Is Wikipedia good on the action principle? (Lagrangian etc.)

[marcus]

Wikipedia is potentially like a supplemental textbook
which is online and instantly available

In another PF context someone was interested in getting
an intuitive layman's idea of topics in these Wikipedia articles:

http://en.wikipedia.org/wiki/Action_principle

http://en.wikipedia.org/wiki/Lagrangian

http://en.wikipedia.org/wiki/Lagrangian_mechanics

http://en.wikipedia.org/wiki/Gauge_theory

Prompted by this other PF member's interest, I looked at these articles and thought (just my personal take) that they are pretty good, for what they try to do. I have not compared what is available at Eric Weisstein's site "World of Physics" or "World of mathematics".

I would like to know what other people think about the Wikipedia treatment. Is there a better online resource for general audience that covers these topics?

A side issue-----things like gauge group and Lagrangian come up in quantum contexts, so why put this thread in Classical?
I think it belongs here because you first understand the ideas in a classical setting, and that makes it easier to apply them in other situations later.

Apparently the idea of "action" (which Euler called "effort" and which several of his contemporaries thought that Nature always chose to minimize) was first investigated by Maupertuis around 1750.
To understand how to get the Euler-Lagrange equation from differentiating the action integral and setting equal to zero the main thing seems to be
that you have to know something from Freshman Calculus called
"integration by parts". The Wikipedia treatment is way way basic and i think that is great----makes it seem accessible from Freshman Calculus
with maybe a little judicious handwaving. Like, if some Frenchman can do it in 1750 can it really be all that hard?

Anyway it's classical, so here's a classical forum thread if anyone wants to comment on the Wiki articles or on the action principle itself and anything related

 

[marcus]

the action principle is great.

here is a picture of Maupertuis, who thought it up

http://consciencia.org/imagens/banco/L-Q/maupertius.html

he has a big fancy wig on

Maupertuis had to spend a year in the arctic---up north of arctic circle in Sweden---because of a disagreement between DesCartes and Newton.

the Cartesians, including the directors of the Paris Observatory which represented 18th Century Big Science,
thought the Earth would narrow down by spinning and look more like a lemon

while Newtonians, ever-mindful of centrifugal force, thought that it would fatten out by spinning and look more like a tangerine or a pumpkin

this lead to a nasty quarrel and the only way to settle it seemed to be
to send a team up north to measure and see if it was
pointy-headed like a lemon, or broad-domed and wide-girthed.

http://www.tornedalen.net/maupertuis/data.htm

this was around 1736, roughly,
it was only ten years later in 1746 that Maupertuis discovered the principle of least action, or (as Euler expressed it) of least "effort"
If he had only known earlier about minimizing effort Maupertius could have stayed at home relaxing on his country estate instead of going off surveying in the arctic. He could have told the French Academy to find somebody else, since he would follow Nature's example and minimize his action.

 

[krab]

That's Maupertuis, not Maupertius.

Wikipedia is available to anyone not only to read, but also to write into, so there is no guarantee, and no general statement can be made concerning its articles. Some may be excellent, but others may even be intentionally misleading; there are no safeguards.

 

[marcus]

That's Maupertuis, not Maupertius.

Wikipedia is available to anyone not only to read, but also to write into, so there is no guarantee, and no general statement can be made concerning its articles. Some may be excellent, but others may even be intentionally misleading; there are no safeguards.

Indeed I realize there is no guarantee with Wikipedia! I know authorship is open. And good work can be "undone" by later editing!
I have monitored the editing sequence of some articles to see if this
has happened to any noticeable extent. Wiki let's you see the editing "history" of its articles----who changed what, who added what.

But my impression is that at the present time there are quite a number of excellent articles there----and I also think the ones I linked to are quite good (for what they are trying to do)

I would like confirmation of this. what do other people think of the Wikipedia articles on Lagrangian, on gauge theory etc.

Thanks for the spell-check on Maupertuis! I go back and correct the spelling.