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Problem and a paradox

  1. Nov 15, 2003 #1
    To start off, I am in my second year of high school physics so please be discriptive if you make reference to any sort of theory. We have begun to study relativity, and two things occurred to me.

    First, assuming that nothing can go faster than the speed of light, could two spaceships traveling in opposite directions go .99c? It would seem to me that since the frame of reference is moving at a speed of .99c, the spaceship moving opposite it would be traveling at a speed of 1.98c. Is this possible?

    Second, it is basic knowledge that the inside of a wheel will spin slower than the outside of a wheel. What happens if the inside of the wheel is spinning at the speed of light? The outside of the wheel must then be moving at a speed that is greater than c or the wheel is tearing itself to pieces.

    Any ideas on what happens in either scenario would be insightful.
     
  2. jcsd
  3. Nov 15, 2003 #2

    HallsofIvy

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    If you are going to talk about relativity, use relativity. In the theory of relativity, the speed of two objects, moving toward each other with speeds of u and v (relative to the same object), relative to one another, is (u+v)/(1+ uv/c2). In the example you give, two spaceships, moving toward one another with speed .99c relative to a planet between them, have speed relative to one another of (.99c+ .99c)/(1+ (.99)(.99))= 1.98c/1.9801= 0.999949c. Awfully close to c but not equal or larger than c.

    How do you get the inside of the wheel moving "at the speed of light"? Any physical object must be moving at a speed below the speed of light which leaves plenty of room of portions of the wheel further out to be moving at higher speeds that are still lower than the speed of light.
     
  4. Nov 15, 2003 #3
    Okay, the wheel was a bad example of what I was thinking about.

    Assuing that it is possible for the speed of light to be attained...

    We have a square shaped spaceship moving at the speed of light.

    A--B
    ||||
    C--D

    What will happen if the ship moves into a turn to follow a circular path long enough to reverse directions. Assume that the corner A will always maintain the speed of light. What will happen to the other corners of the ship? Since the ship is turning the corners B,C, and D must move faster to keep up with corner A throughout the turn. I'm not looking for mathematical proof of anything just theories on what would happen to the object if parts of it needed to exceed the speed of light.
     
  5. Nov 16, 2003 #4
    You must also remember that the mass is relative to an objects resting mass divided by the square root of (1 minus (v^2/c^2)).
    Taking this in account you get that as an object gets closer to c, its mass will increase, and thus the spaceship won't really be able to travel by the speed of light - only a fraction of it.

    //Martin (also in high school)
     
  6. Nov 17, 2003 #5

    turin

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    The coordinate systems of the two ships are skewed. From the frame of reference in which you have defined the motions of the ships, the world line and now line for a given ship are almost indistinguishable. This is the geometric version of the explanation. The algebraic version seems to have already been mentioned. Remember, there were other relativities before Einstein's. Don't get them confused. In Galilean, there is no special speed. In Einstein's, the invariance of the speed of light comes before you even try to think about space ships and laser beams.




    First, I will revise this to say that the tangential velocity of the surface of the axle is 0.99c. Then, assuming that the radius of the axle is much less than the raidus of the outside of the wheel, you certainly have a problem. Let's just say that you do in fact have the axle spinning as mentioned. Then the spokes will spiral outward, and the metallic bonding that holds the atoms of the spokes to each other will break.
     
  7. Nov 17, 2003 #6
    For every movement forward a object of Mass will increase its mass. So the two spaceships travelling head-on will both be increasing their masses, therefore their approaching speeds relative to each other will actually de-crease as they both gain Mass, Assumming both have the same relative speeds.

    Of course you have heard of the zeno Arrow paradox?..if you apply this analogy, then for every movement forward, you have to release your Mass in order to proceed, if you want to achieve a comparable speed to Light, then you have to in effect become Light, this is contained within the E=Mc2. Taking away some of your Mass for every movement forward, increase's your speed (which gives you more Mass!)so in the equation you have to 'shed' your mass, or contract your Mass to achieve Light Speed.

    Light 'Boosting' occurs as you gradually loose mass to speed in a specific ratio, the problem is though at a precise moment you will become 'Tachyon', and will be infact a mirror-particle, coming towards your initial direction of motion. In non technical terms you will be a 'future' you, travelling from a future to a present-time,not the same as your initial scenario of both ships travelling from a Past>>Present-Tense.

    The Tachyon scenario travels opposite from Future>>Present-Tense.
     
    Last edited: Nov 17, 2003
  8. Nov 18, 2003 #7
    ok. but what if the spaceships move in the opposite directions and their speeds relative to the plantet between them are 0.99c...?
     
  9. Nov 18, 2003 #8

    HallsofIvy

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    Didn't you read the first response to this question?:
     
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