what use of classical mechanics [Archive]

SunnyJing

Oct25-04, 08:09 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nI am studying the course-a complete scheme of mechanics in 18th, 19th\ncentury, but I find it is just always denoted as "a passage to\nunderstand quantum mechanics", so it seems no practical use except\nleading to quantum mechanics.\nif so, why do people need to labor on it?\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>I am studying the course-a complete scheme of mechanics in 18th, 19th
century, but I find it is just always denoted as "a passage to
understand quantum mechanics", so it seems no practical use except
leading to quantum mechanics.
if so, why do people need to labor on it?

Arnold Neumaier

Oct25-04, 10:42 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nSunnyJing wrote:\n> I am studying the course-a complete scheme of mechanics in 18th, 19th\n> century, but I find it is just always denoted as "a passage to\n> understand quantum mechanics", so it seems no practical use except\n> leading to quantum mechanics.\n> if so, why do people need to labor on it?\n\nIt is the basis of a lot of engineering. And it is essential to\nget a good understanding of quantum mechanics. Learning the latter\nwithout the former leaves one uneducated about most of nature except\nmicroscopic phenomena.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>SunnyJing wrote:
> I am studying the course-a complete scheme of mechanics in 18th, 19th
> century, but I find it is just always denoted as "a passage to
> understand quantum mechanics", so it seems no practical use except
> leading to quantum mechanics.
> if so, why do people need to labor on it?

It is the basis of a lot of engineering. And it is essential to
get a good understanding of quantum mechanics. Learning the latter
without the former leaves one uneducated about most of nature except
microscopic phenomena.

Arnold Neumaier

John T Lowry

Oct25-04, 10:42 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n"SunnyJing" <pdm190@hotmail.com> wrote in message\nnews:46b99cc6.0410241513.555c302b@posting .google.com...\n>\n>\n>\n> I am studying the course-a complete scheme of mechanics in 18th, 19th\n> century, but I find it is just always denoted as "a passage to\n> understand quantum mechanics", so it seems no practical use except\n> leading to quantum mechanics.\n> if so, why do people need to labor on it?\n\nSince we don\'t really know how this world works, we need all the\nheuristic tips we can find. Classical mechanics has many different ways\nof looking at the same phenomena (Newton\'s laws, Lagrange, Hamiltonian,\ncontact transformations, variational approaches, etc.). Plus most of our\ncommon experience is on the classical level.\n\nJohn Lowry\nFlight Physics\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"SunnyJing" <pdm190@hotmail.com> wrote in message
news:46b99cc6.0410241513.555c302b@posting.google.c om...
>
>
>
> I am studying the course-a complete scheme of mechanics in 18th, 19th
> century, but I find it is just always denoted as "a passage to
> understand quantum mechanics", so it seems no practical use except
> leading to quantum mechanics.
> if so, why do people need to labor on it?

Since we don't really know how this world works, we need all the
heuristic tips we can find. Classical mechanics has many different ways
of looking at the same phenomena (Newton's laws, Lagrange, Hamiltonian,
contact transformations, variational approaches, etc.). Plus most of our
common experience is on the classical level.

John Lowry
Flight Physics

Lou Pecora

Oct25-04, 10:43 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nIn article <46b99cc6.0410241513.555c302b@posting.google.com>, \npdm190@hotmail.com (SunnyJing) wrote:\n\n> I am studying the course-a complete scheme of mechanics in 18th, 19th\n> century, but I find it is just always denoted as "a passage to\n> understand quantum mechanics", so it seems no practical use except\n> leading to quantum mechanics.\n> if so, why do people need to labor on it?\n\nWell, that\'s not a bad reason right there. However, I\'m sorry to hear\nthat classical mechanics is put in that category even today. More\nmodern versions will also show you that studies of classical mechanics\nhave increased, mainly in response to the fact that many classical\nsystems are chaotic and are still not well understood. In addition,\nother areas of physics (fluid dynamics, plasma physics, celestial\nmechanics, statistical mechanics, and, in a certain sense, relativity)\nbuild on classical mechanics. It\'s a good foundation for a lot of other\nphysics.\n\nIt\'s not wasted time to study it. IMHO. In fact, I believe you would\nhave trouble progressing in most areas of physics without it.\n\n-- Lou Pecora (my views are my own)\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <46b99cc6.0410241513.555c302b@posting.google.com>,
pdm190@hotmail.com (SunnyJing) wrote:

> I am studying the course-a complete scheme of mechanics in 18th, 19th
> century, but I find it is just always denoted as "a passage to
> understand quantum mechanics", so it seems no practical use except
> leading to quantum mechanics.
> if so, why do people need to labor on it?

Well, that's not a bad reason right there. However, I'm sorry to hear
that classical mechanics is put in that category even today. More
modern versions will also show you that studies of classical mechanics
have increased, mainly in response to the fact that many classical
systems are chaotic and are still not well understood. In addition,
other areas of physics (fluid dynamics, plasma physics, celestial
mechanics, statistical mechanics, and, in a certain sense, relativity)
build on classical mechanics. It's a good foundation for a lot of other
physics.

It's not wasted time to study it. IMHO. In fact, I believe you would
have trouble progressing in most areas of physics without it.

-- Lou Pecora (my views are my own)

Igor Khavkine

Oct27-04, 10:56 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\npdm190@hotmail.com (SunnyJing) wrote in message news:<46b99cc6.0410241513.555c302b@posting.google. com>...\n> I am studying the course-a complete scheme of mechanics in 18th, 19th\n> century, but I find it is just always denoted as "a passage to\n> understand quantum mechanics", so it seems no practical use except\n> leading to quantum mechanics.\n> if so, why do people need to labor on it?\n\nClassical mechanics is useful in explaining the world around us because\nin many cases quantum effects are negligible. The Hamiltonian formulation\nof classical mechanics can certainly used as a starting point for\nformulating quantum mechanics, but it has many other uses. Many dynamical\nsystems (systems that evolve subject to differential equations) can\nbe cast in Hamiltonian form and analyzed that way.\n\nHope this helps.\n\nIgor\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>pdm190@hotmail.com (SunnyJing) wrote in message news:<46b99cc6.0410241513.555c302b@posting.google.com>...
> I am studying the course-a complete scheme of mechanics in 18th, 19th
> century, but I find it is just always denoted as "a passage to
> understand quantum mechanics", so it seems no practical use except
> leading to quantum mechanics.
> if so, why do people need to labor on it?

Classical mechanics is useful in explaining the world around us because
in many cases quantum effects are negligible. The Hamiltonian formulation
of classical mechanics can certainly used as a starting point for
formulating quantum mechanics, but it has many other uses. Many dynamical
systems (systems that evolve subject to differential equations) can
be cast in Hamiltonian form and analyzed that way.

Hope this helps.

Igor

Frank Hellmann

Oct27-04, 10:56 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\npdm190@hotmail.com (SunnyJing) wrote in message news:<46b99cc6.0410241513.555c302b@posting.google. com>...\n> I am studying the course-a complete scheme of mechanics in 18th, 19th\n> century, but I find it is just always denoted as "a passage to\n> understand quantum mechanics", so it seems no practical use except\n> leading to quantum mechanics.\n> if so, why do people need to labor on it?\n\nThe simple answer: If you don\'t understand classical mechanics,\nparticularly in the Hamiltonian formalism you wont stand a chance in\nQM or GR. The concept introduced there: Lagrangian and Hamiltonian\nmethod, symmetries, and so on, are valid throughout physics. Plus\nclassical mechanics still describes and always will describe a vast\npart of the world.\n\nThere are two boundaries of knowledge in physics: Simplicity and\ncomplexity.\n\nWe can not yet simplify all phenomena into a common framework/theory.\nWe do not have a TOE.\nAlong the path to understanding this, learning classical mechanics is\nbut a stepping stone to quantum mechanics, GR and all the wonderfull\nthings ahead.\n\nThe other is complexity, in a sufficiently complex system (and\nsufficiently complex is remarkably little: three gravitationally\ninteracting bodies in Newtons theory for example) we can write down\nthe equations of motion but we do not understand what they mean, what\nthey say and rpedict. This is also known as chaos theory.\nAlong the path of advancing this classical mechanics is (one of) the\n(possible) framework(s) within which you work to find and reveal the\nhidden and implicit structures that it holds. Check out the beautifull\nKAM theorem for a taste of things on that boundary.\n\n\nHowever, it sounds like your course is historical. Personally I favor\nrevisionist teaching. Teaching shouldn\'t be an accelerated rushing\nthrough the historic development to the present point. Particularly if\nit indeed contains no 20th century material it would obmitt Noethers\ntheorem which would be a crime.\nIf you want to see a good introduction to classical mechanics pick up\nLandau Lifschitz, even though that two is somewhat old fashioned in\nsome aspects.\n\n\n----\nfrank\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>pdm190@hotmail.com (SunnyJing) wrote in message news:<46b99cc6.0410241513.555c302b@posting.google.com>...
> I am studying the course-a complete scheme of mechanics in 18th, 19th
> century, but I find it is just always denoted as "a passage to
> understand quantum mechanics", so it seems no practical use except
> leading to quantum mechanics.
> if so, why do people need to labor on it?

The simple answer: If you don't understand classical mechanics,
particularly in the Hamiltonian formalism you wont stand a chance in
QM or GR. The concept introduced there: Lagrangian and Hamiltonian
method, symmetries, and so on, are valid throughout physics. Plus
classical mechanics still describes and always will describe a vast
part of the world.

There are two boundaries of knowledge in physics: Simplicity and
complexity.

We can not yet simplify all phenomena into a common framework/theory.
We do not have a TOE.
Along the path to understanding this, learning classical mechanics is
but a stepping stone to quantum mechanics, GR and all the wonderfull
things ahead.

The other is complexity, in a sufficiently complex system (and
sufficiently complex is remarkably little: three gravitationally
interacting bodies in Newtons theory for example) we can write down
the equations of motion but we do not understand what they mean, what
they say and rpedict. This is also known as chaos theory.
Along the path of advancing this classical mechanics is (one of) the
(possible) framework(s) within which you work to find and reveal the
hidden and implicit structures that it holds. Check out the beautifull
KAM theorem for a taste of things on that boundary.

However, it sounds like your course is historical. Personally I favor
revisionist teaching. Teaching shouldn't be an accelerated rushing
through the historic development to the present point. Particularly if
it indeed contains no 20th century material it would obmitt Noethers
theorem which would be a crime.
If you want to see a good introduction to classical mechanics pick up
Landau Lifschitz, even though that two is somewhat old fashioned in
some aspects.

----
frank

Van Jacques

Oct27-04, 11:00 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lou Pecora wrote:\n> In article <46b99cc6.0410241513.555c302b@posting.google.com>, \n> pdm190@hotmail.com (SunnyJing) wrote:\n>\n> > I am studying the course-a complete scheme of mechanics in 18th,\n19th\n> > century, but I find it is just always denoted as "a passage to\n> > understand quantum mechanics", so it seems no practical use except\n> > leading to quantum mechanics.\n> > if so, why do people need to labor on it?\n>\n> Well, that\'s not a bad reason right there. However, I\'m sorry to\nhear\n> that classical mechanics is put in that category even today. More\n> modern versions will also show you that studies of classical\nmechanics\n> have increased, mainly in response to the fact that many classical\n> systems are chaotic and are still not well understood. In addition,\n> other areas of physics (fluid dynamics, plasma physics, celestial\n> mechanics, statistical mechanics, and, in a certain sense,\nrelativity)\n> build on classical mechanics. It\'s a good foundation for a lot of\nother\n> physics.\n>\n> It\'s not wasted time to study it. IMHO. In fact, I believe you\nwould\n> have trouble progressing in most areas of physics without it.\n>\n> -- Lou Pecora (my views are my own)\n\nThere is more to modern physics than quantum mechanics. The\nrelativistic\nmechanics of particles must be understood to do physics in any case,\nI it is part of classical mechanics. Classical mechanics has come to\nmean\n"not quantum mechanics", IMO.\n\nThere is also the mechanics of continua, like gases and solids, MHD and\nplasma.\nI have been trying to convince people all my life that its important to\ndo\nall these things relativistically, even at low velocities. This is\nbecause\nthe arena for physics is spacetime, which invites the use of 4-vectors,\nand many relationships are obvious when using 4 vector notation that\none can\'t see if one uses 3 + 1 notation.\n\nAlso, often the EM field puts in an appearance, and what is a\nnonrelativistic\ntheory of the EM field? It is nonsense to even talk about it.\nWhen I say MHD and plasma done with the matter using Galilean inv.\neqns., and the EM field just sort of thrown in on top of this, I wanted\nto scream. I knew my lifes work was to set this right.\n\nHowever, since I lost may place at a University, I have become\nvoiceless,\nand noone pays any attention to what is to me, an obvious problem with\nMHD and plasmas, or any continua.\nIMO, it all is important, and all should be done relativistically.\n\nVan\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lou Pecora wrote:
> In article <46b99cc6.0410241513.555c302b@posting.google.com>,
> pdm190@hotmail.com (SunnyJing) wrote:
>
> > I am studying the course-a complete scheme of mechanics in 18th,
19th
> > century, but I find it is just always denoted as "a passage to
> > understand quantum mechanics", so it seems no practical use except
> > leading to quantum mechanics.
> > if so, why do people need to labor on it?
>
> Well, that's not a bad reason right there. However, I'm sorry to
hear
> that classical mechanics is put in that category even today. More
> modern versions will also show you that studies of classical
mechanics
> have increased, mainly in response to the fact that many classical
> systems are chaotic and are still not well understood. In addition,
> other areas of physics (fluid dynamics, plasma physics, celestial
> mechanics, statistical mechanics, and, in a certain sense,
relativity)
> build on classical mechanics. It's a good foundation for a lot of
other
> physics.
>
> It's not wasted time to study it. IMHO. In fact, I believe you
would
> have trouble progressing in most areas of physics without it.
>
> -- Lou Pecora (my views are my own)

There is more to modern physics than quantum mechanics. The
relativistic
mechanics of particles must be understood to do physics in any case,
I it is part of classical mechanics. Classical mechanics has come to
mean
"not quantum mechanics", IMO.

There is also the mechanics of continua, like gases and solids, MHD and
plasma.
I have been trying to convince people all my life that its important to
do
all these things relativistically, even at low velocities. This is
because
the arena for physics is spacetime, which invites the use of 4-vectors,
and many relationships are obvious when using 4 vector notation that
one can't see if one uses 3 + 1 notation.

Also, often the EM field puts in an appearance, and what is a
nonrelativistic
theory of the EM field? It is nonsense to even talk about it.
When I say MHD and plasma done with the matter using Galilean inv.
eqns., and the EM field just sort of thrown in on top of this, I wanted
to scream. I knew my lifes work was to set this right.

However, since I lost may place at a University, I have become
voiceless,
and noone pays any attention to what is to me, an obvious problem with
MHD and plasmas, or any continua.
IMO, it all is important, and all should be done relativistically.

Van

Joseph.D.Warner

Oct28-04, 01:28 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nSunnyJing wrote:\n> I am studying the course-a complete scheme of mechanics in 18th, 19th\n> century, but I find it is just always denoted as "a passage to\n> understand quantum mechanics", so it seems no practical use except\n> leading to quantum mechanics.\n> if so, why do people need to labor on it?\n\nClassical mechanics can stand on its own. It provides a great basis for\nQuantum Mechanics. The techniques you learn in CM can be applied to QM.\nAlso, there is always the reference of the term in QM to CM to help one\ninitially grasp the meaning of the equation and where it come from.\n\nAway from that CM is the bases for many fields of engineering. When you\ndo graduate you very well may get a job as a Physicist doing QM related\nresearch but you may not. CM will be the way you will interact with\nother people, you will use it to design your experiments along with QM\nbecause you will need to do some engineering yourself if you build new\nresearch equipment.\n\nThen there are whole field of physics related to CM. Classical many-body\ntheory (ex. why are there rings around planets?), chaos theory, orbital\nmechanics for space applications, micro-machining and fluid dynamics to\nname a few.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>SunnyJing wrote:
> I am studying the course-a complete scheme of mechanics in 18th, 19th
> century, but I find it is just always denoted as "a passage to
> understand quantum mechanics", so it seems no practical use except
> leading to quantum mechanics.
> if so, why do people need to labor on it?

Classical mechanics can stand on its own. It provides a great basis for
Quantum Mechanics. The techniques you learn in CM can be applied to QM.
Also, there is always the reference of the term in QM to CM to help one
initially grasp the meaning of the equation and where it come from.

Away from that CM is the bases for many fields of engineering. When you
do graduate you very well may get a job as a Physicist doing QM related
research but you may not. CM will be the way you will interact with
other people, you will use it to design your experiments along with QM
because you will need to do some engineering yourself if you build new
research equipment.

Then there are whole field of physics related to CM. Classical many-body
theory (ex. why are there rings around planets?), chaos theory, orbital
mechanics for space applications, micro-machining and fluid dynamics to
name a few.

robert j. kolker

Nov3-04, 09:37 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Igor Khavkine wrote:\n>\n> Classical mechanics is useful in explaining the world around us because\n> in many cases quantum effects are negligible. The Hamiltonian formulation\n> of classical mechanics can certainly used as a starting point for\n> formulating quantum mechanics, but it has many other uses. Many dynamical\n> systems (systems that evolve subject to differential equations) can\n> be cast in Hamiltonian form and analyzed that way.\n\nAerodynamics is squarely based on classical physics. It is an adequate\nmodelling tool and the starting point for any novel aircraft design.\n\nDitto for turbulent flow in general.\n\nThere are some areas in non-fundamental physics where one cannot do\nbetter than classical theory. To the best of my knowledge no one has\nquantized the Navier Stokes equations (I am no an expert so if someone\nhas information to the contrary please do share it).\n\nBob Kolker\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Igor Khavkine wrote:
>
> Classical mechanics is useful in explaining the world around us because
> in many cases quantum effects are negligible. The Hamiltonian formulation
> of classical mechanics can certainly used as a starting point for
> formulating quantum mechanics, but it has many other uses. Many dynamical
> systems (systems that evolve subject to differential equations) can
> be cast in Hamiltonian form and analyzed that way.

Aerodynamics is squarely based on classical physics. It is an adequate
modelling tool and the starting point for any novel aircraft design.

Ditto for turbulent flow in general.

There are some areas in non-fundamental physics where one cannot do
better than classical theory. To the best of my knowledge no one has
quantized the Navier Stokes equations (I am no an expert so if someone
has information to the contrary please do share it).

Bob Kolker

V. Guruprasad

Nov7-04, 04:05 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 3 Nov 2004 15:37:59 +0000 (UTC),\nrobert j. kolker <nowhere@nowhere.net> wrote:\n> Igor Khavkine wrote:\n>>\n>> Classical mechanics is useful in explaining the world around us because\n>> in many cases quantum effects are negligible. The Hamiltonian formulation\n>> of classical mechanics can certainly used as a starting point for\n>> formulating quantum mechanics, but it has many other uses. Many dynamical\n>> systems (systems that evolve subject to differential equations) can\n>> be cast in Hamiltonian form and analyzed that way.\n>\n> Aerodynamics is squarely based on classical physics. It is an adequate\n> modelling tool and the starting point for any novel aircraft design.\n>\n> Ditto for turbulent flow in general.\n>\n> There are some areas in non-fundamental physics where one cannot do\n> better than classical theory. To the best of my knowledge no one has\n> quantized the Navier Stokes equations (I am no an expert so if someone\n> has information to the contrary please do share it).\n>\n> Bob Kolker\n>\n\nAs I posted a review request containing a URL earlier to this group:\n\nAlso for rigorously deriving quantization itself in the first place from\nstrict mathematical/definitional properties of EM waves*.\n\n(To be precise, we do not need the Hamilton-Jacobi formalism as this\ndoes not depend on the dynamical properties of matter, only on waves.)\n\n\n\n-prasad\n-----------------------------------------------------------------------\n* That\'s classical Maxwell-Hertz EM waves as in Jordan\'s book, not the\nmodern notion of photons following QED. Even SR is not involved.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 3 Nov 2004 15:37:59 +0000 (UTC),
robert j. kolker <nowhere@nowhere.net> wrote:
> Igor Khavkine wrote:
>>
>> Classical mechanics is useful in explaining the world around us because
>> in many cases quantum effects are negligible. The Hamiltonian formulation
>> of classical mechanics can certainly used as a starting point for
>> formulating quantum mechanics, but it has many other uses. Many dynamical
>> systems (systems that evolve subject to differential equations) can
>> be cast in Hamiltonian form and analyzed that way.
>
> Aerodynamics is squarely based on classical physics. It is an adequate
> modelling tool and the starting point for any novel aircraft design.
>
> Ditto for turbulent flow in general.
>
> There are some areas in non-fundamental physics where one cannot do
> better than classical theory. To the best of my knowledge no one has
> quantized the Navier Stokes equations (I am no an expert so if someone
> has information to the contrary please do share it).
>
> Bob Kolker
>

As I posted a review request containing a URL earlier to this group:

Also for rigorously deriving quantization itself in the first place from
strict mathematical/definitional properties of EM waves*.

(To be precise, we do not need the Hamilton-Jacobi formalism as this
does not depend on the dynamical properties of matter, only on waves.)

-prasad
-----------------------------------------------------------------------
* That's classical Maxwell-Hertz EM waves as in Jordan's book, not the
modern notion of photons following QED. Even SR is not involved.