. Planet C sees that A decelerates to zero, then reaccelerates to 99.99999999999999999% the speed of light to dock with B. PLanet C notes that B experienced time dialation the entire time.

    So what is it?

    A) A new universe is created for Planet C that says Colony Ship B experienced time dialation.

    B) Each particle in the universe has a history log showing every velocity change, so paradoxes like this cant happen.
     
  2. jcsd
  3. Mar 24, 2005 #2

    Janus

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    Neither. You need to take the Relativity of Simultaneity into account for planet C and length contraction into account. Assume that Ship A and B synchronize their clocks before A leaves to join B. Now As the ships fly by planet C, Planet C takes note of the Times on the Clocks. He will note that ship B's clock runs about 1 year ahead of Clock A, And that they are only about one light minute apart.

    So A stops (His clock now run at the same rate as C), for 1 min to let B catch up, then speeds back up to B's speed. B's clock, which undergoes time dilation during this time, changes very little, so that when they meet up, B's clock is one year minus 1 minute ahead of A's clock. The same result seen by the ships. No paradox.
     
  4. Mar 24, 2005 #3
    According to A and B, what they see is that they are 1 lightyear apart. C may see length contraction as entirely different thing.

    I meant acceleration and deceleration is an unrealistic 0-c in 1 minute, for mathematical simplicity. The trip though is 1 year, for mathematical simplicity 99.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999% the speed of light.

    The ships have no windows and dont see the outside universe, only radio contact with eachother, and being at rest with eachother.
     
  5. Mar 24, 2005 #4
    Relativity states that Ships A and B being at rest with eachother are a universe unto themselves, being that there is no universal speed of light or speed of rest, and every frame of reference for every particle at rest with eachother is a universe unto itself. So therefore ship A being at lightspeed for a year should experience the time dialation.
     
  6. Mar 24, 2005 #5

    JesseM

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    Dropout, did you read Janus' response? The answer is that different frames define "simultaneity" differently, which means that two events which happened simultaneously in one frame happened at different times in another frame. In A and B's rest frame, up until the moment A accelerated their clocks were synchronized--the event of A's clock striking 12 happened simultaneously with the event of B's clock striking 12, for example. But in C's frame the two clocks were not synchronized--instead he sees B's clock ahead of A's clock, so for example, he might see B's clock strike 12 at the same moment that A's clock strikes 10. So even though he does see A's clock speed up after it accelerates (because A's velocity has decreased rather than increased), A will still be behind B when they meet, simply because B started out so far ahead of A...even though A narrowed the gap by ticking faster, it still did not catch up with B, from the perspective of C's frame. If you like, I can work out an actual numerical example to show just how this works, and why both frames will predict exactly the same answer about what A and B's clocks will read at the moment they meet.
     
    Last edited: Mar 24, 2005
  7. Mar 24, 2005 #6
    Ok, planet C is monitoring the radio transmissions of both ships A and B. When the ships A and B dock and start talking to eachother what will planet C hear them say?


    Ship A, "I experienced time dialation."

    Ship B, "I experienced time dialation."
     
  8. Mar 24, 2005 #7

    Janus

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    Neither. No one ever "experiences" time dilation, it is always measured as happening to the other frame.
     
  9. Mar 25, 2005 #8
    Im not being anal about simultaneouty, and exactly what time they have at their clocks at one particular point in time. I want to know what they said to eachother when they docked. What did they SAY?

    Ship A verbalized something to Ship B, and Planet C was monitoring the entire situation. What did Ship A say?
     
  10. Mar 25, 2005 #9
    drawing in ASCII dont work very well
     
  11. Mar 25, 2005 #10

    Janus

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    Ship A: While I was accelerating towards Ship B, Ship B's clock jumped about a year forward in time.(Ship B's clock ran fast.) While I was traveling at a constant speed towards Ship B and braking to to a stop, Ship B's clock ran slow.
    Ship B: While Ship A acclerated towards me, traveled at a constant speed and braked to a stop, Ship A's clock ran slow by varying amounts depending on its relative velocity WRT to me at the moment.

    Planet C: Both ships Clocks ran slow until Ship A decelerated to a stop and its clock clock kept the same time as mine. Ship B's clock continued to run slow. When Ship B caught up to ship A, ship A accelerated back up to speed with ship B and its clock started to run slow again.
     
  12. Mar 25, 2005 #11

    So your saying ship B verbalized to Ship A, "You aged 1 year, while we only aged a few minutes."
     
  13. Mar 25, 2005 #12
    From the colony's ship point of view during that 1 year. Colony Ship B gets on the radio and transmits across space to Colony Ship A, "Hey thats amazing, our scientists were correct about time dialation, your clock is running slow Colony ship A, since you accelerated towards us and are now traveling at 99.99999999999999% the speed of light."

    PLanet C listens to Colony Ship B's transmission and starts to think, "WTF are they talking about? Colony Ship B is suppose to experience time dialation." A great debate begins on Planet C about the validity of their theories on time dialation after listening to that broadcast.



















    From the colony's ship point of view during that 1 year. Colony Ship B gets on the radio and transmits across space to Colony Ship A, "What is going on Colony ship A? We are reading you accelerated towards us at 99.99999999999999% the speed of light, you should be experiencing time dialation, but we are actually the ones experiencing time dialation. We must already be traveling at 99.99999999999999% the speed of light and you actually slowed down to the universal speed of stop. We will build a telescope to see if we are passing any galaxies up, oh look we just passed a planet C."

    PLanet C listens to Colony Ship B's transmission and starts to think, "Yeah thats right, our scientists were right about relativity."















    I used three numbers for mathematical simplicity.

    A) They are 1 lightyear apart from their point of view, so if they travelled at the speed of light it would take 1 year to get there.

    B) Acceleration is nearly isntant, for simplicity purposes I wouldnt have to get anal about exactly how much time passes during acceleration. Make it 0 to light speed in 1 minute, yeah it would make mush of their bodies but its not theoretically impossible.

    C) Top speed is 99.9999999999999999999999999999999999999999999% the speed of light after acceleration, again its not theoretically impossible for matter to travel that fast.

    So one or the other will age 1 year. Its either one or the other that experiences time dialation. It doesnt really matter what happens enroute, simultaneuty doesnt matter, what matters is after they meet up and determine who experienced time dialation. Once those ships broadcast over the universe a radio wave about what they said, then its written in stone what exactly happened otherwise 2 universes are created each one with different radio waves transmitted across the universe.
     
    Last edited: Mar 25, 2005
  14. Mar 25, 2005 #13
    Im specifically asking what they VERBALIZED to eachother because verbalization is something that cant get bogged down in simultaneouty of events or mathematics. I remember physics classes and the way they bent space in that cone of light in different frames. It was all fine and dandy when dealing with with pulses of light, in fact it made perfect sense.

    What is impossible is for one observer to see this ---.--

    and another observer to see this ...-..
     
  15. Mar 25, 2005 #14
    OH yeah, and another thing that is strange, length contraction.

    Brownian motion on a nuclear scale. In the sun at its hottest spot, you got Hydrogen atoms going close to the speed of light because of speed. Maybe not OUR sun, but atoms in very hot places are being bounced around in a brownian motion that are close to the speed of light.

    At any particular point in time, you can have a Hydrogen atom in one galaxy going 99.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999% the speed of light in exactly the same direction of another Hydrogen atom in another galaxy going just as fast.

    According to length contraction, from an outsiders point of view, those two hydrogen atoms will be right next to eachother, not seperated by millions of light years, but right next to eachother. Most of matter is made up of empty space anyways, our bodies are mostly made up of space, even lead is made up of mostly empty space. What makes length contract? Dont know, but solid matter doesnt exist in the universe anyways, so Im guessing that if your traveling in the same direction your part of the same body that can shrink.
     
  16. Mar 25, 2005 #15

    Janus

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    No, read it again.
     
  17. Mar 25, 2005 #16

    Janus

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    Only if the inhabitants of planet C had no understanding of Relativity. If they understood Relativity and what it predicts, they would have no problem with this at all.
    Again, this would happen only if all the participants did not understand Relativity. For one, in SR there is no such thing as a "universal speed of stop", or absolute frame of rest. If these "scientist's" version of Relativity includes such a frame, then it is not SR.
    You just can't disregard simultaneity, nor the observations of the participants during the trip like that, as they are integral to understanding Relativity. And Relativity says: That while all the participants will agree to what the respective clocks on ship A and B will read when they meet, They will not agree on how they got that way.
     
  18. Mar 25, 2005 #17

    Janus

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    Why?

    Let's use an analogy:

    Person A is standing next to a tree and decides to judge its height by comparing to the thumb of his outstretched arm. It is 20 "thumbs" high.

    Person B is standing a fair distance from the tree and makes the same measurement, he measures the tree to be 2 'thumbs' high.

    To someone not used to the concept of perspective, this would seem impossible. How can two people see two different heights in the same tree?

    The same thing happens with Relativity, in this case our Observers are viewing the same space-time interval from different perspectives. They are seeing the same "Reality", but are just seeing it from different viewpoints.
     
  19. Mar 25, 2005 #18

    Janus

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    The amount of energy it would take to get a hydrogen atom up this speed would rival the entire energy output of a total galaxy.
    From an outsiders point of view they are millions of light years apart. From their own point of view, they are much further apart. and it is the galaxies that are close together. This brings up the point of Simultaneity again. If particle A is passing through galaxy A at same time as particle B is passing through Galaxy B according to the inhabitant of the Galaxies, then according to the particles, they do not. One particle passes through its galaxy before the other does.
    Length contracts because it is a measurement, and in SR it is measurements made between frames that have relative motion WRT each other that are effected.
     
  20. Mar 26, 2005 #19
    So your saying Planet C is going to hear a totally different radio transmission then Ships A and B.

    So planet C's going to hear Ship A say, "Hey B, you experienced time dialation."

    And Ship A is going to say to Ship B, "Hey I experienced time dialation."


    Only one radio transmission can be transmitted across the universe for all to hear, it may be received slow to some or fast to others, but there can only be one radio transmission.
     
    Last edited: Mar 26, 2005
  21. Mar 26, 2005 #20

    Chronos

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    Dropout, read a book. If you don't understand the question, it is unlikely you will understand the answer.
     
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