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#19
Mar3010, 05:48 PM

P: 894




#20
Mar3010, 06:21 PM

P: 1,540

I know someone (online) who is a numerical relativist working on the 2body problem at The API in Jena (Germany), but if he's on this forum I don't know what his nickname is. He's a recent PhD so I'd say that would work... maybe I can ask him to come here, or I can relay a question to him if you like?



#21
Mar3010, 06:36 PM

P: 53

Simulation = nbody numerical integration. So is there some GR software that can do Solar system or is GR good just for black holes? 


#22
Mar3010, 06:47 PM

P: 53

I have no idea why I typed QM where I clearly meant to say GR.
 Can GR model the Solar system and can you point any such software? Write down the equation and I will do it in less than 5 hours. Are you not a programmer? Surely once you have a function to evolute motion of two bodies, like two black holes, then of course you should be able to plug in any number bodies and solve the nbody problem two by two, that's what computers do, why would that be any more waste than doing spinning black holes? Are you really saying that no one ever even bothered to check those GR equations by simulating complete Solar system? Why then do you think those equations are better than Newton's equations, how can you verify them otherwise, by observing black holes collisions ? 


#23
Mar3010, 07:15 PM

P: 986

It is not necessary to use numerical GR to model solar system, because solar system can be modelled analytically to a high degree of accuracy. GR corrections to Newton's law are in good agreement with experiment.
Black hole collisions, on the other hand, can't be modelled analytically, numerical simulations are the way to go. 


#24
Mar3010, 09:06 PM

P: 894

But more than that, it is a waste of computer time because you don't seem to understand how massive these calculations are. Especially with your 5 hour comment. Since you clearly do not know this field, can you please calm the tone down some, for if you are asking questions of "experts"/students you might as well trust their advice in the field you do not know, or why bother asking? So, to address the implicit question: Why are the computations so involved? In Newtonian mechanics, the gravitational force is instantaneous at a distance, and spacetime is not an active player. The state is given merely by the position and velocity of the bodies. These are the only things you need to keep track of. Now in GR the spacetime itself is dynamic. So depending on how finely you want to "grid" spacetime, you have a HUGE number of state variables to keep track of. To see modifications from the simple "1 body approximation" I explained above, to use full GR for the solar system would require a tremendous amount of computation time just to get that extra little corrections (which could probably be done much easier with a different GR approximation, like Linearized GR, which is reminescent of solving electrodynamics equations ... since it is linear, many EM type approximations can be applied). And why do we think GR is better than Newtonian gravity? It has already been explained to you multiple times now that Newtonian gravity already couldn't explain the planetary motion to the degree of experimental accuracy in Einstein's time when he proposed GR. Let's make this very clear right now. Are you denying that Newton's gravity cannot explain the precession of mercury (already mentioned to you previously)? Are you actually claiming these must be error in measurements since it disagrees with Newton? If you are here to promote the Newtonian view over Relativity, I am not interested in having this discussion any further. 


#25
Mar3010, 09:12 PM

P: 1,540

@Dunnis: You think that ANY nBody problem is solvable in GR hm? The 2body is unsolved, and 3+ is considered IMPOSSIBLE. Your ignorance of the field, and the nature of how PDE's work is staggering given your arrogance and boorish manner. You have little to say, no concept of what you're talking about, yet you say it loudly and rudely in the faces of those who tried to help you.
If you want to be deluded, plese be so in private eh? 


#26
Mar3010, 09:20 PM

P: 894

If you can only relay questions, I guess what I wrote in post 9 is along the lines of what I'm curious about. I have a feeling my ignorance of the field would require some translating before those are useful questions though. Probably the most approachable question is this: Naively, when I look at Einstein's equations, it only gives information for the Ricci curvature ... so how do you determine the Weyl curvature evolution in numerical GR? My understanding is that in analytic solutions they use symmetry arguments and boundary conditions at infinity to constrain the form of the metric, which effectively puts in the Weyl terms. Maybe that is not correct, but even if it is along the right track, in dynamic situations you don't have those luxuries. Naively it looks like the Weyl curvature can just evolve however it wants (I assume that is wrong for some reason though). 


#27
Mar3010, 09:42 PM

P: 451

I would hope that there is some way to give an initial placement and velocity to Nbodies and then through some sort of relaxation technique take an initial guessed (known wrong) spacetime condition and relax it to the correct spacetime condition. On the coordinates the paper offered in an earlier post covers some of this. They use two systems of coordinates one fixed and one deformable. The issue is in GR you do not have a fixed cartesian (sic) grid the spacetime deforms! So what do you simulate? Give me a lever and a place to stand and I will move the Earth, in this case give me a place to stand and I will simulate GR. 


#28
Mar3010, 10:50 PM

Sci Advisor
P: 674

That said, something like the solar system does not need full GR. It is adequate to use what is called the postNewtonian approximation of it. This assume weak fields and slow speeds to analytically simplify the equations. The result can be simulated without much effort. The very lowest order corrections have a similar effect to making the gravitational field of the Sun look like it is coming from a somewhat more oblate object. This kind of thing is included in modern simulations of the solar system. 


#29
Mar3010, 11:17 PM

Sci Advisor
P: 8,365



#30
Mar3010, 11:19 PM

Sci Advisor
P: 674

This requires writing Einstein's equation in terms of geometric objects intrinsic to the hypersurfaces. They all have an intrinsic (3D) metric as well as an extrinsic curvature. These things can be related to the 4D curvature (and therefore Einstein's equation) using the GaussCodazzi equations. You also have to worry about how the hypersurfaces stack on top of each other. This is parameterized by a lapse function ("relative time separation between leaves") and a shift vector ("shearing between leaves"). The lapse and shift are not constrained by Einstein's equation, and must be specified. Bad choices quickly lead to singular coordinate systems (and crashed computers). In terms of these variables, Einstein's equation reduces to a pair of constraint equations and a pair of evolution equations for 3metric and extrinsic curvature. The constraints are analogous to Laplace equations, and do not involve time derivatives. If they are satisfied on one hypersurface, one can show that use of the evolution equations alone guarantees that they are satisfied on all other hypersurfaces. The problem of specifying initial data is very difficult. So is the boundary problem. There are also a lot of subtleties with precisely which form of the Einstein equation to use, which variables are most efficient (the ones I outlined above aren't the best for numerical stability), lapse and shift choices, etc. Although I'm not working in numerical relativity, I have a fair bit of knowledge about it if you have more specific questions. 


#31
Mar3110, 05:53 AM

P: 53




#32
Mar3110, 06:04 AM

P: 53

@Dragger: My angry friend, with slight amusement I acknowledge your emotional distress, but I do not recall to have been talking to you before, so can you just tell me what is it we are arguing about and what did I say to make you cry?  You are confusing analytical and dynamical "solution", former is 'exact' and later is 'approximation', by definition. You surely do not mean to deny that classical modeling of the sun, planets and all their moons  with high degree of precision and absolute stability through millions of years of simulated time  would be impossible, do you?



#33
Mar3110, 06:53 AM

P: 1,540

I think that's enough playing footsie, don't you? The point of the 2body problem, beyond the actual model, is that when we talk about it we mean the EXACT solution. Again, obviously, when I say that 3+ is unsolvable, I am again speaking of EXACT solutions. You seem to be a codejockey with delusions "above your station" so to speak. You were told quite a while ago that you were pursuing a deadend, a "waste of computer time", and instead of accepting that as the state of affairs, you've reformulated your original pointless query into a new one. The answer is the same, and it's the one Nabeshin, Justin Levy, and Hamster gave you. Like it or not. You're acting like a moderately well educated (I say moderate given "you're" instead of "your"... always a giveaway) brat. If what you're asking for is so easy, why not hit the old internet and find that equation? Better yet, find something simpler and see if you really CAN do any of what you claim. Btw, this whole post is absolutely SOAKED in my angry tears.  @JustinLevy: I've invited him to join us here, or if he'd prefer not to, to relay your question. I suspect he might come over here, if he isn't already however. 


#34
Mar3110, 07:29 AM

P: 53

..it's waaaaste of time... it's sooo unnecessary. Awww, you had me at "hello". [edit: someone actually edited my post and removed the part where I said how amused I was with this comment, so I'll just follow Dragger's example, put 'rotating head' and call this person delusional, as that seem to the a proper and allowed way to communicate around here. Hilarious indeed.] 


#35
Mar3110, 07:36 AM

P: 1,540

@Dunnis: "The simple case scenario with only two planets" :Rofl: ... Well, it's been nice knowing you on this site Dunnis, but I think the rest of us will be wishing you Adieu fairly soon. Insulting other users (one of which, not me) was trying to help you, is a quick way to feel the wintery freshness of BAN.
Oh, and... "No, but I would like to know how was that conclusion made, when and by whom."... ok... try Google, or a textbook, or school! You want to be spoonfed GR... not going to happen, for you, or anyone. 


#36
Mar3110, 11:23 AM

Sci Advisor
P: 674

http://arxiv4.library.cornell.edu/abs/0802.3371: This paper shows that the solar system is significantly more stable over very long time scales with postNewtonian corrections. trsnew.jpl.nasa.gov/dspace/bitstream/2014/8903/1/021476.pdf: This states that PN effects have been included in ephemeris calculations needed for spacecraft navigation since the 1960's. http://arxiv.org/abs/astroph/0701612: PN Nbody simulation. There are (and have been) experiments of many kinds in the solar system that accurately test the PN equations and look for deviations that might signal a problem with GR. 


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