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I Energy of gravitational waves

  1. Feb 17, 2016 #1
    So everyone knows that the energy of a photon is E = hf, I assume this is just because light also has a particle nature. But how do we calculate the energy of a gravitational wave, because from memory classical wave equations have a mass component to calculate 'kinetic' associated energy, and I assume space-time doesn't have a mass?

    I have another question which is, can matter absorb this energy from the gravitational wave, and if so, how?
    And if not, well where is the energy actually going, because if it just travels outward through the universe forever unable to interact with matter again, than that is pretty close to actually destroying the energy.

    Thanks
     
  2. jcsd
  3. Feb 17, 2016 #2

    bcrowell

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    E=hf is a universal relation. It applies to photons, electrons, and (assuming they exist) gravitons. It has nothing to do with mass. If you know the frequency of a graviton, then hf is its energy.

    But you do not need E=hf to calculate the energy of a gravitational wave, or of an electromagnetic wave. Classically, the energy content of these waves is proportional to the square of the amplitude.

    Yes: https://en.wikipedia.org/wiki/Sticky_bead_argument

    But only a vanishingly small fraction of any gravitational wave's energy will ever be absorbed by matter. Gravitational waves interact only very slightly with matter.

    No, it's not being destroyed, merely diluted (if you ignore cosmological Doppler shifts). The situation is exactly the same as with electromagnetic waves emitted by a star.

    As a side note, energy is not conserved in general relativity. For example, the energy of an electromagnetic wave gets smaller over time (as measured by an observer moving with the Hubble flow) due to cosmological Doppler shifts.
     
  4. Feb 17, 2016 #3

    jambaugh

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    Firstly the hf formula applies to individual quanta, it would (assuming a quantization of gravitational waves) also apply to the hypothetical graviton. However this is a quantum mechanical result giving the smallest unit of energy for these respective wave quanta. In general EM waves will have an energy which is a function of their amplitudes. So too with gravity waves. I would refer you to any good textbook on GR (Misner, Thorne, and Wheeler is a big ole book o fun in that regard).

    As to how matter might absorb energy from a gravity wave, when you do the math with the electromagnetic case you find that you can express absorption of energy in terms of the incoming wave moving the charges around in such a way that they radiate their own waves which in part cancel the incoming wave. That would be how it would happen in a gravity wave case as well. Imagine for example a moon orbiting a planet in a highly elliptical orbit. If a gravity wave passes while the moon is nearing the closest approach it could perturb the orbit into one of higher total energy. (It could also do the reverse and of course the system itself is already radiating its own tiny gravity waves).
     
  5. Feb 17, 2016 #4
    That is interesting that it applies to electrons etc. too.
    I wasn't saying it had anything to do with mass, what I was saying was that the classical (non quanta) energy of a wave equations I'd seen from memory were proportional to mass.

    So you're saying that space-time is comprised of gravitons? I don't actually know what a graviton is, you're only just reminding me about the word.
    So gravitons have a discrete duality too, like photons?

    oh yeah, square of amplitude, but how do you know the amplitude?

    Yeah well if it interacts than it must just be diluted.

    So the expansion of the universe means that it isn't a closed energy system....within the hubble sphere.

    So even after the discovery the 'graviton' (whatever that is) is still hypothetical?
    Thanks for the book tips.
    Ah so Gravitational energy is absorved by matter in proportion to the mass of the matter it interacts with and how much that induces gravitational waves. Hence why the interaction is so small.

    Thanks
     
  6. Feb 17, 2016 #5

    bcrowell

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    We don't really know because we don't have a theory of quantum gravity, but the most likely description is that gravitons are the gravitational *excitations* of the vacuum, just as photons are the electromagnetic *excitations* of the vacuum.

    You can use a measure of spacetime curvature. (Or in linearized gravity, a common approach is to quantify the wave by the deviation of the metric from the standard Lorentzian form.)

    No, energy simply isn't conserved in GR for a cosmological spacetime. We have a FAQ about this: https://www.physicsforums.com/threads/what-is-the-total-mass-energy-of-the-universe.506985/
     
  7. Feb 17, 2016 #6
    So it isn't space-time that is getting bigger with the expansion of the universe? There are more gravitons or something? (theoretically) And what does a graviton have to do with time, why is it 'space-time'? (and not just a vacuum?)
    Thanks for the link
     
  8. Feb 18, 2016 #7

    bcrowell

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    I don't know what you mean by this or how it connects to what we've been talking about.

    No.
     
  9. Feb 23, 2016 #8
    I think you should think more stringy to understand the problem.
    gravity cannot be quantized in our 4 dimensional world. Gravity waves are spacetime by itself. This means that we cannot find gravitons, because for us in our 4 dimensional world it will always look like spacetime and IS spacetime and never interacts like particles in quantummechanics.
    So if we find a multiverse or a superspace then we find it as gravitons producing spacetime. This means that we will only find the dualty expression in higher dimensions.
    e.g. if we find a superspace by a rotating universe, then we can find maybe another universe and describe it as 3 D brane interacting with another 3 D brane and then we can find gravitation as gravitons between the 2 branes.
    This is the stringy view on this and is completely going compatible with GR. This is explaining the quadropol property and the problem that we cannot quantize gravitation. Every try to explain gravitation as kind of quantized graviton in our 3 D Brane Universe will end with headache
     
  10. Mar 8, 2016 #9

    jambaugh

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    tim9000 Re: discovering the graviton... we discovered gravitational waves (classically and just barely) which is a far cry from observing quantized gravitational interactions. I doubt we would ever have the means to do so directly... we'd have to come up with some indirect evidence like how energy loss in orbital systems indicates radiation of gravity waves classically. Consider how far we would be from discovering the photo-electric effect if we just barely could detect AM radio waves (and didn't have eyes to even know light existed other than theoretically as very high freq radio.)

    MacRudi, careful there buddy, just because we can model something in extra dimensions doesn't mean those dimensions are real. Also its not about "gravitons producing space-time" which is not very sensible as a statement. Production of anything is implicitly a temporal process happening within some space-time structure.
    I fear you misunderstand what a graviton is as a concept. A graviton is the hypothetical quantized gravitational interaction so it would be e.g. quantized gravity waves. We do not construct our models of space-time out of a superposition of gravitational waves and thus can't even speak of modeling space-time itself using gravitons. (For one thing the math is terribly non-linear.) You are correct (and in agreement with most experts) in that a new paradigm is needed.

    Also be aware that the concept of gravity as space-time curvature is itself a model... indistinguishable, due to the equivalence principle, from a proper force. The EP says we *can* model gravity as curved space-time. The proper geometry is therefore unobservable (unless we accept as a gauge condition that there are no "extra" gravitational fields). I appreciate your enthusiasm for string/brane "theory" but it is very premature to argue which approach will work. History is full of silly predictions of that type. However let me argue the contrary to your position. The principle failure of field theory to describe gravitation was irreconcilable divergences (non-renormalizable). This is a problem of over counting not under counting. Introduction of more dimensions may make the renormalization achievable but it is aggravating the problem by introducing more unobservable structure. One is inventing infinities to cancel infinities. The base issue is the divergences themselves which really need to be addressed directly rather than renormalized away. The issue resides in the foundation of field theory which itself needs modification. Its like adding on to a house to compensate for a flaw in the foundation, things will still be a bit off square.

    Now string/brane theories are not properly field theories (quite) and so may potentially be able to circumvent the flaws but heuristically I believe they move in the wrong direction. (Less not more). I personally believe we need to step away from treating space-time as physical. In spite of beauty of the geometric model of Einstein's general relativity one must keep firmly in mind that "It's only a model."(like Camelot :D ).

    Of course if I had more answers to these issues I would be working in far higher position then I currently hold.
     
  11. Mar 12, 2016 #10
    It is for me more the intuitive view on this. It looks more and more, that we cannot find lagrangian physics above our 3 D Brane. All calculations and modells are now so far concluded, that we see lagrangian physics in our 3 D brane and yang mill and Lie algebra works for it. But not above. So it is the intuitive view, how we have to see gravity from all modells, we know now.
    Sure the GR is a model, which is working well for our 3 D Brane. It is perfect for us to calculate. It is a model like the conformal field theory for our 3 D Brane. For me it is intuitively the right thinking to see it more as phenomenology for us to see in our 3 D brane. But not as ontological description.
    Please if you are into this research can you help me to understand the 2 M Brane to 5 M Brane developement? I started a new thread for this.
     
  12. Mar 12, 2016 #11
    The probability that a post is read is proportional to a negative power of its length, likewise is the probability of it being understood. If that post is a reaction to another lengthy post multiply with another small factor. If you precede by an abstract and add a conclusion of a few lines I'll be happy to read it !
     
  13. Mar 24, 2016 #12

    ohwilleke

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    I'm not clear how we know that h is universal.
     
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