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Groups > sci.physics.relativity > #593386
| From | Thomas 'PointedEars' Lahn <PointedEars@web.de> |
|---|---|
| Newsgroups | sci.physics.relativity |
| Subject | Re: Why Does the Metric contain a minus sign? |
| Date | 2022-10-13 22:09 +0200 |
| Organization | PointedEars Software (PES) |
| Message-ID | <12100779.O9o76ZdvQC@PointedEars.de> (permalink) |
| References | <8b322777-1913-4360-bce8-555912ea9237n@googlegroups.com> |
George Hammond wrote:
> Explanations for the minus sign in the 4 x 4 space-time Metric range from
> Thermodynamics to Euclidean versus Hyperbolic geometry. ..... I however
> think there is a simpler explanation, namely –
>
> The minus sign is required in order to reproduce the Lorentz
> transformation of special relativity. The correctness of the Lorentz
> transformation is experimentally proven beyond any question whatsoever.
> Therefore the minus sign is EXPERIMENTALLY REQUIRED. .... My question to
> you is: – is this a correct answer to the question, YES or NO?
No. Because, contrary to what especially science journalists with their
clickbait headings often want to make laypeople believe, that is NOT how
science works. There is NO experiment that can prove *any* theory beyond a
reasonable doubt. That is not what we do. We do experiments to *falsify*
theories, to weed out the bad ones. And when that fails (provided it it was
falsifiable, i.e. actually a theory), the respective theory becomes more
worthy of consideration.
But (if you also accept just one fundamental experimental fact) it is
*mathematically* required: It is a *logical* consequence of that fact.
A derivation that I still find very nice (and may have been introduced by
either Minkowski or Einstein) is that of the Minkowski metric merely from
two simple assumptions:
1. Light travels at the speed c, so it travels the distance c Δt in the
duration Δt (for all observers).
2. The Pythagorean theorem holds in flat spacetime, and so distances may
be expressed as the square root of the sum of squares of differences
between the spatial coordinates of two points (Euclidean metric).
For light,
c Δt = √(Δx² + Δy² + Δz²)
⇒ c² Δt² = Δx² + Δy² + Δz²
⇔ c² Δt² − Δx² − Δy² − Δz² = 0
When we make the intervals infinitesimal, we obtain
c² dt² − dx² − dy² − dz² = 0. (1)
We may call the value RHS “ds²” and find that light follows null spacetime
geodesics where ds² = 0. In general, for flat spacetime we have then one
form of the Minkowski metric
ds² = c² dt² − dx² − dy² − dz².
You can see that you can multiply eq. (1) by −1 to obtain equivalently
−c² dt² + dx² + dy² + dz² = 0,
and so you can also say
ds² = −c² dt² + dx² + dy² + dz²
if you prefer that.
It is "just a small step" from there to a full-blown spacetime metric that
works for all objects and spacetime intervals given a particular spacetime
geometry.
Notice the beauty of this. It does not require any assumptions about
clocks, lengths, or relations between observers. Just a constant speed of
light and basic geometry
And, in fact, even the Lorentz factor and "time dilation" pops out of it
*automagically*:
(ds/dt)² = c² − (dx/dt)² − (dy/dt)² − (dz/dt)²
= c² − [(dx/dt)² + (dy/dt)² + (dz/dt)²]
= c² − v²
= c² (1 − v²/c²)
= c² (1 − v²/c²)
⇔ (ds/c)² = dt² (1 − v²/c²)
⇔ dτ = dt √(1 − v²/c²) = dt/γ.
PointedEars
--
“Science is empirical: knowing the answer means nothing;
testing your knowledge means everything.”
—Dr. Lawrence M. Krauss, theoretical physicist,
in “A Universe from Nothing” (2009)
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Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-10 09:12 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-10 11:13 -0700
Re: Why Does the Metric contain a minus sign? Mandy Stabile <alts@ilnnnbsl.ed> - 2022-10-10 18:37 +0000
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-10 16:32 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-12 09:26 -0700
Re: Why Does the Metric contain a minus sign? Athel Cornish-Bowden <acornish@imm.cnrs.fr> - 2022-10-12 19:38 +0200
Re: Why Does the Metric contain a minus sign? Chip Gabrielli <eici@apeciill.bl> - 2022-10-13 17:17 +0000
Re: Why Does the Metric contain a minus sign? Woodrow Adessi <reds@odirsodo.er> - 2022-10-13 22:00 +0000
Re: Why Does the Metric contain a minus sign? nospam@de-ster.demon.nl (J. J. Lodder) - 2022-10-12 21:03 +0200
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-13 22:09 +0200
Re: Why Does the Metric contain a minus sign? Maciej Wozniak <maluwozniak@gmail.com> - 2022-10-13 23:18 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-14 10:25 -0700
Re: Why Does the Metric contain a minus sign? Woodrow Adessi <reds@odirsodo.er> - 2022-10-14 17:36 +0000
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-14 11:23 -0700
Re: Why Does the Metric contain a minus sign? Woodrow Adessi <reds@odirsodo.er> - 2022-10-14 19:50 +0000
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-14 23:55 +0200
Re: the 'PointedEars' Lahn, the braindead uneducated, unskilled and unemployed scumbag Woodrow Adessi <reds@odirsodo.er> - 2022-10-14 22:03 +0000
Re: the 'PointedEars' Lahn, the braindead uneducated, unskilled and unemployed scumbag "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2022-10-14 15:45 -0700
Re: the 'PointedEars' Lahn, the braindead uneducated, unskilled and unemployed scumbag whodat <whodaat@void.nowgre.com> - 2022-10-14 18:01 -0500
Re: the 'PointedEars' Lahn, the braindead uneducated, unskilled and unemployed scumbag Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-15 02:40 +0200
Re: the 'PointedEars' Lahn, the braindead uneducated, unskilled and unemployed scumbag William Stickers <bill.stickers@innocent.com> - 2022-10-17 11:09 +0100
Re: the 'PointedEars' Lahn, the braindead uneducated, unskilled and unemployed scumbag whodat <whodaat@void.nowgre.com> - 2022-10-17 07:49 -0500
Re: the 'PointedEars' Lahn, the braindead uneducated, unskilled and unemployed scumbag Maciej Wozniak <maluwozniak@gmail.com> - 2022-10-17 08:25 -0700
Re: the 'PointedEars' Lahn, the braindead uneducated, unskilled and unemployed scumbag "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2022-10-15 12:47 -0700
Re: the 'PointedEars' Lahn, the braindead uneducated, unskilled and unemployed scumbag Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-17 01:10 +0200
Re: the 'PointedEars' Lahn, the braindead uneducated, unskilled and unemployed scumbag whodat <whodaat@void.nowgre.com> - 2022-10-16 22:09 -0500
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-15 00:03 +0200
Re: Why Does the Metric contain a minus sign? Woodrow Adessi <reds@odirsodo.er> - 2022-10-14 22:06 +0000
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-14 23:54 +0200
Re: Why Does the Metric contain a minus sign? Woodrow Adessi <reds@odirsodo.er> - 2022-10-14 22:18 +0000
Re: Why Does the Metric contain a minus sign? whodat <whodaat@void.nowgre.com> - 2022-10-14 17:56 -0500
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-15 02:37 +0200
Re: Why Does the Metric contain a minus sign? whodat <whodaat@void.nowgre.com> - 2022-10-14 21:33 -0500
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-15 20:09 +0200
Re: Why Does the Metric contain a minus sign? whodat <whodaat@void.nowgre.com> - 2022-10-15 13:25 -0500
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-17 00:55 +0200
Re: Why Does the Metric contain a minus sign? whodat <whodaat@void.nowgre.com> - 2022-10-16 22:02 -0500
Re: Why Does the Metric contain a minus sign? Joaquin Cuocco <cicu@acacqjuc.co> - 2022-10-17 14:59 +0000
Re: Why Does the Metric contain a minus sign? Jim Pennino <jimp@gonzo.specsol.net> - 2022-10-17 08:23 -0700
Re: Why Does the Metric contain a minus sign? Joaquin Cuocco <cicu@acacqjuc.co> - 2022-10-17 17:30 +0000
Re: Why Does the Metric contain a minus sign? Jim Pennino <jimp@gonzo.specsol.net> - 2022-10-17 10:38 -0700
Re: Why Does the Metric contain a minus sign? Joaquin Cuocco <cicu@acacqjuc.co> - 2022-10-17 18:43 +0000
Re: Why Does the Metric contain a minus sign? Jim Pennino <jimp@gonzo.specsol.net> - 2022-10-17 12:19 -0700
Re: Why Does the Metric contain a minus sign? Joaquin Cuocco <cicu@acacqjuc.co> - 2022-10-17 18:48 +0000
Re: Why Does the Metric contain a minus sign? Jim Pennino <jimp@gonzo.specsol.net> - 2022-10-17 12:20 -0700
Re: Why Does the Metric contain a minus sign? Joaquin Cuocco <cicu@acacqjuc.co> - 2022-10-17 20:08 +0000
Re: Why Does the Metric contain a minus sign? Jim Pennino <jimp@gonzo.specsol.net> - 2022-10-17 14:22 -0700
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-15 02:33 +0200
Re: Why Does the Metric contain a minus sign? rotchm <rotchm@gmail.com> - 2022-10-14 17:40 -0700
Re: Why Does the Metric contain a minus sign? whodat <whodaat@void.nowgre.com> - 2022-10-14 21:44 -0500
Re: yet another lurking imbecile *rotchm* uneducated and unskilled like hell Everet Baldini <rvia@nildiden.ii> - 2022-10-15 18:18 +0000
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-14 23:41 +0200
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-14 18:04 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-14 18:08 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-14 18:36 -0700
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-15 03:35 +0200
Re: Why Does the Metric contain a minus sign? whodat <whodaat@void.nowgre.com> - 2022-10-14 21:40 -0500
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-15 19:54 +0200
Re: the lurking imbecile *Thomas 'PointedEars' Lahn* putting the foot in his mouth again Everet Baldini <rvia@nildiden.ii> - 2022-10-15 18:10 +0000
Re: the lurking imbecile *Thomas 'PointedEars' Lahn* putting the foot in his mouth again whodat <whodaat@void.nowgre.com> - 2022-10-15 14:04 -0500
Re: Why Does the Metric contain a minus sign? Everet Baldini <rvia@nildiden.ii> - 2022-10-15 18:40 +0000
Re: Why Does the Metric contain a minus sign? whodat <whodaat@void.nowgre.com> - 2022-10-15 13:53 -0500
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-17 00:41 +0200
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-15 03:37 +0200
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-14 19:09 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-15 01:39 -0700
Re: Why Does the Metric contain a minus sign? whodat <whodaat@void.nowgre.com> - 2022-10-14 21:42 -0500
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-15 03:44 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-15 03:51 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-15 10:34 -0700
Re: Why Does the Metric contain a minus sign? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-10-15 19:58 +0200
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-17 13:33 -0700
Re: Why Does the Metric contain a minus sign? Joaquin Cuocco <cicu@acacqjuc.co> - 2022-10-17 22:25 +0000
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-17 17:27 -0700
Re: Why Does the Metric contain a minus sign? Wilbert Sciacca <wcsc@iccstcwa.ia> - 2022-10-18 17:57 +0000
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-18 12:31 -0700
Re: Why Does the Metric contain a minus sign? Wilbert Sciacca <wcsc@iccstcwa.ia> - 2022-10-18 19:47 +0000
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-18 14:29 -0700
Re: Why Does the Metric contain a minus sign? Wilbert Sciacca <wcsc@iccstcwa.ia> - 2022-10-18 21:46 +0000
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-18 18:01 -0700
Re: Why Does the Metric contain a minus sign? Wilbert Sciacca <wcsc@iccstcwa.ia> - 2022-10-19 19:43 +0000
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-19 17:40 -0700
Re: Why Does the Metric contain a minus sign? Wilbert Sciacca <wcsc@iccstcwa.ia> - 2022-10-20 15:03 +0000
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-20 12:42 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-20 19:39 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-20 19:50 -0700
Re: Why Does the Metric contain a minus sign? Ricardo Bassani <isis@nbcroiad.ai> - 2022-10-21 09:04 +0000
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-21 04:37 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-21 16:49 -0700
Re: Why Does the Metric contain a minus sign? larry harson <larryharson66@gmail.com> - 2022-10-15 14:04 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-15 19:00 -0700
Re: Why Does the Metric contain a minus sign? George Hammond <ghammond928@gmail.com> - 2022-10-16 11:14 -0700
Re: Why Does the Metric contain a minus sign? Everet Baldini <rvia@nildiden.ii> - 2022-10-16 18:20 +0000
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