HDTenEightyP/NetNews huggingface dataset:
Newsgroups: sci.physics


I've been struggling with the concept of covariant derivative for some time.
I'd like to add my $0.02 and my $0.50 questions to this thread.

Here goes,

A covariant derivative need only be an operation that adds one covariant
index to any tensor. Consider a Reimmanian space.

For a scalar I this is simply

          i
I  = dI/dx  , where the derivatives are partials.
 ;i

For a covariant tensor of 1st rank (order, whatever) A

            j   k
A   = dA /dx - G  A
 i;j    i       ij k

as I'm sure you all know. G can be formed from any non-singular covariant
rank 2 tensor. The "connection" is an additional restraint that need not
be imposed to insure the tensor character of the resulting tensor. 

Ok that was my $0.02 worth, now for the $0.50 questions,

John Baez writes:

>2) The covariant derivative only requires a tangent vector at one point
>of the manifold.  The price you pay is this: to define it you need to
>choose a connection on the (tangent bundle of) the manifold.  Of course,
>such a connection - the Levi-Civita connection - comes for free if your
>manifold has a Riemann metric on it.

Hmm.... If I look at the covariant derivative of the scalar I above, all
I need to know are the partial derivatives of I at the points that I want
the derivative. Let me just talk about one point. Then I need to know
I(x1,x2,,,) only, that is know the scalar as a function of the coordinates
at the point is question.

In the general case, I need to know G, which means I need to know the
tensor in question as a function of coordinates, and the covariant tensor
of rank 2 used for the derivative as a function of the coordinates, both
at the point in question.

One question is this, how does knowing a tangent vector at one point
give me enough information to compute a covariant derivative?

Another question is about the connection. As I stated above, I don't
see the need for a connection to establish a covariant derivative.
Is this just a matter of definition?

Enough for now.

--------------------------------------------------------------------
Ric Peregrino   c/o Hewlett Packard Co.    I represent only myself
ric@spd.hp.com  1501 Page Mill Rd Bldg 5M  I may be wrong, maybe not
415-857-7526    Palo Alto, CA 94304        Do DC photons exist?
--------------------------------------------------------------------
Newsgroups: sci.physics
From: mmjsas@iesd.auc.dk (Michael Melgaard)
Subject: Gravitation - Book Needed
Organization: Mathematics and Computer Science, Aalborg University
Distribution: sci.physics
Date: 5 Nov 92 12:47:59

I would like to know if anyone could tell me where to get the textbook
"Gravitation" written by Charles Misner, Kip Thorne and John A.
Wheeler back in 1970. 

Please E-mail to mmjsas@iesd.auc.dk 
Newsgroups: sci.physics
From: johnf@uhheph.phys.hawaii.edu (John Flanagan)
Subject: Re: Barbie is Right! (was: Mattel on women)
Organization: University of Hawaii, Dept. of Physics & Astronomy
Date: Sun, 8 Nov 1992 23:15:21 GMT

In article <1992Nov8.013814.18382@Princeton.EDU>
ajackson@ernie.Princeton.EDU (Andrew William Jackson) writes:
>
>Men are inherently better at math than women are.  Culture is not a force
>unto itself but a reflection of our fundimental nature.

That's nice, dear.

--John
-- 
John Flanagan                          ||"Pretty boys
johnf@uhheph.phys.hawaii.edu           || with the sunshine faces
U. of Hawaii, Dept. of Physics & Astro.|| <mumble mumble>..."
2505 Correa Rd., Honolulu, HI 96822    ||   -- My Bloody Valentine
From: un025720@wvnvms.wvnet.edu
Newsgroups: sci.physics
Subject: JCPDS files.....
Date: 5 Nov 92 15:28:57 GMT
Organization: West Virginia Network for Educational Telecomputing


  Could someone tell me if there is a data base or ftp site available to
access JCPDS (x-ray powder diffraction files).
Thanks.
manjula ibrahim
From: parson_r@cubldr.colorado.edu (Robert Parson)
Subject: "Anderson-Higgs Mechanism" (Re: Solid-State doesn't use QED!)
Organization: University of Colorado, Boulder
Date: Sun, 8 Nov 1992 22:19:20 GMT

In article <MATT.92Nov8120704@physics.berkeley.edu>, matt@physics.berkeley.edu (Matt Austern) writes:
> In article <BxEuvI.59p@wsrcc.com> alison@wsrcc.com (Alison Chaiken) writes:
> 
>> What is the Anderson-Higgs mechanism?  My very limited understanding
>> of the Higgs mechanism is that a new gauge boson (which would be
>> called a collective mode in solid-state) is postulated to explain how
>> the fundamental particles (which would be the quasiparticles) obtain
>> their different mass energies (which would be the effective mass).
> 
> When high-energy theorists talk about the Higgs mechanism, what they
> mean is somewhat more general than that.  It's just how if a gauge
> symmetry is broken spontaneously, then there aren't any Goldstone
> bosons, but, instead, the gauge bosons become massive.
 
> My understanding is that solid-state theorists do indeed work with
> models in which this happens.  (e.g., massive photons in
> superconductors) 

 Yes, that's the context of Anderson's work, published in 1958 (in the
immediate aftermath of BCS).  There were a number of questions (excuse
me, my memory is very vague on this) concerning the gauge-invariance of
BCS. Anderson showed that the gauge invariance of the electromagnetic
field in a superconductor led to the existence of longitudinal plasmons
with a nontrivial dispersion relation (nonzero effective mass). Five
years later he published a paper that considered the implications of the
mechanism for quantum field theory (Phys. Rev. _130_, 439, 1963.) I don't
 know to what extent he anticipated Higgs et al. in this latter work.

See, for example, _Quantum Many-Particle Systems_, by Negele and Orland,
p. 222.

Robert (getting out of his depth as usual.)
Newsgroups: sci.physics
From: merithew@uxa.cso.uiuc.edu (robert merithew)
Subject: Re: jokes & sexisim in physics
Organization: University of Illinois at Urbana
Date: Sat, 7 Nov 1992 00:31:12 GMT
Keywords: sexism women women-physicists

carl@aoa.aoa.utc.com (Carl Witthoft) writes:

>x
>Men just don't get it.
>One of the things we don't get is that it's absurd for a bunch
>of men to pontificate as to whether certain jokes are offensive
>to women 

The question is not which jokes are 'offensive to women'.  You don't
have to be a woman to be offended by a sexist joke.  Maybe it's 'which
jokes alienate women' i.e. which jokes tell women they don't belong in
this group.

>and whether this is part of the reason women avoid
>science (or for that matter football).
>Women know.  The sooner men stop speaking for them and listening
>to them, the better.

When men participate in the discussion of gender bias in a field, they
are *not* necessarily speaking *for* women.

Do you think that men posting about sexism in this forum somehow
prevents men from listening to women?

I think sexism is not just a women's problem.  It is a 'people'
problem, and people should be able to work together to help solve it.
I don't see why men should be excluded from the discussion.

--
  Robert Merithew                                        r-merithew@uiuc.edu
  grad student, Dept. of Physics
  University of Illinois at Urbana-Champaign
From: lml@vision.ummed.edu (Lawrence Mark Lifshitz)
Newsgroups: sci.physics
Subject: Covariant vs. Lie Derivative in Gen. Rel.?
Date: 10 Nov 92 17:32:24 GMT
Organization: University of Massachusetts Medical Center


I have been trying to learn General Relativity by reading Robert Wald's 
book and have become confused about the difference between a
covariant derivative contracted with a vector and a Lie
derivative in the direction of the vector.  Any help clarifying
the distinction would be appreciated. Specifically:

If D_a (ie, D sub a) is the unique derivative operator induced by
the metric which has the property D_a g_bc = 0  (page 35) then the
derivative of a Tensor (T^b1b1..._c1c2...) when transported in a 
direction t^a (ie, t superscipt a) is  t^a D_a T^b1b2..._c1c2 ...

But the definition of Lie derivative of a tensor with respect
to a vector v^a is defined on page 439 as the limit of the
diffence of the tensor and its pullback divided by t, the
parameterization of the curve along which T is being moved
(v^a is the tangent to the curve at the current position).
How is this different from v^a D_a T ?  Wald clearly
presents it as different since on page 441 (eq. C.2.13)
he shows that L_v u_a  (ie, the Lie derivative of the dual vector
u_a in the direction v^b) = v^b D_b u_a + u_b D_a v^b .
If the Lie derivate were equal to the covariant derivative
then the second term would not be there.

So, conceptually, what is the difference between the two?
Does one require a different type of topogical space or
parameterization?  Mathematically how do they differ?
thanks in advance.

			Larry.
Newsgroups: sci.physics
From: dwr2560@zeus.tamu.edu (RING, DAVID WAYNE)
Subject: Re: Question on Hawking radiation
Summary: Why don't extremal black holes radiate?
News-Software: VAX/VMS VNEWS 1.41    
Organization: Texas A&M University, Academic Computing Services
Date: Sat, 7 Nov 1992 01:05:00 GMT

brahm@cco.caltech.edu (David E. Brahm) writes...
>Can anyone explain why extreme Reissner-Nordstrom black holes (Q=M) [or
>charged Kerr solutions, L^2 + Q^2 = M^2] have a vanishing Hawking
>temperature (T=0)?  The virtual-particle picture would make me erroneously
>believe that positively-charged particles would spew out from the vicinity
>of a positively-charged black hole.  My guess is that it has something to
>do with the inner horizon (r-) going to zero.
>[* This question is originally due to Dr. Stephen Hsu at Harvard *]

A stationary observer just outside the horizon does not accelerate (as measured
from outside, i.e. if she is lowered from infinity on a string the string has
no tension). Thus, what looks like a particle pair from outside, looks like a
particle pair in a local inertial frame. And pair production from nothing is
forbidden in inertial frames.

But this suggests another harder question: how can the surface gravity be
zero???

BTW If you talk to Steve, say hi for me. :-)

Dave Ring
dwr2560@zeus.tamu.edu
From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Subject: Re: Religion and Science don't mix
Organization: University of Virginia
Date: Fri, 6 Nov 1992 18:47:57 GMT

In article <1992Nov6.011331.25635@sierra.com> ande@sierra.com (Ande Rychter) writes:
>In 26495 Angelo J. Paguia writes:
>
>> "... The two [ie religion and science] don't mix and do not contradict 
>>  nor support each other."
>
>You are right.  But they can displace each other.  And that's what's
>happening in this country right now.  (Guess which one is doing the 
>displacing.  Hint: Think of Oral Roberts) -AR

     If this is so, it is probably partly because certain people 
     keep insisting that science says that there can be no God, and
     that belief in a God and science are necessarily incompatible.  
     Guess this shows what many people consider more important?

                         dale bass

-- 
C. R. Bass                                          crb7q@virginia.edu        
Department of Mechanical, 
     Aerospace and Nuclear Engineering
University of Virginia                              (804) 924-7926
Newsgroups: sci.physics
From: cegtitd@prism.gatech.EDU (Tim Dodd)
Newsgroups: sci.physics
Subject: Re: Religion & Physics Don't Mix
Date: 9 Nov 92 21:22:44 GMT
Organization: Georgia Institute of Technology

In article <BxGnLw.J8A@unixhub.SLAC.Stanford.EDU| sschaff@roc.SLAC.Stanford.EDU (Stephen F. Schaffner) writes:
|In article <74170@hydra.gatech.EDU|, cegtitd@prism.gatech.EDU (Tim Dodd) writes:
||| In article <BxB855.7Mq@unixhub.SLAC.Stanford.EDU| 
|sschaff@roc.SLAC.Stanford.EDU (Stephen F. Schaffner) writes:
|
|
||| |It seems pretty clear to me that the concept of meaning that you espouse is 
||| |itself meaningless under your own definition (meaning does not, after all, 
||| |refer to anything observable), and is in fact a philosophical rather than 
||| |a scientific statement.  
||| 
||| Au contraire:  I defined "meaning" in an earlier post.  It most certainly
||| refers to something real.
||| 
|
|	I'm sorry, I must have missed the part where you showed that the 
|concept of meaning was empirically verifiable (I believe that was one of your 
|requirements for meaning).  Could you run that part by me again?

Alright, one more time!  :-)

"Meaning" refers to the semantic mapping, or correspondence, between a word
and the thing to which the word refers.  If it cannot be shown that a word
has a referent, then it is by definition meaningless.

If you regard this definition as rendering "meaning" meaningless, stop &
think about how you understood this sentence.  If there were no semantic
mappings between words and their referents, this entire note would have
been meaningless drivel.

Tim
-- 
Tim Dodd, Research Scientist, Georgia Tech:  cegtitd@prism.gatech.edu
Newsgroups: sci.physics
From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Subject: Re: Religion & Physics Don't Mix
Organization: University of Virginia
Date: Fri, 6 Nov 1992 18:32:40 GMT

In article <6201@tuegate.tue.nl> johan@blade.stack.urc.tue.nl (Johan Wevers) writes:
>Cameron Randale Bass writes:
>
>>>> Actually, most core doctrine is taken on faith.  There ain't no
>>>> way to determine the 'truth' of faith.  It's 'true' until the 
>>>> last adherent dies, after which may be debate.
>
>>>You can believe in something that can be proven wrong. What's the point?
>
>> I don't know?  Does there have to be a 'point'?
>
>Yes. If something is proven wrong and you still believe in it you're
>views about the world are inconsistent.

     I don't think you understand.  There may well be a difference
     between 'reality' and 'appearance'.  And, this 'proving wrong'
     is a very tricky business outside of science.

>> You seem to be having difficulties with delineation between
>> science and religion.  Let me help you out, if you're talking about
>> 'gods' your rules for science do not necessarily apply.  Similarly,
>> in science there is no place for unfalsifiable concepts like 'God'.
>
>Hmmm. I conclude from this that your opinion about science is an
>instrumentalistic one: you use it to describe some things you want
>to measure.

     You may *not* conclude that my views are 'instrumentalistic'.
     That does not, however, mean that I only recognize my own view as
     the sole valid viewpoint.

>My view is realistic: I believe that there exists a reality, independant
>wether we know this or not. The main thing QM has to learn us about this
>is that the interaction between observers and the rest of reality is not
>always neglectable.

     So you agree that there exist leprechauns, whether we see them or not?

>Therefore, I believe in only one reality. This reality can be described
>by science. I've never seen any hint that there exists anything more.

     Feel free.  Recognize, however, that there are other, perfectly
     valid, 'realities'.  In fact, every major religion has a different 
     'reality', Machian positivism represents another one.

     You can no more prove them wrong than you can prove you exist.

                            dale bass

-- 
C. R. Bass                                          crb7q@virginia.edu        
Department of Mechanical, 
     Aerospace and Nuclear Engineering
University of Virginia                              (804) 924-7926
Newsgroups: sci.physics,sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Covariant vs. Lie Derivative in Gen. Rel.?
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Thu, 12 Nov 92 21:11:26 GMT

In article <1drukoINN801@darkstar.UCSC.EDU> ask@ucscb.UCSC.EDU (Andrew Stanford Klingler) writes:
>
>
>JB:
>
>>
>>To repeat: The connection allows you to compare tangent vectors at two
>>points of the manifold given only a curve connecting them; the Lie
>>derivative requires a whole vector field, to generate a flow that "drags
>>tensors along". 
>>
>The distinction you're making sounds kind of phony; after all one can
>define a connection using a vector field or a field of one-forms (I may
>be limiting myself to principal fiber bundles here).  It seems like the
>flow is just buried in the structure for a connection (in some sense a
>connection gets you "more than a flow" - the local family of geodesics
>through a point).  Without a connection, you have no way to compare vectors
>at two different points, so you have to transport tensors out, then back
>to the same point and compare them there.  With a connection, you have
>"flow in every direction" (geodesics thru the point) so parallel transport
>vectors from a point to any other point and compare them there.  From this
>point of view Lie derivatives and covariant derivatives represent the
>same geometric thing, I think.  Am I way wrong here?

I can't really estimate your rightness or wrongness.  Of course both
derivatives amount to ways of comparing vectors at different points.
However, the Lie derivative L_v w(x) at the point x of a vector field w
with respect to a vector field v does NOT just depend on the value of v
at the point x, while the covariant derivative D_v w(x) only depends on
the value of v at the point x.  The price one pays, of course, is that
to define D_v w(x) we need an extra structure, the connection.  But on
the up side, the covariant derivative is defined for all vector bundles
(equipped with connection) while the Lie derivative only works for the
tangent bundle and its relatives (tensor bundles).  

Another way of saying it, from a more global and algebraic perspective,
is that D_v w is linear in v (thinking of vector fields as a module over
the ring of smooth functions) while L_v w is not.






From: selee@hpcc01.corp.hp.com (Lee Say Eng)
Date: Fri, 13 Nov 1992 08:40:47 GMT
Subject: Need HELP !
Organization: the HP Corporate notes server
Newsgroups: sci.physics


I have been trying without much success to find the amount of
damage that a machine part will suffer when it is impacted by 
a moving body.  I understand that when the kinetic energy of
the moving body exceeds the maximum elastic strain energy of
the machine part, the part will (if we neglect the inertia of
the part and the energy dissipated during impact) either suffer
some permanent deformation or be crushed at the location where
the cross-sectional area is minimum.   I however do not know
how to find by how much the part will be crushed in such a case.
It could be found experimentally but it would also be beneficial
to be able to theoretically predict things.  The material is
pretty brittle but to simplify things, it might be easier to
ignore failure by crack propagation.  Any help will be greatly
appreciated.   


		     ********
		     * mass *  |  Free falling mass
		     *  m   *  |  from height h 
		     ********  V


                               |
                               |
                               V
		       ****  ---  Distance that will
          Machine     *    * ---  be crushed ??
           Part      *      *  ^
                    *        * |
                   *          *
              ___ *___________ * _____
	      ////////////////////////
		    Rigid Base
                 
  
  Data known regarding machine part:  
  
		Dimensions/geometry 
		Young's Modulus, E
		Compressive strength
		Ultimate tensile strength

Thanks in advance,

Alan Phang

alan@hpmalr50.mal.hp.com
From: sichase@csa1.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.physics
Subject: Re: No big crunch?
Date: 6 Nov 1992 12:47 PST
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
Distribution: world
NNTP-Posting-Host: 128.3.254.196
News-Software: VAX/VMS VNEWS 1.41    

In article <6NOV199211570602@csa1.lbl.gov>, sichase@csa1.lbl.gov (SCOTT I CHASE) writes...
> 
>>     However, getting back on track it is silly to say that a theory that in 
>>     some sense avoids internal inconsistency has passed some sort of 
>>     valid scientific 'test'.  It's like patting oneself on the back
>>     for not having assumed ii equals 3 and ii equals 5 at the same
>>     time.  
> 
>Perhaps it seems that way to a mechanical engineer.  However, I assure you
>that it really works that way in particle physics.  Internally consistent
>theories come much more easily in classical physics than in quantum field
>theory.  Over the fifty-odd years of particle physics history, internal 
>consistency has repeatedly been a useful way of discovering new physics.

Lest I get more hate mail from engineers, let me state for the record
that I did not intend to make a disparaging statement about Dale, or 
engineers in general.

I only meant to say that although it might seem silly to someone who's
daily work is in classical physics, mathematical consistency is a very 
valuable guide for searching out physically correct models in particle
physics.  It is not logically necessary for this to be the case, but 
I know from long experience that it is so.

-Scott
--------------------
Scott I. Chase			"It is not a simple life to be a single cell,
SICHASE@CSA2.LBL.GOV		 although I have no right to say so, having
				 been a single cell so long ago myself that I 
				 have no memory at all of that stage of my 
				 life." - Lewis Thomas
From: dsg@impmh.uucp (Dave Gordon)
Newsgroups: sci.physics
Subject: Re: New Group sci.physics.orthodox
Date: 9 Nov 92 14:27:26 GMT
Organization: Integrated Micro Products Ltd

In <1deevpINNl33@bigboote.WPI.EDU> phillies@bigwpi.WPI.EDU (George D. Phillies) writes:
>
>My motivation for this is the suspicion that this group 
>is not in contact with the physics community at all.  
>Note that approximately two months ago I posted an 
>announcement of a tenure-track physics opening at my
>institution.  Before the ad appeared in Physics Today,
>a month later, we received perhaps two applications.  
>We'renow up to around 60, with an end-of-the-year 
>deadline.  Since people usually tell their friends and 
>students about job openings, I infer that well under 1%
>of the real physics community actually reads this group.

On the other hand, it could be that a lot of the readers of this
group, even within "the real physics community" are not interested
in an opening at your institution - because they're on the other
side of the world!
-- 

===============================================================================
Dave | dsg@imp.co.uk | +44 753 516599 | <this space is deliberately left blank>
===============================================================================
        You are in a little maze of twisty standards, all different
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Newsgroups: sci.physics,sci.math