Talk:Fermat's principle

Issues resolved or rendered moot as of 30 September 2019:

Untitled

Template:Smallrejected in June 2003. — Gavin R Putland (talk) 11:58, 29 September 2019 (UTC). Template:Collapse

Better image

I think this image should be translated and used or perhaps just added and leaving the original image. Any thoughts? Cristan 23:00, 13 November 2006 (UTC).

Template:Stale-small. Implicitly rejected? For the time being, and perhaps for the long term, I have cited a standard rare-to-dense refraction diagram in connection with the lifeguard analogy. — Gavin R Putland (talk) 13:03, 29 September 2019 (UTC).

Proof?

File:Yes check.svg Resolved (I hope) by: (i) adding a "Derivation" section; (ii) mentioning, in the "Analogies" subsection, the deduction of the classical path of a particle from its wave function; and (iii) linking to the article on Snell's law, which includes a derivation of that law from Fermat's principle. — Gavin R Putland (talk) 11:58, 29 September 2019 (UTC).

Not entirely.Extent content to see why it is ambiguous. Nikosbinis (talk) 11:22, 22 August 2023 (UTC)

Better statement

File:Yes check.svg Resolved (I hope) in the rewrite of August 2019, if not earlier. — Gavin R Putland (talk) 11:53, 29 September 2019 (UTC). Template:Collapse

Extremum principle of mechanics

File:Yes check.svg Resolved (I hope) under the headings "Analogies" and "Modern version". — Gavin R Putland (talk) 13:21, 29 September 2019 (UTC). Template:Collapse

"Incompleteness of the principle"

File:Yes check.svg Resolved.  The first part (May 2009) was promptly resolved by deleting the offending passage. The second part (January 2011) refers to an earlier version and (I hope) has now been resolved in the "Derivation" section. — Gavin R Putland (talk) 09:37, 30 September 2019 (UTC).

Not really "time", since velocity is phase velocity, not group velocity

File:Yes check.svg Resolved.  This section seems to refer to an earlier version of the article. In any case, the article now distinguishes the "ray velocity" from the "phase velocity" and the "group velocity". — Gavin R Putland (talk) 10:36, 30 September 2019 (UTC). Template:Collapse

Not Least, but Extremum

File:Yes check.svg Resolved, but not by claiming an extremum. The stationarity in the traversal time is either a local minimum or something more complicated; it is never a local maximum if all modes of variation are taken into account. (Search text for "maximum".)

 — Gavin R Putland (talk) 15:17, 29 September 2019 (UTC). Template:Collapse

Ptolemy

I added a reference to Ptolemys work and his influence in Alhacen´s work.--Knight1993 (talk) 15:07, 10 April 2010 (UTC).

File:Yes check.svg OK.  In later amendments, Ptolemy has been dropped for want of specifics; but Alhacen is still mentioned in the Notes, and other characters have been added. — Gavin R Putland (talk) 15:03, 29 September 2019 (UTC).

The "Modern version" is not clearly stated

File:Yes check.svg Resolved (quietly) by defining "ray velocity". While a negative index doesn't mean a negative group velocity, it does mean a negative ray velocity, hence a negative contribution to the notional traversal time. — Gavin R Putland (talk) 10:14, 30 September 2019 (UTC). Template:Collapse

Same old error

File:Yes check.svg Resolved  by defining the "ray index" and distinguishing the "ray velocity" from the phase and group velocities. — Gavin R Putland (talk) 10:39, 30 September 2019 (UTC). Template:Collapse

Deleted final sentence of introductory section

I removed statement about Hamiltonian optics that seems better suited to and appears at that page; also who the heck is Winston - either Newton or Lagrange, but even correcting that - it seems out of context to bring this up here. Netrapt (talk) 23:29, 17 December 2011 (UTC).

File:Yes check.svg OK, but moot due to later amendments. Hence it is also moot that "Winston" could be William Whiston. — Gavin R Putland (talk) 14:11, 29 September 2019 (UTC).

External links modified

Template:Stale-small; the reference has been replaced by a later version. — Gavin R Putland (talk) 13:46, 29 September 2019 (UTC). Template:Collapse

Complete rewrite

The issues addressed so far include the following:

• I hope the "Derivation" makes it clear why traversal time is more important than length.
• The "Derivation" doesn't merely treat Fermat's principle as the "definition" of a ray, but explains why such a theoretical definition ought to correspond to empirical ones (line of sight; narrow beam).
• The ray index is distinguished from the usual refractive index.
• The ray velocity is distinguished from both the phase velocity and the group velocity (see "Notes").
• The subsection on Hamilton's principle has been rearranged for easier and more frequent comparison with the references. (Disclosure: This is the subsection that I know least about; I tend to take Fermat's principle on its own terms.)
• "Quantum electrodynamics" is not currently mentioned in the draft. Correct me if I'm wrong, but I understand that for matter waves, Fermat's principle for the phase/ray velocity corresponds to Maupertuis's principle for the group velocity. I'm not sure if it's helpful to include that. (And if I can understand it, it isn't really QED!) (P.S.: Matter waves and the classical path are now mentioned briefly under "Analogies", with two references. — Gavin R Putland (talk) 08:47, 28 August 2019 (UTC).)
• Euclid is relegated to the "Notes" due to uncertain authorship. (P.S.: After checking against Sabra, Euclid is now mentioned in the References, citing his Optics, not the pseudo-Euclidean Catoptrics. — Gavin R Putland (talk) 23:15, 27 August 2019 (UTC).)
• Ptolemy is no longer mentioned; I think the information would need to be more specific if it were to warrant inclusion. Ibn al-Haytham is not quite a precedent and has been relegated to the "Notes". The same "Note" mentions Boelmans, who did scoop Fermat, albeit not in terms of time.
• Oh, and Huygens' principle is not "earlier" than Fermat's.

— Gavin R Putland (talk) 15:04, 23 August 2019 (UTC).

A specific objection is that the lead paragraph is rather formidable. Why not start with the principle of least time, which is what Fermat said, and then in later paragraphs introduce waves and extrema? And what the heck is stasimochrome? Did you make that up, or can you source that terminology? Is your derivation and approach following sources more generally? There's a ton to check here. Dicklyon (talk) 14:49, 28 August 2019 (UTC)

Template:Reply to Thank you. I hope my latest edit addresses most of these concerns. In particular, it belatedly occurs to me that the place to define a ray path as a "path of stationary traversal time" is immediately before we justify that definition in terms of lines of sight and narrow beams. That gets rid of the need to coin a separate term to be used only eight times. Template:Facepalm  P.S.: That edit was on 29 August. Belated signature: Gavin R Putland (talk) 14:55, 29 September 2019 (UTC).

unnecessarily complicated

I could not understand this article, I really wish math and science wikis had summaries that curious lay people could parse. not sure why an encyclopedia would require so much prior knowledge like a academic article 2600:1702:1DA0:1700:911C:95B2:7E98:B039 (talk) 20:27, 1 February 2023 (UTC)

IMO this drive-by comment is not substantiated in any way. Maybe the lede could be a bit cleaner but compared with other pages this one has nice long ramp up. Nice work! Johnjbarton (talk) 16:25, 27 May 2023 (UTC)

Equivalence to Huygens' construction

The section is original research. According to Born and Wolf and to Hecht, Fresnel modified Huygens' construction by adding interference so at best we could claim that Fermat and Fresnel principle are equivalent. However the section has no source that supports this claim. Thus this derivation is an invention as far as we can tell. Johnjbarton (talk) 01:35, 2 January 2025 (UTC)