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Superluminal hypothetical

  1. Feb 19, 2007 #1
    Example:

    If you had a car that could travel quicker than the speed of light (Theoretically speaking), and there was another car infront of you travelling at the same speed, how would the light from your headlights travel ?

    From what i understand light always travels at the same speed, never changes, so considering we are moving quicker than the speed of light, would the light still hit the car infront and shine on the rear of it ???
    :surprised
     
    Last edited: Feb 19, 2007
  2. jcsd
  3. Feb 19, 2007 #2

    pervect

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    There's a short proof by Charles Dodgson, aka Lewis Caroll, that illustrates the dangers of asking questions like "If you had a car that could travel quicker than the speed of light". It goes like this:


    IF 2+2=5, I am the king of England.

    2+2=5. But 2+2=4. Therfore 5=4. Therfore 2=1.

    Me and the king are 2, but 2=1. Therfore me and the king are 1. Therfore I am the king of England.


    The basic issue is that it is nonsense (if one assumes that special relativity is true) to assume that one has a car that goes faster than light.

    And as Charles Dodgson (aka Lewis Caroll) illustrates, once you start assuming nonsense, you can prove nonsense with complete and total rigor. Another way of putting this: garbage in, garbage out.

    If you have some other theoretical context other than SR in mind you need to:
    1) specify the context
    2) find some forum relevant to that context (it should be obvious that in the SR&GR forum, we will assume that posters are asking questions about relativity.)
     
  4. Feb 19, 2007 #3
    Thanks for that great total nonsense answer that wasted 23 seconds of my life reading that terrific response.... If you dont know the answer or have no idea, best keep your fingers in your pockets and dont type anything at all.

    <irrelevant link deleted - Zz>

    I assume you posted your response in the wrong forum.

    Dont get cheesy with me.
     
    Last edited by a moderator: Feb 20, 2007
  5. Feb 20, 2007 #4
    The relativity equations disalow v>c. So, if you want to know what will happen in your scenariio you would need to write your own equations. Do you think you can try that?
     
  6. Feb 20, 2007 #5
    Special relativity provides a framework/model for reality. If someone poses a question within that framework, then people who understand SR can at least try and answer that question.

    In your question, you have assumed something that SR doesn't allow. Putting the words "theoretically speaking" doesn't help: theoretically speaking, there are no massive particles that can travel at speed c relative to any inertial frame.

    If you can suggest or refer to another model of reality which allows a car to be moving faster than the speed of light, and people here are sufficiently expert in this other model, then perhaps they may be able to help.

    The point is that SR is a highly consistent framework: if you assume one of its results are false (in this case the condition on massivle particles) then you can expect to lead to contradictions (as you have done regarding light leaving the headlights). Note that this is no real problem for SR: there are no such things as massive faster-than-c particles, so there will never be a problem of emitted light from these objects. Even if we are speaking theoretically.
     
    Last edited: Feb 20, 2007
  7. Feb 20, 2007 #6
    No they don't. They only disallow speed above c in vacuo
    So there are situations where cars could be made to travel faster than light. - In water for example. So threoretically it IS possible.

    Some see this as proof of the invalidity of SR..
     
  8. Feb 20, 2007 #7

    pervect

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    I really find it very hard to believe that you're actually looking for an answer to your question - I think you are just trying to have a silly argument.

    On the off-chance that you are serious, I'll point out that your "question" is a well-known logical fallacy, called "The fallacy of many questions". Here's a short Wiki quote on the topic:

    http://en.wikipedia.org/wiki/Fallacy_of_many_questions

     
    Last edited by a moderator: Feb 20, 2007
  9. Feb 20, 2007 #8
    Actually, no they do not. There is nothing in relativity's postulates that requires a particle to have a time-like path.

    If particles could travel faster than the speed of light it would mean that cause and effect are not truely distinct entities. Imagine two boxes at rest in our frame - box A releases a tachyon (recoiling in doing so), the tachyon travels and is absorbed by box B (giving it momentum). Since causality is no longer frame invarient, we can go to a frame which claims the exact opposite (box B was the one that recoiled and emitted the tachyon, and box A absorbed it).

    Even though tachyons are still proposed and discussed for various reasons to this very day in literature, it is the distinctness between cause and effect which people hold so precious that makes them often declare v<=c (or alternatively, lack of experimental evidence of tachyons). It is not demanded by the postulates of relativity.

    If A is moving faster than B and start at the same point, will B overtake A? No, by the very definition of "faster". And it doesn't matter what frame you ask the question, for even though cause-effect get jumbled, if we analyze it in one frame and see that the light never hits the car in front, it will not hit the car in front in any frame.

    So no, the light would not hit the car in front.

    But as pervect mentioned in the very first reply, this is a non-sense question. For the car sitting in your driveway could not ever go faster than the speed of light, since anything starting under the speed of light (even if propelled with infinite energy) would still travel under the speed of light. You'd have to have a car built out of particles already travelling faster than the speed of light! :) But if you just wanted a discussion on faster than light objects, I hope I helped satisfy some of your curiousity.
     
    Last edited: Feb 20, 2007
  10. Feb 20, 2007 #9
    I didn't write postulates. I wrote equations. Would you try plugging in v>c into the Lorentz transforms?

    Agreed.
     
  11. Feb 20, 2007 #10
    I can't define an inertial reference frame for something moving at the speed of light either. Does that mean relativity disallows photons? No, of course not.

    Or does this somehow prevent us from making calculations about situations with photons? No, of course not again. We can analyze a situation in any inertial frame that is convenient; we don't need the rest frame. Similarly with tachyons.
     
  12. Feb 20, 2007 #11
    Then you should have no problem working the v>c into the Lorentz transforms, right?
     
  13. Feb 20, 2007 #12
    PERVECT... no im being serious here...


    Im being serious, not kidding. Im trying to understand bits and pieces here.

    So it is impossible for any solid mass to travel at c even if we had unlimited amounts of power to propel this solid mass through space?

    Would it be fair to say C is the universal speed limit and we could only ever travel / move 99% of C's velocity ?
     
    Last edited: Feb 20, 2007
  14. Feb 20, 2007 #13

    jtbell

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    Well, there's no such thing as truly unlimited energy, of course. No matter how much energy we have available, we cannot propel a material object to the speed of light. Given enough energy, we can get as close we we like, but the closer the speed gets to c, the harder it gets to go further.

    Or, to put it another way, no matter how much energy we've pumped into the object and gotten it correspondingly close to c, it still takes an infinite amount more energy to get it the rest of the way to c.

    Actually, we can do better than that with particle accelerators. For example, an electron with 50 GeV of energy is moving at 0.99999999995c (I hope I counted the 9's right :uhh: )
     
  15. Feb 20, 2007 #14
    What would it be like," Einstein wondered, "to run beside a light beam at the speed of light?" Normal adults would squelch such a question or forget it. Einstein was different. He played with this question for 10 years. The more he pondered, the more questions arose. Suppose, he asked himself, that you were riding on the end of a light beam and held a mirror before your face. Would you see your reflection?

    According to classical physics, you would not -- because light leaving your face would have to travel faster than light in order to reach the mirror. But Einstein could not accept this. It didn't feel right. It seemed ludicrous that you would look into a mirror and see nothing. Einstein imagined rules for a universe that would allow you to see your reflection in a mirror while riding a light beam. Only years later did he undertake proving his theory mathematically. <spam link deleted - Zz>
     
    Last edited by a moderator: Feb 20, 2007
  16. Feb 20, 2007 #15

    Your getting alot warner here Robert in touching the subject and topics im intrested in learning. There are so many awsome questions Einstein had answered / unanswered, it puzzles me for weeks/months/years thinking of the same examples but no way of testing these theories. How would you replicate such a theory ? How could you prove that your reflection would be non visible ?

    Can someone explain the old theory he had, if you throw a tennis ball in a moving train travelling at C (we know it cant but this is the example), to you the ball looks like its travelling at a normal throwing speed 30kmp because your in the train for example. But to the outside observer the ball is travelling at 30kmp + C (train speed).

    And why/how can an Atomic Clock (this has been tested) be shown to have a difference in time after being flown in a jet at the speed of sound for a few hours. They compared it to a synchornised Atomic clock on the ground.. there was a very slight difference. Einstein beleived if this speed of the jet was alot faster the time difference would hence be alot more.

    I think he beleived light could be bent to modify time, you can travel forward but not backward is what he beleived. VERY intresting topics if you can find a way of actualy proving these theories are true/false.
     
  17. Feb 20, 2007 #16

    pervect

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    Yes, it is impossible for a material body to reach the speed of light, no matter how much energy is applied to it, or how long or how hard it accelerates.

    Consider a rocket accelerating at a proper acceleration (the sort that an accelerometer measures) of 1G (i.e. one Earth gravity, about 10 m /s^2).

    According to special relativity, he rocket can accelerate for 1g indefinitely, without ever reaching the speed of light. (Newtonian physics incorrectly predicts that the rocket would reach the speed of light in approximately 1 year).

    In terms of time T elapsed as measured on the rocket, the velocity of the rocket relative to its launchpad will be

    http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

    v = c * tanh(a T /c)

    where tanh is the hyperbolic tangent. Because tanh(x) is always <1, the velocity will always be lower than the speed of light.

    (We've assumed here that the rocket is moving through the flat, Minkowski space-time of special relativity - i.e. we've assumed that there is no gravity to complicate matters, and we've ignored cosmological issues such as the expansion of the universe, to keep things simple).

    The reason for this can be understood purely in terms of a branch of physics called kinematics, which describes how bodies move without worying about what makes them move (i.e. forces). The argument that it would require infinite energy to accelerate an object to the speed of light is also correct, but I think this is more roundabout than the kinematic explanation.

    What happens is that the velocity of the rocket will increase at 1g (i.e about 10 m/s per second) relative to an observer moving along with the rocket.

    The velocity increase relative to an inertial "launchpad observer" will be smaller. This is due to the way velocities in special relativity add. See for instance

    http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

    For two objects moving in the same direction

    v = (v1 + v2) / (1 + v1 v2 / c^2)

    Basically, the speed of light can be and is regarded in special relativity as an absolute speed limit, one which no material body can reach, no matter how long or how hard it accelerates.
     
  18. Feb 21, 2007 #17
    Are you purposely quoting things that you didn't take time to read?

    I clearly stated, in the very text that you quoted, that it isn't necessary to define a rest frame of a photon or a tachyon to analyze situations containing them. If you disagree, please explain why.
     
  19. Mar 10, 2007 #18
    let's say we have 3 cars...all three are traveling a little faster than half the speed of light...and lets say two of the cars are traveling in one direction and the other car is traveling in the opposite direction...

    i'll name two of the cars A1 and A2, and the other car traveling in the opposite direction, B...

    if A1 is in front of A2 and A2 has it's headlights on, will the rear bumper of A1 be illuminated when seen from car B?
     
  20. Mar 10, 2007 #19

    russ_watters

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    Certainly yes. Just because A1 and B are both moving away from A2 at a little over .5C (according to A2), doesn't mean A1 and B will measure each other to be moving at greater than C wrt each other.
     
  21. Mar 10, 2007 #20
    thanks for the quick response. this is interesting to me. maybe I'm just a little slow today, but why is it that A1 and B wouldn't be moving greater than C wrt to each other?
     
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