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Two objects moving towards each other.

  1. Mar 11, 2014 #1
    So im trying to understand some of the ideas of relativity but there is one thing i don't get. I understand that if one object were sent at .99 c and from that object another were launched at .99c the object would appear to be at .99c for the moving object but below the speed of light for an outside observer because time is just slowed down for the first bullet so it appears to be at .99c for the bullet but just below c and above .99c for and outside observer. The thing i do not understand is why if two objects were moving in opposite directions near the speed of light an observer on one of the objects would see the other going slower than the speed of light. Shouldn't it appear much faster because time is slowed in the fast object. Or does it have to do with the time dilation factor on the object. Also if object A and B were going at .99c towards each other why would an observer see it below the speed of light. I just want and explanation, no math or questioning the speed of the objects please because that is the easy way out.
    I've heard that in the time, time would be slowed so much on the too intersecting that it would be impossible to measure, does this make sense? It sounds wrong to me, what if the same scenerio happened with two objects of speeds just above .5c
    Last edited: Mar 11, 2014
  2. jcsd
  3. Mar 11, 2014 #2
    If you were on earth looking up at the two objects, you would see them approaching each other at far above the speed of light. Just below 2c I believe. The people on board due to time dilation, length contration and other distorting factors would measure things totally differently than you, and below light speed. Thats what their clocks and tape measures would show. Whats odd is you would both be correct!
  4. Mar 11, 2014 #3


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    Staff: Mentor

    If A is approaching me from the left at speed ##u## and B is approaching me from the right at speed ##v## (both speeds less than ##c##, of course), I will report that the distance between them is shrinking at the speed ##u+v##, just as you would expect. However, I'm not seeing anything moving faster than light; I'm seeing two things both moving at less than the speed of light.

    A will report he is at rest, I'm moving towards him at speed ##u##, and B is moving towards him at speed:$$w=\frac{u+v}{1+\frac{uv}{c^2}}$$
    Try plugging in some numbers and you'll see that this always comes out less than ##c##. This is the "relativistic velocity addition" formula, and googling for that phrase will find you much more information.

    B will report that he is at rest, I'm moving towards him at speed ##v##, and A is moving towards him at the same speed ##w##, again calculated according to that formula.

    Note that my motion is completely irrelevant as long we're careful about defining ##u## and ##v## as speeds relative to me.
  5. Mar 11, 2014 #4
    So if object A and B are going towards each other at .99c and their is one stationary object, the stationary object will seem to be at .99c but object B traveling at .99c towards object A which is going the other way at .99c will seem to be only slightly faster because time is slowed significantly and the object only appears to be slightly faster because of this? Sounds kind of unassuring but makes some sense.
  6. Mar 11, 2014 #5
    But the objects are approaching each other at almost twice the speed of light from the middle persons frame of reference. So you CAN move two objects in certain ways faster than the speed of light, depending on your frame of reference. Away from each other or towards each other. (While neither object is actually exceeding c.)
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