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Nicolaas Vroom
Sep9-04, 03:03 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Starting point of this posting is chapter 15.3\n"Advance of the perihelion of Mercury"\nthe pages 195 to 198 in the book\n"Introducing Einstein\'s Relativity" by Ray d\'Inverno.\n\nIMO the whole purpose of this exercise is to calculate\nwith a model the future positions of the planets\n(i.e. Mercury) solely based on past observations\n(positions) as acurate as possible.\n\nIn order to do this you need a 3D grid of measuring\nrods and clocks. The clocks are located at the cross\nsections of the rods and the clocks are all synchronised\nwith a clock at the origin.\nIn order to predict you need a model. One model can be\neq. 15.25 which is the relativistic version of Binet\'s eq.\nand differs from Newton\'s by the presence of the last term.\n\nUsing this 3D grid and the clocks you can perform\nthe past observations of the positions of the planets.\nThis is important because eq. 15.25 contains constants.\nIMO the only correct way to calculate those constants\n(for example m) is to use eq. 15.25 based on past\nobservations.\n\nOne parameter discussed is proper time tau.\nIn the grid there are no moving clocks involved.\nOn the other hand if you attach a clock onto Mercury\nand you synchronise this clock with the nearest clock\nfrom the grid, you will see that this moving clock\nconstantly runs behind the nearest clock from the grid\n(based on its moving position) and that this difference\nis increasing (at variable rate).\n\nI expect that in order to calculate proper time tau\nyou can also use eq. 8.16 i.e. as a function of v and c.\nI expect that v is measured with the clocks from the\n3D grid.\n\nIN eq 15.22 a constant k is calculated by means\nof a factor dtau/dt (multiplied by 1-2m/r).\nI expect that k is only a constant because r is variable.\n\nWhat amases me that in equation 15.25 the factor k\nhas disappeared. Does this mean that the concept\nproper time is of less importance inorder to calculate\nthe precession of Mercury ?\n\nHow do I compare the above with the following\nsentence from\nhttp://arxiv.org/PS_cache/gr-qc/pdf/0103/0103044.pdf\nThe Meaning of Einstein\'s Equation\nAuthors: John C. Baez, Emory F. Bunn\nat page 3 of 19:\n"Thus the concept of inertial frame, so important in SR\nis banned from GR"\n\nNicolaas Vroom\nhttp://users.pandora.be/nicvroom/\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Starting point of this posting is chapter 15.3
"Advance of the perihelion of Mercury"
the pages 195 to 198 in the book
"Introducing Einstein's Relativity" by Ray d'Inverno.

IMO the whole purpose of this exercise is to calculate
with a model the future positions of the planets
(i.e. Mercury) solely based on past observations
(positions) as acurate as possible.

In order to do this you need a 3D grid of measuring
rods and clocks. The clocks are located at the cross
sections of the rods and the clocks are all synchronised
with a clock at the origin.
In order to predict you need a model. One model can be
eq. 15.25 which is the relativistic version of Binet's eq.
and differs from Newton's by the presence of the last term.

Using this 3D grid and the clocks you can perform
the past observations of the positions of the planets.
This is important because eq. 15.25 contains constants.
IMO the only correct way to calculate those constants
(for example m) is to use eq. 15.25 based on past
observations.

One parameter discussed is proper time \tau.
In the grid there are no moving clocks involved.
On the other hand if you attach a clock onto Mercury
and you synchronise this clock with the nearest clock
from the grid, you will see that this moving clock
constantly runs behind the nearest clock from the grid
(based on its moving position) and that this difference
is increasing (at variable rate).

I expect that in order to calculate proper time \tau
you can also use eq. 8.16 i.e. as a function of v and c.
I expect that v is measured with the clocks from the
3D grid.

IN eq 15.22 a constant k is calculated by means
of a factor dtau/dt (multiplied by 1-2m/r).
I expect that k is only a constant because r is variable.

What amases me that in equation 15.25 the factor k
has disappeared. Does this mean that the concept
proper time is of less importance inorder to calculate
the precession of Mercury ?

How do I compare the above with the following
sentence from
http://arxiv.org/PS_cache/gr-qc/pdf/0103/0103044.pdf
The Meaning of Einstein's Equation
Authors: John C. Baez, Emory F. Bunn
at page 3 of 19:
"Thus the concept of inertial frame, so important in SR
is banned from GR"

Nicolaas Vroom
http://users.pandora.be/nicvroom/

Nicolaas Vroom
Oct1-04, 04:22 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n"Nicolaas Vroom" &lt;nicolaas.vroom@pandora.be&gt;\nschreef in bericht news:HHB%c.240136\\$mA5.12401702@phobos.telenet-ops.be...\n&gt;\n&gt; In order to do this you need a 3D grid of measuring\n&gt; rods and clocks. The clocks are located at the cross\n&gt; sections of the rods and the clocks are all synchronised\n&gt; with a clock at the origin.\n\nOne of the best url\'s to study such a grid is the following:\nhttp://www.astro.utu.fi/EGal/elg/ELG3D.html\nThe two main questions are:\n1. Is such a grid the right tool to study GR\n(Finally in order to simulate the planet Mercury)\n2. If yes: What is the metric (tensor) involved.\n\nThe "centre" of the grid shows the Milkway galaxy\nas a large yellow dot and 3 other major galaxies.\nEach of those galaxies is surrounded by a cloud\nof smaller galaxies in red.\n\nHowever the same grid can be used as a part of\nour Milkyway galaxy.\nThe Yellow dot in the centre is than the Sun\nsurrounded by local stars.\n\nAt an even smaller scale the centre is still the Sun\nsurrounded by planets.\n\nWhat ever the scale at the crossing points of the\ngrids there are clocks (and a light), all synchronised.\nWhen you look at clocks on the grid, all clocks show\nexactly the same time.\nHowever that is not what you see when you are\nat the center of the grid.\nWhen you are at the center of the grid and when there\nare no masses involved and when you look along the\nline x=0 all clocks at different distances show a different\ntime (as a function of distance and c).\nIn fact you only see the first clock (light).\n\nWhen the whole grid only contains one object (one mass)\nthe object moves in a perfect straight line through the grid.\n\nSuppose this object crosses the line x=0 very close to the\nclock which shows 6.00\n(Suppose all the clocks show ONE hour difference)\nSuppose the clock at the center shows 12.00.\nThe question is what will be observed by an observer\nat the center ?\nThe observer will not see the clocks at 11.00, 10.00, 9.00\n8.00 7.00 and 6.00 but the observer will be able\nto see the clocks (light from the clocks) at 5.00 and earlier\nbecause light from those clocks is bended by the (moving)\nmass. (This only for a small period of time)\n\nHowever, and this is important, you do not have to include\nthis light bending in order to describe the movent of your\nmoving object. (i.e. all the objects)\n\nSuppose the center of the grid shows the Sun and there\nis only one planet (the Earth)\nSuppose the Earth crosses the line x=0 twice\nat x= x0 and x= -x0. Suppose there are two clocks\nfixed at the grid and there is one moving clock.\nSuppose you synchronise your moving clock with\nthe clock at x=x0.\nWhat will happen that your moving clock will run\nbehind the two fixed clocks after one revolution\nand that this discrepancy will increase after each\nrevolution.\nHowever, again, you do not have to include this behavior\n(slow down) of the moving clock to include in order to\ndescribe the movent of your moving object. (and objects)\n\nBut you must take it into account when you convert\nearth based observations into grid based "observations"\nand vice versa.\nThe same with light bending.\nThis becomes more complex when the sun itself is moving\nin your grid, but the concept is the same.\n\nThe final question to answer is what is the metric of the grid.\n\nWhat is the proper time in the grid ?\n\n&gt; Nicolaas Vroom\n&gt; http://users.pandora.be/nicvroom/\n&gt;\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Nicolaas Vroom" <nicolaas.vroom@pandora.be>
schreef in bericht news:HHB%c.240136$mA5.12401702@phobos.telenet-ops.be...
>
> In order to do this you need a 3D grid of measuring
> rods and clocks. The clocks are located at the cross
> sections of the rods and the clocks are all synchronised
> with a clock at the origin.

One of the best url's to study such a grid is the following:
http://www.astro.utu.fi/EGal/elg/ELG3D.html
The two main questions are:
1. Is such a grid the right tool to study GR
(Finally in order to simulate the planet Mercury)
2. If yes: What is the metric (tensor) involved.

The "centre" of the grid shows the Milkway galaxy
as a large yellow dot and 3 other major galaxies.
Each of those galaxies is surrounded by a cloud
of smaller galaxies in red.

However the same grid can be used as a part of
our Milkyway galaxy.
The Yellow dot in the centre is than the Sun
surrounded by local stars.

At an even smaller scale the centre is still the Sun
surrounded by planets.

What ever the scale at the crossing points of the
grids there are clocks (and a light), all synchronised.
When you look at clocks on the grid, all clocks show
exactly the same time.
However that is not what you see when you are
at the center of the grid.
When you are at the center of the grid and when there
are no masses involved and when you look along the
line x=0 all clocks at different distances show a different
time (as a function of distance and c).
In fact you only see the first clock (light).

When the whole grid only contains one object (one mass)
the object moves in a perfect straight line through the grid.

Suppose this object crosses the line x=0 very close to the
clock which shows 6.00
(Suppose all the clocks show ONE hour difference)
Suppose the clock at the center shows 12.00.
The question is what will be observed by an observer
at the center ?
The observer will not see the clocks at 11.00, 10.00, 9.00
8.00 7.00 and 6.00 but the observer will be able
to see the clocks (light from the clocks) at 5.00 and earlier
because light from those clocks is bended by the (moving)
mass. (This only for a small period of time)

However, and this is important, you do not have to include
this light bending in order to describe the movent of your
moving object. (i.e. all the objects)

Suppose the center of the grid shows the Sun and there
is only one planet (the Earth)
Suppose the Earth crosses the line x=0 twice
at x= x0 and x= -x0. Suppose there are two clocks
fixed at the grid and there is one moving clock.
Suppose you synchronise your moving clock with
the clock at x=x0.
What will happen that your moving clock will run
behind the two fixed clocks after one revolution
and that this discrepancy will increase after each
revolution.
However, again, you do not have to include this behavior
(slow down) of the moving clock to include in order to
describe the movent of your moving object. (and objects)

But you must take it into account when you convert
earth based observations into grid based "observations"
and vice versa.
The same with light bending.
This becomes more complex when the sun itself is moving
in your grid, but the concept is the same.

The final question to answer is what is the metric of the grid.

What is the proper time in the grid ?

> Nicolaas Vroom
> http://users.pandora.be/nicvroom/
>