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Travelling the Same speed as a photon

  1. May 1, 2013 #1
    Hi, i have a question about SR. would happen if two bodies were moving away from each other at exactly .50c, and one body emitted a beam of light the opposite way it was travelling just as the other was passing? I know that simultanety is relative, but what if someone moving on the body that emitted the light adjusted their timing perfectly so that it would be emitted just as the other body saw them passing by in its reference frame.

    Sorry if this doesn't make sense, and I'm sure there's a flaw in this scenario somewhere, but I just can't figure it out.
     
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  3. May 1, 2013 #2

    Doc Al

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    Nothing special. Realize that their relative velocity is only about .8c, not c as you might have thought. (Neither body is traveling at the same speed as a photon. That can't happen.)

    What did you think would happen?
     
  4. May 1, 2013 #3

    phinds

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    The speed of light is has nothing to do with the speed of the emitting object. In the scenario you describe ... well, let me restate it to be sure I'm clear:

    Let's say one spaceship is traveling along the X-axis in the positive direction and the other is traveling along the X-axis in the negative direction. Both are traveling at .5c The both reach the origin at the same time and at exactly that time they both emit a beam of light in their forward direction. Each will now see two beams of light moving away from them at c (this is a bit imprecise since you don't see a beam of light that is not hitting your eye, but I assume you get what I mean), one from themselves and one from the other spaceship.
     
  5. May 1, 2013 #4
    I wasn't sure to be honest. So this brings me to another question: can the relative velocity between two objects be equal to or greater than c?
     
    Last edited: May 1, 2013
  6. May 1, 2013 #5
    Yes, if neither object is at rest in the chosen reference frame, the relative speed can be anything equal or lower than 2c.
    Consider for example two photons going in opposite directions. This reaches the extreme case of a relative velocity of 2c.

    NOTE: The objects themselves will never measure a relative velocity equal to or greater than c. To calculate this measurement, you have to do a Lorentz transformation to the rest frame of one of the objects, in which the other object will still travel slower than c.
     
    Last edited: May 1, 2013
  7. May 1, 2013 #6

    Nugatory

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    The relative velocity between two objects cannot exceed c - but this is the relative velocity between the two objects, not what some third observer moving relative to both of them might observe.

    If you're approaching me from the left at .75c and someone else is approaching me in the opposite direction, from the right, at .75c you and he are both moving at .75c relative to me.

    He is not, however, moving at 1.5c relative to you. You see yourself at rest, me moving towards you at .75c, and the other guy is beyond me and approaching at .96c, not the 1.5 that you'd get if you just added .75 and .75.

    Google for "relativistic velocity addition" to see how I came up with .96c (and check my math too :smile:)
     
  8. May 1, 2013 #7

    Fredrik

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    Just in case this apparent contradiction confuses the OP, the difference is that espen180 and nugatory are using the term "relative velocity" in different ways. Many of us use the term "relative velocity" only like this: The velocity of B relative to A is the coordinate velocity of B in a coordinate system comoving with A. But there are also many people who use the term "relative velocity" for the rate at which the coordinate difference between A and B is increasing, even if the coordinate system isn't comoving with either A or B. The latter kind of "relative velocity" can exceed c. The former can't.
     
  9. May 1, 2013 #8
    I've seen the word "closing velocity" for that, although that may only be applicable if the objects are getting closer together.
     
  10. May 1, 2013 #9

    phinds

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    The opposite is "recession velocity" and that term is frequently used --- objects at the outer region of our observable universe have a recession velocity (relative to us) of about 3c.
     
  11. May 1, 2013 #10
    Thanks guys. So let me see if I understand:

    If I'm moving at some velocity and another object is moving away from me, space and time will warp to make sure that I never see the object moving away as fast (or faster than) light.

    If I'm a stationary observer I can see two objects moving away from each other with a combined speed of > c, but each of their speed will never exceed c relative to me.
     
  12. May 2, 2013 #11

    Nugatory

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    Pretty much right.

    Of course "space and time will warp..." is a hand-wavy and unscientific description of something that can be precisely expressed in math, but it's close enough here.

    Be careful about saying things like "if I'm a stationary observer...". There's no "if" to it - as far as you are concerned, you are always at rest and everything else is moving around you. This matters, because if you aren't careful you can slip into the fallacy of thinking that some things are "really" moving and other things are "really" at rest.
     
  13. May 2, 2013 #12

    Fredrik

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    If "warp" means "curve", then the answer is that there's nothing like that going on in special relativity. But the effect you're talking about is still a consequence of the properties of spacetime, and the convention that statements about what we "see" are really statements about the coordinates assigned by the inertial coordinate system in which we're stationary at the spatial origin (x=y=z=0).

    The word "see" is potentially misleading, because what you actually see depends on when the light reaches you, and what you "see" in the sense discussed here doesn't.
     
  14. May 2, 2013 #13
    Do you mean the recession velocity of two distant objects with respect to us?
     
  15. May 2, 2013 #14

    phinds

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    No, I mean what I said. ALL objects at the edge of our observable universe are receding from us at about 3c.

    Two objects in opposite directs from us would be receding from each other at about 6c
     
  16. May 3, 2013 #15
    I don't think it's possible for an object to have a coordinate velocity greater than c with respect to an inertial frame.
     
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