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Speed of light shot from behind

  1. Sep 11, 2012 #1
    The speed of light in a vacuum is constant because it participates in no inertial reference frame. If I am moving at 300m per second and shoot a beam of light ahead of me that beam travels at 300,000m per second irrespective of my speed or my motion. If I increase my speed, time slows down such that the speed of light from my perspective never changes.

    I assume that the speed of light is constant from my perspective if I am traveling forward and a beam of light from far behind me is shot in my direction. If I am moving at 300m per second, the beam fired from behind me must seem to make up that speed in order to remain constant. Of course, that beam doesn’t actually increase its speed; there must be a variation in time. Does time speed up so the speed of light remains constant?
  2. jcsd
  3. Sep 11, 2012 #2


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    The bolded text above is wrong. As far as you are concerned, you are never moving at 300m/sec. You are sitting still while the rest of the world is moving backwards at 300m/sec. So from your point of view there's nothing surprising about the light from behind approaching you at 300,000km/sec (BTW, that's km not m) nor the light you've sent ahead moving away from you at that speed. You don't need any time dilation or other relativistic weirdness at all.

    Now what does the guy who is watching you float by at 300 m/sec sec see? He also measures both beams of light moving at 300,000km/sec, using the exact same argument: as far as he's concerned he's at rest watching two light beams move at the speed of light. Again, no time dilation or other relativistic weirdness is needed to explain his experience.

    You only need to invoke relativity to explain how rest-guy sees one beam of light closing the distance between it and the ship at a rate of 300,000km-300m every second and the other beam of light increasing the distance between it and the ship at a rate of 300,000km-300m, while the ship guy sees both both rates to be 300,000km/sec (and vice versa for ship-guy looking at the light beams approaching and moving away from rest-guy). That's the result of the two observers measuring each other's time and space differently.
  4. Sep 11, 2012 #3


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    Now that's an interesting comment. I wonder what you mean by that. If I were to use your words, I would say that the speed of light in a vacuum is constant because it participates in all inertial frames identically.

    So what do you mean by your statement? Are you talking about the fact that every inertial observer will measure the round-trip speed of light to be the same value? Or are you talking about the unmeasurable one-way speed of light that is assigned to be the same value as part of Einstein's definition of an inertial reference frame?
    Same question: are you talking about measuring the speed of a beam of light that you emit under different states of inertial motion, or are you talking about the assigned speed of light according to different reference frames in which you are at rest?
    Again, same question: are you talking about measuring the speed of a beam of light that someone else emitted who was not at rest with respect to you, or are you talking about the assigned speed of light from a moving source according to a frame in which you are at rest?
  5. Sep 12, 2012 #4
    I was going to reply in a similar way, as that comment sounds upside down - two people, one thought! :smile:

    I would say that the speed of light in vacuum is invariant because it is possible to set it to the same value in all inertial frames (ah yes I find your "assign" also very clear).
    "Constant" in the second postulate relates to a single inertial frame and refers to the same in all directions, independent of the motion of the source.
  6. Sep 12, 2012 #5
    I think my question is simpler than what I set out before. Let me see if I can clarify what I want to know.

    If I am pursuing a beam of light, I will measure it moving away from me at 300,000km/s. If I accelerate, the beam will still move away from me at 300,000km/s. I assume that if I slow down that beam will still move away from me at 300,000km/s.

    As I understand special relativity, the beam doesn’t actually accelerate or decelerate along with my acceleration and deceleration. Instead, time slows down as I accelerate so that my measurement of the speed of the light beam never changes.

    This time suppose a beam of light is chasing me. My measurement shows that the beam approaches me at 300,000km/s. If I accelerate, my measurement again shows it approaches me at 300,000km/s, and if I decelerate, my measurement still shows that the beam approaches me at 300,000km/s.

    If the paragraph immediately above is right, and if time slows when I am chasing the beam of light, then does time accelerate or decelerate when the beam chases me?
  7. Sep 12, 2012 #6
    "Pursuing a beam of light" and "If I accelerate" indicates that you are moving wrt your reference system. In such considerations, that beam will not still move away from you at 300,000km/s. The normal rules of vector addition apply in a single reference system. That relative speed as determined with a reference system in which you are moving is c-v (in Newspeak this is called "closing speed").

    But the earlier answers were already to the point; I wonder if you really understood them? Without understanding the basics of setting up an inertial reference frame (more precisely a standard inertial coordinate system), it can be too confusing.
  8. Sep 12, 2012 #7
    It is not as simple as saying "time slows so your measurement stays the same".
    It is not just time dilation that you will observe, it is time slanting and shifting, more pronounced the further away from you. Relativity of simultaneity makes it so your new "now" after acceleration will be different than your previous "now". Things behind you that you thought already happened, would have yet to happen again after your acceleration, and the opposite in front of you. Length contraction would make things and distances seem smaller, but despite that the light pulse chasing you will be even further behind you, simply because in your new slanted "now", it would not have yet travelled as far as it had travelled in your previous point of view...
    In a sense you can claim that the pulse behind you (and all other objects really) moved back in time, jumped to an earlier moment, because of your acceleration.
    With a large enough constant proper acceleration and/or a large enough distance from the pulse, that effect can overcome the distance contraction effect and the speed of light itself, and so the pulse may never catch up... at least if you could keep accelerating forever.

    A similar pulse in front of you is also an interesting case... it would appear to have jumped forward in time. If it was pointed towards you, it would be closer to you, if it was pointed away from you, it would now be even further away... very unintuitive, considering you just accelerated towards it, but unless I messed something up, that is exactly what will happen. The more you accelerate to try to catch up with a far away light pulse, the further away it will be from you, despite increasing length contraction.
  9. Sep 12, 2012 #8
    It would be better to say that regardless of your speed relative to Earth or some other reference body, that the light ray travels at c. Bringing the act of acceleration into it complicates matters. But it's true that as long as you are not accelerating, the speed of light is always c, you can regard yourself as being at rest, and it doesn't matter what the speeds of Earth, your spaceship, or whatever else are in your reference frame are.

    No. Time dilation is not something that happens to you. Time dilation is the result of the relationship between TWO bodies in relative motion: an observer, and a clock moving relative to him. It is not something that can be said to be happening to YOU alone. Time does not slow down: you observer your own clock always to tick at the same rate, regardless of whatever else might be going on outside. And that is the definition of time: that which is measured by a clock.

    In other words, when you are in motion relative to, say, the Earth, the Earth observer will measure your clock to tick more slowly than his own. You will also measure the Earth's clock to tick more slowly than your own. Both observers are correct, and there is no answer to the question of which clock is "really" slow. Neither observer "experiences" the time dilation. It's always happening to the other guy.

    Nor is there any answer to "why" the light ray always is observed at c. That is a postulate that we use to explain everything else.
  10. Sep 12, 2012 #9


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    Thanks for answering my questions--you want to know what you can measure with regard to the speed of light beams that either you are pursuing or that are chasing you.

    First off, I would encourage you to read the wikipedia article, One-way speed of light.

    Now let's think about how you can measure the speeds of those beams of light. Here's what I would suggest for measuring a beam that is chasing you: You take a long rigid structure and install a shutter at the far end so the light beam can be interrupted. You also place a light source on the far side of the shutter that can be interrupted at the same time so that when you open the shutter, both light beams can progress toward you. Whenever you open the shutter, you will detect that both beams arrive at your location at the exact same time. You can repeat the experiment with light beams from different sources that are known to be moving away from you or towards you at different rates. You can also repeat the experiment after you have accelerated to any new inertial state.

    Now with regard to light beams that you are pursuing: this is a little more complicated but you can take the same apparatus and move to the other end. But then you will need to have a couple light detectors that can determine if the two light beams arrive at the same time. But if you think about it, it's really the same experiment, isn't it? It's only a matter of when you make the measurement of the light beams--either before they reach you or after they pass you--correct? Now you don't really think it will make any difference do you?

    Please note in these measurements, you are not assigning a value to the speed of the light beams, you are just comparing the speed of an externally sourced light beam to one that is local to you and you always conclude that as long as you are inertial (non-accelerating) they are the same speed but you haven't measured what that speed is.

    Does this all make sense to you?
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