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"> 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/
"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/