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

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

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

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

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.

* - 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.

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

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.

"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

"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.