Deutsch English Français Italiano |
<covariance-20240809191541@ram.dialup.fu-berlin.de> View for Bookmarking (what is this?) Look up another Usenet article |
Path: ...!weretis.net!feeder8.news.weretis.net!fu-berlin.de!uni-berlin.de!individual.net!not-for-mail From: ram@zedat.fu-berlin.de (Stefan Ram) Newsgroups: sci.physics.research Subject: Re: The momentum - a cotangent vector? Date: Fri, 09 Aug 2024 13:54:17 PDT Organization: Stefan Ram Lines: 39 Approved: Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com (sci.physics.research) Expires: 1 Jul 2025 11:59:58 GMT Message-ID: <covariance-20240809191541@ram.dialup.fu-berlin.de> References: <cotangent-20240806233433@ram.dialup.fu-berlin.de> <v8vbib$2fuke$1@dont-email.me> <vector-20240807201044@ram.dialup.fu-berlin.de> X-Trace: individual.net fF061y55D7OCBR7lepDuIgHauf9XyQvivxkbwN0R/mCVssY+2Og2c5D+6e Cancel-Lock: sha1:pkMZWZsJ7YhdxrTHSIpcnt9olkY= sha256:5+steFNJfBB6dvuMvKKbsOZ5FU6vk0LYHbR/DR84Y2Q= X-Forwarded-Encrypted: i=2; AJvYcCXhf81kkMDuTai0OA2IYUAZvLOMVHHj11nMOGp4Jg1RXrhVKN6tbvsEovxtF7lP6VOd9kNeaAyIZHnEFBmcmZurT5KfF8+CW7w= X-Orig-X-Trace: news.uni-berlin.de ptovoQDdwDJmsYlS2/LfCgxSEeRm3yOJIn9jy281HAZE01 X-Copyright: (C) Copyright 2024 Stefan Ram. All rights reserved. X-No-Archive-Readme: "X-No-Archive" is set, because this prevents some X-No-Html: yes X-ZEDAT-Hint: RO Bytes: 3427 ram@zedat.fu-berlin.de (Stefan Ram) wrote or quoted: >Explaining objects by their transformation behavior is >classic physicist stuff. A mathematician, on the other hand, >defines what an object /is/ first, and then the transformation >behavior follows from that definition. These notions can be somewhat personified by the persons of /Albert Einstein/ and /Hermann Minkowski/. Einstein's focus was on the algebraic properties of his theory of relativity, specifically the equations that express its laws and their behavior under transformations, known as /covariance/. The fulfillment of the principle of relativity is demonstrated through often tedious algebraic manipulations. The equations of the theory are transformed using Lorentz transformations, showing that the resulting equations maintain their form. In contrast, Minkowski emphasized the geometric properties of the theory, focusing on the geometric units that remain unchanged behind the transformations, which is referred to as /invariance/. Minkowski ensures the fulfillment of the principle of relativity through entirely different means. The only structures allowed in constructing a theory are the invariants of spacetime. This restriction guarantees compatibility with the principle of relativity and allows for the verification of its fulfillment through inspection. BTW: The word "tensor" for Ricci and Levi-Civita's "contravariant and covariant systems" was introduced by Einstein and Grossmann. I pulled this info (about Einstein, Minkowski, and Grossmann) from "General covariance and the foundations of general relativity: eight decades of dispute" (1993-03) by John D. Norton. I also read somewhere - can't remember where right now - that Einstein didn't actually name his theory "theory of relativity". That title, like "Big Bang" or "black hole", was thrown out there by a journalist or a critic. (Maybe Einstein picked it up later on.) So, it's kind of ironic that some folks today blame Einstein for giving his "theory of relativity" a name that doesn't really fit.