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*From*: John Denker <jsd@av8n.com>*Date*: Thu, 21 Jan 2010 17:13:54 -0700

On 01/20/2010 09:44 PM, Stefan Jeglinski wrote:

I like the idea pedagogically of an argument that doesn't

resort to blatant/circular assertions about the form of KE. However,

Landau/Lifshitz do not expound further either, beyond these few

words. I think I understand the second part, essentially that the

isotropy of space cannot support a preferred direction, but it's

unclear to me how the homogeneity of space and time lead to L being a

function of v alone.

It's easy to demonstrate that the L&L argument is

bogus.

As the saying goes, it's bad luck to prove things

that aren't true.

Their argument sorta proves one thing, but they

claim to have proved something else. I would be

quite willing to believe some sufficiently-careful

statements about what terms *cannot* be in the

Lagrangian ... but to leap from there to statements

about what terms *must* be in the Lagrangian is

just crazy.

Specifically, I am willing to believe that there

cannot be a term containing just plain naked v all

by itself. That would have the wrong symmetry.

On the other hand, the electromagnetic Lagrangian

contains a term in j•A which is first order in j,

which is tantamount to being first order in v. A

term in plain naked j would be disallowed for the

same reasons plain naked v would be disallowed.

There are pretty good symmetry arguments why the

Lagrangian density should be a scalar ... not just

a 3D Galilean scalar, but also a 4D Lorentz scalar.

We must not leap from there to any notion that the

Lagrangian will only contain terms that are second

order in v. As others have pointed out, terms in

|v| are allowed by symmetry, as well as just about

any hypothetical function of |v|. Also terms in

v•A are allowed; this is not a vague hypotheses,

but known good physics.

===============

And now for a book review: If you are ever reading

Landau and Lifshitz and you come to a passage that

you don't understand, you reeeally need to consider

the possibility that the passage is wrong, misleading,

or at best highly open to misinterpretation.

In particular, their "proofs" are notorious. If you're

lucky, they state a conclusion that is true enough as

a matter of fact, but then "prove" it using a "proof"

that proves nothing of the sort.

If you're not so lucky, the conclusion is not entirely

true, but instead is subject to all sorts of provisos

that they don't bother to mention.

For these reasons I consider the whole series of books

to be a pedagogical disaster area.

====

On happier note, if you want to learn about classical

mechanics -- and learn a lot of other good stuff along

the way -- I recommend

Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer

_Structure and Interpretation of Classical Mechanics_

http://mitpress.mit.edu/SICM/

The whole thing is available for free on the web, but

once you get into it you may well decide to buy the

hardcopy. The table of contents is at:

http://mitpress.mit.edu/SICM/book-Z-H-4.html

Modern. State of the art.

Lucid.

Abounding in good worked examples.

You'll get far more out of this book than you possibly

could get out of L&L.

**Follow-Ups**:**Re: [Phys-l] symmetries of the Lagrangian***From:*Stefan Jeglinski <jeglin@4pi.com>

**References**:**[Phys-l] Landau on Lagrangian***From:*Stefan Jeglinski <jeglin@4pi.com>

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