Jump to content

Main Page: Difference between revisions

From The Invariance Itself
← Older editNewer edit →

BFP Rauch (talk | contribs)

4 user groups
811 edits
No edit summary
No edit summary
Line 62: Line 62:
       <h2 id="mp-hamilton-h2" style="margin: 0; padding: 8px 10px; background-color: #cedff2; border-bottom: 1px solid #a2a9b1; font-size: 1.2em; font-weight: bold;">Hamilton's Principle</h2>
       <h2 id="mp-hamilton-h2" style="margin: 0; padding: 8px 10px; background-color: #cedff2; border-bottom: 1px solid #a2a9b1; font-size: 1.2em; font-weight: bold;">Hamilton's Principle</h2>
       <div id="mp-hamilton" style="padding: 10px;">
       <div id="mp-hamilton" style="padding: 10px;">
Of all the ways a ball could fly from your hand to a window, it takes one. Of all
Newton's laws, Maxwell's equations, general relativity and the Standard Model are each formulated as an action via Hamilton's Principle.  In every case the equations of motion are consequences rather than starting points. Conservation
the paths light could follow from a lamp to your eye, it takes one. Physics has a
single answer to why: along the true path, a quantity called the '''action''' is
''stationary''.
 
The claim of this volume is that this is not one principle among many, but the
deepest thing physics knows. Newton's laws, Maxwell's equations, general
relativity and the Standard Model are each stated as an action, and in every case
the equations of motion are consequences rather than starting points. Conservation
of energy, momentum and charge are not separate laws at all — [[Hamilton's principle/Mathematics/Noether's first theorem|Noether proved]] they follow from
of energy, momentum and charge are not separate laws at all — [[Hamilton's principle/Mathematics/Noether's first theorem|Noether proved]] they follow from
the action's symmetries. New theories are now built by writing the action a
the action's symmetries. New models are now built by writing the action a
symmetry permits and letting the dynamics follow, which is how electromagnetism
symmetry permits and letting the dynamics follow.  This is how electromagnetism
and gravity are derived here and how the nuclear forces were found. And the
and gravity were derived and how the nuclear forces were found. Hamilton's Principle alone survives the passage to quantum mechanics intact: the action
principle alone survives the passage to quantum mechanics intact: the action
becomes the phase carried by every possible history, and the classical path is
becomes the phase carried by every possible history, and the classical path is
simply where those phases fail to cancel.
simply where those phases fail to cancel. The action is the deepest thing physics knows.
 
 
[[File::OPL-HP-F-01.png|thumb|right|upright=1.5|Deriving a truth path]]


* [[Hamilton's principle/Mathematics/The Jacobi condition and conjugate points|Stationary is not least]] — the long way round a great circle obeys the same rule at every point, and is plainly not the shortest. [[:File:OPL-HP-F-05.png|See the diagram]].
* [[Hamilton's principle/Mathematics/The Jacobi condition and conjugate points|Stationary is not least]] — the long way round a great circle obeys the same rule at every point, and is plainly not the shortest. [[:File:OPL-HP-F-05.png|See the diagram]].

Revision as of 07:02, 9 September 2026

IPSUM INVARIANS: The Invariance Itself

the public record of the invariance program.
183 articles · 6 active editors · 3,878 edits

Introduction

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur.

Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium, totam rem aperiam, eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.

(Full article...)

The Current Program (Round 3)

Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci velit, sed quia non numquam eius modi tempora incidunt ut labore et dolore magnam aliquam quaerat voluptatem.

(Program of record...)  ·  Open items

Program History

Temporibus autem quibusdam et aut officiis debitis aut rerum necessitatibus saepe eveniet ut et voluptates repudiandae sint et molestiae non recusandae. Itaque earum rerum hic tenetur a sapiente delectus.

  • Round 1 – nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit.
  • Round 2 – quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est.
  • Round 2 review – omnis dolor repellendus ut aut reiciendis voluptatibus maiores alias consequatur.
  • Round 3 opening – aut perferendis doloribus asperiores repellat, sed quia consequuntur magni dolores.

(Full record...)  ·  Archive

Hamilton's Principle

Newton's laws, Maxwell's equations, general relativity and the Standard Model are each formulated as an action via Hamilton's Principle. In every case the equations of motion are consequences rather than starting points. Conservation of energy, momentum and charge are not separate laws at all — Noether proved they follow from the action's symmetries. New models are now built by writing the action a symmetry permits and letting the dynamics follow. This is how electromagnetism and gravity were derived and how the nuclear forces were found. Hamilton's Principle alone survives the passage to quantum mechanics intact: the action becomes the phase carried by every possible history, and the classical path is simply where those phases fail to cancel. The action is the deepest thing physics knows.


[[File::OPL-HP-F-01.png|thumb|right|upright=1.5|Deriving a truth path]]

(Full article...)

Noether's 1st Theorem

Quis autem vel eum iure reprehenderit qui in ea voluptate velit esse quam nihil molestiae consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla pariatur.

(Full article...)

The Work of James Clerk Maxwell

On Physical Lines of Force

Lines of force about a bar magnet


In four instalments between March 1861 and February 1862, James Clerk Maxwell filled space with spinning cells and little rolling particles, to explain the mechanics behind magnetic fields. His machine was wrong. On the way to building it, he wrote down the displacement current, derived the speed of light from two electrical measurements that had nothing to do with optics, and founded field theory.

A 65-page reading edition: Maxwell's argument in his own order and register, the modern equations derived from his results, and a plain-language explainer for every major idea.

(Full article...)

Featured plate

Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Quis autem vel eum iure reprehenderit qui in ea voluptate velit esse quam nihil molestiae consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla pariatur.

Plate placeholder – browse all plates

Other areas of Ipsum Invarians

  • All pages – ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
  • Recent changes – nisi ut aliquip ex ea commodo consequat duis aute irure.
  • Categories – dolor in reprehenderit in voluptate velit esse cillum dolore.
  • Special pages – eu fugiat nulla pariatur excepteur sint occaecat cupidatat.
  • Sandbox – non proident, sunt in culpa qui officia deserunt mollit anim.
  • Upload – id est laborum sed ut perspiciatis unde omnis iste natus error.

Ipsum Invarians languages

Totam rem aperiam, eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.

Language editions are not yet configured. Set them up with interwiki links or Extension:Translate.

Consult the User's Guide for information on using the wiki software.

Getting started

Invarians Logo
Retrieved from "https://invarians.org/index.php?title=Main_Page&oldid=375"