Path: csiph.com!fu-berlin.de!uni-berlin.de!individual.net!not-for-mail From: Thomas Heger Newsgroups: sci.physics.relativity Subject: Re: Annotated version of SRT Date: Fri, 20 May 2022 09:32:46 +0200 Lines: 56 Message-ID: References: <0837699b-4179-4249-9a72-98371b5c05b8n@googlegroups.com> <60f21ac0-1bf9-49a7-9c86-89e270fc07cbn@googlegroups.com> <59b45a30-48b0-430c-8910-fab1ff643051n@googlegroups.com> <52fe5433-4dcd-434c-905f-44e649e5b8f5n@googlegroups.com> <4e587415-9f7b-4ad9-b5ad-8a7b498ccef9n@googlegroups.com> <315799b5-db63-4608-a85f-9456228cebe9n@googlegroups.com> Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: individual.net 6Mf2oUYEtKER3s5g0xm9Cg5yePcgFsChWR5yCtCUBr3+WvJvWq Cancel-Lock: sha1:JxlWF/ALYJvjGNz/WUjrR05nQm4= User-Agent: Mozilla/5.0 (Windows NT 6.0; WOW64; rv:31.0) Gecko/20100101 Thunderbird/31.4.0 In-Reply-To: Xref: csiph.com sci.physics.relativity:585640 Am 18.05.2022 um 19:02 schrieb JanPB: > On Sunday, May 15, 2022 at 12:53:05 PM UTC-7, I wrote: >> >>> He used partial derivatives, for what there was no >>> reason, because the other variables (y/eta and z/zeta) were not involved. >> >> They were but their values were identically zero, so Einstein >> didn't include them in the equation. > > Sorry, I got carried away by the other part of the derivation. Here the answer > is that the derivatives wrt y and z are not present because in the first tau > equation the variable x' is not present in the y and z slots of tau. x' is not a variable! x' denotes the location of the mirror at rest in k, but measured in K-coordinates. That position is in some distance d from the emitter of the zero spot of k. This distance was not named 'd', nor even mentioned, but should exist. Therefore, I assume d would be the name for the disatnce between emitter and mirror in k. d is arbitrary (because not specified), but assumed as a constant value, because the mirror is assumed to be at rest in k. The position of the mirror is moving in K as x', but that does not make x' a variable. > That's why in order to calculate dtau/dy and dtau/dz it's necessary to set up > tau equations with the y and z variables present (that's what setting up the > mirror in the Y and Z directions does). What is dtau/dy? tau is a time measure in k and y a coordinate in K. So: how do we interpret dtau/dy? something like: a small variation of the y-coordinate in K is corresponding to a small variation of the time tau in k? As that is absurd, we need to aply the other meaning of 'tau' here, which is a function! That function is a coordinate transformation between k and K. The input values of tau are four vectors in k and the output corresponding four-vectors in K. To use partial derrivatives was actually correct, because only one coordinate y was considered. But Einstein used x', which is NOT a variable of that function. TH