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Homework Help: Hypothetical time travel & time dilation

  1. Jan 10, 2010 #1
    1. The problem statement, all variables and given/known data

    <Q1> “Super Ted”, a famous children’s TV cartoon character, has
    just leant of an evil deed carried out by “Texas Pete” who had opened a
    farm gate at A and let all the sheep out onto the
    train tracks and roads. It shows that everything was normal until Super Ted boarded the train at B and did some magic
    to make sure that the train arrived at A before Texas Pete
    opened the farm gate. Note : At A, departure was at 16:13 and at B, at 16:45

    (a) Assuming that the distance D between B and A
    is 30 km (in ref frame S), and Super Ted can break the law of
    Physics about being able to get mass up to (and beyond the
    speed of light), how many times faster than the speed of light
    must the train travel to achieve the arrival time at A ?

    (cool.gif (b) Now “Texas Pete”: is captured and given a community service
    order to round up all the sheep using a
    giant vacuum cleaner. If there are 3000 million sheep and these
    have an average separation between them of 10m (in stationary
    reference frame S), then at what sub-light speed (V wrt S) must
    “Texas Pete” travel in order to capture all the sheep in t’=60
    seconds of his time in reference frame S’? Note: you may
    completely ignore the relativistic mass increase resulting from
    cumulative inelastic collisions (captures of) with sheep.

    <Q2> Consider two alien creatures, a senile old green Soup Dragon that
    lives close to the centre of a 600m diameter asteroid and a relativistic-
    velocity capable Iron Chicken. The Soup Dragon is in the rest reference
    frame S. The Iron Chicken is in reference frame S’ and when triggered
    can jump up to a speed of 0.8C instantly, and likewise can stop
    immediately from 0.8c down to 0c. However despite its speed, the Iron
    Chicken is not a very clever animal. The Iron Chicken is initially at rest
    wrt S, however when it sees an explosion it will immediately make flight
    at 0.8c directly towards the explosion, and if it sees a second explosion then it will stop immediately. Now the Soup Dragon needs a change in
    diet and decides it wants some chicken ingredient to go into its soup pot,
    situated very close to the centre of the asteroid. If the soup dragon has
    some very precise timed detonator explosives, that it has synchronized
    from its central position, what time difference δt between two explosions
    will bring the Iron Chicken to rest at the precise centre of the asteroid?
    Hint: a Minkowski diagram will simplify the solution to the problem.


    2. Relevant equations


    3. The attempt at a solution

    Q1 Part a) is a hypothetical question about
    time travel. I say hypothetical because we cannot accelerate matter
    up to the speed of light. But suppose we could, and had a velocity
    > c e.g. 2c, or 5c etc. What effect would this have on the time
    dilation effect? Does it actually lead to time travel or not?
    If not then I'd like to explain why not, as you see it. I Tried drawing a Minkowski
    diagram, to see if this helps? Part b) of 1 I looked at the equation for time dilation, to see if that is of any use but I'm still confused.

    Q2 I draw four vertical world lines, one for the Chicken's initial position,
    one for the centre of the asteroid, and two others for the
    explosive devices.I know that If something is stationary it moves along a vertical
    line. Information of the explosion travels at the speed of light - this
    is a 45deg line. The chicken must see the light of the explosion before
    it can jump to sub light speed. Anything at sub light speed travels along a line that lies between the
    vertical and the 45 deg light cone. However, I am unsure about which equation gives the correct δt?
  2. jcsd
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