Path: csiph.com!news.mixmin.net!weretis.net!feeder1.news.weretis.net!news.solani.org!.POSTED!not-for-mail From: Thomas 'PointedEars' Lahn Newsgroups: sci.physics.relativity Subject: Re: The Necessity Alternate Theories Date: Sat, 10 Oct 2015 19:08:31 +0200 Organization: PointedEars Software (PES) Lines: 80 Message-ID: <2065293.R244bDITXT@PointedEars.de> References: <4368209.GPKBEtnK0j@PointedEars.de> <1730284.XuYReIBpc4@PointedEars.de> <2452749.ojeSIZT1PQ@PointedEars.de> <1994224.nhiJk4n2FN@PointedEars.de> <3272666.zKxLX75AIR@PointedEars.de> <1753439.1rgGCj0DGj@PointedEars.de> <2448822.LE9lmc8zEI@PointedEars.de> Reply-To: Thomas 'PointedEars' Lahn Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: 8Bit X-Trace: solani.org 1444496913 8581 eJwNxcEBwCAIA8CVhJJQx6kB9h/B3ufw0KgMgoHBRHylxX0q3NdmeeA/20bthTG1yl71QY7OBRoAEbs= (10 Oct 2015 17:08:33 GMT) X-Complaints-To: abuse@news.solani.org NNTP-Posting-Date: Sat, 10 Oct 2015 17:08:33 +0000 (UTC) User-Agent: KNode/4.14.2 X-User-ID: eJwFwQkBwDAIA0BLDU8AOYUV/xJ250pwwug0X1+tvle9vimMFyVFyQ1MNqiD3ug8PNoTbxHpKxOUx9w2/EPKFRQ= Cancel-Lock: sha1:G9YftEkJE5DTa8f73rIePgAtg74= X-NNTP-Posting-Host: eJwFwYERADAEBLCVOP4xjqruP0ITGJUTTtDx8ChWPOwER5kVu4FCvltZRzZdr1nbbEg0+QEGExBq Xref: csiph.com sci.physics.relativity:366737 Natalina Nazvarova wrote: > Thomas 'PointedEars' Lahn wrote: >> Thomas 'PointedEars' Lahn wrote: >>> Natalina Nazvarova wrote: >>>> But does not imply that so many have to be zeroed. >>> >>> But it does; that is how you write the metric tensor for Minkowski >>> spacetime. Otherwise the spacetime would not be a Minkowski one, it >>> would not be flat (measuring distances would depend on the >>> four-position). >>> >>> And if you replace the components with their values in the expansion >>> above, you can see that only the summands where µ = ν remain as the >>> coefficients of those where µ ≠ ν are all 0. (That is what multiplying >>> with a diagonal matrix left-hand side does.) >>> >>> Leaving only >>> ds² = g_µν dx^µ dx^ν = g_00 dx^0 dx^0 + g_11 dx^1 dx^1 >>> + g_22 dx^2 dx^2 + g_33 dx^3 dx^3 > > What is this?? This is the metric partially expanded (on the g_µν where µ ≠ ν) by writing what Einstein summation notation (in which the general metric is expressed) actually means. When you expand it completely, by replacing g_00, g_11, g_22 and g_33 (the g_µν where µ = ν) with the corresponding values of the components of the metric tensor, you will see that the result is precisely what I used as basis of deriving the equation for calculating the proper time interval in Minkowski spacetime. >> Sorry for the confusion, of course it is >> = g_00 dx^0 dx^0 − g_11 dx^1 dx^1 − g_22 dx^2 dx^2 − g_33 dx^3 dx^3. >> instead. > > Which is still incorrect of course. It is _not_ “*still* incorrect”, but it *is* incorrect because the minus sign comes from the tensor’s components, in particular g_11, g_22, and g_33, instead. Which is why I had canceled and deleted that posting 8 minutes before you replied to it. > […] [as] you postulated already, as that being "a vector" (without having > the demanded UNIT vectors attached at it). So you have not done your homework (#1) yet. > Then your another blunder, Unfortunately, despite my sincere efforts, you still have no clue what you are talking about. > that those terms should stand for "values". They do: g_00 = c² g_11 = −1 g_22 = −1 g_33 = −1 All the other components of the metric tensor/matrix are 0, which means that the summands vanish when the tensor/matrix is multiplied with the vectors. Homework assignment #2: Write in explicit matrix/vector form, using variables for the component values only, the equation for muliplying a 4 × 4 matrix with a 4-vector. PointedEars -- Q: Who's on the case when the electricity goes out? A: Sherlock Ohms. (from: WolframAlpha)