View Full Version : inertial reference frames
alistair
Jun12-04, 07:20 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>I can make a local inertial reference frame in a gravitational field\nby creating a frame that is small but close to the source of curvature\nof space-time.\nAlternatively I can make a local inertial reference frame by creating\na frame that is large but a long distance from the source of curvature\nof space-time.\nIf the reference frame has a mass, is there a quantitative\nrelationship in general relativity between the mass/size of the frame\nand its distance from the source of curvature of space-time?\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>I can make a local inertial reference frame in a gravitational field
by creating a frame that is small but close to the source of curvature
of space-time.
Alternatively I can make a local inertial reference frame by creating
a frame that is large but a long distance from the source of curvature
of space-time.
If the reference frame has a mass, is there a quantitative
relationship in general relativity between the mass/size of the frame
and its distance from the source of curvature of space-time?
Igor Khavkine
Jun13-04, 09:39 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>\nOn Sat, 12 Jun 2004 12:20:55 +0000, alistair wrote:\n\n> If the reference frame has a mass, is there a quantitative relationship in\n> general relativity between the mass/size of the frame and its distance\n> from the source of curvature of space-time?\n\nA reference frame is a figment of imagination also known as a coordinate\nsystem. It has as much mass as the contents of a bag full of integers.\n\nIgor\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>On Sat, 12 Jun 2004 12:20:55 +0000, alistair wrote:
> If the reference frame has a mass, is there a quantitative relationship in
> general relativity between the mass/size of the frame and its distance
> from the source of curvature of space-time?
A reference frame is a figment of imagination also known as a coordinate
system. It has as much mass as the contents of a bag full of integers.
Igor
tessel@tum.bot
Jun22-04, 03:13 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>On Sat, 12 Jun 2004, alistair wrote:\n\n> I can make a local inertial reference frame in a gravitational field by\n> creating a frame that is small but close to the source of curvature of\n> space-time. Alternatively I can make a local inertial reference frame by\n> creating a frame that is large but a long distance from the source of\n> curvature of space-time.\n\nIn curved spacetimes, "local Lorentz frames" are defined in frame bundle.\nEach such frame consists of a quadruple of unit norm vector fields,\nmutually orthogonal, one timelike and three spacelike, with the timelike\ncurves corresponding to the world lines of a family of "observers".\n\nApparently you want to think of the quadruple at one event as allowing you\nto construct a "very small" inertial frame in a "very small" piece of the\ntangent space to that event, and then project into M itself. Clearly,\nthis should work, if you proceed with sufficient care.\n\n> If the reference frame has a mass, is there a quantitative relationship\n> in general relativity between the mass/size of the frame and its\n> distance from the source of curvature of space-time?\n\nSuggestion: think about Rindler observers in Minkowski spacetime. Can you\nset up and answer an analogous question? Can you now relate your\ndiscussion of a suitable Rindler scenario to an attempt to construct a\n"small" and "almost inertial" frame at some "location" in a Schwarzschild\nvacuum?\n\n"T. Essel" (hiding somewhere in cyberspace)\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>On Sat, 12 Jun 2004, alistair wrote:
> I can make a local inertial reference frame in a gravitational field by
> creating a frame that is small but close to the source of curvature of
> space-time. Alternatively I can make a local inertial reference frame by
> creating a frame that is large but a long distance from the source of
> curvature of space-time.
In curved spacetimes, "local Lorentz frames" are defined in frame bundle.
Each such frame consists of a quadruple of unit norm vector fields,
mutually orthogonal, one timelike and three spacelike, with the timelike
curves corresponding to the world lines of a family of "observers".
Apparently you want to think of the quadruple at one event as allowing you
to construct a "very small" inertial frame in a "very small" piece of the
tangent space to that event, and then project into M itself. Clearly,
this should work, if you proceed with sufficient care.
> If the reference frame has a mass, is there a quantitative relationship
> in general relativity between the mass/size of the frame and its
> distance from the source of curvature of space-time?
Suggestion: think about Rindler observers in Minkowski spacetime. Can you
set up and answer an analogous question? Can you now relate your
discussion of a suitable Rindler scenario to an attempt to construct a
"small" and "almost inertial" frame at some "location" in a Schwarzschild
vacuum?
"T. Essel" (hiding somewhere in cyberspace)
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