Robittybob1 Posted March 27, 2016 Author Posted March 27, 2016 (edited) That is the view of the effect of a linear polarized wave on the x and y dimensions (where z is the direction of travel); i.e. you are looking along the z axis (direction of propagation). Linear polarization is seen looking "edge on" to the pair of black holes (http://arxiv.org/abs/1602.03840). Movement is relative remember. So if you shift the point of view, then the point at the center in that diagram will move relative to the new central point. I wasn't shifting the point just reducing its size till the diagram became a point. The central point won't be moving, it will just be a point. LIGO only works because the test particles are far apart (4 km). You can't reduce LIGO to a point on the z axis and expect it to work IMO. Edited March 27, 2016 by Robittybob1
Strange Posted March 27, 2016 Posted March 27, 2016 I wasn't shifting the point just reducing its size till the diagram became a point. The central point won't be moving, it will just be a point. Of course. Motion is relative. If you look at a point, there is nothing to compare it to. LIGO only works because the test particles are far apart (4 km). You can't reduce LIGO to a point on the z axis and expect it to work IMO. Of course.
Robittybob1 Posted March 27, 2016 Author Posted March 27, 2016 (edited) Of course. Motion is relative. If you look at a point, there is nothing to compare it to. Of course. But that doesn't happen if the GW is a 3D spiral. One side of the point (the reduced ring of test particles) will feel a strain before the other. It will wobble. I haven't had to think it through too much, but if the plane wavefront approached along the z axis but the wavefront at an angle to the z axis one side of the point would be touched before the opposite side. Can you see that? Edited March 27, 2016 by Robittybob1
swansont Posted March 27, 2016 Posted March 27, 2016 I wasn't shifting the point just reducing its size till the diagram became a point. The central point won't be moving, it will just be a point. The animation still tells you what's going on. The arrows are the direction and amplitude of the strain. First vertical, then horizontal. If you change the polarization you shift the direction of the oscillation. But that doesn't happen if the GW is a 3D spiral. So the notion of it being a spiral would be wrong, if it disagrees with what GR says.
geordief Posted March 27, 2016 Posted March 27, 2016 (edited) Have you got a supercomputer handy for the simulations? There is no equation that will allow you to calculate this. This image is looking "head on" to the approaching wave. Just imagine that in 3 dimensions .... If there is a black hole at 3 o clock (off the page) are all the vectors in that graphic lengthened towards the "east" ? (And of course the vectors pointing "west" would be shortened proportionally) Does the gravitational wave cause passing perturbations in the local gravitational field and do the vectors due to the gravitational waves add linearly to the vectors in the local gravity field? Edited March 27, 2016 by geordief
Strange Posted March 27, 2016 Posted March 27, 2016 If there is a black hole at 3 o clock (off the page) are all the vectors in that graphic lengthened towards the "east" ? (And of course the vectors pointing "west" would be shortened proportionally) I have no idea. But I doubt it is that simple. Does the gravitational wave cause passing perturbations in the local gravitational field Effectively, yes. That is what a gravitational wave is. and do the vectors due to the gravitational waves add linearly to the vectors in the local gravity field? No. It is non-linear.
Robittybob1 Posted March 28, 2016 Author Posted March 28, 2016 (edited) ..... So the notion of it being a spiral would be wrong, if it disagrees with what GR says. GR is a very complex calculation where for ease of finding solutions they make approximations, so from a large distance they would treat a spiral as a circle, or in this case a 3D spiral approximates a sphere. Now I would agree to that if the GW was from a point source. It is more than likely the source is the binary masses operating in unison so the source could likened to the two ends of a dumbbell, and hence a quadrupolar wave comes out, you won't get that quadrupolar wave from a point source. It is definitely not a point source. I was hoping from the analysis of those equations we would see if GR was treating it as a point source. Let me have some time to do the math please. If there is a black hole at 3 o clock (off the page) are all the vectors in that graphic lengthened towards the "east" ? (And of course the vectors pointing "west" would be shortened proportionally) Does the gravitational wave cause passing perturbations in the local gravitational field and do the vectors due to the gravitational waves add linearly to the vectors in the local gravity field? I think they would but they can be neglected as they are even across the surface i.e both ends of the LIGO would have the same g due to the Earth. Strange has said the opposite because "they are nonlinear". The test masses in LIGO are always in the Earth's gravitational field, which is perpendicular to the LIGO arms so those parts are non linear. But the GW could come in from any angle so at times it won't be all nonlinear. If you were alongside a black hole the test masses would be affected by the gravity of the BH but since they would all accelerate toward the BH at the same rate. So the GW would still move the test particles in the same pattern. The animation still tells you what's going on. The arrows are the direction and amplitude of the strain. First vertical, then horizontal. If you change the polarization you shift the direction of the oscillation. So the notion of it being a spiral would be wrong, if it disagrees with what GR says. Thought for the day: if the 3D structure of a GW was a sphere or a circle from a point source all symmetrical rotating bodies would be able to produce GWs. Edited March 27, 2016 by Robittybob1
Robittybob1 Posted March 28, 2016 Author Posted March 28, 2016 3 equations: [latex]\omega=\sqrt{G(m_1+m_2)/r^3}[/latex] [latex]h_{+} = -\frac{1}{R}\, \frac{G^2}{c^4}\, \frac{2 m_1 m_2}{r} (1+\cos^2\theta) \cos\left[2\omega(t - R/c)\right][/latex] [latex]h_{\times} = -\frac{1}{R}\, \frac{G^2}{c^4}\, \frac{4 m_1 m_2}{r}\, (\cos{\theta})\sin \left[2\omega(t-R/c)\right][/latex] 1
Mordred Posted March 28, 2016 Posted March 28, 2016 3 equations: [latex]\omega=\sqrt{G(m_1+m_2)/r^3}[/latex] [latex]h_{+} = -\frac{1}{R}\, \frac{G^2}{c^4}\, \frac{2 m_1 m_2}{r} (1+\cos^2\theta) \cos\left[2\omega(t - R/c)\right][/latex] [latex]h_{\times} = -\frac{1}{R}\, \frac{G^2}{c^4}\, \frac{4 m_1 m_2}{r}\, (\cos{\theta})\sin \left[2\omega(t-R/c)\right][/latex] Nice your finally posting latex. Well done now post your understanding of those equations. PS +1
swansont Posted March 28, 2016 Posted March 28, 2016 Here's a question for Rb1 that occurred to me: In GR we have waves, and a quantum theory would have gravitons. Based on your interpretation here, what would the path of a graviton be? (because in E&M we have waves but we also have a photon description, and there's often confusion of what the wave represents)
geordief Posted March 28, 2016 Posted March 28, 2016 (edited) No. It is non-linear. Could you throw me a tidbit and explain it a general introductory way why(or how) these vectors -the arrows you have shown in the animation in in your post#48- don't add linearly? Is it because they are not actually vectors but their equivalent in spacetime ? They wouldn't be tensors ,would they? Or are they just a schematic representation and not to be taken at all literally? PS :Sorry I can't work out how to put multiple posts into replies..... Edited March 28, 2016 by geordief
Strange Posted March 28, 2016 Posted March 28, 2016 Could you throw me a tidbit and explain it a general introductory way why(or how) these vectors -the arrows you have shown in the animation in in your post#48- don't add linearly? Is it because they are not actually vectors but their equivalent in spacetime ? Because to calculate the sum of two gravitational waves requires mathematics I don't understand! But you can't just add the vectors, you would need to calculate the total effect from the equations that describe the (changing) curvature of space-time. I am told (by people who would be able to do this) that the results will not be a sum of the waveforms.
swansont Posted March 28, 2016 Posted March 28, 2016 Because to calculate the sum of two gravitational waves requires mathematics I don't understand! But you can't just add the vectors, you would need to calculate the total effect from the equations that describe the (changing) curvature of space-time. I am told (by people who would be able to do this) that the results will not be a sum of the waveforms. Since the space is curved (and as such triangles don't have angles that add to 180º) this doesn't seem surprising.
geordief Posted March 28, 2016 Posted March 28, 2016 (edited) Because to calculate the sum of two gravitational waves requires mathematics I don't understand! But you can't just add the vectors, you would need to calculate the total effect from the equations that describe the (changing) curvature of space-time. I am told (by people who would be able to do this) that the results will not be a sum of the waveforms. Is " the sum of two gravitational waves" correct terminology in this case ? The black hole to the right of the animation (the one that I put there in my mind's eye) is not actually producing gravitational waves is it? Would it be correct to refer to that gravitational field (at the point where it meets the gravitational wave ) as a "standing wave" ? or just a field with "curved fronts" that look like a wavefront. So ,if my terminology is correct (or comprehensible) then I was asking how this "standing wave" (= the local gravitational field) interacts with the disturbance caused by the binary black hole . I appreciate that it is non linear. but I am interested to learn (if I have) that both are basically the same beast -one is static and the other dynamic . I hope I am seeing that right. Edited March 28, 2016 by geordief
Robittybob1 Posted March 28, 2016 Author Posted March 28, 2016 (edited) Here's a question for Rb1 that occurred to me: In GR we have waves, and a quantum theory would have gravitons. Based on your interpretation here, what would the path of a graviton be? (because in E&M we have waves but we also have a photon description, and there's often confusion of what the wave represents) I'm just going to answer this in an off the cuff as I can comprehend the situation. If there was just 1 BH and if there were gravitons producing the gravity around the BH the effective graviton field would be centered on the center of mass (COM) of the one BH. If there were 2 BHs (non orbiting) and there were gravitons producing the gravity around the BHs the effective graviton field would be the summation centered on the center of mass (COM) of EACH of the BHs which effectively is the COM of both (the barycenter). If there were 2 BHs (orbiting each other) they would be binary black holes (BBH) and if there were gravitons producing the gravity around the BHs the effective graviton field would be the summation centered on the center of mass (COM) of EACH of the BHs. But now the center of mass (COM) of EACH of the BHs is moving in space relative to an observer so the observer will be getting waves of gravitons depending on the geometry of the BBH and the speed of the graviton. So from a very long way away it might appear for ease of calculation that the effect is from the COM (R in the above formulas #59 http://www.scienceforums.net/topic/94060-what-is-the-best-3d-description-of-gravitational-waves/page-3#entry913453)and the waves are spherical around this R). For the formulas can't be used to describe the waves closer in because they don't originate from the barycenter but the COM each mass forming the barycenter, and the distances to these COMs varies, depending on separation and orbital speed, (calculated by finding omega). So we would have a BBH geometry, waves (of gravitons) and the effect of gravitons on mass (yet to be discovered). I haven't mentioned path of a graviton - maybe we will work that one out in the thread on the Shapiro effect of BBHs. I would tend to think a graviton is not influenced by mass so the graviton always travel "straight" unlike light. No matter how massive a BH gets the gravitons still get out so the rules about gravitational time dilation can't apply to gravitons. BHs stop EM getting out but don't stop gravitons. Am I saying light and gravitons travel at different speeds? They seem too when coming out of BHs at least. Edited March 28, 2016 by Robittybob1
swansont Posted March 28, 2016 Posted March 28, 2016 Could you throw me a tidbit and explain it a general introductory way why(or how) these vectors -the arrows you have shown in the animation in in your post#48- don't add linearly? Is it because they are not actually vectors but their equivalent in spacetime ? They wouldn't be tensors ,would they? Or are they just a schematic representation and not to be taken at all literally? What do you think is supposed to add linearly? AFAICT the animation tells you how much stretching you get as a function of distance from the central point (and of time) Strain is a fractional change in length, so larger lengths will see more lengthening. IOW, you should expect to see larger arrows further from the central point. I haven't mentioned path of a graviton - maybe we will work that one out in the thread on the Shapiro effect of BBHs. I would tend to think a graviton is not influenced by mass so the graviton always travel "straight" unlike light. So what is spiralling?
Robittybob1 Posted March 28, 2016 Author Posted March 28, 2016 (edited) ... So what is spiralling? Gravitational waves are waves of gravitons (gravitational effect) and the effective amplitudes (or strength of effect) is a pattern like a 3D spiral (like water out of the garden sprinkler each one of the droplets is going straight but there is the overall image of a spiral of water. Stand close to it and you will get waves of water at intervals 2 per revolution). Edited March 28, 2016 by Robittybob1
Strange Posted March 28, 2016 Posted March 28, 2016 Is " the sum of two gravitational waves" correct terminology in this case ? The black hole to the right of the animation (the one that I put there in my mind's eye) is not actually producing gravitational waves is it? Sorry, I misunderstood. I thought you were talking about the interaction of waves from different sources (perhaps because I had just read something about that). I assume the interaction of the waves with a static source, such as a black hole, is also non-trivial. Would it be correct to refer to that gravitational field (at the point where it meets the gravitational wave ) as a "standing wave" ? or just a field with "curved fronts" that look like a wavefront. I would say a (statically) curved surface is a better analogy.
geordief Posted March 28, 2016 Posted March 28, 2016 (edited) What do you think is supposed to add linearly? AFAICT the animation tells you how much stretching you get as a function of distance from the central point (and of time) Strain is a fractional change in length, so larger lengths will see more lengthening. IOW, you should expect to see larger arrows further from the central point. Well I never expected anything to add linearly. My question was not rhetorical (as phrased it can be taken either way I see now but I actually intended it to be taken in a "neutral" way) . It was straight bat -a request for further clarification. But to address your question as to what I expected to be added it was (a) those "vectors" in Strange's animation in post #48 and (b) (if they exist) corresponding vectors associated with the pre-existing gravity field through which that gravitational wave is passing (I added a "convenient" black hole to the right hand side of the animation -off the page - to highlight /emphasize this existing gravitational field. I have no doubt my question holds many confusing misconceptions but I have tried to be as clear as I can Perhaps I could have more simply asked " What is the mechanism whereby a gravitational wave interacts/combines with the gravity field through which it passes?" Sorry, I misunderstood. I thought you were talking about the interaction of waves from different sources (perhaps because I had just read something about that). I assume the interaction of the waves with a static source, such as a black hole, is also non-trivial. I would say a (statically) curved surface is a better analogy. thanks I think I have had enough lessons for the time being Edited March 28, 2016 by geordief
Robittybob1 Posted March 28, 2016 Author Posted March 28, 2016 Well I never expected anything to add linearly. My question was not rhetorical (as phrased it can be taken either way I see now but I actually intended it to be taken in a "neutral" way) . It was straight bat -a request for further clarification. But to address your question as to what I expected to be added it was (a) those "vectors" in Strange's animation in post #48 and (b) (if they exist) corresponding vectors associated with the pre-existing gravity field through which that gravitational wave is passing (I added a "convenient" black hole to the right hand side of the animation -off the page - to highlight /emphasize this existing gravitational field. I have no doubt my question holds many confusing misconceptions but I have tried to be as clear as I can Perhaps I could have more simply asked " What is the mechanism whereby a gravitational wave interacts/combines with the gravity field through which it passes?" Edit : I see Strange has cross posted with me in reply to my last question and so I will have a look at it now. A more easy to understand question would be what if there were two BBHs (a total of 4 BHs) producing GWs at the same time. Do their vectors add?
swansont Posted March 28, 2016 Posted March 28, 2016 Well I never expected anything to add linearly. My question was not rhetorical (as phrased it can be taken either way I see now but I actually intended it to be taken in a "neutral" way) . It was straight bat -a request for further clarification. But to address your question as to what I expected to be added it was (a) those "vectors" in Strange's animation in post #48 and (b) (if they exist) corresponding vectors associated with the pre-existing gravity field through which that gravitational wave is passing (I added a "convenient" black hole to the right hand side of the animation -off the page - to highlight /emphasize this existing gravitational field. I have no doubt my question holds many confusing misconceptions but I have tried to be as clear as I can Perhaps I could have more simply asked " What is the mechanism whereby a gravitational wave interacts/combines with the gravity field through which it passes?" These are two separate issues. The animation in post 48 is showing the strain — the stretching of spacetime. But you mention the gravity field, and that's the curvature of the spacetime. Those are not the same thing.
Robittybob1 Posted March 28, 2016 Author Posted March 28, 2016 Swansont - did my answers help? #66 and #68 Can you see why a 3D sphere makes sense?
Strange Posted March 28, 2016 Posted March 28, 2016 A more easy to understand question would be what if there were two BBHs (a total of 4 BHs) producing GWs at the same time. Do their vectors add? That is the question I thought was being asked. They do combine, but not in a simple way like light waves.
geordief Posted March 28, 2016 Posted March 28, 2016 These are two separate issues. The animation in post 48 is showing the strain — the stretching of spacetime. But you mention the gravity field, and that's the curvature of the spacetime. Those are not the same thing. to a layman it seems like they are closely related though. Is the connection that mass (et al) curves spacetime and that gravitational waves (as an analogy) "pass a current" through that curvature?
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