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Galactic Simulations and the propagation of Gravity
This posting arose out of a discussion on Galactic simulations. Why do
simulations assume gravity is propagated instantaneously? The answer is it is difficult to calculate anything different and the inaccuracies are small. "But surely you can simply say that the gravity we see is the gravity d/c ago where d is the distance?" No it is not as simple as that. Let us look at the retarded potential electromagnetically. http://en.wikipedia.org/wiki/Retarded_potential Here we are integrating with t' = t-|x - x'|/c. BUT we are integrating POTENTIALS and not fields. To get an electromagnetic field we have to differentiate. It is NOT simply a case of an electric field |x-x'|/c ago. The theory of retarded potentials tells us, amongst other things, that if we put a sinusoidal voltage on a piece of wire we will get radiation which varies to the square of the size for short lengths of wire. So far so good. What happens for gravity? http://en.wikipedia.org/wiki/Gravitational_waves Well our gravitational "potential" is a lot more complicated than the electromagnetic case. To get gravitational pull you need to take a tensor and differentiate twice. In fact if we have "gravity" going round our loop of wire we get a fourth power law. Calculating the true gravitational field, with GTR included is thus rather complicated. Is an instantaneous rate of travel for gravity justified. For 600km/s with relative velocities a lot smaller it probably is. A full calculation is not justified in complexity terms. In fact t'=|x-x'|/c would in fact be more wrong. You see a body is surrounded by its gravitational field which travels with it. If two bodies pass each other at speed the second body will see this gravitational field. In fact the best "fudge factor" would probably be to do a calculation on the basis of SPECIAL Relativity. - Ian Parker |
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Galactic Simulations and the propagation of Gravity
Ian Parker wrote:
This posting arose out of a discussion on Galactic simulations. Why do simulations assume gravity is propagated instantaneously? The answer is it is difficult to calculate anything different and the inaccuracies are small. "But surely you can simply say that the gravity we see is the gravity d/c ago where d is the distance?" No it is not as simple as that. Let us look at the retarded potential electromagnetically. http://en.wikipedia.org/wiki/Retarded_potential Here we are integrating with t' = t-|x - x'|/c. BUT we are integrating POTENTIALS and not fields. To get an electromagnetic field we have to differentiate. It is NOT simply a case of an electric field |x-x'|/c ago. The theory of retarded potentials tells us, amongst other things, that if we put a sinusoidal voltage on a piece of wire we will get radiation which varies to the square of the size for short lengths of wire. So far so good. What happens for gravity? http://en.wikipedia.org/wiki/Gravitational_waves Well our gravitational "potential" is a lot more complicated than the electromagnetic case. To get gravitational pull you need to take a tensor and differentiate twice. In fact if we have "gravity" going round our loop of wire we get a fourth power law. Calculating the true gravitational field, with GTR included is thus rather complicated. Is an instantaneous rate of travel for gravity justified. For 600km/s with relative velocities a lot smaller it probably is. A full calculation is not justified in complexity terms. In fact t'=|x-x'|/c would in fact be more wrong. You see a body is surrounded by its gravitational field which travels with it. If two bodies pass each other at speed the second body will see this gravitational field. In fact the best "fudge factor" would probably be to do a calculation on the basis of SPECIAL Relativity. - Ian Parker If gravitational lightspeed delay were integrated into summed massed points in galaxies the dynamics calculations would be much slower - even in customized hardware and supercomputers. Publication would be hampered. Darlings of empirical confabulation like Dark Matter might fall out of fashion. If everybody agrees a model is valid, what difference does it make if it does not model observation? No dissenters! The singular error is to make a real time prediction. Christ coming back is good. Christ coming back next Thursday is bad. SUSY proton decay is good. Super-Kamiokande looking for proton decay on schedule is bad. NINJA loans are good, for all MBAs know tomorrow - when payment is due - is aways put off into future quarters where its value has been inflated away into insignificance. Tomorrow having arrived last Thursday is bad. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 |
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Galactic Simulations and the propagation of Gravity
On 23 Feb, 16:19, Uncle Al wrote:
* - Ian Parker If gravitational lightspeed delay were integrated into summed massed points in galaxies the dynamics calculations would be much slower - even in customized hardware and supercomputers. *Publication would be hampered. *Darlings of empirical confabulation like Dark Matter might fall out of fashion. You have to make a compromise at some point. - Ian Parker |
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Galactic Simulations and the propagation of Gravity
Ian Parker wrote:
This posting arose out of a discussion on Galactic simulations. Why do simulations assume gravity is propagated instantaneously? The answer is it is difficult to calculate anything different and the inaccuracies are small. Better answer: as long as one stays well away from any black holes or super-massive objects, the Newtonian approximation to GR is adequate for most of these computations [#]. In this approximation, gravity does not propagate, and its effects are indeed instantaneous. [#] for a 1-solar-mass star, this approximation is very good anywhere outside the orbit of mercury. In galactic computations stars don't get nearly that close. So only near to objects much more massive than the sun is there likely to be a problem. Note that for a specified accuracy one can COMPUTE how far one must stay from any given object. The way this is reconciled with the finite "speed of gravity" in the full theory is that the Green's function for the linear approximation to GR has propagation at c, but like electrodynamics it "extrapolates" from the retarded position and gives an answer very close to that obtained by using the instantaneous position of the source. The Newtonian approximation then applies v c to this. In fact the best "fudge factor" would probably be to do a calculation on the basis of SPECIAL Relativity. No. Stick to known approximations to GR, for which the limitations and error bounds are known. Your guess does not carry with it knowledge of its range of validity or an estimate of the error involved, and thus is quite dangerous. Tom Roberts |
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Galactic Simulations and the propagation of Gravity
On Feb 23, 7:53*pm, Tom Roberts wrote:
Ian Parker wrote: This posting arose out of a discussion on Galactic simulations. Why do simulations assume gravity is propagated instantaneously? The answer is it is difficult to calculate anything different and the inaccuracies are small. Better answer: as long as one stays well away from any black holes or super-massive objects, the Newtonian approximation to GR is adequate for most of these computations [#]. In this approximation, gravity does not propagate, and its effects are indeed instantaneous. If c is infinite in its frame, sure. Gravity is ties to dimensions. It comes automatically in the third dimension. We won't feel the gravitational wave effects of a Supernovae explosion instantaneously. The gravitational waves or pulses caught on camera sending a wave on the environment propagated with the speed of light. * * * * [#] for a 1-solar-mass star, this approximation is very good * * * * anywhere outside the orbit of mercury. In galactic * * * * computations stars don't get nearly that close. So only near * * * * to objects much more massive than the sun is there likely to * * * * be a problem. Note that for a specified accuracy one can * * * * COMPUTE how far one must stay from any given object. The way this is reconciled with the finite "speed of gravity" in the full theory is that the Green's function for the linear approximation to GR has propagation at c, but like electrodynamics it "extrapolates" from the retarded position and gives an answer very close to that obtained by using the instantaneous position of the source. The Newtonian approximation then applies v c to this. Gravity can form waves and can be created as 'mass that is not there' (dark matter). The definition of mass is the amount of particles a system has. Gravity automatically grows with 'body' and is tied to three dimensions naturally, meaning moving from a two dimensional motion to a three dimensional motion adds mass (theoretical physics), while moving down on dimensions reduces mass. Mass adds to forces and 'body'. In fact the best "fudge factor" would probably be to do a calculation on the basis of SPECIAL Relativity. No. Stick to known approximations to GR, for which the limitations and error bounds are known. Your guess does not carry with it knowledge of its range of validity or an estimate of the error involved, and thus is quite dangerous. No, use your own mind, it is the only way to find the answers. |
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Galactic Simulations and the propagation of Gravity
* - Ian Parker
If gravitational lightspeed delay were integrated into summed massed points in galaxies the dynamics calculations would be much slower - even in customized hardware and supercomputers. *Publication would be hampered. *Darlings of empirical confabulation like Dark Matter might fall out of fashion. You have to make a compromise at some point. * - Ian Parker There cannot be obligations by a system of government leader. |
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Galactic Simulations and the propagation of Gravity
So you solve the Helmholtz equation rather than the Laplace equation for
the gravitational potential, what is the big deal? Q Ian Parker wrote: This posting arose out of a discussion on Galactic simulations. Why do simulations assume gravity is propagated instantaneously? The answer is it is difficult to calculate anything different and the inaccuracies are small. "But surely you can simply say that the gravity we see is the gravity d/c ago where d is the distance?" No it is not as simple as that. Let us look at the retarded potential electromagnetically. http://en.wikipedia.org/wiki/Retarded_potential Here we are integrating with t' = t-|x - x'|/c. BUT we are integrating POTENTIALS and not fields. To get an electromagnetic field we have to differentiate. It is NOT simply a case of an electric field |x-x'|/c ago. The theory of retarded potentials tells us, amongst other things, that if we put a sinusoidal voltage on a piece of wire we will get radiation which varies to the square of the size for short lengths of wire. So far so good. What happens for gravity? http://en.wikipedia.org/wiki/Gravitational_waves Well our gravitational "potential" is a lot more complicated than the electromagnetic case. To get gravitational pull you need to take a tensor and differentiate twice. In fact if we have "gravity" going round our loop of wire we get a fourth power law. Calculating the true gravitational field, with GTR included is thus rather complicated. Is an instantaneous rate of travel for gravity justified. For 600km/s with relative velocities a lot smaller it probably is. A full calculation is not justified in complexity terms. In fact t'=|x-x'|/c would in fact be more wrong. You see a body is surrounded by its gravitational field which travels with it. If two bodies pass each other at speed the second body will see this gravitational field. In fact the best "fudge factor" would probably be to do a calculation on the basis of SPECIAL Relativity. - Ian Parker -- CO2 at 390 ppm and counting, put a tiger in your tank -- ESSO commercial |
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Galactic Simulations and the propagation of Gravity
On 24 Feb, 02:53, Tom Roberts wrote:
Ian Parker wrote: This posting arose out of a discussion on Galactic simulations. Why do simulations assume gravity is propagated instantaneously? The answer is it is difficult to calculate anything different and the inaccuracies are small. Better answer: as long as one stays well away from any black holes or super-massive objects, the Newtonian approximation to GR is adequate for most of these computations [#]. In this approximation, gravity does not propagate, and its effects are indeed instantaneous. * * * * [#] for a 1-solar-mass star, this approximation is very good * * * * anywhere outside the orbit of mercury. In galactic * * * * computations stars don't get nearly that close. So only near * * * * to objects much more massive than the sun is there likely to * * * * be a problem. Note that for a specified accuracy one can * * * * COMPUTE how far one must stay from any given object. The way this is reconciled with the finite "speed of gravity" in the full theory is that the Green's function for the linear approximation to GR has propagation at c, but like electrodynamics it "extrapolates" from the retarded position and gives an answer very close to that obtained by using the instantaneous position of the source. The Newtonian approximation then applies v c to this. In fact the best "fudge factor" would probably be to do a calculation on the basis of SPECIAL Relativity. No. Stick to known approximations to GR, for which the limitations and error bounds are known. Your guess does not carry with it knowledge of its range of validity or an estimate of the error involved, and thus is quite dangerous. You are, of course, absolutely right. I looked up the Lense-Thirring effect http://en.wikipedia.org/wiki/Frame-dragging This appears to be the main GTR effect and like gravitational ways the force varies according to (v/c)^2 (unlike magnetism which varies as v/ c). Hence Lense-Thirring is the fudge factor to use. Gravity travels instananeously otherwise. It is instantaneous at the stately pace of the Sun. Papers seem to have been published showing that in neutron stars you assume normal gravity AFTER LT has been callculated. - Ian Parker BTW - LT has recently been verified by an ESA spacecraft. |
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Galactic Simulations and the propagation of Gravity
"Ian Parker" schreef in bericht ... This posting arose out of a discussion on Galactic simulations. Why do simulations assume gravity is propagated instantaneously? The answer is it is difficult to calculate anything different and the inaccuracies are small. I do not agree with this opinion. If you want to simulate the position of the planet Mercury using Newton's Law than you will find that there is a discrepancy between calculated and observed positions. "But surely you can simply say that the gravity we see is the gravity d/c ago where d is the distance?" If you take the above formula into account using Newton's Law and you assume that the speed of gravity is c than you will find that the oveall size of our solar system starts to increase. If you assume that the speed of gravity is a little larger than c than your simulation of Mercury will match observations. Again using Newton's Law. No it is not as simple as that. Let us look at the retarded potential electromagnetically. http://en.wikipedia.org/wiki/Retarded_potential Here we are integrating with t' = t-|x - x'|/c. BUT we are integrating POTENTIALS and not fields. To get an electromagnetic field we have to differentiate. It is NOT simply a case of an electric field |x-x'|/c ago. The theory of retarded potentials tells us, amongst other things, that if we put a sinusoidal voltage on a piece of wire we will get radiation which varies to the square of the size for short lengths of wire. So far so good. The problem is you cannot test this based on observations. The distances on earth are too small. What happens for gravity? http://en.wikipedia.org/wiki/Gravitational_waves Well our gravitational "potential" is a lot more complicated than the electromagnetic case. To get gravitational pull you need to take a tensor and differentiate twice. In fact if we have "gravity" going round our loop of wire we get a fourth power law. Calculating the true gravitational field, with GTR included is thus rather complicated. That is correct. I have doubt if people can use GTR to do a simulation of our solarsystem using GTR. Case 1 Performing a simulation of our solarsystem from scratch using Newton's Law in its simplest form is a rather complicated exercise. What you need are the positions, velocities and masses of all the objects involved at a certain moment t0. In fact what you need is a fixed coordinate system and a fixed clock at the origin of that system. If you position your self at the sun and you look towards the planets and by sheer luck they are all positioned at one point in the sky than you know that the true position at that moment is not in a straight line. You have to make corrections based on your observations in order to find the true positions at the same moment tx. You have to do that multiple times in order to calculate the masses of the objects using Newton's Law. (that have the closest match with all observations) Case 2 If you modify Newton's Law and include gravity propagation than you have to repeat this whole last process of finding the initial position and masses of your solar system. Case 3 Using GTR this whole process is much more complex starting from scratch. What you have to do is described in paragraph 13.1 at the book Introducing Einstein's relativity by Ray d'Inverno namely: "To solve the field equations which consist of ten equations connecting twenty quantities namely the ten components of gab and Tab each" I think you have to add: twenty quantities for each object included. But that is not all. You have to match the results of those calcultions using the same observations as in Case 1 Is an instantaneous rate of travel for gravity justified. For 600km/s with relative velocities a lot smaller it probably is. A full calculation is not justified in complexity terms. In fact t'=|x-x'|/c would in fact be more wrong. You see a body is surrounded by its gravitational field which travels with it. If two bodies pass each other at speed the second body will see this gravitational field. In fact the best "fudge factor" would probably be to do a calculation on the basis of SPECIAL Relativity. Using Newton's Law (Case 1) and Special Relativity IMO is wrong. The same for Case 2. My understanding based on what other people write is this newsgroup is that there is no issue of Gravity Propagation using GTR to describe the movement of galactic objects. As such no SR is required. - Ian Parker Nicolaas Vroom http://users.pandora.be/nicvroom |
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Galactic Simulations and the propagation of Gravity
"Nicolaas Vroom" wrote in message ... "Ian Parker" schreef in bericht ... This posting arose out of a discussion on Galactic simulations. Why do simulations assume gravity is propagated instantaneously? The answer is it is difficult to calculate anything different and the inaccuracies are small. I do not agree with this opinion. I do not agree with your opinion of this opinion. |
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