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Spacetime diagrams and proper time

  1. Jun 17, 2008 #1
    Hey guys,

    Can someone please explain to me this image:
    from the page

    What i do understand:
    I understand the concept of light cones
    I understand that the units used for the axes means the lines are a 45 degree angle indicate the particle/causaility horizon thing (i think)
    I think i understand that non parallel worldlines implies relativistic effects taking place
    I dont understand what the red line thing is.

    So yeh i dont get much of this, any help would be appriciated =)

  2. jcsd
  3. Jun 17, 2008 #2
    I dabble in relativity more than cosmology, but I think I can help a little here. In a normal spacetime diagram in Special Relativity a line at 45 degrees represents the worldline of a light ray. Anything moving slower than the speed of light is tilted at less than than 45 degrees from the vertical and a verticle line is the worldline of a stationary object that is going forward in time which could for example represent the Earth. So usually there are no worldlines tilted at more than 45 degrees to the vertical.

    In cosmology the expansion of spacetime itself allows objects to recede at greater than the speed of light relative to the Earth as long as they are restricted to moving at the speed of light or less locally relative to the the local spacetime. The little light cones on the tilted worldlines indicate the allowed velocities locally in that region. In other words the rules of Special Relativity only apply locally. The expansion of space effectively "carries" objects along with it a bit like a conveyor belt. The red line indicates the path of a photon emitted near the horizon of the visible universe when it first became transparent to light. At that time the universe was about 300,000 years old so it is reasonable to ask why the photon took over 13 billion years to arrive at the Earth. The reason is that the photon, for part of its journey was moving against a flow of spacetime that was moving so fast the photon was actually losing ground and receding from us. Gradually with the passage of time it finds itself in regions of spacetime that are receding from us less rapidly and eventually makes headway to arrive at the Earth having taken the scenic route. If you look carefully and if the diagram has been drawn correctly, you should be able to see that the red worldline is always parallel to the one the edges of a local light cone. The expansion of space during its journey "stretches" the wavelength greatly redshifting it to the microwave wavelength that we see now as the CMBR. The diagram also shows that if the age of the universe is about 13.7 billion years old that the particles furthest away from us that we can actually see are lot further away from us than 13.7 billion light years now. Hope that helps :)
  4. Jun 19, 2008 #3
    ah yes of course. what i didnt understand is why some of the cones were tilted but theyre like that as viewed from A. Cheers =D
  5. Jun 19, 2008 #4
    Sorry, just to clarify on that image, the worldlines are moving apart in the past because of cosmic expansion and as we go back in time expansion speeds up so eventually we get a 'turning point' on our light cone where the speed was the same as light and then it goes back to when it exceeded c and goes back to a single point in space and time. I think.
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