Hamilton's principle/Chronology - Revision history

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	A timeline of the subject, from the first variational principle in physics to the		A timeline of the subject, from the first variational principle in physics to the
	explanation of why such principles exist.		explanation of why such principles exist.

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			{{DISPLAYTITLE:Hamilton's principle — Chronology}}
	A timeline of the subject, from the first variational principle in physics to the		A timeline of the subject, from the first variational principle in physics to the
	explanation of why such principles exist.		explanation of why such principles exist.
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	reported by secondary literature and are not independently confirmed. See		reported by secondary literature and are not independently confirmed. See
	[[Hamilton's principle/Sources]].		[[Hamilton's principle/Sources]].

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New page

A timeline of the subject, from the first variational principle in physics to the
explanation of why such principles exist.

Dates are of first statement or first publication, as marked. Where this volume's
source survey could not verify a claim, the entry says so; see
[[Hamilton's principle/Sources]].

== The seventeenth century ==

[[File:OPL-HP-F-21.png|thumb|right|400px|Chronology of the action principle.]]

{| class="wikitable"
! date !! event !! page
|-
| 1621 || Snel derives the law of refraction and does not publish it || —
|-
| 1637 || Descartes publishes the refraction law, assuming light moves faster in a dense medium || [[Hamilton's principle/History/Least time before least action]]
|-
| 1656 || Huygens invents the pendulum clock and begins looking for a curve of equal-time descent || [[Hamilton's principle/Applications/The brachistochrone]]
|-
| 1662 || '''Fermat''', ''Synthesis ad refractiones''. Derives the same law from the opposite assumption, on the postulate that nature operates by the easiest and readiest ways || [[Hamilton's principle/History/Least time before least action]]
|-
| 1691 || The hanging chain is shown to be a catenary and not a parabola || [[Hamilton's principle/Applications/The catenary]]
|-
| 1696 || Johann Bernoulli poses the brachistochrone problem || [[Hamilton's principle/Applications/The brachistochrone]]
|}

== The eighteenth century ==

[[File:OPL-HP-F-58.png|thumb|right|400px|The two long gaps in the subject's history.]]

{| class="wikitable"
! date !! event !! page
|-
| 1743 || '''d'Alembert''', ''Traité de dynamique''. Reduces dynamics to statics by treating inertia as a force || [[Hamilton's principle/History/d'Alembert and virtual work]]
|-
| 15 Apr 1744 || '''Maupertuis''' reads the ''Accord'' to the Académie. Action is speed times distance, with no mass. Printed 1748 || [[Hamilton's principle/History/Maupertuis and the 1744 memoir]]
|-
| 1744 || '''Euler''', ''Methodus inveniendi''. The first treatise on the calculus of variations; the action principle appears in its second appendix || [[Hamilton's principle/History/Euler and the Methodus inveniendi]]
|-
| 1746 || Maupertuis extends the definition of action to include mass, in a Berlin memoir || [[Hamilton's principle/History/Maupertuis and the 1744 memoir]]
|-
| 1750s || Lagrange sends Euler a variational derivation of the Euler-Lagrange equation. Euler adopts it and names the calculus of variations || [[Hamilton's principle/History/Lagrange and the Mecanique analytique]]
|-
| 1751–53 || The '''Maupertuis-Koenig affair'''. The Berlin Academy declares the Leibniz letter a forgery; the letter is now generally held authentic || [[Hamilton's principle/History/The Maupertuis-Koenig affair]]
|-
| 1786 || '''Legendre''' proposes his condition and believes it sufficient. Lagrange finds the error || [[Hamilton's principle/Mathematics/The Legendre condition]]
|-
| 1788 || '''Lagrange''', ''Mécanique analytique'', first edition. Mechanics as analysis, with no diagrams || [[Hamilton's principle/History/Lagrange and the Mecanique analytique]]
|}

== The nineteenth century ==

{| class="wikitable"
! date !! event !! page
|-
| 1811–15 || Lagrange's second edition, described by him as in many respects a new work || [[Hamilton's principle/History/Lagrange and the Mecanique analytique]]
|-
| 1833 || Hamilton announces the dynamical principle in the ''Dublin University Review'' || [[Hamilton's principle/History/Hamilton 1834 and 1835]]
|-
| 1834 || '''Hamilton''', ''On a General Method in Dynamics''. The characteristic function and the law of varying action. Corrects ''least'' to ''stationary'' in passing || [[Hamilton's principle/Mathematics/Action as a function of its endpoints]]
|-
| 1835 || Hamilton's ''Second Essay'' introduces the function modern texts call the action || [[Hamilton's principle/History/Hamilton 1834 and 1835]]
|-
| 1837 || '''Jacobi''' supplies the conjugate-point condition, closing the gap Legendre left || [[Hamilton's principle/Mathematics/The Jacobi condition and conjugate points]]
|-
| 1842–43 || Jacobi's Königsberg lectures. Reduces Hamilton's two equations to one || [[Hamilton's principle/History/Jacobi]]
|-
| 1850 || '''Foucault''' measures light as slower in a dense medium, settling the question against Descartes and Maupertuis, and for Fermat || [[Hamilton's principle/History/Least time before least action]]
|-
| 1866 || Jacobi's ''Vorlesungen über Dynamik'' published, fifteen years after his death || [[Hamilton's principle/History/Jacobi]]
|-
| later 19th c. || '''Weierstrass''' supplies the excess function and the theory of strong minima || [[Hamilton's principle/Mathematics/The Weierstrass excess function]]
|}

== The twentieth century ==

{| class="wikitable"
! date !! event !! page
|-
| 1915 || General relativity published. Energy conservation in it becomes contested || [[Hamilton's principle/Applications/The Einstein-Hilbert action]]
|-
| 26 Jul 1918 || '''Noether''', ''Invariante Variationsprobleme'', presented to the Göttingen Scientific Society. Two theorems; the second settles the Hilbert assertion || [[Hamilton's principle/History/Noether 1918]]
|-
| 1926 || '''Schrödinger''' constructs wave mechanics by completing Hamilton's optical-mechanical analogy || [[Hamilton's principle/Applications/The optical-mechanical analogy]]
|-
| 1942 || Feynman's doctoral thesis on the principle of least action in quantum mechanics. Published 2005 || [[Hamilton's principle/History/Feynman 1948]]
|-
| 1948 || '''Feynman''', ''Space-Time Approach to Non-Relativistic Quantum Mechanics''. The sum over paths || [[Hamilton's principle/Applications/The Feynman path integral]]
|-
| 1971 || Tavel's English translation of Noether, fifty-three years after publication || [[Hamilton's principle/History/Noether 1918]]
|}

== Two long silences ==

The timeline has two gaps worth naming, because each is longer than it looks and
each was ended by the same kind of act.

'''1662 to 1744, eighty-two years.''' Fermat's principle stood as an isolated
result about light. Nobody extended a variational principle to matter until
Maupertuis and Euler did so independently in the same year.

'''1834 to 1926, ninety-two years.''' Hamilton observed that mechanics and ray
optics obey the same equation. Ray optics is the short-wavelength approximation to
wave optics, so mechanics should be the short-wavelength approximation to
something. Nobody pursued it, because there was no evidence of a wavelength and
nothing to be waving. Schrödinger then completed the analogy by working it
backwards.

The second silence is the more striking. The observation was published, the
inference is short, and the mathematics needed was in place the whole time. What
was missing was a reason to believe the missing corner existed.

== A pattern in the corrections ==

Four moments in the timeline are corrections rather than discoveries, and they run
in the same direction.

Lagrange corrects Legendre in 1786: a local condition is not sufficient.

Hamilton corrects the name in 1834: not least, but stationary.

Jacobi supplies the reason in 1837: minimality fails past a conjugate point.

Weierstrass supplies the rest later in the century: a path can lose to competitors
close in position but not in slope.

'''Every one of them weakens a claim.''' The subject's history is largely the
history of finding out that ''least'' was too strong a word, and the process took
from 1786 to the end of the century.

Feynman's 1948 account then removes the word's basis entirely: nothing is
minimised, because nothing is choosing.

== Dates this volume could not verify ==

Several entries above rest on secondary sources rather than on documents this
volume has opened.

Verified against ESTABLISHED sources: the 1834 and 1835 essays, and Noether's 1918
paper by way of its translation.

Everything else in these tables — including the Huygens, Bernoulli, Galileo,
Legendre, Jacobi, Foucault and Schrödinger entries — is editorial. Dates are as
reported by secondary literature and are not independently confirmed. See
[[Hamilton's principle/Sources]].

← Older revision		Revision as of 04:59, 16 September 2026
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	Dates are of first statement or first publication, as marked. Where this volume's		Dates are of first statement or first publication, as marked. Where this volume's
	source survey could not verify a claim, the entry says so; see		source survey could not verify a claim, the entry says so; see
	[[Hamilton's principle/Sources]].		[[Hamilton's principle/Sources\|Sources]].

	== The seventeenth century ==		== The seventeenth century ==
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	\| 1621 \|\| Snel derives the law of refraction and does not publish it \|\| —		\| 1621 \|\| Snel derives the law of refraction and does not publish it \|\| —
	\|-		\|-
	\| 1637 \|\| Descartes publishes the refraction law, assuming light moves faster in a dense medium \|\| [[Hamilton's principle/History/Least time before least action]]		\| 1637 \|\| Descartes publishes the refraction law, assuming light moves faster in a dense medium \|\| [[Hamilton's principle/History/Least time before least action\|Least time before least action]]
	\|-		\|-
	\| 1656 \|\| Huygens invents the pendulum clock and begins looking for a curve of equal-time descent \|\| [[Hamilton's principle/Applications/The brachistochrone]]		\| 1656 \|\| Huygens invents the pendulum clock and begins looking for a curve of equal-time descent \|\| [[Hamilton's principle/Applications/The brachistochrone\|the brachistochrone]]
	\|-		\|-
	\| 1662 \|\| '''Fermat''', ''Synthesis ad refractiones''. Derives the same law from the opposite assumption, on the postulate that nature operates by the easiest and readiest ways \|\| [[Hamilton's principle/History/Least time before least action]]		\| 1662 \|\| '''Fermat''', ''Synthesis ad refractiones''. Derives the same law from the opposite assumption, on the postulate that nature operates by the easiest and readiest ways \|\| [[Hamilton's principle/History/Least time before least action\|Least time before least action]]
	\|-		\|-
	\| 1691 \|\| The hanging chain is shown to be a catenary and not a parabola \|\| [[Hamilton's principle/Applications/The catenary]]		\| 1691 \|\| The hanging chain is shown to be a catenary and not a parabola \|\| [[Hamilton's principle/Applications/The catenary\|the catenary]]
	\|-		\|-
	\| 1696 \|\| Johann Bernoulli poses the brachistochrone problem \|\| [[Hamilton's principle/Applications/The brachistochrone]]		\| 1696 \|\| Johann Bernoulli poses the brachistochrone problem \|\| [[Hamilton's principle/Applications/The brachistochrone\|the brachistochrone]]
	\|}		\|}

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	! date !! event !! page		! date !! event !! page
	\|-		\|-
	\| 1743 \|\| '''d'Alembert''', ''Traité de dynamique''. Reduces dynamics to statics by treating inertia as a force \|\| [[Hamilton's principle/History/d'Alembert and virtual work]]		\| 1743 \|\| '''d'Alembert''', ''Traité de dynamique''. Reduces dynamics to statics by treating inertia as a force \|\| [[Hamilton's principle/History/d'Alembert and virtual work\|d'Alembert and virtual work]]
	\|-		\|-
	\| 15 Apr 1744 \|\| '''Maupertuis''' reads the ''Accord'' to the Académie. Action is speed times distance, with no mass. Printed 1748 \|\| [[Hamilton's principle/History/Maupertuis and the 1744 memoir]]		\| 15 Apr 1744 \|\| '''Maupertuis''' reads the ''Accord'' to the Académie. Action is speed times distance, with no mass. Printed 1748 \|\| [[Hamilton's principle/History/Maupertuis and the 1744 memoir\|Maupertuis and the 1744 memoir]]
	\|-		\|-
	\| 1744 \|\| '''Euler''', ''Methodus inveniendi''. The first treatise on the calculus of variations; the action principle appears in its second appendix \|\| [[Hamilton's principle/History/Euler and the Methodus inveniendi]]		\| 1744 \|\| '''Euler''', ''Methodus inveniendi''. The first treatise on the calculus of variations; the action principle appears in its second appendix \|\| [[Hamilton's principle/History/Euler and the Methodus inveniendi\|Euler and the Methodus inveniendi]]
	\|-		\|-
	\| 1746 \|\| Maupertuis extends the definition of action to include mass, in a Berlin memoir \|\| [[Hamilton's principle/History/Maupertuis and the 1744 memoir]]		\| 1746 \|\| Maupertuis extends the definition of action to include mass, in a Berlin memoir \|\| [[Hamilton's principle/History/Maupertuis and the 1744 memoir\|Maupertuis and the 1744 memoir]]
	\|-		\|-
	\| 1750s \|\| Lagrange sends Euler a variational derivation of the Euler-Lagrange equation. Euler adopts it and names the calculus of variations \|\| [[Hamilton's principle/History/Lagrange and the Mecanique analytique]]		\| 1750s \|\| Lagrange sends Euler a variational derivation of the Euler-Lagrange equation. Euler adopts it and names the calculus of variations \|\| [[Hamilton's principle/History/Lagrange and the Mecanique analytique\|Lagrange and the Mecanique analytique]]
	\|-		\|-
	\| 1751–53 \|\| The '''Maupertuis-Koenig affair'''. The Berlin Academy declares the Leibniz letter a forgery; the letter is now generally held authentic \|\| [[Hamilton's principle/History/The Maupertuis-Koenig affair]]		\| 1751–53 \|\| The '''Maupertuis-Koenig affair'''. The Berlin Academy declares the Leibniz letter a forgery; the letter is now generally held authentic \|\| [[Hamilton's principle/History/The Maupertuis-Koenig affair\|the Maupertuis-Koenig affair]]
	\|-		\|-
	\| 1786 \|\| '''Legendre''' proposes his condition and believes it sufficient. Lagrange finds the error \|\| [[Hamilton's principle/Mathematics/The Legendre condition]]		\| 1786 \|\| '''Legendre''' proposes his condition and believes it sufficient. Lagrange finds the error \|\| [[Hamilton's principle/Mathematics/The Legendre condition\|the Legendre condition]]
	\|-		\|-
	\| 1788 \|\| '''Lagrange''', ''Mécanique analytique'', first edition. Mechanics as analysis, with no diagrams \|\| [[Hamilton's principle/History/Lagrange and the Mecanique analytique]]		\| 1788 \|\| '''Lagrange''', ''Mécanique analytique'', first edition. Mechanics as analysis, with no diagrams \|\| [[Hamilton's principle/History/Lagrange and the Mecanique analytique\|Lagrange and the Mecanique analytique]]
	\|}		\|}

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	! date !! event !! page		! date !! event !! page
	\|-		\|-
	\| 1811–15 \|\| Lagrange's second edition, described by him as in many respects a new work \|\| [[Hamilton's principle/History/Lagrange and the Mecanique analytique]]		\| 1811–15 \|\| Lagrange's second edition, described by him as in many respects a new work \|\| [[Hamilton's principle/History/Lagrange and the Mecanique analytique\|Lagrange and the Mecanique analytique]]
	\|-		\|-
	\| 1833 \|\| Hamilton announces the dynamical principle in the ''Dublin University Review'' \|\| [[Hamilton's principle/History/Hamilton 1834 and 1835]]		\| 1833 \|\| Hamilton announces the dynamical principle in the ''Dublin University Review'' \|\| [[Hamilton's principle/History/Hamilton 1834 and 1835\|Hamilton 1834 and 1835]]
	\|-		\|-
	\| 1834 \|\| '''Hamilton''', ''On a General Method in Dynamics''. The characteristic function and the law of varying action. Corrects ''least'' to ''stationary'' in passing \|\| [[Hamilton's principle/Mathematics/Action as a function of its endpoints]]		\| 1834 \|\| '''Hamilton''', ''On a General Method in Dynamics''. The characteristic function and the law of varying action. Corrects ''least'' to ''stationary'' in passing \|\| [[Hamilton's principle/Mathematics/Action as a function of its endpoints\|Action as a function of its endpoints]]
	\|-		\|-
	\| 1835 \|\| Hamilton's ''Second Essay'' introduces the function modern texts call the action \|\| [[Hamilton's principle/History/Hamilton 1834 and 1835]]		\| 1835 \|\| Hamilton's ''Second Essay'' introduces the function modern texts call the action \|\| [[Hamilton's principle/History/Hamilton 1834 and 1835\|Hamilton 1834 and 1835]]
	\|-		\|-
	\| 1837 \|\| '''Jacobi''' supplies the conjugate-point condition, closing the gap Legendre left \|\| [[Hamilton's principle/Mathematics/The Jacobi condition and conjugate points]]		\| 1837 \|\| '''Jacobi''' supplies the conjugate-point condition, closing the gap Legendre left \|\| [[Hamilton's principle/Mathematics/The Jacobi condition and conjugate points\|the Jacobi condition and conjugate points]]
	\|-		\|-
	\| 1842–43 \|\| Jacobi's Königsberg lectures. Reduces Hamilton's two equations to one \|\| [[Hamilton's principle/History/Jacobi]]		\| 1842–43 \|\| Jacobi's Königsberg lectures. Reduces Hamilton's two equations to one \|\| [[Hamilton's principle/History/Jacobi\|Jacobi]]
	\|-		\|-
	\| 1850 \|\| '''Foucault''' measures light as slower in a dense medium, settling the question against Descartes and Maupertuis, and for Fermat \|\| [[Hamilton's principle/History/Least time before least action]]		\| 1850 \|\| '''Foucault''' measures light as slower in a dense medium, settling the question against Descartes and Maupertuis, and for Fermat \|\| [[Hamilton's principle/History/Least time before least action\|Least time before least action]]
	\|-		\|-
	\| 1866 \|\| Jacobi's ''Vorlesungen über Dynamik'' published, fifteen years after his death \|\| [[Hamilton's principle/History/Jacobi]]		\| 1866 \|\| Jacobi's ''Vorlesungen über Dynamik'' published, fifteen years after his death \|\| [[Hamilton's principle/History/Jacobi\|Jacobi]]
	\|-		\|-
	\| later 19th c. \|\| '''Weierstrass''' supplies the excess function and the theory of strong minima \|\| [[Hamilton's principle/Mathematics/The Weierstrass excess function]]		\| later 19th c. \|\| '''Weierstrass''' supplies the excess function and the theory of strong minima \|\| [[Hamilton's principle/Mathematics/The Weierstrass excess function\|the Weierstrass excess function]]
	\|}		\|}

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	! date !! event !! page		! date !! event !! page
	\|-		\|-
	\| 1915 \|\| General relativity published. Energy conservation in it becomes contested \|\| [[Hamilton's principle/Applications/The Einstein-Hilbert action]]		\| 1915 \|\| General relativity published. Energy conservation in it becomes contested \|\| [[Hamilton's principle/Applications/The Einstein-Hilbert action\|the Einstein-Hilbert action]]
	\|-		\|-
	\| 26 Jul 1918 \|\| '''Noether''', ''Invariante Variationsprobleme'', presented to the Göttingen Scientific Society. Two theorems; the second settles the Hilbert assertion \|\| [[Hamilton's principle/History/Noether 1918]]		\| 26 Jul 1918 \|\| '''Noether''', ''Invariante Variationsprobleme'', presented to the Göttingen Scientific Society. Two theorems; the second settles the Hilbert assertion \|\| [[Hamilton's principle/History/Noether 1918\|Noether 1918]]
	\|-		\|-
	\| 1926 \|\| '''Schrödinger''' constructs wave mechanics by completing Hamilton's optical-mechanical analogy \|\| [[Hamilton's principle/Applications/The optical-mechanical analogy]]		\| 1926 \|\| '''Schrödinger''' constructs wave mechanics by completing Hamilton's optical-mechanical analogy \|\| [[Hamilton's principle/Applications/The optical-mechanical analogy\|the optical-mechanical analogy]]
	\|-		\|-
	\| 1942 \|\| Feynman's doctoral thesis on the principle of least action in quantum mechanics. Published 2005 \|\| [[Hamilton's principle/History/Feynman 1948]]		\| 1942 \|\| Feynman's doctoral thesis on the principle of least action in quantum mechanics. Published 2005 \|\| [[Hamilton's principle/History/Feynman 1948\|Feynman 1948]]
	\|-		\|-
	\| 1948 \|\| '''Feynman''', ''Space-Time Approach to Non-Relativistic Quantum Mechanics''. The sum over paths \|\| [[Hamilton's principle/Applications/The Feynman path integral]]		\| 1948 \|\| '''Feynman''', ''Space-Time Approach to Non-Relativistic Quantum Mechanics''. The sum over paths \|\| [[Hamilton's principle/Applications/The Feynman path integral\|the Feynman path integral]]
	\|-		\|-
	\| 1971 \|\| Tavel's English translation of Noether, fifty-three years after publication \|\| [[Hamilton's principle/History/Noether 1918]]		\| 1971 \|\| Tavel's English translation of Noether, fifty-three years after publication \|\| [[Hamilton's principle/History/Noether 1918\|Noether 1918]]
	\|}		\|}

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	Legendre, Jacobi, Foucault and Schrödinger entries — is editorial. Dates are as		Legendre, Jacobi, Foucault and Schrödinger entries — is editorial. Dates are as
	reported by secondary literature and are not independently confirmed. See		reported by secondary literature and are not independently confirmed. See
	[[Hamilton's principle/Sources]].		[[Hamilton's principle/Sources\|Sources]].