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Speed of light and dark matter

  1. Apr 5, 2013 #1
    First off, I'm not a physicist (as I'm sure is evident by my multi-part question), but I'm hoping someone will be kind enough to explain this in basic terms.

    Part the first: I'm wondering if someone can explain to me in layman's terms why the speed of light is essentially the universal speed limit?

    Part the second: Why does dark matter have to respect the speed of light speed-limit (and how do we know that it does?)

    Thanks!
     
  2. jcsd
  3. Apr 5, 2013 #2

    mathman

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    The simple answer is that it would take an infinite amount of energy to speed up anything to the speed of light (relativity theory). This applies to all matter (dark and ordinary).
     
  4. Apr 5, 2013 #3
    the speed of light is a universal speed limit because no one could measure the speed of anything more than that of light, not even of the light.
     
  5. Apr 5, 2013 #4

    Dale

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    That isn't true. Simply set up some synchronized clocks a known distance apart and check the time on each as the object goes by. That will give you the speed regardless of if it is slower or faster than light.
     
  6. Apr 5, 2013 #5
    The way you're thinking about this is a little inside out. The universal speed limit is a property of the geometry of spacetime. The fact that light travels at the speed limit really is telling us something about light, not something about the speed limit. What it's telling us is that light is massless. We can see this by considering how energy works in special relativity. And object of mass m moving at speed v will have energy given by
    [tex]E = \frac{mc^2}{\sqrt{1-\left(\frac{v}{c}\right)^2}}.[/tex]

    If we examine this equation, we can see that, when v=c, the energy becomes infinite unless the object's mass is 0. And, we can also see that the energy of an object with m=0 will be 0 unless v=c. In the case where v=c and m=0, this equation is actually indeterminate, which turns out to happen because massless objects can actually have any amount of energy without it changing their speed.

    So, it isn't that something about light affects how everything else moves. It's that a property of the way the universe works both determines how fast light moves and, for the same reason, restricts how everything else moves, as well.

    Dark matter has to obey the speed limit for the same reason that everything else does - the speed limit is an underlying property of spacetime itself.
     
  7. Apr 6, 2013 #6
    @ DaleSpam
    As far as I know the concept of synchronization of clocks is lost at the relativistic speed and we can not measure the absolute time and distance so measuring the speed is not simply division of distance and time but we need to take account of frame of reference, time delation and the whole special relativity. And it says that nothing can move faster than the light. for simplicity just try to do a thaught experiment:
    let's say two observer O1 and O2 are close to each other and they synchronised their clocks. Now they go away from each other with their clock at a distance 300000 km. for which light takes almost 1 sec. to travel. Now if they are able to see the clocks of each other, observer O1 would find that the clock of O2 is 1 sec behind of his own clock and same would go for observer O2.
    Now suppose, an object is moving with infinte speed, i.e. a particle reaches instantenously to observer O2 whenever it is realsed by the observer O1. It will take no time but as the clocks are showing the time difference of 1 sec., so, for both the observers, it will take 1 sec to travel the distance as they have their clocks synchronised locally. Thus both the observer will find the speed of the particle is same as the speed of light.
     
    Last edited: Apr 6, 2013
  8. Apr 6, 2013 #7
    But it is not possible to measure infinite speed. But i agree with DaleSpam is that we can measure something below infinite speed.If something travels faster than light,it will take less than 1 second and both observer will agree on it as their clocks go at the same rate. You used the context of infinite speed,we cannot measure infinite speed as we can't know what is the answer for 1 divided by 0.
     
  9. Apr 6, 2013 #8

    Nugatory

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    You have misunderstood Dalespam's answer. Synchronization is only lost between clocks that are moving relative to one another. It's OK to have two synchronized clocks one kilometer apart and not moving relative to each other; they will remain synchronized and one km apart for as long as I need them, and that's what Dalespam is describing.

    If I'm standing next to one clock when it reads zero, and I shoot a bullet at the other clock... The bullet hits the other clock and stops it. I then slowly walk over to the other clock and look at it, and see that it read one second when it was stopped by the bullet. I know that the speed of the bullet was 1 km/sec in a frame of reference in which I and the clocks are at rest, and I've used my synchronized clocks to discover this.
     
  10. Apr 6, 2013 #9
    @ash64449 and Nugatory
    First I would like to address that the synchronisation is lost when no observer is moving. for this I take example of three spaceship at rest observing a star:
    Untitled.jpg
    Suppose we have three spaceship A, B, and C. The spaceship is not at the same distance from star as shown in the figure above. Every pilot has synchronised his clock with others. One night they observed an abnormal event on a star. Next day, they met with each other and discussed the events took place on the star. They agreed on everything except timing of the event (we can easily figure it out why it is so). And I see that the synchronisation is lost anyway.
    Now take the example of bullet. At the speed of bullet we never take relativistic correction. But when we talk about the velocity of light we must take care of relativity.

    Untitled1.jpg
    In case of bullet the distance between the target and firing position is remain same, i.e. X=X0. But when bullet would be moving comparable with the speed of light then,
    X=X0*√(1-(v2/c2). Now the distace between the two point is function of the speed. So if you say that we can measure the speed of a particle (we are mesuring because the velocity is unknown) that is heigher than or cmparable to the speed of light, then I doubt how we can find the speed when we do not know the relativistic distance between them as it is a function of velocity itself. The same we can have if we measure the time between the two events, i.e. it also needs relativistic correction.
     
    Last edited: Apr 6, 2013
  11. Apr 6, 2013 #10
    Not if they have the least understand of physics. The light from the star will reach them at different times. Of course all along they have slightly different measurement of the distance to the star, and so the differing times of observation for them are understood in terms of that different distance for A, B, and C so they come up with the same time for the initial event, before its light was sent to each of them. What you said is true only if they imagine the speed of light to be infinite.
     
  12. Apr 6, 2013 #11

    Nugatory

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    No, they still agree about the timing of the events on the star. The light from the events on the star hits their eyes at different times, but because they know about light travel time, they also understand that the the events happened sometime before the light hit their eyes. So the guy who is four light-minutes away from the star sees something happen at four minutes past midnight, the guy who is two light-minutes away from the star sees something happen at two minutes past midnight, and they both agree that it really happened at the same time time, midnight - as long as they are at rest relative to one another so can maintain clock synchronization.

    Time dilation, length contraction, relativity of simultaneity are what's left over after you've allowed for light transmission times.
     
  13. Apr 6, 2013 #12

    Nugatory

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    Now you're making an easy problem difficult. Speed is defined to be distance traveled divided by time of travel (using a reference frame in which the observer is at rest - speed is a frame-dependent quantity even in ordinary classical physics). The relativistic effects of the bullet's speed are irrelevant unless we want to calculate how things look to the bullet.
     
    Last edited: Apr 6, 2013
  14. Apr 6, 2013 #13
    if the speed of light were infinite, the time of observing the event would be same as it reaches to A, B and C simultaneously irrespective to their distance from the star.
    you guys again assuming the distance to be known. :)
     
  15. Apr 6, 2013 #14
    Relativity matters only when speed of the bullet is comparable to the speed of light whether we see how things look like to the bullet or to our position as the bullet is moving w.r.t to us and we are moving w.r.t. to the bullet with the same speed.
     
  16. Apr 6, 2013 #15

    ZapperZ

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    This is incorrect. Do you use relativistic addition all the time? After all, according to an observer in another galaxy, you are moving very, very, very fast!

    If the bullet is not moving relative to you, no matter how fast it looks from another frame, that bullet isn't relativistic to you.

    Zz.
     
  17. Apr 6, 2013 #16

    Nugatory

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    yes, of course. And then the correction for light travel time would be even easier because the travel time would always be zero. But I'm not sure of the significance of this point because no one in this thread is suggesting that the speed of light might be infinite.

    Of course we are... Because in principle the distance can always be measured.
     
    Last edited: Apr 6, 2013
  18. Apr 6, 2013 #17
    I see my error regarding infinite speed. The issue is that people do not make determination of when an event occurred without knowing how far away something is.
     
  19. Apr 6, 2013 #18
    If A, B, and C have synchronized their clocks, they presumably have measurements regarding how far away they are from one another. If they all agree to send out pulses of light at time t1, each will receive the others' pulses at different times. This won't confuse them about their clocks being in synch because they know the light has to travel to get to them.
     
  20. Apr 6, 2013 #19
    yes .. if the speed of the bullet is high enough (comparable to the speed of light), relativity is always there to play a role. But when speed is very low even 1000km/s, there is no need to take relativistic corrction. You can see when we deal with the nutrinos or high energy particles from outer space falling on the atmosphere of the earth, we take relativistic correction.
     
  21. Apr 6, 2013 #20

    ZapperZ

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    But what does this have anything to do with what I was responding to. You clearly stated that it doesn't matter as long as something is moving close to c in any frame. I'm saying it does! If the bullet is moving at 0.9 c in some frame, but I am in the same ref. frame as the bullet, I see the bullet is not moving, and I do not have to use any relativistic correction of any kind!

    Zz.
     
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