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Groups > sci.physics.relativity > #376988 > unrolled thread
| Started by | JanPB <filmart@gmail.com> |
|---|---|
| First post | 2016-02-23 17:05 -0800 |
| Last post | 2016-02-26 15:02 -0800 |
| Articles | 20 on this page of 134 — 18 participants |
Back to article view | Back to sci.physics.relativity
Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-23 17:05 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-23 22:28 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-23 22:47 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-23 23:01 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-23 23:04 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-23 23:27 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-23 23:28 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-23 23:40 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-24 00:21 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Maciej Woźniak <mlwozniak@wp.pl> - 2016-02-24 10:39 +0100
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-24 12:59 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-24 13:12 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Odd Bodkin <bodkinodd@gmail.com> - 2016-02-24 08:46 -0600
Re: Schwarzschild's paper and the uniqueness of the solution "Paul B. Andersen" <relativity@paulba.no> - 2016-02-24 19:54 +0100
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-24 01:20 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-24 01:39 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Maciej Woźniak <mlwozniak@wp.pl> - 2016-02-24 11:12 +0100
Re: Schwarzschild's paper and the uniqueness of the solution Odd Bodkin <bodkinodd@gmail.com> - 2016-02-24 08:37 -0600
Re: Schwarzschild's paper and the uniqueness of the solution "Dono," <sa_ge@comcast.net> - 2016-02-24 07:16 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-24 22:31 -0800
Re: Schwarzschild's paper and the uniqueness of the solution "Dono," <sa_ge@comcast.net> - 2016-02-25 06:30 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-25 09:11 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-25 16:13 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 09:38 -0800
Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-25 17:44 +0000
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 09:50 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Odd Bodkin <bodkinodd@gmail.com> - 2016-02-25 11:51 -0600
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 09:57 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Odd Bodkin <bodkinodd@gmail.com> - 2016-02-25 12:05 -0600
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 10:19 -0800
Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-25 18:13 +0000
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 10:21 -0800
Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-25 18:05 +0000
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 09:48 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Jackpol11@hotmail.com - 2016-02-25 14:06 -0500
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-25 12:35 -0800
Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-25 21:44 +0000
Re: Schwarzschild's paper and the uniqueness of the solution Jackpol11@hotmail.com - 2016-02-25 17:37 -0500
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-25 15:11 -0800
Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 12:44 +0000
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-26 06:57 -0800
Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 14:59 +0000
Re: Schwarzschild's paper and the uniqueness of the solution Gary Harnagel <hitlong@yahoo.com> - 2016-02-26 07:36 -0800
Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 18:45 +0000
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-26 07:37 -0800
Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 19:36 +0000
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-26 07:50 -0800
Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 18:47 +0000
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-26 11:44 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-25 15:47 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-25 16:00 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-25 16:09 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Odd Bodkin <bodkinodd@gmail.com> - 2016-02-25 18:29 -0600
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-25 18:43 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-26 23:04 +0100
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-26 14:59 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-26 16:19 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-27 10:27 +0100
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-27 17:55 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 12:13 +0100
Re: Schwarzschild's paper and the uniqueness of the solution Emigdio Sophronius <emigg@augustvisitors.org> - 2016-02-28 11:37 +0000
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 12:56 +0100
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 08:03 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 18:13 +0100
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 18:26 +0100
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 09:36 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 18:50 +0100
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 09:54 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 20:40 +0100
Re: Schwarzschild's paper and the uniqueness of the solution Emigdio Sophronius <emigg@augustvisitors.org> - 2016-02-28 19:44 +0000
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 12:20 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Emigdio Sophronius <emigg@augustvisitors.org> - 2016-02-28 20:58 +0000
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 13:02 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 12:31 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-29 22:40 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 10:54 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 07:30 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 17:46 +0100
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 08:51 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Emigdio Sophronius <emigg@augustvisitors.org> - 2016-02-28 17:01 +0000
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 07:34 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-03 15:15 -0600
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-03-03 19:54 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 08:48 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Fuller <fuller.david@hotmail.com> - 2016-02-28 09:13 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 10:09 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Fuller <fuller.david@hotmail.com> - 2016-03-06 10:56 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 18:19 +0100
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 09:24 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 18:34 +0100
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 09:44 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 19:12 +0100
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 10:19 -0800
Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 11:17 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-01 17:06 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-03-01 17:54 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-01 19:41 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-03-04 01:17 +0100
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-03 17:12 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-03-03 17:53 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-03 22:19 -0600
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-03 21:36 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-10 11:14 -0600
Re: Schwarzschild's paper and the uniqueness of the solution Maciej Woźniak <mlwozniak@wp.pl> - 2016-03-10 18:32 +0100
Re: Schwarzschild's paper and the uniqueness of the solution Luigi Durante <luigdu@jaccappo.org> - 2016-03-10 20:22 +0000
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-10 13:02 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Luigi Durante <luigdu@jaccappo.org> - 2016-03-10 21:08 +0000
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-10 13:19 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Luigi Durante <luigdu@jaccappo.org> - 2016-03-10 21:27 +0000
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-10 14:04 -0800
Re: Schwarzschild's paper and the uniqueness of the solution "Paul B. Andersen" <relativity@paulba.no> - 2016-03-11 13:33 +0100
Re: Schwarzschild's paper and the uniqueness of the solution Maciej Woźniak <mlwozniak@wp.pl> - 2016-03-10 22:49 +0100
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-10 14:20 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-03-05 05:24 +0100
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-04 21:36 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-03-04 22:50 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-03-05 11:24 +0100
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-05 20:07 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-03 14:49 -0600
Re: Schwarzschild's paper and the uniqueness of the solution Helénē Swanhild <helenes@gardenclosure.org> - 2016-03-03 21:40 +0000
Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-03 18:58 -0600
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-03 14:04 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-03-03 17:46 -0800
Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-03 22:21 -0600
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-25 16:42 -0800
Re: Schwarzschild's paper and the uniqueness of the solution "Paul B. Andersen" <relativity@paulba.no> - 2016-02-26 20:00 +0100
Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 19:03 +0000
Re: Schwarzschild's paper and the uniqueness of the solution John Gogo <jfgogo22@yahoo.com> - 2016-02-25 19:36 -0800
Re: Schwarzschild's paper and the uniqueness of the solution alsor@interia.pl - 2016-02-26 09:36 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-26 11:33 -0800
Re: Schwarzschild's paper and the uniqueness of the solution alsor@interia.pl - 2016-02-26 12:05 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-26 12:47 -0800
Re: Schwarzschild's paper and the uniqueness of the solution alsor@interia.pl - 2016-02-26 14:16 -0800
Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-26 15:02 -0800
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| From | Emigdio Sophronius <emigg@augustvisitors.org> |
|---|---|
| Date | 2016-02-28 11:37 +0000 |
| Message-ID | <naum6k$orh$1@gioia.aioe.org> |
| In reply to | #377393 |
Thomas 'PointedEars' Lahn wrote: >> It is an undefined object in mathematics unless you use non-standard >> analysis or something similar. > > Already shown by me to be wrong. Yes, you are wrong. No need to show. We can just assume.
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| From | Thomas 'PointedEars' Lahn <PointedEars@web.de> |
|---|---|
| Date | 2016-02-28 12:56 +0100 |
| Message-ID | <2313164.RIS2ONplPl@PointedEars.de> |
| In reply to | #377394 |
The ’nym-shifting troll posted as "Emigdio Sophronius": > Thomas 'PointedEars' Lahn wrote: >>> It is an undefined object in mathematics unless you use non-standard >>> analysis or something similar. >> >> Already shown by me to be wrong. > > Yes, you are wrong. No need to show. We can just assume. As we can see here again, the ’nym-shifting troll can neither read nor write English properly. *PLONK* PointedEars -- Q: Who's on the case when the electricity goes out? A: Sherlock Ohms. (from: WolframAlpha)
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| From | David Waite <waitedavid1618@yahoo.com> |
|---|---|
| Date | 2016-02-28 08:03 -0800 |
| Message-ID | <b3f841bc-09c0-4158-9d9e-d96af45bd218@googlegroups.com> |
| In reply to | #377395 |
On Sunday, February 28, 2016 at 4:56:17 AM UTC-7, Thomas 'PointedEars' Lahn wrote: >On Sunday, February 28, 2016 at 4:13:08 AM UTC-7, Thomas 'PointedEars' Lahn wrote: > (c² 0 0 0) > g_µν = (0 −1 0 0) > (0 0 −1 0) > (0 0 0 −1) If you're going to be pedantic about Jan's semantics than I will be about your definitions. It is utterly ridiculous to define your terms in such a way that a tensor has different units carried by different elements when its not necessary to do so. Just get a brain and define x0 by ct rather than t so that it has all elements with the same units.
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| From | Thomas 'PointedEars' Lahn <PointedEars@web.de> |
|---|---|
| Date | 2016-02-28 18:13 +0100 |
| Message-ID | <2877801.KmaYAJ1YTX@PointedEars.de> |
| In reply to | #377409 |
David Waite wrote:
> On Sunday, February 28, 2016 at 4:56:17 AM UTC-7, Thomas 'PointedEars'
> Lahn wrote:
>> On Sunday, February 28, 2016 at 4:13:08 AM UTC-7, Thomas 'PointedEars'
>> Lahn wrote:
>> (c² 0 0 0)
>> g_µν = (0 −1 0 0)
>> (0 0 −1 0)
>> (0 0 0 −1)
>
> If you're going to be pedantic about Jan's semantics than I will be about
> your definitions. It is utterly ridiculous to define your terms in such a
> way that a tensor has different units carried by different elements when
> its not necessary to do so. Just get a brain and define x0 by ct rather
> than t so that it has all elements with the same units.
That is the third time now (I can see that you have posted a fourth time as
I was writing this). How more often are you going to post this (what I
think is nonsense as you are confusing the signature with the metric)?
I think I am following convention here. To recapture, I made the following
substitutions to arrive and the summantion notation (now superscript not
following paranthesis meaning the index in a contravariant tensor, not an
exponent):
ds² = (c)² (dt)² − (dx)² − (dy)² − (dz)²
= (c)² (dx⁰)² − (dx¹)² − (dx²)² − (dx³)²
= g₀₀ dx⁰ dx⁰ − g₁₁ dx¹ dx¹ − g₂₂ dx² dx² − g₃₃ dx³ dx³
How is “g” going to look like if I “define x0 by ct rather than t”?
There is no “t” there; there is “dt”.
PointedEars
--
Q: What did the nuclear physicist post on the laboratory door
when he went camping?
A: 'Gone fission'.
(from: WolframAlpha)
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| From | Thomas 'PointedEars' Lahn <PointedEars@web.de> |
|---|---|
| Date | 2016-02-28 18:26 +0100 |
| Message-ID | <4017562.QSWATVsR6p@PointedEars.de> |
| In reply to | #377417 |
Thomas 'PointedEars' Lahn wrote:
> I think I am following convention here. To recapture, I made the
> following substitutions to arrive and the summantion notation (now
> superscript not following paranthesis meaning the index in a contravariant
> tensor, not an exponent):
>
> ds² = (c)² (dt)² − (dx)² − (dy)² − (dz)²
> = (c)² (dx⁰)² − (dx¹)² − (dx²)² − (dx³)²
> = g₀₀ dx⁰ dx⁰ − g₁₁ dx¹ dx¹ − g₂₂ dx² dx² − g₃₃ dx³ dx³
Sorry, I meant of course:
= g₀₀ dx⁰ dx⁰ + g₁₁ dx¹ dx¹ + g₂₂ dx² dx² + g₃₃ dx³ dx³
> How is “g” going to look like if I “define x0 by ct rather than t”?
>
> There is no “t” there; there is “dt”.
PointedEars
--
Q: Where are offenders sentenced for light crimes?
A: To a prism.
(from: WolframAlpha)
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| From | David Waite <waitedavid1618@yahoo.com> |
|---|---|
| Date | 2016-02-28 09:36 -0800 |
| Message-ID | <4a3ebdff-6fb6-4683-9ad6-f2fd2dd68472@googlegroups.com> |
| In reply to | #377422 |
On Sunday, February 28, 2016 at 10:26:31 AM UTC-7, Thomas 'PointedEars' Lahn wrote: > Thomas 'PointedEars' Lahn wrote: > > > I think I am following convention here. To recapture, I made the > > following substitutions to arrive and the summantion notation (now > > superscript not following paranthesis meaning the index in a contravariant > > tensor, not an exponent): > > > > ds² = (c)² (dt)² − (dx)² − (dy)² − (dz)² > > = (c)² (dx⁰)² − (dx¹)² − (dx²)² − (dx³)² > > = g₀₀ dx⁰ dx⁰ − g₁₁ dx¹ dx¹ − g₂₂ dx² dx² − g₃₃ dx³ dx³ > > Sorry, I meant of course: > > = g₀₀ dx⁰ dx⁰ + g₁₁ dx¹ dx¹ + g₂₂ dx² dx² + g₃₃ dx³ dx³ > > > How is “g” going to look like if I “define x0 by ct rather than t”? > > > > There is no “t” there; there is “dt”. > > > PointedEars > -- > Q: Where are offenders sentenced for light crimes? > A: To a prism. > > (from: WolframAlpha) I already told you, defining x0=ct it becomes > > (1 0 0 0) > > g_µν = (0 −1 0 0) > > (0 0 −1 0) > > (0 0 0 −1)
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| From | Thomas 'PointedEars' Lahn <PointedEars@web.de> |
|---|---|
| Date | 2016-02-28 18:50 +0100 |
| Message-ID | <4473018.da5nk44eqV@PointedEars.de> |
| In reply to | #377424 |
David Waite wrote: > On Sunday, February 28, 2016 at 10:26:31 AM UTC-7, Thomas 'PointedEars' > Lahn wrote: >> Thomas 'PointedEars' Lahn wrote: >> > I think I am following convention here. To recapture, I made the >> > following substitutions to arrive and the summantion notation (now >> > superscript not following paranthesis meaning the index in a >> > contravariant tensor, not an exponent): >> > >> > ds² = (c)² (dt)² − (dx)² − (dy)² − (dz)² >> > = (c)² (dx⁰)² − (dx¹)² − (dx²)² − (dx³)² >> > = g₀₀ dx⁰ dx⁰ − g₁₁ dx¹ dx¹ − g₂₂ dx² dx² − g₃₃ dx³ dx³ >> >> Sorry, I meant of course: >> >> = g₀₀ dx⁰ dx⁰ + g₁₁ dx¹ dx¹ + g₂₂ dx² dx² + g₃₃ dx³ dx³ >> >> > How is “g” going to look like if I “define x0 by ct rather than t”? >> > >> > There is no “t” there; there is “dt”. >> […] > > I already told you, defining x0=ct it becomes >> > (1 0 0 0) >> > g_µν = (0 −1 0 0) >> > (0 0 −1 0) >> > (0 0 0 −1) Unsursprisingly, you have not answered the question that I asked. PointedEars -- Q: What did the nuclear physicist post on the laboratory door when he went camping? A: 'Gone fission'. (from: WolframAlpha)
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| From | David Waite <waitedavid1618@yahoo.com> |
|---|---|
| Date | 2016-02-28 09:54 -0800 |
| Message-ID | <81b3df83-ec1a-4dff-a1da-8a07ca3a83da@googlegroups.com> |
| In reply to | #377427 |
On Sunday, February 28, 2016 at 10:50:29 AM UTC-7, Thomas 'PointedEars' Lahn wrote:
> David Waite wrote:
>
> > On Sunday, February 28, 2016 at 10:26:31 AM UTC-7, Thomas 'PointedEars'
> > Lahn wrote:
> >> Thomas 'PointedEars' Lahn wrote:
> >> > I think I am following convention here. To recapture, I made the
> >> > following substitutions to arrive and the summantion notation (now
> >> > superscript not following paranthesis meaning the index in a
> >> > contravariant tensor, not an exponent):
> >> >
> >> > ds² = (c)² (dt)² − (dx)² − (dy)² − (dz)²
> >> > = (c)² (dx⁰)² − (dx¹)² − (dx²)² − (dx³)²
> >> > = g₀₀ dx⁰ dx⁰ − g₁₁ dx¹ dx¹ − g₂₂ dx² dx² − g₃₃ dx³ dx³
> >>
> >> Sorry, I meant of course:
> >>
> >> = g₀₀ dx⁰ dx⁰ + g₁₁ dx¹ dx¹ + g₂₂ dx² dx² + g₃₃ dx³ dx³
> >>
> >> > How is “g” going to look like if I “define x0 by ct rather than t”?
> >> >
> >> > There is no “t” there; there is “dt”.
> >> […]
> >
> > I already told you, defining x0=ct it becomes
> >> > (1 0 0 0)
> >> > g_µν = (0 −1 0 0)
> >> > (0 0 −1 0)
> >> > (0 0 0 −1)
>
> Unsursprisingly, you have not answered the question that I asked.
I did, twice, fleebrain, but you didn't answer mine. This is the Thomas 'PointedEars' Lahn challenge just for you.
Here is an exact solution to Einstein's field equations(one of mine):
ds^2={dct^2/[(1-(A*|z|/c^2))^2]}-[(1-(A*|z|/c^2))^(2n)]dx^2-[(1-(A*|z|/c^2))^(2n/(n-1))]dy^2-[(1-(A*|z|/c^2))^((2*(n^2-2n+2))/(n-1))]dz^2
which is vacuum for |z| greater than 0. Find the stress-energy tensor for the sheet at z=0.
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| From | Thomas 'PointedEars' Lahn <PointedEars@web.de> |
|---|---|
| Date | 2016-02-28 20:40 +0100 |
| Message-ID | <56D34D33.6050709@PointedEars.de> |
| In reply to | #377429 |
David Waite wrote:
> On Sunday, February 28, 2016 at 10:50:29 AM UTC-7, Thomas 'PointedEars'
> Lahn wrote:
>> Unsursprisingly, you have not answered the question that I asked.
>
> I did, twice,
I think we can agree on that you have answered the question that I asked in
this subthread *in a way* twice as you have posted *a possible, correct*
metric for Minkowski spacetime.
I had previously been unaware that
c dt = d(ct)
holds for constants c and differentials dt [1], so that
ds² = c² dt² − dx² − dy² − dz²
= (c dt)² − dx² − dy² − dz²
= (d(ct))² − dx² − dy² − dz²
= (dx⁰)² − (dx¹)² − (dx²)² − (dx³)² (x⁰ := ct)
= g₀₀ (dx⁰)² + g₁₁ (dx¹)² + g₂₂ (dx²)² + g₃₃ (dx³)²
with
(1 0 0 0)
g_µν = (0 −1 0 0) = diag(+1,−1,−1,−1)
(0 0 −1 0)
(0 0 0 −1)
which is probably what you mean. It then happens that the metric (tensor) g
is identical to the signature of the space when written as diagonal
matrix/tensor η, whereas both are generally related by the identity
g_αβ ≡ ∂ξ^α∕∂x^µ ∂ξ^β∕∂x^ν η_αβ
(see also: <http://mathworld.wolfram.com/MetricTensor.html>).
However, you have _not_ answered my *other* question regarding the form of
ds² in Einstein summation convention then, which is why I had to figure that
out for myself:
ds² = g_µν dx^µ dx^ν = c² dt² − dx² − dy² − dz²
still holds with your metric g and definition of x⁰, as can be seen above.
Had you been more forthcoming and less name-calling, we could have resolved
this earlier.
I maintain, however, that the metric that I posted also is standard notation
and not in any way wrong, and I have to reiterate that with natural units
where c = 1 (which is common in relativistic physics), our metrics are
identical.
See also: <http://mathworld.wolfram.com/MinkowskiMetric.html>
> fleebrain, but you didn't answer mine. […]
And do you think that your insults will effect that I consider your red
herring, or reading further postings from you at all?
So much for “logical responses”.
PointedEars
___________
[1] <https://en.wikipedia.org/wiki/Differential_of_a_function#Properties>
<https://de.wikipedia.org/wiki/Differential_(Mathematik)#Rechenregeln>
--
Q: How many theoretical physicists specializing in general relativity
does it take to change a light bulb?
A: Two: one to hold the bulb and one to rotate the universe.
(from: WolframAlpha)
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| From | Emigdio Sophronius <emigg@augustvisitors.org> |
|---|---|
| Date | 2016-02-28 19:44 +0000 |
| Message-ID | <naviml$c5v$2@gioia.aioe.org> |
| In reply to | #377439 |
Thomas 'PointedEars' Lahn wrote: > I had previously been unaware that > > c dt = d(ct) What an idiot. lol. You are strong, man, in tensors.
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| From | David Waite <waitedavid1618@yahoo.com> |
|---|---|
| Date | 2016-02-28 12:20 -0800 |
| Message-ID | <dd95619a-e74c-4811-8255-03c2b68fd723@googlegroups.com> |
| In reply to | #377440 |
On Sunday, February 28, 2016 at 12:44:24 PM UTC-7, Emigdio Sophronius wrote: > Thomas 'PointedEars' Lahn wrote: > > > I had previously been unaware that > > > > c dt = d(ct) > > What an idiot. lol. You are strong, man, in tensors. Ah so you need to go back to elementary school and learn ppmdas. dct=d(ct), moron.
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| From | Emigdio Sophronius <emigg@augustvisitors.org> |
|---|---|
| Date | 2016-02-28 20:58 +0000 |
| Message-ID | <navn28$k57$1@gioia.aioe.org> |
| In reply to | #377443 |
David Waite wrote: > On Sunday, February 28, 2016 at 12:44:24 PM UTC-7, Emigdio Sophronius > wrote: >> Thomas 'PointedEars' Lahn wrote: >> >> > I had previously been unaware that >> > >> > c dt = d(ct) >> >> What an idiot. lol. You are strong, man, in tensors. > > Ah so you need to go back to elementary school and learn ppmdas. > dct=d(ct), moron. I called him an idiot, but since you insist, David Waste :) Is c not a constant, idiot!
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| From | David Waite <waitedavid1618@yahoo.com> |
|---|---|
| Date | 2016-02-28 13:02 -0800 |
| Message-ID | <f8e7ce57-ae55-4b9b-bc75-b79d9f3c7f89@googlegroups.com> |
| In reply to | #377446 |
On Sunday, February 28, 2016 at 1:58:52 PM UTC-7, Emigdio Sophronius wrote: > David Waite wrote: > > > On Sunday, February 28, 2016 at 12:44:24 PM UTC-7, Emigdio Sophronius > > wrote: > >> Thomas 'PointedEars' Lahn wrote: > >> > >> > I had previously been unaware that > >> > > >> > c dt = d(ct) > >> > >> What an idiot. lol. You are strong, man, in tensors. > > > > Ah so you need to go back to elementary school and learn ppmdas. > > dct=d(ct), moron. > > I called him an idiot, but since you insist, David Waste :) Is c not a > constant, idiot! About 2 seconds after I posted, I relized that you were talking to him and not telling me that it wasn't and deleted the response post, but apparently the groups lag is atrocious.
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| From | David Waite <waitedavid1618@yahoo.com> |
|---|---|
| Date | 2016-02-28 12:31 -0800 |
| Message-ID | <3d751c34-199c-4147-8ef2-898838d57272@googlegroups.com> |
| In reply to | #377439 |
On Sunday, February 28, 2016 at 12:40:38 PM UTC-7, Thomas 'PointedEars' Lahn wrote:
> However, you have _not_ answered my *other* question regarding the form of
> ds² in Einstein summation convention then, which is why I had to figure that
> out for myself:
>
> ds² = g_µν dx^µ dx^ν = c² dt² − dx² − dy² − dz²
You didn't have questions you had false assertions which you ignored the answer to. As I said plainly stated,
x⁰=ct
x¹=x
x²=y
x³=z
ds²=dct²-dx²-dy²-dz²
then you get
ds²=(dx⁰)²-(dx¹)²-(dx²)²-(dx³)²
>> > (1 0 0 0)
>> > g_µν = (0 −1 0 0)
>> > (0 0 −1 0)
>> > (0 0 0 −1)
and its signature is (+,-,-,-).
And YOU still haven't answered my question and until you do you should stop being a crank making assertions about things you obviously don't know anything about. Here is an exact solution to Einstein's field equations(one of mine)
ds^2={dct^2/[(1-(A*|z|/c^2))^2]}-[(1-(A*|z|/c^2))^(2n)]dx^2-[(1-(A*|z|/c^2))^(2n/(n-1))]dy^2-[(1-(A*|z|/c^2))^((2*(n^2-2n+2))/(n-1))]dz^2
which is vacuum for |z| greater than 0. Find the stress-energy tensor for the sheet at z=0.
Tell me when you're going to admit you don't know crap about the subject matter and so can't answer it so I can put the answer back up at my site as I temporarily removed it so you couldn't get it from me.
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| From | David Waite <waitedavid1618@yahoo.com> |
|---|---|
| Date | 2016-02-29 22:40 -0800 |
| Message-ID | <8a328ba9-caaa-42d6-bce2-a2cc49d6e2f1@googlegroups.com> |
| In reply to | #377439 |
On Sunday, February 28, 2016 at 12:40:38 PM UTC-7, Thomas 'PointedEars' Lahn wrote: > Since we've fully verified now that you don't actually know anything about it and won't be able to answer the challenge, you can find the answer to the challenge put to you at http://www.modernrelativitysite.com/domain216.gif Guess it was a bad idea to troll Jan being pedantic about semantics.
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| From | David Waite <waitedavid1618@yahoo.com> |
|---|---|
| Date | 2016-02-28 10:54 -0800 |
| Message-ID | <e8f5f4e8-a2ba-407e-a5bc-1f64c1e70c02@googlegroups.com> |
| In reply to | #377427 |
On Sunday, February 28, 2016 at 10:50:29 AM UTC-7, Thomas 'PointedEars' Lahn wrote: > David Waite wrote: > > > On Sunday, February 28, 2016 at 10:26:31 AM UTC-7, Thomas 'PointedEars' > > Lahn wrote: > >> Thomas 'PointedEars' Lahn wrote: > >> > I think I am following convention here. You're following crapwiki actually. There actually isn't one single set of conventions for general relativity's tensor calculus because I can count on my fingers and toes the number of people who have understood general relativity since Einstein. I'm just telling you what you should be doing. > >> > There is no “t” there; there is “dt”. So it just occurs to me that not only am I talking to a crank that makes assertions about tensors he knows nothing about but that he doesn't even have calculus as a prerequisite. Ok, so dt means an infinitesimal displacement in t. As such, c*dt=dct c²*dt²=(dct)² or for those who aren't to stupid to get it, dct². So you define for the Minkowski spacetime x⁰=ct x¹=x x²=y x³=z and the Minkowski rank2 covariant metric tensor expressed as a matrix IS THEN, >> > (1 0 0 0) >> > g_µν = (0 −1 0 0) >> > (0 0 −1 0) >> > (0 0 0 −1) Nice and elegant, with all the same units for all the elements since so long as you're using rectilinear coordinates, it isn't necessary to do otherwise and its signature is (+,-,-,-).
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| From | David Waite <waitedavid1618@yahoo.com> |
|---|---|
| Date | 2016-02-28 07:30 -0800 |
| Message-ID | <4e20cce1-58d0-43a3-9ab0-3f623d007829@googlegroups.com> |
| In reply to | #377393 |
> (c² 0 0 0) > g_µν = (0 −1 0 0) > (0 0 −1 0) > (0 0 0 −1) If you're going to be pedantic about Jan's semantics than I will be about your definitions. It is utterly ridiculous to define your terms in such a way that a tensor has different units carried by different elements. Just get a brain and define x0 by ct rather than t so that it has all elements with the same units.
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| From | Thomas 'PointedEars' Lahn <PointedEars@web.de> |
|---|---|
| Date | 2016-02-28 17:46 +0100 |
| Message-ID | <1911315.W5DvsoVRud@PointedEars.de> |
| In reply to | #377404 |
David Waite wrote: >> (c² 0 0 0) >> g_µν = (0 −1 0 0) >> (0 0 −1 0) >> (0 0 0 −1) > > If you're going to be pedantic about Jan's semantics than I will be about > your definitions. It is utterly ridiculous to define your terms in such a > way that a tensor has different units carried by different elements. Utter nonsense. PointedEars -- Q: How many theoretical physicists specializing in general relativity does it take to change a light bulb? A: Two: one to hold the bulb and one to rotate the universe. (from: WolframAlpha)
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| From | David Waite <waitedavid1618@yahoo.com> |
|---|---|
| Date | 2016-02-28 08:51 -0800 |
| Message-ID | <c6edecde-39da-438a-87d4-a370ebaf2a40@googlegroups.com> |
| In reply to | #377411 |
On Sunday, February 28, 2016 at 9:46:06 AM UTC-7, Thomas 'PointedEars' Lahn wrote: > Utter nonsense. Argument from incredulity isn't logical Mr.Spock. You were wrong so you didn't have a valid response.
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| From | Emigdio Sophronius <emigg@augustvisitors.org> |
|---|---|
| Date | 2016-02-28 17:01 +0000 |
| Message-ID | <nav95k$1qnb$1@gioia.aioe.org> |
| In reply to | #377411 |
Thomas 'PointedEars' Lahn wrote: >>> (c² 0 0 0) >>> g_µν = (0 −1 0 0) >>> (0 0 −1 0) >>> (0 0 0 −1) >> >> If you're going to be pedantic about Jan's semantics than I will be >> about your definitions. It is utterly ridiculous to define your terms >> in such a way that a tensor has different units carried by different >> elements. > > Utter nonsense. PointedEars You don't know what a tensors stands for, especially in Physics. Is not a data storage, idiot. What am I crazy?? I am talking to an almost half of an engineer.
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