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Groups > sci.physics.relativity > #401877 > unrolled thread
| Started by | JanPB <filmart@gmail.com> |
|---|---|
| First post | 2016-12-14 22:50 -0800 |
| Last post | 2017-02-14 14:06 -0800 |
| Articles | 20 on this page of 368 — 25 participants |
Back to article view | Back to sci.physics.relativity
Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-14 22:50 -0800
Re: Zero-area Sagnac path and its residual time delay "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2016-12-14 23:35 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-15 09:03 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-15 10:53 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-15 10:56 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-15 11:03 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-15 11:13 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-15 11:27 -0800
Re: Zero-area Sagnac path and its residual time delay Lauretta Nagle <uattea@aeuatte.au> - 2016-12-16 18:05 +0000
Re: Zero-area Sagnac path and its residual time delay Poutnik <poutnik4nntp@gmail.com> - 2016-12-17 01:57 +0100
Re: Zero-area Sagnac path and its residual time delay Lauretta Nagle <uattea@aeuatte.au> - 2016-12-17 17:46 +0000
Re: Zero-area Sagnac path and its residual time delay John Heath <heathjohn2@gmail.com> - 2016-12-18 08:29 -0800
Re: Zero-area Sagnac path and its residual time delay Jacquelyn Schiffer <euefhqheeoeeSfaJn@euefhqhee.eeSfaJn.eue> - 2016-12-21 19:58 +0000
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2016-12-22 08:36 -0600
Re: Zero-area Sagnac path and its residual time delay Darleen Sloop <aolenD@nedfdealln.org> - 2016-12-22 21:05 +0000
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-15 12:54 -0800
Re: Zero-area Sagnac path and its residual time delay Lauretta Nagle <uattea@aeuatte.au> - 2016-12-16 17:57 +0000
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-20 14:02 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-15 09:32 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-15 11:02 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-15 11:08 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-15 11:31 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-15 11:40 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-15 12:00 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-15 13:01 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-15 13:07 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-15 13:10 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-15 13:41 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-15 15:21 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-16 15:46 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-16 21:32 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-19 22:40 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2016-12-20 11:08 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2016-12-20 14:00 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2016-12-16 12:54 -0800
Re: Zero-area Sagnac path and its residual time delay Lauretta Nagle <uattea@aeuatte.au> - 2016-12-16 21:16 +0000
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2016-12-16 17:09 -0800
Re: Zero-area Sagnac path and its residual time delay Lauretta Nagle <uattea@aeuatte.au> - 2016-12-17 17:40 +0000
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2016-12-18 09:45 -0800
Re: Zero-area Sagnac path and its residual time delay Gary Harnagel <hitlong@yahoo.com> - 2016-12-18 10:38 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2016-12-18 11:02 -0800
Re: Zero-area Sagnac path and its residual time delay Gary Harnagel <hitlong@yahoo.com> - 2016-12-18 16:14 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2016-12-19 12:13 -0800
Re: Zero-area Sagnac path and its residual time delay Gary Harnagel <hitlong@yahoo.com> - 2016-12-19 14:09 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2016-12-20 10:46 -0800
Re: Zero-area Sagnac path and its residual time delay Gary Harnagel <hitlong@yahoo.com> - 2016-12-20 16:33 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2016-12-24 07:01 -0800
Re: Zero-area Sagnac path and its residual time delay numbernumber1964@gmail.com - 2016-12-19 12:39 -0800
Re: Zero-area Sagnac path and its residual time delay Gary Harnagel <hitlong@yahoo.com> - 2016-12-19 14:18 -0800
Re: Zero-area Sagnac path and its residual time delay Darron Borton <ororrt@orrtnorr.info> - 2016-12-20 03:38 +0000
Re: Zero-area Sagnac path and its residual time delay Gary Harnagel <hitlong@yahoo.com> - 2016-12-19 19:49 -0800
Re: Zero-area Sagnac path and its residual time delay numbernumber1964@gmail.com - 2016-12-19 14:43 -0800
Re: Zero-area Sagnac path and its residual time delay Gary Harnagel <hitlong@yahoo.com> - 2016-12-19 16:22 -0800
Re: Zero-area Sagnac path and its residual time delay Darron Borton <ororrt@orrtnorr.info> - 2016-12-20 03:34 +0000
Re: Zero-area Sagnac path and its residual time delay numbernumber1964@gmail.com - 2016-12-19 16:26 -0800
Re: Zero-area Sagnac path and its residual time delay Gary Harnagel <hitlong@yahoo.com> - 2016-12-19 18:31 -0800
Re: Zero-area Sagnac path and its residual time delay Darron Borton <ororrt@orrtnorr.info> - 2016-12-20 03:32 +0000
Re: Zero-area Sagnac path and its residual time delay numbernumber1964@gmail.com - 2016-12-20 11:03 -0800
Re: Zero-area Sagnac path and its residual time delay numbernumber1964@gmail.com - 2016-12-20 11:19 -0800
Re: Zero-area Sagnac path and its residual time delay furthermore123456@gmail.com - 2016-12-20 12:54 -0800
Re: Zero-area Sagnac path and its residual time delay furthermore123456@gmail.com - 2016-12-20 12:55 -0800
Re: Zero-area Sagnac path and its residual time delay furthermore123456@gmail.com - 2016-12-20 13:04 -0800
Re: Zero-area Sagnac path and its residual time delay furthermore123456@gmail.com - 2016-12-20 13:07 -0800
Re: Zero-area Sagnac path and its residual time delay numbernumber1964@gmail.com - 2016-12-21 12:31 -0800
Re: Zero-area Sagnac path and its residual time delay numbernumber1964@gmail.com - 2016-12-22 15:20 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2016-12-24 07:19 -0800
Re: Zero-area Sagnac path and its residual time delay dancouriann@gmail.com - 2017-01-24 07:47 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-24 07:56 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-24 08:50 -0800
Re: Zero-area Sagnac path and its residual time delay dancouriann@gmail.com - 2017-01-24 09:59 -0800
Re: Zero-area Sagnac path and its residual time delay dancouriann@gmail.com - 2017-01-24 10:16 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-24 11:11 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-24 11:45 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-24 11:58 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-24 12:06 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-24 12:47 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-24 14:13 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-24 14:31 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-24 14:37 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-25 00:07 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-25 07:54 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-25 11:25 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-27 16:15 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-27 17:29 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-01-28 01:19 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-28 18:35 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-01-28 21:08 -0800
Re: Zero-area Sagnac path and its residual time delay "Paul B. Andersen" <relativity@paulba.no> - 2017-01-29 10:49 +0100
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-01-29 02:41 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-01-29 10:23 -0600
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-01-29 16:22 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-01-29 20:40 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-01-29 22:50 -0600
Re: Zero-area Sagnac path and its residual time delay "David (Lord Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2017-01-29 21:28 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-30 08:21 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-30 08:17 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-01-30 16:08 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-30 16:30 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-30 16:59 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-30 17:12 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-30 20:49 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-30 20:58 -0800
Re: Zero-area Sagnac path and its residual time delay Poutnik <poutnik4nntp@gmail.com> - 2017-01-31 07:38 +0100
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-31 11:40 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-01-31 11:51 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-31 12:08 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-01-31 13:01 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-31 13:22 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-01-31 14:37 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-31 15:29 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-02-01 12:02 -0800
Re: Zero-area Sagnac path and its residual time delay Odd Bodkin <bodkinodd@gmail.com> - 2017-02-01 14:12 -0600
Re: Zero-area Sagnac path and its residual time delay mlwozniak@wp.pl - 2017-02-02 00:01 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-02-02 10:21 -0800
Re: Zero-area Sagnac path and its residual time delay Odd Bodkin <bodkinodd@gmail.com> - 2017-02-02 12:44 -0600
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-01 13:06 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-31 12:19 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-31 12:24 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-31 12:30 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-31 13:19 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-01-31 15:39 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-31 17:40 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-01 15:58 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-01 16:28 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-01 23:54 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-02 07:04 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-02 09:36 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-02 10:04 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-02 10:39 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-02 12:58 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-02 14:27 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-02 15:36 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-02 16:00 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-02 19:23 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-02 19:49 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-03 00:23 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-03 06:34 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-03 08:17 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-03 08:30 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-02 16:48 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-02 18:44 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-02-02 15:15 -0800
Re: Zero-area Sagnac path and its residual time delay Odd Bodkin <bodkinodd@gmail.com> - 2017-02-02 17:20 -0600
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-02-02 15:34 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-02 16:43 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-02-02 18:30 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-02 16:42 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-28 10:39 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-27 18:27 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-01-29 11:26 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-30 08:23 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-01-27 10:57 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-27 17:37 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-01-27 23:50 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-27 21:55 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-28 11:29 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-28 18:31 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-01-28 20:45 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-01-30 08:14 -0800
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-01-28 20:00 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-01-29 11:45 -0600
Re: Zero-area Sagnac path and its residual time delay "David (Lord Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2017-01-29 10:13 -0800
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-01-28 19:10 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-05 21:40 -0600
Re: Zero-area Sagnac path and its residual time delay Emmaline Coots <ealoa@loealoioa.los> - 2017-02-06 06:33 +0000
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-06 22:07 -0600
Re: Zero-area Sagnac path and its residual time delay Emmaline Coots <ealoa@loealoioa.los> - 2017-02-07 09:18 +0000
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-06 07:01 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-06 15:37 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-06 16:30 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-08 12:14 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-08 10:39 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-12 14:43 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-12 19:35 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-13 12:39 -0800
Re: Zero-area Sagnac path and its residual time delay Sanjuanita Peeples <naalu@nwmeela.org> - 2017-02-13 21:06 +0000
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-13 13:10 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-13 14:38 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-13 15:47 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-13 16:08 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-13 16:31 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-13 17:21 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-13 19:00 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-13 19:24 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-13 19:51 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-13 22:10 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-13 23:47 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-14 06:11 -0800
Re: Zero-area Sagnac path and its residual time delay Python <python@python.invalid> - 2017-02-14 15:20 +0100
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-14 07:14 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-14 13:42 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-14 13:30 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-14 22:50 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 00:28 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 06:11 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 11:13 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 11:31 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 11:45 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 11:52 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 12:02 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 12:20 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 13:43 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 14:29 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 14:44 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 14:49 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 14:53 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-15 13:46 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 13:49 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 14:31 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 14:52 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 15:03 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-15 20:28 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 19:24 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 19:39 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 19:44 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 21:05 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 21:25 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-16 08:22 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 08:39 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-16 16:02 -0800
Re: Zero-area Sagnac path and its residual time delay Sanjuanita Peeples <naalu@nwmeela.org> - 2017-02-16 16:53 +0000
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 13:40 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 13:46 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 15:11 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 13:48 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 15:18 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 15:42 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 16:12 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 17:42 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-16 22:35 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 20:46 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 21:16 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 21:22 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 21:37 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 21:45 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 21:58 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 22:11 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 22:22 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 22:32 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 22:40 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 22:42 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 23:26 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-16 23:57 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-16 21:50 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 20:03 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 21:07 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 21:21 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 21:53 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 22:14 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 22:33 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-17 17:06 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-17 16:43 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-18 04:52 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-18 07:09 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-18 12:41 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-18 21:16 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-18 21:39 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-18 23:57 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-19 07:10 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-19 10:17 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-19 08:27 -0800
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-02-16 15:24 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 15:43 -0800
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-02-16 16:23 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 17:45 -0800
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-02-16 19:31 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 19:46 -0800
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-02-19 10:26 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-19 10:59 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 11:52 -0800
Re: Zero-area Sagnac path and its residual time delay Sanjuanita Peeples <naalu@nwmeela.org> - 2017-02-15 20:44 +0000
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 13:44 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 14:30 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 14:46 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 14:50 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 14:56 -0800
Re: Zero-area Sagnac path and its residual time delay Sanjuanita Peeples <naalu@nwmeela.org> - 2017-02-16 16:16 +0000
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 11:32 -0800
Re: Zero-area Sagnac path and its residual time delay Sanjuanita Peeples <naalu@nwmeela.org> - 2017-02-16 21:00 +0000
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 13:29 -0800
Re: Zero-area Sagnac path and its residual time delay Sanjuanita Peeples <naalu@nwmeela.org> - 2017-02-17 12:26 +0000
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-02-13 22:36 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-13 22:45 -0800
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-02-16 15:49 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-16 15:54 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-16 16:16 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-13 23:35 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-13 22:14 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-13 23:54 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-14 10:51 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-14 09:02 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-14 13:46 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-15 11:19 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-15 09:39 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-15 11:42 -0800
Re: Zero-area Sagnac path and its residual time delay mlwozniak@wp.pl - 2017-02-15 23:47 -0800
Re: Zero-area Sagnac path and its residual time delay Sanjuanita Peeples <naalu@nwmeela.org> - 2017-02-14 12:43 +0000
Re: Zero-area Sagnac path and its residual time delay Poutnik <poutnik4nntp@gmail.com> - 2017-02-14 14:04 +0100
Re: Zero-area Sagnac path and its residual time delay Sanjuanita Peeples <naalu@nwmeela.org> - 2017-02-15 16:08 +0000
Re: Zero-area Sagnac path and its residual time delay Poutnik <poutnik4nntp@gmail.com> - 2017-02-15 17:29 +0100
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-07 10:42 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-07 11:05 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-07 15:30 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-07 15:31 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-07 15:38 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-07 16:43 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-07 18:04 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-08 11:58 -0600
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-08 10:23 -0800
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-01-28 19:22 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-01-29 22:58 -0600
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-01-30 23:32 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-01-31 16:06 -0600
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-02-01 05:56 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-01 13:04 -0800
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-02-02 03:52 -0800
Re: Zero-area Sagnac path and its residual time delay Tom Roberts <tjroberts137@sbcglobal.net> - 2017-02-04 12:45 -0600
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-02-04 13:55 -0800
Re: Zero-area Sagnac path and its residual time delay Larry Harson <johnmcandrew66@gmail.com> - 2017-02-05 12:49 -0800
Re: Zero-area Sagnac path and its residual time delay RichD <r_delaney2001@yahoo.com> - 2017-02-03 09:19 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-03 09:47 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-02-03 11:19 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-03 12:46 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-02-03 13:30 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-03 14:14 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-03 21:43 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-03 21:42 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-04 12:42 -0800
Re: Zero-area Sagnac path and its residual time delay Emmaline Coots <ealoa@loealoioa.los> - 2017-02-05 01:33 +0000
Re: Zero-area Sagnac path and its residual time delay Python <python@python.invalid> - 2017-02-05 03:20 +0100
Re: Zero-area Sagnac path and its residual time delay Emmaline Coots <ealoa@loealoioa.los> - 2017-02-05 06:03 +0000
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-05 00:09 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-06 06:51 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-07 01:58 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-07 05:48 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-07 21:09 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-07 21:40 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-08 00:35 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-08 03:24 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-08 05:47 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-08 08:51 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-08 09:29 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-08 19:32 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-08 19:49 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-08 20:04 -0800
Re: Zero-area Sagnac path and its residual time delay Python <python@python.invalid> - 2017-02-09 05:15 +0100
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-08 20:33 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-09 02:05 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-09 07:13 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-13 00:05 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-13 07:57 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-13 10:29 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-13 11:09 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-13 11:16 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-13 12:51 -0800
Re: Zero-area Sagnac path and its residual time delay JanPB <filmart@gmail.com> - 2017-02-13 13:08 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-09 01:38 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-09 07:12 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-09 08:09 -0800
Re: Zero-area Sagnac path and its residual time delay Emmaline Coots <ealoa@loealoioa.los> - 2017-02-09 16:13 +0000
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-09 08:13 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-09 09:56 -0800
Re: Zero-area Sagnac path and its residual time delay "Dono," <sa_ge@comcast.net> - 2017-02-09 10:04 -0800
Re: Zero-area Sagnac path and its residual time delay Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2017-02-09 10:14 -0800
Re: Zero-area Sagnac path and its residual time delay "Paul B. Andersen" <relativity@paulba.no> - 2017-01-25 09:59 +0100
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-01-29 11:36 -0800
Re: Zero-area Sagnac path and its residual time delay alsor@interia.pl - 2017-02-04 14:08 -0800
Zero-area Sagnac path and its residual time delay "David (Lord Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2017-02-14 14:06 -0800
Page 9 of 19 — ← Prev page 1 … 7 8 [9] 10 11 … 19 Next page →
| From | Tom Roberts <tjroberts137@sbcglobal.net> |
|---|---|
| Date | 2017-01-29 11:45 -0600 |
| Message-ID | <3KOdnWMAgpnKtxPFnZ2dnUU7_83NnZ2d@giganews.com> |
| In reply to | #407068 |
On 1/28/17 1/28/17 1:29 PM, JanPB wrote: > [the rest is correct] > > 2. Even a stationary frame whose spatial coordinates are expressed in terms of, say, > spherical coordinates will likewise result in extra derivative terms to Maxwell's equations, Not when curl and div are properly expressed in terms of those coordinates -- standard practice in physics. (This does NOT mean they are covariant, see below.) This cannot be done for rotating coordinates, because curl and div are spatial (3-D) only, and for rotating coordinates space and time are not orthogonal. > You probably think that simply replacing "div", "curl" etc. by their equivalent expressions > in other coordinate systems (spherical, etc., like on the inner cover of Jackson) constitutes > covariance but this is NOT what "covariant" means! Covariance is NOT about merely > sweeping some extra terms under an existing label and calling the result "being of the same > form": all you've done is simply assigning the same symbol to a different thing and calling > it "the same". Hmmmm. I basically agree. But then, Maxwell's equations cannot possibly be covariant when expressed in terms of E and B, because those are not tensors. At base this is a problem with using the term "covariant" and applying it to Maxwell's equations; this meaning of "covariant" is a rather slippery concept, and you merely touch on the subtleties. The proper approach is to discuss the Lagrangian and discuss whether it is invariant under certain transformations (such as changes of coordinates onto which it is projected). Then it is obvious that the Lagrangian is not invariant under translations along a rotating axis, but is invariant under translations along any axis of an inertial frame. Tom Roberts
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| From | "David (Lord Kronos Prime) Fuller" <fuller.david@hotmail.com> |
|---|---|
| Date | 2017-01-29 10:13 -0800 |
| Message-ID | <9f58cd12-80b4-46ce-934e-9763ae663420@googlegroups.com> |
| In reply to | #407130 |
Tom Roberts wrote:
On 1/28/17 1/28/17 1:29 PM, JanPB wrote:
> [the rest is correct]
>
> 2. Even a stationary frame whose spatial coordinates are expressed in terms of, say,
> spherical coordinates will likewise result in extra derivative terms to Maxwell's equations,
Not when curl and div are properly expressed in terms of those coordinates --
standard practice in physics. (This does NOT mean they are covariant, see below.)
This cannot be done for rotating coordinates, because curl and div are spatial
(3-D) only, and for rotating coordinates space and time are not orthogonal.
> You probably think that simply replacing "div", "curl" etc. by their equivalent expressions
> in other coordinate systems (spherical, etc., like on the inner cover of Jackson) constitutes
> covariance but this is NOT what "covariant" means! Covariance is NOT about merely
> sweeping some extra terms under an existing label and calling the result "being of the same
> form": all you've done is simply assigning the same symbol to a different thing and calling
> it "the same".
Hmmmm. I basically agree. But then, Maxwell's equations cannot possibly be
covariant when expressed in terms of E and B, because those are not tensors.
At base this is a problem with using the term "covariant" and applying it to
Maxwell's equations; this meaning of "covariant" is a rather slippery concept,
and you merely touch on the subtleties. The proper approach is to discuss the
Lagrangian and discuss whether it is invariant under certain transformations
(such as changes of coordinates onto which it is projected).
Then it is obvious that the Lagrangian is not invariant under
translations along a rotating axis, but is invariant under
translations along any axis of an inertial frame.
Tom Roberts
E/(Z0)^2 = B
https://goo.gl/photos/z3d8eN12uMDBpKSy9
https://goo.gl/photos/SY9gFTE6cR8q5MCz9
https://goo.gl/photos/HdheFmjY2EHs94YG8
https://goo.gl/photos/7E8CtiXdDfhRcWmp7
https://goo.gl/photos/q6LfxwTVUCHYbEUb7
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| From | Larry Harson <johnmcandrew66@gmail.com> |
|---|---|
| Date | 2017-01-28 19:10 -0800 |
| Message-ID | <7ed24838-e9fa-4bfc-9bfe-2145fd7d465a@googlegroups.com> |
| In reply to | #407042 |
On Saturday, January 28, 2017 at 5:55:58 AM UTC, Dono, wrote: > On Friday, January 27, 2017 at 9:50:16 PM UTC-8, tjrob137 wrote: > > On 1/27/17 1/27/17 7:37 PM, Dono, wrote: > > > On Friday, January 27, 2017 at 8:57:15 AM UTC-8, tjrob137 wrote: > > >> This depends on what you mean by "Maxwell's equations". > > >> The usual meaning is a set of 4 equations involving the curl and divergence > > >> of E and B fields -- these equations are NOT covariant, they apply ONLY in > > >> inertial coordinates and if you transform them to rotating coordinates extra > > >> terms arise due to the non-orthogonality of the coordinates > > > > > > There are no "extra terms", you don't know what you are talking about. I have > > > a pretty good ideas what transforms you are considering, they are not the > > > correct transforms. The correct transforms leave the 4 Maxwell equations > > > invariant. > > > > Please display these transforms. > > > > Tom Roberts > > Chapter 47 in Moller's book. They are quite complicated, much more complicated than the naive and incorrect ones you are using. I have a link to the book, chapter 47 here: https://archive.org/stream/theoryofrelativi029229mbp#page/n137/mode/2up It does an analysis of a particle in constant circular motion relative to the series of comoving rest frames which aren't frames rotating at some constant angular velocity. In the chapter 52 on electrodynamics, I can't see any derivation of Maxwell's equations for rotating frames, maybe you have a later edition or it's done elsewhere? Cheers, Larry Harson
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| From | Tom Roberts <tjroberts137@sbcglobal.net> |
|---|---|
| Date | 2017-02-05 21:40 -0600 |
| Message-ID | <8fKdnRtFWrOwbQrFnZ2dnUU7_83NnZ2d@giganews.com> |
| In reply to | #407042 |
On 1/27/17 1/27/17 11:55 PM, Dono, wrote: > Chapter 47 in Moller's book. OK. I borrowed a copy from the library. A perusal of chapter 47 shows that Dono made a GROSS ERROR in reading, and compounded his error via arrogance and an inability (or refusal) to THINK about what he was saying. As several of us pointed out, essentially everything he said about this is just plain wrong. Moller's book was written in 1951/52. It shows its age in many ways, and I do NOT recommend it to a modern reader. But other than presentation style and archaic notation, I found nothing wrong. Dono's reading failure first appears in the title of chapter 47: "Successive rest systems of a particle ... in constant circular motion". That is, Moller is computing the transforms from the inertial frame of the center to the "successive rest systems" of the particle -- each "rest system" is of course an inertial frame, and every one of the transforms he computes is a "special Lorentz transform" [#], but there is a different transform and "rest system" for each value of the time coordinate \tau. [#] By this phrase Moller means a transform between inertial frames with parallel Cartesian spatial axes. See his discussion in Section II following eq. 24. This was referenced in Ch. 47, but apparently Dono did not bother to look it up, as it would have cleared up his confusion and avoided this whole nonsense. Moller NEVER transforms to rotating coordinates (or a "rotating frame") as Dono has repeatedly asserted. He is transforming to inertial frames, using a different frame for each value of t. So it happens that Dono was correct when he said the equations are invariant when Moller's transforms are applied. But he was WRONG in thinking this applied to a rotating system, Moller was transforming to inertial frames. Essentially everything Dono said about this is wrong, and Moller does not support his claims, because Moller NEVER transformed to a rotating frame, that was DONO'S MISTAKE IN READING. Dono compounded his error and displayed his foolishness by asserting: > 2. A light ray emitted in a rotating frame propagates in a straight line in > the respective frame and appears curved (due to a complicated aberration) in > an inertial frame. This is just plain wrong. Light in vacuum follows a null geodesic path, and such a path is NOT a straight line relative to a rotating frame (unless it is along the rotation axis); it _IS_ a straight line in an inertial frame. This is so independent of how the light is emitted (I'm ignoring Dono's confusion in using the phrase "light ray", which is AMBIGUOUS when applied to a rotating system). Dono also falsely asserted: > 3. Maxwell laws are fully covariant, they have the same exact form in a > uniformly rotating frame as in an inertial frame. and > The em wave equations are the SAME in the rotating frame.as in the inertial > frame. These are also just plain wrong. Dono confused himself here -- Moller's transforms of Ch. 47 actually do keep Maxwell's equations' form unchanged, BECAUSE THEY ARE TRANSFORMS BETWEEN INERTIAL FRAMES. Dono misread Moller and thinks Moller's transforms are to "a uniformly rotating frame" when they are NOT. Dono made numerous other false claims related to this. They are all wrong, because they are all based on: a) his MIS-READING of Moller, b) his inability to THINK about what he is saying, and c) his arrogance. Tom Roberts
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| From | Emmaline Coots <ealoa@loealoioa.los> |
|---|---|
| Date | 2017-02-06 06:33 +0000 |
| Message-ID | <o795at$fmg$1@gioia.aioe.org> |
| In reply to | #408046 |
Tom Roberts wrote: > These are also just plain wrong. Dono confused himself here -- Moller's > transforms of Ch. 47 actually do keep Maxwell's equations' form > unchanged, BECAUSE THEY ARE TRANSFORMS BETWEEN INERTIAL FRAMES. Dono > misread Moller and thinks Moller's transforms are to "a uniformly > rotating frame" when they are NOT. Dono made numerous other false claims > related to this. They are all wrong, Except that you can't transform among inertial rotating frames. While you transform for one, the other already moved a milimeter.
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| From | Tom Roberts <tjroberts137@sbcglobal.net> |
|---|---|
| Date | 2017-02-06 22:07 -0600 |
| Message-ID | <psGdnR8fe8hx2gTFnZ2dnUU7_81j4p2d@giganews.com> |
| In reply to | #408052 |
On 2/6/17 2/6/17 12:33 AM, Emmaline Coots wrote: > Except that you can't transform among inertial rotating frames. There is no such thing as "inertial rotating frames" -- the two adjectives are mutually exclusive. Tom Roberts
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| From | Emmaline Coots <ealoa@loealoioa.los> |
|---|---|
| Date | 2017-02-07 09:18 +0000 |
| Message-ID | <o7c3cm$spm$1@gioia.aioe.org> |
| In reply to | #408182 |
Tom Roberts wrote: > On 2/6/17 2/6/17 12:33 AM, Emmaline Coots wrote: >> Except that you can't transform among inertial rotating frames. > > There is no such thing as "inertial rotating frames" -- the two > adjectives are mutually exclusive. Tom Roberts Indeed, but you said it first. That's why I said the above. You probably not want to read.
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| From | "Dono," <sa_ge@comcast.net> |
|---|---|
| Date | 2017-02-06 07:01 -0800 |
| Message-ID | <113e1901-2587-4ebc-86e3-25af7b15596a@googlegroups.com> |
| In reply to | #408046 |
On Sunday, February 5, 2017 at 7:40:35 PM UTC-8, tjrob137 wrote: > On 1/27/17 1/27/17 11:55 PM, Dono, wrote: > > Chapter 47 in Moller's book. > > OK. I borrowed a copy from the library. A perusal of chapter 47 shows that Dono > made a GROSS ERROR in reading, and compounded his error via arrogance and an > inability (or refusal) to THINK about what he was saying. As several of us > pointed out, essentially everything he said about this is just plain wrong. > > Moller's book was written in 1951/52. It shows its age in many > ways, and I do NOT recommend it to a modern reader. But other than > presentation style and archaic notation, I found nothing wrong. > > Dono's reading failure first appears in the title of chapter 47: "Successive > rest systems of a particle ... in constant circular motion". That is, Moller is > computing the transforms from the inertial frame of the center to the > "successive rest systems" of the particle -- each "rest system" is of course an > inertial frame, and every one of the transforms he computes is a "special > Lorentz transform" [#], but there is a different transform and "rest system" for > each value of the time coordinate \tau. > Yes. Obviously. > [#] By this phrase Moller means a transform between inertial > frames with parallel Cartesian spatial axes. See his discussion > in Section II following eq. 24. This was referenced in Ch. 47, > but apparently Dono did not bother to look it up, as it would > have cleared up his confusion and avoided this whole nonsense. > > Moller NEVER transforms to rotating coordinates (or a "rotating frame") as Dono > has repeatedly asserted. Moller is transforming from the inertial frame of the hub into the frame comoving with the ROTATING particle. To an imbecile like Tom Roberts, this is not a rotating frame. To the rest of the people, this is a rotating frame. > He is transforming to inertial frames, using a > different frame for each value of t. > Yes. > So it happens that Dono was correct when he said the equations are invariant > when Moller's transforms are applied. Cretin Tom Roberts finally gets it. > But he was WRONG in thinking this applied > to a rotating system, Moller was transforming to inertial frames. > Moller is transforming from the inertial frame of the hub into the frame comoving with the ROTATING particle. To an imbecile like Tom Roberts, this is not a rotating frame. To the rest of the people, this is a rotating frame. > Essentially everything Dono said about this is wrong, and Moller does not > support his claims, because Moller NEVER transformed to a rotating frame, that > was DONO'S MISTAKE IN READING. > Moller is transforming from the inertial frame of the hub into the frame comoving with the ROTATING particle. To an imbecile like Tom Roberts, this is not a rotating frame. To the rest of the people, this is a rotating frame. To wit, Moller's transforms are reprised by a few other papers that deal with transformations between inertial and rotating frames. Well done, old fart.
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| From | JanPB <filmart@gmail.com> |
|---|---|
| Date | 2017-02-06 15:37 -0800 |
| Message-ID | <50448e89-dfbf-41a2-9825-45cfbf783c64@googlegroups.com> |
| In reply to | #408092 |
On Monday, February 6, 2017 at 7:01:46 AM UTC-8, Dono, wrote: > On Sunday, February 5, 2017 at 7:40:35 PM UTC-8, tjrob137 wrote: > > On 1/27/17 1/27/17 11:55 PM, Dono, wrote: > > > Chapter 47 in Moller's book. > > > > OK. I borrowed a copy from the library. A perusal of chapter 47 shows that Dono > > made a GROSS ERROR in reading, and compounded his error via arrogance and an > > inability (or refusal) to THINK about what he was saying. As several of us > > pointed out, essentially everything he said about this is just plain wrong. > > > > Moller's book was written in 1951/52. It shows its age in many > > ways, and I do NOT recommend it to a modern reader. But other than > > presentation style and archaic notation, I found nothing wrong. > > > > Dono's reading failure first appears in the title of chapter 47: "Successive > > rest systems of a particle ... in constant circular motion". That is, Moller is > > computing the transforms from the inertial frame of the center to the > > "successive rest systems" of the particle -- each "rest system" is of course an > > inertial frame, and every one of the transforms he computes is a "special > > Lorentz transform" [#], but there is a different transform and "rest system" for > > each value of the time coordinate \tau. > > > > Yes. Obviously. > > > > [#] By this phrase Moller means a transform between inertial > > frames with parallel Cartesian spatial axes. See his discussion > > in Section II following eq. 24. This was referenced in Ch. 47, > > but apparently Dono did not bother to look it up, as it would > > have cleared up his confusion and avoided this whole nonsense. > > > > Moller NEVER transforms to rotating coordinates (or a "rotating frame") as Dono > > has repeatedly asserted. > > Moller is transforming from the inertial frame of the hub into the frame comoving with the ROTATING particle. No. He is constructing a _family_ of Lorentz transformations: for each proper time tau of the particle, he has a corresponding Lorentz transformation from a fixed inertial system S to an _inertial_ system S'(tau) that's momentarily co-moving with the particle at the instant tau. This is what formulas (136) and (137) are for (I'm using the 1st edition of the book for reference). The alpha_ik there are matrix elements of the (tau-dependent) Lorentz transformation. A family of systems S'(tau) does NOT constitute a "rotating frame" and a family of Lorentz transformations to them does NOT constitute a transformation to any "rotating frame". (Question: if it were a frame, what would be its hypersurface t=const.? BE SPECIFIC.) > To an imbecile like Tom Roberts, this is not a rotating frame. Save your tongue, Tom is correct: family of inertial frames is NOT the same as rotating frame. You have a lot of thinking things over ahead of you if you think otherwise. > To the rest of the people, this is a rotating frame. This is a "rotating frame" to no-one competent in this field. Trust me. -- Jan
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| From | "Dono," <sa_ge@comcast.net> |
|---|---|
| Date | 2017-02-06 16:30 -0800 |
| Message-ID | <a39c1a05-c040-4b84-8b84-a8f87b2fa589@googlegroups.com> |
| In reply to | #408163 |
On Monday, February 6, 2017 at 3:38:00 PM UTC-8, JanPB wrote:
> On Monday, February 6, 2017 at 7:01:46 AM UTC-8, Dono, wrote:
> > On Sunday, February 5, 2017 at 7:40:35 PM UTC-8, tjrob137 wrote:
> > > On 1/27/17 1/27/17 11:55 PM, Dono, wrote:
> > > > Chapter 47 in Moller's book.
> > >
> > > OK. I borrowed a copy from the library. A perusal of chapter 47 shows that Dono
> > > made a GROSS ERROR in reading, and compounded his error via arrogance and an
> > > inability (or refusal) to THINK about what he was saying. As several of us
> > > pointed out, essentially everything he said about this is just plain wrong.
> > >
> > > Moller's book was written in 1951/52. It shows its age in many
> > > ways, and I do NOT recommend it to a modern reader. But other than
> > > presentation style and archaic notation, I found nothing wrong.
> > >
> > > Dono's reading failure first appears in the title of chapter 47: "Successive
> > > rest systems of a particle ... in constant circular motion". That is, Moller is
> > > computing the transforms from the inertial frame of the center to the
> > > "successive rest systems" of the particle -- each "rest system" is of course an
> > > inertial frame, and every one of the transforms he computes is a "special
> > > Lorentz transform" [#], but there is a different transform and "rest system" for
> > > each value of the time coordinate \tau.
> > >
> >
> > Yes. Obviously.
> >
> >
> > > [#] By this phrase Moller means a transform between inertial
> > > frames with parallel Cartesian spatial axes. See his discussion
> > > in Section II following eq. 24. This was referenced in Ch. 47,
> > > but apparently Dono did not bother to look it up, as it would
> > > have cleared up his confusion and avoided this whole nonsense.
> > >
> > > Moller NEVER transforms to rotating coordinates (or a "rotating frame") as Dono
> > > has repeatedly asserted.
> >
> > Moller is transforming from the inertial frame of the hub into the frame comoving with the ROTATING particle.
>
> No. He is constructing a _family_ of Lorentz transformations: for each
> proper time tau of the particle, he has a corresponding Lorentz
> transformation from a fixed inertial system S to an _inertial_ system S'(tau)
> that's momentarily co-moving with the particle at the instant tau.
>
> This is what formulas (136) and (137) are for (I'm using the 1st edition
> of the book for reference). The alpha_ik there are matrix elements of
> the (tau-dependent) Lorentz transformation.
>
> A family of systems S'(tau) does NOT constitute a "rotating frame" and
> a family of Lorentz transformations to them does NOT constitute a
> transformation to any "rotating frame".
>
So, {according to you) the frames co-ROTATING with the ROTATING Sagnac mirrors are not the appropriate frames for describing the effects of light propagation between said mirrors. Interestrng
> (Question: if it were a frame, what would be its hypersurface t=const.?
> BE SPECIFIC.)
>
Take your attitude and stuff it up your ass.
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| From | Tom Roberts <tjroberts137@sbcglobal.net> |
|---|---|
| Date | 2017-02-08 12:14 -0600 |
| Message-ID | <BtOdnR7_9saA_QbFnZ2dnUU7_83NnZ2d@giganews.com> |
| In reply to | #408166 |
On 2/6/17 2/6/17 6:30 PM, Dono, wrote:
> So, {according to you) the frames co-ROTATING with the ROTATING Sagnac
> mirrors [...]
Among the frames to which Moller transforms, there _IS_ no such frame. Moller's
family of inertial frames has only a SINGLE POINT of the rotating system at rest
[#], not even an entire mirror (much less multiple mirrors). That is, there is
no inertial frame in which all of the Sagnac mirrors are at rest, BECAUSE THEY
ARE ROTATING AND MOLLER'S INERTIAL FRAMES ARE NOT.
[#] Read his Ch. 47 -- he is discussing a pointlike particle.
Tom Roberts
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| From | "Dono," <sa_ge@comcast.net> |
|---|---|
| Date | 2017-02-08 10:39 -0800 |
| Message-ID | <29f3ecbd-b522-45c7-97c9-ac360296a850@googlegroups.com> |
| In reply to | #408416 |
On Wednesday, February 8, 2017 at 10:14:59 AM UTC-8, tjrob137 wrote: > That is, there is > no inertial frame in which all of the Sagnac mirrors are at rest, BECAUSE THEY > ARE ROTATING AND MOLLER'S INERTIAL FRAMES ARE NOT. > I did not say that, cretin What I said is that two mirrors (at least the point of light reflection) ARE being described accurately by Moller's formalism. In such frames, the Maxwell equations have the same exact form as in an inertial frame (you agreed to that). Now, what you did not agree, is that Maxwell equations are AKSO invariant wrt the transform: Stubborn Cretin, Maxwell's equations are invariant to the rotation transform. Therefore the solutions in the frame of the rotating are identical to the ones in the inertial frame of the hub. You can try it too, rather than blathering your idiocies. The transform is: x' |cos \omega*t sin \omega*t 0 0 | x y'= |-sin \omega*t cos \omega*t 0 0 | y z' | 0 0 1 0 | z t' | 0 0 0 1 | t Can you STFU for a little while and prove this to yourself? Or are you as incompetent when it comes rto calculations as the PCH idiot?
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| From | Tom Roberts <tjroberts137@sbcglobal.net> |
|---|---|
| Date | 2017-02-12 14:43 -0600 |
| Message-ID | <SdqdnfbXs9JqVT3FnZ2dnUU7_8zNnZ2d@giganews.com> |
| In reply to | #408420 |
On 2/8/17 2/8/17 12:39 PM, Dono, wrote: > Maxwell's equations are invariant to the rotation transform. Therefore the > solutions in the frame of the rotating are identical to the ones in the > inertial frame of the hub. This is not true, for the rotation transform YOU give. You CLEARLY have not performed the exercise you want me to do. > The transform is: > x' |cos \omega*t sin \omega*t 0 0 | x > y'= |-sin \omega*t cos \omega*t 0 0 | y > z' | 0 0 1 0 | z > t' | 0 0 0 1 | t OBVIOUSLY you have not actually applied this transform to the Maxwell's equations. Or if you think you did, then you did it incorrectly. The ME are NOT invariant under this transform. This is NOT Moller's transform: Moller uses \tau in his rotation matrix; \tau is his PARAMETER representing the particle's proper time -- YOU used t, which is the TIME COORDINATE. That difference is central to your error: it is the difference between transforming to a succession of inertial frames parameterized by \tau and transforming to rotating coordinates. MOLLER is transforming to the inertial frame in which the particle is at rest at proper time \tau. MOLLER'S transforms are Lorentz transforms, with a different one applying at each value of \tau. YOUR transform does go to a rotating frame, and after applying it the div' and curl' operators will have derivatives by t (can be converted to t') [#]. Those derivatives will form EXTRA TERMS that make the equations not invariant; in fact those terms correspond (distantly) to the "centrifugal and Coriolis forces" of classical mechanics. [#] just LOOK at your transform for x': x' = cos(\omega t) x + sin(\omega t) y That is OBVIOUSLY a function of t, x, and y. When you compute div' and curl' they will NECESSARILY include terms in d/dt. In another post discussing Moller's transforms you said: > Interestingly, the transforms preserve the invariant E^2-(Bc)^2 as well as the relation of gauge. OF COURSE, because each of Moller's transforms is a Lorentz transform between two inertial frames, and it is well known that the ME are invariant under such a transform, and that E^2-B^2 is invariant under them. You also said this about Moller's transforms: > They aren't "Lorentz". They don't look anything like Lorentz. OBVIOUSLY you have not looked at his book; or if you did you did not really understand it. The family of transforms he displays in Sect. 47, eq. IV.164, is a family of Lorentz transforms parametrized by \tau (the particle's proper time, NOT the time coordinate). That is, for each and every value of \tau the transform is a Lorentz transform; he is transforming to a different inertial frame for each value of \tau -- THAT'S WHAT HE SAYS AND WHAT HE DOES. Not only have you been quite careless here, and arrogantly refused to consider your own mistakes, you have also failed to understand what a rotating frame actually is and how it behaves. In particular, while the ME are invariant under a FIXED rotation, they are most definitely NOT invariant under a transform to a rotating frame. Now elevate your eyes to the very first sentence of yours I quoted above, and see how carelessly you phrased it, failing to make the important distinction I made in my last sentence. Tom Roberts
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| From | "Dono," <sa_ge@comcast.net> |
|---|---|
| Date | 2017-02-12 19:35 -0800 |
| Message-ID | <131a99c4-675a-4584-ac35-20bd46a15782@googlegroups.com> |
| In reply to | #408958 |
On Sunday, February 12, 2017 at 12:43:41 PM UTC-8, tjrob137 wrote: > On 2/8/17 2/8/17 12:39 PM, Dono, wrote: > > Maxwell's equations are invariant to the rotation transform. Therefore the > > solutions in the frame of the rotating are identical to the ones in the > > inertial frame of the hub. > > This is not true, for the rotation transform YOU give. You CLEARLY have not > performed the exercise you want me to do. > > > The transform is: > > x' |cos \omega*t sin \omega*t 0 0 | x > > y'= |-sin \omega*t cos \omega*t 0 0 | y > > z' | 0 0 1 0 | z > > t' | 0 0 0 1 | t > > OBVIOUSLY you have not actually applied this transform to the Maxwell's > equations. Or if you think you did, then you did it incorrectly. The ME are NOT > invariant under this transform. > Actually, unlike you, I DID the calculations. Do them or STFU. > This is NOT Moller's transform: Moller uses \tau in his rotation matrix; \tau is > his PARAMETER representing the particle's proper time -- YOU used t, which is > the TIME COORDINATE. > Yes, these are DIFFERENT transforms from Moller's. But BOTH leave the ME invariant. > That difference is central to your error: it is the difference > between transforming to a succession of inertial frames > parameterized by \tau and transforming to rotating coordinates. > Imbecile, I KNOW what I am doing. Do the calculations and prove me wrong. You will finf that it is YOU who i wrong. > YOUR transform does go to a rotating frame, and after applying it the div' and > curl' operators will have derivatives by t (can be converted to t') [#]. Those > derivatives will form EXTRA TERMS that make the equations not invariant; in fact > those terms correspond (distantly) to the "centrifugal and Coriolis forces" of > classical mechanics. > There are no extra terms, imbecile. Unlike you, I DID the calculations.
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| From | JanPB <filmart@gmail.com> |
|---|---|
| Date | 2017-02-13 12:39 -0800 |
| Message-ID | <4b0748fc-d3fc-406a-8cd5-7fe0d14314cf@googlegroups.com> |
| In reply to | #408991 |
On Sunday, February 12, 2017 at 7:35:15 PM UTC-8, Dono, wrote:
> On Sunday, February 12, 2017 at 12:43:41 PM UTC-8, tjrob137 wrote:
> > On 2/8/17 2/8/17 12:39 PM, Dono, wrote:
> > > Maxwell's equations are invariant to the rotation transform. Therefore the
> > > solutions in the frame of the rotating are identical to the ones in the
> > > inertial frame of the hub.
> >
> > This is not true, for the rotation transform YOU give. You CLEARLY have not
> > performed the exercise you want me to do.
> >
> > > The transform is:
> > > x' |cos \omega*t sin \omega*t 0 0 | x
> > > y'= |-sin \omega*t cos \omega*t 0 0 | y
> > > z' | 0 0 1 0 | z
> > > t' | 0 0 0 1 | t
> >
> > OBVIOUSLY you have not actually applied this transform to the Maxwell's
> > equations. Or if you think you did, then you did it incorrectly. The ME are NOT
> > invariant under this transform.
> >
>
> Actually, unlike you, I DID the calculations. Do them or STFU.
You must have made a mistake somewhere. I'm posting a proof below but
first a quick observation: when changing the coordinates in Maxwell's
equations, it is NOT enough to replace all the coordinate derivative
operators by those of the new system: it is ALSO necessary to adjust
the electric and magnetic vectors E and B _as well_. This is _not trivial_,
even for a Lorentz transformation, let alone a for a curvilinear
one like your rotating system.
This adjustment of E and B is _not_ the same as the transformation of
the derivative operators. This is because E and B fields in whatever
coordinates are defined by the mechanical results of _forces_ they
generate, and these forces, unlike the derivative operators, do not
transform linearly. For example, whenever one says "Maxwell's
equations are invariant under Lorentz transformations", this means BOTH
derivative operators AND E and B are changed in a certain way.
Just wanted to state it clearly to avoid further confusion.
Now the proof that Maxwell's equations do not retain their form in the
rotating coordinates you've written above. Actually I'm not going to
brute-force the calculation but instead set up an experiment which
we'll view from both the lab (inertial) coordinates and the above rotating
system. The conclusion will be that at least one of Maxwell's equations
_in its standard form_ will clearly FAIL in the rotating system.
Which means in the rotating system Maxwell's equations develop extra
terms, sort of like "F=ma" develops extra terms in rotating coordinates
(the usual three fictitious forces).
So here is the setup. I believe it's correct (I doodled it while on my
train to work):
* the lab coordinate system is the standard Cartesian xyz,
* your system rotates around the z-axis with angular speed \omega
(from now on I'm going to write "w" instead of "\omega"), as this is
what your matrix says. The angular velocity _vector_ points _down_
along the z-axis, given your choice of the minus sign before the sines
(this is unimportant),
* imagine a circular conducting wire in the xy-plane with the origin
at its center. Assume there is a steady current I flowing through it.
We are going to examine the E and B fields in the lab system and likewise
the corresponding E' and B' fields in the rotating system. We'll conclude
that E' and B' CANNOT satisfy Maxwell's equations in their standard form
in the rotating system.
To gather enough information about E and B, we imagine a bunch of charged
particles in space, each of charge q, and rotating in the same fashion as
your rotating coordinate system (so to keep them on their circular tracks
around the z-axis, imagine them mounted on some mechanical contraption
designed to maintain this constraint).
Because the wire is electrically neutral, we have E = 0. OTOH due to the
nonzero I, we have a nonzero B given by the Biot-Savart law. Because the
aforementioned cloud of particles is moving wrt to the lab system, the
particles experience the Lorentz force F = q v x B, where a particle
at position r has the linear velocity v = w x r.
The above E and B satisfies Maxwell's equations in the standard form.
Now let's examine this setup in the rotating coordinates. First of all,
all the particles in it are _stationary_, therefore NO MATTER what B' is
(the magnetic field as observed by the rotating system), they experience
_no_ magnetic (Lorentz) force. But they of course _do_ experience _a_ force[#]
simply because they did so as measured by the (say) mechanical strain of
the contraption mentioned earlier which is a coordinate-independent
phenomenon.
[#] ignoring the centripetal and centrifugal forces, resp., as they
are obviously equal.
Therefore, the electromagnetic force experienced in the rotating system
must be due only to the electric field E'. And we know this force is equal
to the Lorentz force of the lab system:
E' = F/q = v x B
And this is where Maxwell's equations fail. Not sure if all of them fail,
I only checked Gauss' law:
(*) div E' = (charge density)/e0
(e0 = "epsilon-zero", aka. "permittivity of free space").
On the one hand the wire is neutral (charge density = 0), hence the
right-hand side is zero.
On the other hand:
div E' = div (v x B) = B . (curl v) - v . (curl B)
("." means scalar product)
But v = w x r, so:
curl v = curl (w x r) = 2w k (k - the z-axis unit vector)
and since we assume Maxwell in the standard form holds in the lab, we have:
curl B = m0 I
(m0 = "mu-zero", aka. "vacuum permeability", also note that the second
term in Ampere's law drops out:
(1/c^2) * @E'/@t = 0
...since E' is independent of time due to the cylindrical symmetry of our
setup.
So we get for the left-hand side of (*):
div E' = 2w B . k - m0 v . I
...and there is no reason (none that I can tell anyway) that the two
terms on the right-hand side above should cancel in general.
So if Maxwell's equations hold in the rotating system without any extra
terms, then div E' is both zero and nonzero there which is a contradiction.
QED.
--
Jan
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| From | Sanjuanita Peeples <naalu@nwmeela.org> |
|---|---|
| Date | 2017-02-13 21:06 +0000 |
| Message-ID | <o7t74o$1t21$1@gioia.aioe.org> |
| In reply to | #409108 |
JanPB wrote:
> Because the wire is electrically neutral, we have E = 0. OTOH due to the
> nonzero I, we have a nonzero B given by the Biot-Savart law. Because the
> aforementioned cloud of particles is moving wrt to the lab system, the
> particles experience the Lorentz force F = q v x B, where a particle at
> position r has the linear velocity v = w x r.
What you are saying here is that you displace the free electrons/charge
carriers in the wire by rotating the wire??
> The above E and B satisfies Maxwell's equations in the standard form.
>
> Now let's examine this setup in the rotating coordinates. First of all,
> all the particles in it are _stationary_,
Definitely not, but symmetrically distributed.
> therefore NO MATTER what B' is
> (the magnetic field as observed by the rotating system), they experience
> _no_ magnetic (Lorentz) force. But they of course _do_ experience _a_
> force[#]
> simply because they did so as measured by the (say) mechanical strain of
> the contraption mentioned earlier which is a coordinate-independent
> phenomenon.
Yes.
> [#] ignoring the centripetal and centrifugal forces, resp., as they are
> obviously equal.
Yes, but you cannot ignore them.
> Therefore, the electromagnetic force experienced in the rotating system
> must be due only to the electric field E'. And we know this force is
> equal to the Lorentz force of the lab system:
> E' = F/q = v x B
> And this is where Maxwell's equations fail. Not sure if all of them
> fail, I only checked Gauss' law:
> (*) div E' = (charge density)/e0
> (e0 = "epsilon-zero", aka. "permittivity of free space").
> On the one hand the wire is neutral (charge density = 0), hence the
> right-hand side is zero. On the other hand:
> div E' = div (v x B) = B . (curl v) - v . (curl B)
> ("." means scalar product) But v = w x r, so:
> curl v = curl (w x r) = 2w k (k - the z-axis unit vector)
> and since we assume Maxwell in the standard form holds in the lab, we
> have: curl B = m0 I
> (m0 = "mu-zero", aka. "vacuum permeability", also note that the second
> term in Ampere's law drops out:
> (1/c^2) * @E'/@t = 0
> ...since E' is independent of time due to the cylindrical symmetry of
> our setup. So we get for the left-hand side of (*):
> div E' = 2w B . k - m0 v . I
> ...and there is no reason (none that I can tell anyway) that the two
> terms on the right-hand side above should cancel in general.
> So if Maxwell's equations hold in the rotating system without any extra
> terms, then div E' is both zero and nonzero there which is a
> contradiction. QED. -- Jan
It depends on the coordinates of that E'. Is zero when symmetric, non zero
otherwise. I am just guessing here.
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| From | JanPB <filmart@gmail.com> |
|---|---|
| Date | 2017-02-13 13:10 -0800 |
| Message-ID | <c4481d0f-c20c-457d-a6d6-22455c3c8d85@googlegroups.com> |
| In reply to | #409112 |
On Monday, February 13, 2017 at 1:06:38 PM UTC-8, Sanjuanita Peeples wrote: > JanPB wrote: > > > Because the wire is electrically neutral, we have E = 0. OTOH due to the > > nonzero I, we have a nonzero B given by the Biot-Savart law. Because the > > aforementioned cloud of particles is moving wrt to the lab system, the > > particles experience the Lorentz force F = q v x B, where a particle at > > position r has the linear velocity v = w x r. > > What you are saying here is that you displace the free electrons/charge > carriers in the wire by rotating the wire?? No, no, sorry for being unlcear. The wire has its own charges forming the current. What I mean is a bunch of test charges all over the place (constrained to circle the z-axis) designed to simply test the fields E, B and E', B' in the usual textbook way. -- Jan
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| From | "Dono," <sa_ge@comcast.net> |
|---|---|
| Date | 2017-02-13 14:38 -0800 |
| Message-ID | <29f9c233-03c0-4478-892d-3a5b0a53db1e@googlegroups.com> |
| In reply to | #409108 |
On Monday, February 13, 2017 at 12:39:45 PM UTC-8, JanPB wrote: > On Sunday, February 12, 2017 at 7:35:15 PM UTC-8, Dono, wrote: > > On Sunday, February 12, 2017 at 12:43:41 PM UTC-8, tjrob137 wrote: > > > On 2/8/17 2/8/17 12:39 PM, Dono, wrote: > > > > Maxwell's equations are invariant to the rotation transform. Therefore the > > > > solutions in the frame of the rotating are identical to the ones in the > > > > inertial frame of the hub. > > > > > > This is not true, for the rotation transform YOU give. You CLEARLY have not > > > performed the exercise you want me to do. > > > > > > > The transform is: > > > > x' |cos \omega*t sin \omega*t 0 0 | x > > > > y'= |-sin \omega*t cos \omega*t 0 0 | y > > > > z' | 0 0 1 0 | z > > > > t' | 0 0 0 1 | t > > > > > > OBVIOUSLY you have not actually applied this transform to the Maxwell's > > > equations. Or if you think you did, then you did it incorrectly. The ME are NOT > > > invariant under this transform. > > > > > > > Actually, unlike you, I DID the calculations. Do them or STFU. > > You must have made a mistake somewhere. I'm posting a proof below but > first a quick observation: when changing the coordinates in Maxwell's > equations, it is NOT enough to replace all the coordinate derivative > operators by those of the new system: it is ALSO necessary to adjust > the electric and magnetic vectors E and B _as well_. ...which is precisely what I did. One needs to find the transforms E' and B' as a function of E and B. > This is _not trivial_, > even for a Lorentz transformation, let alone a for a curvilinear > one like your rotating system. > I agree. Nevertheless , I had no trouble deriving them. > This adjustment of E and B is _not_ the same as the transformation of > the derivative operators. I agree. > This is because E and B fields in whatever > coordinates are defined by the mechanical results of _forces_ they > generate, and these forces, unlike the derivative operators, do not > transform linearly. Yes. > For example, whenever one says "Maxwell's > equations are invariant under Lorentz transformations", this means BOTH > derivative operators AND E and B are changed in a certain way. > No issue. > Just wanted to state it clearly to avoid further confusion. > > Now the proof that Maxwell's equations do not retain their form in the > rotating coordinates you've written above. Actually I'm not going to > brute-force the calculation but instead set up an experiment which > we'll view from both the lab (inertial) coordinates and the above rotating > system. The conclusion will be that at least one of Maxwell's equations > _in its standard form_ will clearly FAIL in the rotating system. False. Now I need to find what you did wrong. > Which means in the rotating system Maxwell's equations develop extra > terms, sort of like "F=ma" develops extra terms in rotating coordinates > (the usual three fictitious forces). > You have a bias, all you are going to do is to confirm your bias. > So here is the setup. I believe it's correct (I doodled it while on my > train to work): > > * the lab coordinate system is the standard Cartesian xyz, > > * your system rotates around the z-axis with angular speed \omega > (from now on I'm going to write "w" instead of "\omega"), as this is > what your matrix says. The angular velocity _vector_ points _down_ > along the z-axis, given your choice of the minus sign before the sines > (this is unimportant), > > * imagine a circular conducting wire in the xy-plane with the origin > at its center. Assume there is a steady current I flowing through it. > ok > We are going to examine the E and B fields in the lab system and likewise > the corresponding E' and B' fields in the rotating system. We'll conclude > that E' and B' CANNOT satisfy Maxwell's equations in their standard form > in the rotating system. > OK > To gather enough information about E and B, we imagine a bunch of charged > particles in space, each of charge q, and rotating in the same fashion as > your rotating coordinate system (so to keep them on their circular tracks > around the z-axis, imagine them mounted on some mechanical contraption > designed to maintain this constraint). > > Because the wire is electrically neutral, we have E = 0. OTOH due to the > nonzero I, we have a nonzero B given by the Biot-Savart law. Because the > aforementioned cloud of particles is moving wrt to the lab system, the > particles experience the Lorentz force F = q v x B, where a particle > at position r has the linear velocity v = w x r. > > The above E and B satisfies Maxwell's equations in the standard form. > > Now let's examine this setup in the rotating coordinates. First of all, > all the particles in it are _stationary_, therefore NO MATTER what B' is > (the magnetic field as observed by the rotating system), they experience > _no_ magnetic (Lorentz) force. But they of course _do_ experience _a_ force[#] > simply because they did so as measured by the (say) mechanical strain of > the contraption mentioned earlier which is a coordinate-independent > phenomenon. > > [#] ignoring the centripetal and centrifugal forces, resp., as they > are obviously equal. > > Therefore, the electromagnetic force experienced in the rotating system > must be due only to the electric field E'. And we know this force is equal > to the Lorentz force of the lab system: > > E' = F/q = v x B > No, you don't, this is where you went wrong. There is no reason to surmise that E'=F/q > And this is where Maxwell's equations fail. Not sure if all of them fail, > I only checked Gauss' law: > > (*) div E' = (charge density)/e0 > Now you are completely in the weeds, everything else you try after the false assumption above will fail.
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| From | JanPB <filmart@gmail.com> |
|---|---|
| Date | 2017-02-13 15:47 -0800 |
| Message-ID | <a3d2033e-5401-44d4-9a04-dab07f23da02@googlegroups.com> |
| In reply to | #409129 |
On Monday, February 13, 2017 at 2:38:22 PM UTC-8, Dono, wrote:
> On Monday, February 13, 2017 at 12:39:45 PM UTC-8, JanPB wrote:
> > On Sunday, February 12, 2017 at 7:35:15 PM UTC-8, Dono, wrote:
> > > On Sunday, February 12, 2017 at 12:43:41 PM UTC-8, tjrob137 wrote:
> > > > On 2/8/17 2/8/17 12:39 PM, Dono, wrote:
> > > > > Maxwell's equations are invariant to the rotation transform. Therefore the
> > > > > solutions in the frame of the rotating are identical to the ones in the
> > > > > inertial frame of the hub.
> > > >
> > > > This is not true, for the rotation transform YOU give. You CLEARLY have not
> > > > performed the exercise you want me to do.
> > > >
> > > > > The transform is:
> > > > > x' |cos \omega*t sin \omega*t 0 0 | x
> > > > > y'= |-sin \omega*t cos \omega*t 0 0 | y
> > > > > z' | 0 0 1 0 | z
> > > > > t' | 0 0 0 1 | t
> > > >
> > > > OBVIOUSLY you have not actually applied this transform to the Maxwell's
> > > > equations. Or if you think you did, then you did it incorrectly. The ME are NOT
> > > > invariant under this transform.
> > > >
> > >
> > > Actually, unlike you, I DID the calculations. Do them or STFU.
> >
> > You must have made a mistake somewhere. I'm posting a proof below but
> > first a quick observation: when changing the coordinates in Maxwell's
> > equations, it is NOT enough to replace all the coordinate derivative
> > operators by those of the new system: it is ALSO necessary to adjust
> > the electric and magnetic vectors E and B _as well_.
>
> ...which is precisely what I did. One needs to find the transforms E' and B' as a function of E and B.
>
>
> > This is _not trivial_,
> > even for a Lorentz transformation, let alone a for a curvilinear
> > one like your rotating system.
> >
>
> I agree. Nevertheless , I had no trouble deriving them.
>
>
> > This adjustment of E and B is _not_ the same as the transformation of
> > the derivative operators.
>
> I agree.
>
>
> > This is because E and B fields in whatever
> > coordinates are defined by the mechanical results of _forces_ they
> > generate, and these forces, unlike the derivative operators, do not
> > transform linearly.
>
> Yes.
>
> > For example, whenever one says "Maxwell's
> > equations are invariant under Lorentz transformations", this means BOTH
> > derivative operators AND E and B are changed in a certain way.
> >
>
> No issue.
>
>
> > Just wanted to state it clearly to avoid further confusion.
> >
> > Now the proof that Maxwell's equations do not retain their form in the
> > rotating coordinates you've written above. Actually I'm not going to
> > brute-force the calculation but instead set up an experiment which
> > we'll view from both the lab (inertial) coordinates and the above rotating
> > system. The conclusion will be that at least one of Maxwell's equations
> > _in its standard form_ will clearly FAIL in the rotating system.
>
> False. Now I need to find what you did wrong.
>
>
> > Which means in the rotating system Maxwell's equations develop extra
> > terms, sort of like "F=ma" develops extra terms in rotating coordinates
> > (the usual three fictitious forces).
> >
>
> You have a bias, all you are going to do is to confirm your bias.
>
>
> > So here is the setup. I believe it's correct (I doodled it while on my
> > train to work):
> >
> > * the lab coordinate system is the standard Cartesian xyz,
> >
> > * your system rotates around the z-axis with angular speed \omega
> > (from now on I'm going to write "w" instead of "\omega"), as this is
> > what your matrix says. The angular velocity _vector_ points _down_
> > along the z-axis, given your choice of the minus sign before the sines
> > (this is unimportant),
> >
> > * imagine a circular conducting wire in the xy-plane with the origin
> > at its center. Assume there is a steady current I flowing through it.
> >
>
> ok
>
>
> > We are going to examine the E and B fields in the lab system and likewise
> > the corresponding E' and B' fields in the rotating system. We'll conclude
> > that E' and B' CANNOT satisfy Maxwell's equations in their standard form
> > in the rotating system.
> >
>
> OK
>
> > To gather enough information about E and B, we imagine a bunch of charged
> > particles in space, each of charge q, and rotating in the same fashion as
> > your rotating coordinate system (so to keep them on their circular tracks
> > around the z-axis, imagine them mounted on some mechanical contraption
> > designed to maintain this constraint).
> >
> > Because the wire is electrically neutral, we have E = 0. OTOH due to the
> > nonzero I, we have a nonzero B given by the Biot-Savart law. Because the
> > aforementioned cloud of particles is moving wrt to the lab system, the
> > particles experience the Lorentz force F = q v x B, where a particle
> > at position r has the linear velocity v = w x r.
> >
> > The above E and B satisfies Maxwell's equations in the standard form.
> >
> > Now let's examine this setup in the rotating coordinates. First of all,
> > all the particles in it are _stationary_, therefore NO MATTER what B' is
> > (the magnetic field as observed by the rotating system), they experience
> > _no_ magnetic (Lorentz) force. But they of course _do_ experience _a_ force[#]
> > simply because they did so as measured by the (say) mechanical strain of
> > the contraption mentioned earlier which is a coordinate-independent
> > phenomenon.
> >
> > [#] ignoring the centripetal and centrifugal forces, resp., as they
> > are obviously equal.
> >
> > Therefore, the electromagnetic force experienced in the rotating system
> > must be due only to the electric field E'. And we know this force is equal
> > to the Lorentz force of the lab system:
> >
> > E' = F/q = v x B
> >
>
> No, you don't, this is where you went wrong. There is no reason to surmise that E'=F/q
Ah, you are probably right. I'll try to fix it tonight. The reason I wrote
it was a momentary lapse of reason when I assumed "constant linear speed"
(of the test particle) meant "constant linear velocity" (which of course it
isn't).
If that velocity _were_ constant (for example if the wire was a straight line
instead of circle) then Newton's "F = dp/dt" would indeed imply the equality
of forces as I wrote it above (since the two forces would then differ by
"d/dt(a constant vector)", i.e. they would differ by zero).
But in this case the linear velocity vector v circles around so the correct
expression is probably something like:
E' = F/q + (some extra term)
I'll see if I can calculate that extra and we'll see if the contradiction
still persists.
--
Jan
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| From | "Dono," <sa_ge@comcast.net> |
|---|---|
| Date | 2017-02-13 16:08 -0800 |
| Message-ID | <b122096f-6d79-410d-bfe0-5fc5d5ba3d0b@googlegroups.com> |
| In reply to | #409132 |
On Monday, February 13, 2017 at 3:47:48 PM UTC-8, JanPB wrote: > On Monday, February 13, 2017 at 2:38:22 PM UTC-8, Dono, wrote: > > On Monday, February 13, 2017 at 12:39:45 PM UTC-8, JanPB wrote: > > > On Sunday, February 12, 2017 at 7:35:15 PM UTC-8, Dono, wrote: > > > > On Sunday, February 12, 2017 at 12:43:41 PM UTC-8, tjrob137 wrote: > > > > > On 2/8/17 2/8/17 12:39 PM, Dono, wrote: > > > > > > Maxwell's equations are invariant to the rotation transform. Therefore the > > > > > > solutions in the frame of the rotating are identical to the ones in the > > > > > > inertial frame of the hub. > > > > > > > > > > This is not true, for the rotation transform YOU give. You CLEARLY have not > > > > > performed the exercise you want me to do. > > > > > > > > > > > The transform is: > > > > > > x' |cos \omega*t sin \omega*t 0 0 | x > > > > > > y'= |-sin \omega*t cos \omega*t 0 0 | y > > > > > > z' | 0 0 1 0 | z > > > > > > t' | 0 0 0 1 | t > > > > > > > > > > OBVIOUSLY you have not actually applied this transform to the Maxwell's > > > > > equations. Or if you think you did, then you did it incorrectly. The ME are NOT > > > > > invariant under this transform. > > > > > > > > > > > > > Actually, unlike you, I DID the calculations. Do them or STFU. > > > > > > You must have made a mistake somewhere. I'm posting a proof below but > > > first a quick observation: when changing the coordinates in Maxwell's > > > equations, it is NOT enough to replace all the coordinate derivative > > > operators by those of the new system: it is ALSO necessary to adjust > > > the electric and magnetic vectors E and B _as well_. > > > > ...which is precisely what I did. One needs to find the transforms E' and B' as a function of E and B. > > > > > > > This is _not trivial_, > > > even for a Lorentz transformation, let alone a for a curvilinear > > > one like your rotating system. > > > > > > > I agree. Nevertheless , I had no trouble deriving them. > > > > > > > This adjustment of E and B is _not_ the same as the transformation of > > > the derivative operators. > > > > I agree. > > > > > > > This is because E and B fields in whatever > > > coordinates are defined by the mechanical results of _forces_ they > > > generate, and these forces, unlike the derivative operators, do not > > > transform linearly. > > > > Yes. > > > > > For example, whenever one says "Maxwell's > > > equations are invariant under Lorentz transformations", this means BOTH > > > derivative operators AND E and B are changed in a certain way. > > > > > > > No issue. > > > > > > > Just wanted to state it clearly to avoid further confusion. > > > > > > Now the proof that Maxwell's equations do not retain their form in the > > > rotating coordinates you've written above. Actually I'm not going to > > > brute-force the calculation but instead set up an experiment which > > > we'll view from both the lab (inertial) coordinates and the above rotating > > > system. The conclusion will be that at least one of Maxwell's equations > > > _in its standard form_ will clearly FAIL in the rotating system. > > > > False. Now I need to find what you did wrong. > > > > > > > Which means in the rotating system Maxwell's equations develop extra > > > terms, sort of like "F=ma" develops extra terms in rotating coordinates > > > (the usual three fictitious forces). > > > > > > > You have a bias, all you are going to do is to confirm your bias. > > > > > > > So here is the setup. I believe it's correct (I doodled it while on my > > > train to work): > > > > > > * the lab coordinate system is the standard Cartesian xyz, > > > > > > * your system rotates around the z-axis with angular speed \omega > > > (from now on I'm going to write "w" instead of "\omega"), as this is > > > what your matrix says. The angular velocity _vector_ points _down_ > > > along the z-axis, given your choice of the minus sign before the sines > > > (this is unimportant), > > > > > > * imagine a circular conducting wire in the xy-plane with the origin > > > at its center. Assume there is a steady current I flowing through it. > > > > > > > ok > > > > > > > We are going to examine the E and B fields in the lab system and likewise > > > the corresponding E' and B' fields in the rotating system. We'll conclude > > > that E' and B' CANNOT satisfy Maxwell's equations in their standard form > > > in the rotating system. > > > > > > > OK > > > > > To gather enough information about E and B, we imagine a bunch of charged > > > particles in space, each of charge q, and rotating in the same fashion as > > > your rotating coordinate system (so to keep them on their circular tracks > > > around the z-axis, imagine them mounted on some mechanical contraption > > > designed to maintain this constraint). > > > > > > Because the wire is electrically neutral, we have E = 0. OTOH due to the > > > nonzero I, we have a nonzero B given by the Biot-Savart law. Because the > > > aforementioned cloud of particles is moving wrt to the lab system, the > > > particles experience the Lorentz force F = q v x B, where a particle > > > at position r has the linear velocity v = w x r. > > > > > > The above E and B satisfies Maxwell's equations in the standard form. > > > > > > Now let's examine this setup in the rotating coordinates. First of all, > > > all the particles in it are _stationary_, therefore NO MATTER what B' is > > > (the magnetic field as observed by the rotating system), they experience > > > _no_ magnetic (Lorentz) force. But they of course _do_ experience _a_ force[#] > > > simply because they did so as measured by the (say) mechanical strain of > > > the contraption mentioned earlier which is a coordinate-independent > > > phenomenon. > > > > > > [#] ignoring the centripetal and centrifugal forces, resp., as they > > > are obviously equal. > > > > > > Therefore, the electromagnetic force experienced in the rotating system > > > must be due only to the electric field E'. And we know this force is equal > > > to the Lorentz force of the lab system: > > > > > > E' = F/q = v x B > > > > > > > No, you don't, this is where you went wrong. There is no reason to surmise that E'=F/q > > Ah, you are probably right. I'll try to fix it tonight. The reason I wrote > it was a momentary lapse of reason when I assumed "constant linear speed" > (of the test particle) meant "constant linear velocity" (which of course it > isn't). > > If that velocity _were_ constant (for example if the wire was a straight line > instead of circle) then Newton's "F = dp/dt" would indeed imply the equality > of forces as I wrote it above (since the two forces would then differ by > "d/dt(a constant vector)", i.e. they would differ by zero). > > But in this case the linear velocity vector v circles around so the correct > expression is probably something like: > > E' = F/q + (some extra term) > > I'll see if I can calculate that extra and we'll see if the contradiction > still persists. > > -- > Jan Let me help you some more: you will not be able to get the correct result based on dynamics considerations, so, you will get wedged again. You will need to get the resulting transforms of the E,B starting from base principles, without invoking forces. I am telling you that in order to help you avoid more wasted time.
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