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Thread: Save the Universe

  1. #1 Save the Universe 
    Senior Member MaxPayne's Avatar
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    As light shifts from lower wavelength to higher wavelength, the energy of photon decreases (T/f)

    Where is this lost energy going to? WHERE????????

    Is this energy equivalent to the kinetic energy of the moving source or observer?

    Why is it that the velocity of the source could affect the wavelength; and yet has no effect on the velocity of light?
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  2. #2  
    Administrator Markus Hanke's Avatar
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    Where is this lost energy going to? WHERE????????
    The question is meaningless, because energy is a frame-dependent quantity. In a curved space-time, the frame of the emitter and the receiver do not stand on an equal footing; the frequency of the photon changes because the clocks in one of the frames are gravitationally dilated ( i.e. there is curvature in the time direction ). Because of the presence of curvature, there is also no global notion of energy conservation; energy is conserved everywhere locally, but ( even though this is counterintuitive ) the local notion of energy does not make sense globally in a curved space-time.

    Why is it that the velocity of the source could affect the wavelength; and yet has no effect on the velocity of light?
    Because light cannot be accelerated. Once it leaves the emitter, the only thing that can affect light is the global geometry of space-time itself; light follows null geodesics through a curved space-time.
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  3. #3  
    Senior Member MaxPayne's Avatar
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    The question is meaningless, because energy is a frame-dependent quantity. In a curved space-time, the frame of the emitter and the receiver do not stand on an equal footing; the frequency of the photon changes because the clocks in one of the frames are gravitationally dilated ( i.e. there is curvature in the time direction ). Because of the presence of curvature, there is also no global notion of energy conservation; energy is conserved everywhere locally, but ( even though this is counterintuitive ) the local notion of energy does not make sense globally in a curved space-time.
    Of course!! this is what you have been trying to put in my brain, that energy is frame dependent and while rest mass is not.
    Complexities and technicalities aside energy isn't a quantity that can be taken for granted.
    gravitationally dilated???? Why?
    About energy? Are you saying that total energy of the universe isn't conserved. I have been told that, at quantum level particles are formed utilizing zero energy, Are you referring to that?

    Also tell me how can I make sense of curved space time? Am not very good at visualizing things.
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    Senior Member MaxPayne's Avatar
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    Because light cannot be accelerated. Once it leaves the emitter, the only thing that can affect light is the global geometry of space-time itself; light follows null geodesics through a curved space-time.
    Yes,but why wavelength changes?...Is it because of the fact that the wavelength of light is a function of time which is frame dependent while velocity of the light is constant.
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  5. #5  
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    Quote Originally Posted by MaxPayne View Post
    Yes,but why wavelength changes?...Is it because of the fact that the wavelength of light is a function of time which is frame dependent while velocity of the light is constant.
    That sounds right to me!
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    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by MaxPayne View Post
    Of course!! this is what you have been trying to put in my brain, that energy is frame dependent and while rest mass is not.
    Yes, exactly. That caused me immense headaches when I first learned relativity.

    gravitationally dilated???? Why?
    Because in the vicinity ( and inside ) regions with non-zero energy-momentum space-time is curved, most notably in the time direction. If you compare two clocks, one far away and one close to the mass/energy distribution, you will find that the latter one ticks at a slower rate. That is gravitational time dilation. A photon is like an elementary clock - as it falls through a gravitational field its frequency must change, since time itself changes as compared to some far-away reference clock.

    About energy? Are you saying that total energy of the universe isn't conserved.
    There is no universally accepted definition for the term "total energy of the universe", so I can't answer this in any meaningful way. Note that I didn't really talk about the universe as such, just about the global gravitational field in some region around a body.

    Also tell me how can I make sense of curved space time? Am not very good at visualizing things.
    That is a very good question, to which, unfortunately, I have no final answer. All visualisations of curved space-time I have seen thus far are in some way flawed and lead to misunderstandings if not utilised correctly. You can try this for the space part of curvature :



    And play around a little with these to visualise the effect on time :

    http://www.adamtoons.de/physics/gravitation.swf
    Wolfram Demonstrations Project

    Yes,but why wavelength changes?...Is it because of the fact that the wavelength of light is a function of time which is frame dependent while velocity of the light is constant.
    Yes, that is pretty much it
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    Senior Member MaxPayne's Avatar
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    Thanks
    Yes, but the space time should exist within the object also. There is a lot of space in the basement.
    If you look at the above picture it looks as if the field lines are emanating from the center of earth.And in the simulation the lines seem to bend away from the center as mass increases, shouldn't it be bending inwards? Why?Why?
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  8. #8  
    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by MaxPayne View Post
    Yes, but the space time should exist within the object also.
    It does, but the metric in the interior of a mass is different from the vacuum solution since the energy-momentum tensor no longer vanishes there, so one has to solve the full Einstein equations.

    If you look at the above picture it looks as if the field lines are emanating from the center of earth.
    Bear in mind that this is only an analogy, a rough schematic, to illustrate the principle; in actual fact there is no field, and no field lines - there is only geometry.

    And in the simulation the lines seem to bend away from the center as mass increases, shouldn't it be bending inwards? Why?Why?
    It bends outwards because the curvature in time is actually positive; what this tells us is that time is dilated, i.e. clocks run slower closer to a massive body. I know this is counterintuitive, but mathematically correct. Few things in GR are quite what intuition would have us believe, and the twice-cursed "rubber sheet analogy" has done a lot of damage by giving people a flawed visualisation aid.
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