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GEMVG1 (gemvg1@aol.com) wrote:
: Please help me - this is going to sound very, very stupid, and I know that
: all of you are professors and clever people like that, but I have a
: physics problem that I need help with. I am doing a project at school into
: gravity and potential energy etc., but it is really bad, because I don't
: know enough background theory behind it. We are dropping balls in a box of
: sand, and we have to see how much sand is displaced, or the diameter of
: the crater, and so on. We have to make quantitative predictions (e.g., I
: predict that the diameter of the crater will be the square root of the
: height), but because I don't know the exact topic behind the project, I
: don't know how to make a good prediction. I have looked in all the physics
: books at my local library (there isn't a physics library that I can go
: to), but they have nothing of relevance in. Also, my physics teacher said
: that there are equations that do give the exact diameter/volume/? of a
: crater, but he won't give them to us, because he has lost them. I am
: really desperate for help, and I am sorry to trouble everyone. If anyone
: can help, I would be very grateful.
: Yours sincerely, 
: Claire
: GEMVG1@aol.com 
My advice is to not worry about the exact equations determining the
crater size (in any case they are complicated and not likely to be
easily understood). A great physics project is simply *finding out*
what variables (height, oject size, object shape, sand mean size ...)
that do determine the crater size experimentally. Then you are 
actually *doing* real physics and not just taking the word of someone
"expert" .
-- 
Lawrence R. Mead (lrmead@whale.st.usm.edu) 
ESCHEW OBFUSCATION ! ESPOUSE ELUCIDATION !
http://www-dept.usm.edu/~scitech/phy/mead.html 

-*--------
Russell: 
>> It may be that the theory that Artese outlines above remains
>> useful for literary criticism.  But Artese would be hard pressed
>> to find a linguist who believes that this is how language
>> actually works.  Chomsky has pointed out that if children had to
>> explicitly learn every rule of a natural language's grammar, they
>> could not learn language, because they are never presented enough
>> information to do so.
In article <326DECC7.4A98@nwu.edu>, brian artese   wrote:
> Nothing in the exposition above says anything about "rules of 
> grammar."  I'm not trying avoid the issue you raise here -- it's 
> definitely worth talking about -- but I just don't see how it 
> connects to the simple issue of signification that I was raising. ...
The inadequacy of input applies perhaps more to learning words
than to learning grammar rules.  I hope I can make this more 
clear, below.
> A boy sees something.  What does he see?  He doesn't see 'furiousness' 
> -- he sees some particular material phenomenon, e.g., he sees somebody 
> shouting, someone with a furrowed brow, somebody striking something.  
> Assuming that the boy has, at this point, a very small vocabulary, when 
> he hears somebody say 'that guy was furious,' then the only thing the 
> boy knows is that the particular brand of semi-violent emotive behavior 
> that he's just witnessed can be described as 'furious.'  So when he sees 
> somebody playing football, he may very well say that he's 'furious.'  Or 
> when he witnesses a lunatic raving in the street, he could be 'furious.' 
> The child's understanding of fury is, at this point, nebulous.  When 
> does it get pared down?  It begins when he learns what is *not*, by 
> convention, considered to be 'fury' -- when he learns the word for 
> 'lunacy,' (in the case of the madman) or 'aggressive play' (in the case 
> of the ball player), etc.  The word takes on even more precision when he 
> learns to place the term on a relative scale *with other similar words*, 
> like 'disgruntled' -- which the child hears used in relation to behavior 
> that isn't quite as violent and emotive.
Children do make mistakes learning words.  The problem with the
theory above is that the mistakes they make are too few and too
different in kind for the theory above to explain how words are
learned.  (This is the connection with what I wrote above.)  To
understand how children learn what words signify, linguists are
forced to deal with the fact that a child has a large amount of
non-linguistic knowledge that comes to bear when the child is
learning speech.  Some of this is learned prior to learning
words.  Some of it is built-in: the human child innately attends
to certain kinds of things in first learning about the world and
in interactions with other people.  The child who is acquiring
the word "furious" is very likely already familiar with fury, in
both herself and others, and to learn the word "furious" only has
to learn its connection with what the child already knows.
Having learned this, the child will figure out (without having to
be told) many of the connections between furious and other words,
for example, that being "furious" makes her brother "hit" their
mother.
This is vastly oversimplified.  Note, well, that I am not denying
some of the processes that Artese describes.  In particular, 
(1) many words, especially those that carry subtle shades,
gradations, extremes, and other inflections, are learned wholy
through their relationship to other words (though only rarely
with respect to what the word does NOT signify), (2) once a child
has sufficient language, it can be used to indicate what other
words signify, especially in conjunction with experience (for
example, a biology teacher pointing to something and saying "the
bluish-grey knot is the ganglion"), and (3) our understanding of
some words change with experience.  Most likely, a child would
not learn the word "furious" as I describe above, but rather a
simpler word, namely "mad."
What linguists do deny is that the processes Artese describes
are adequate explanation of how children learn what words 
signify.  They are not.
> ... You need to be careful when you say things like 'When a boy 
> sees a furious person...' which presumes that the meaning of
> 'furious' is transmitted at the outset, before we even begin
> talking about the exchange between the phenomenon and the 
> boy.
No.  It presumes that the boy is familiar with fury, even if he
lacks the words for it.  Modern literary theory is almost
hilarious in its desparation to deny non-linguistic knowledge.
But linguists and cognitive scientists know that language cannot
be explained apart from this.  In this regard, I again suggest
that Artese reads something on modern linguistics and cognitive
science, if not the Pinker book I book I suggested, then the book
that Haneef recommends.
> ... the very presumption that de Saussure deflates.
Refering to Saussure on such issues is very much like referring
to Aristotle's biology for descriptions of how animal life
reproduces.  Saussure stands at the head of linguistics much as
Aristotle stands at the head of biology, and they both deserve
respect for their work when the fields were new, but the fields
have progressed far beyond them.  
Turpin:
>> ... Obviously people *do* learn new words entirely through 
>> their association with other words, but only *after* they 
>> have learned a core vocabulary which is learned in other 
>> fashion.
Artese:
> Wow.  Do you have a list of the words in this "core vocabulary"?
> Talk about your linguistic feats!  Holy cow.  A core vocabulary. 
> Which words in our language didn't make the cut? 
Don't be silly.  If I had wanted to say any of the things you
wrongly infer, I would have stated them very clearly.  All I
pointed out, quite correctly, is that the processes Artese
describes for word acquisition can work only *after* some
language is already learned, which leaves the question: how
was it learned?  
Russell
-- 
 Newton plain doesn't work, even as an approximation, 
 except within certain limits.        -- Moggin

G*rd*n wrote:
> 
> taboada@mtha.usc.edu (Mario Taboada):
> |       More importantly, you need the calculus to properly formulate
> | concepts like instantaneous velocity and acceleration, without which
> | kinematics cannot be studied "exactly".  ...
> 
> What do you mean by "properly formulate"?  I drive my car
> around, intuiting instantaneous velocity and acceleration,
> without performing even informal thumbnail calculus.  Or
> does my nervous system do it sneakily out of sight of
> my consciousness?
> 
The latter; this is your kinesthetic awareness.
What Mati isn't coming to grips with is that the mechanic or the
car enthusiast, the gymnast and the skater, all have a very great
awareness and intuitive understanding of mechanics.  This comes
from their everyday acquaintance and use of it.
Michael Faraday, one of the leading scientists of the first half
of the last century, was very fond of inquiring from the "mechanics
and artisans" for insights into their crafts, and how they accomplished
things.  Many things are known that haven't been explained, and 
Faraday worked at understanding some of them ... and he was very
successful at this!
However, Faraday knew no calculus; he was self-educated, and never
learned anything beyond high school mathematics.
Though Faraday is perhaps better known as an experimentalist, he 
certainly had an understanding of what he was doing ... it was no
accident that he discovered electromagnetic induction.  He used his
concept of "lines of force", which requires sophisticated mathematical
modeling to fully explore analytically.
What the mathematics gives you is the ability to explore areas where
you have no intuition; you can sometimes (a la Einstein or Dirac) discover 
something that nobody expected.  And once the basic ideas are understood,
one can formalize the whole enterprise mathematically, making it much
easier to work with (for the mathematically literate!), and making it
easier to learn.
The mathematics is always very important if you are going to design
something. This is why engineers learn gobs of math.
Best Regards, Peter
generally

I wrote:
>	...  You assigned Hippolyte's words to Derrida. ...
	That should have been spelled "Hyppolite."  (Caught that one,
but don't nobody ever rely on my spelling -- it's _not_ guaranteed.)
-- moggin

psalzman@landau.ucdavis.edu (Peter Salzman) writes:
Dear Peter--
> I'm working on a project to solve a one dimensional, time dependent
> Schrodinger's equation with a potential that involves an integral.
> 
>      2          /
>     d u        |                du 
>   K ---    +  L| blah dr   =    --                K and L are complex.
>     dr^2       |                dt
>                /
> 
> I've never solved a PDE numerically.  I was hoping for some good advice
> on how to start.  Specifically, I'd like to know what software is out
> there that could do something like this.  
> 
> My first reaction was to try to do it on mathematica because I don't know
> how to do complex numbers with c, and the results are easily graphable.
> However, I hear that MMA is slow.  I also heard that it loses precision (is 
> this true??) quickly.
As another poster has already said, *don't* use Mathematica.  I spent
many hours simulating a Schrodinger eqn in Mathematica with little
success -- Mathematica just got too bogged down on such a large-scale
iteratation.
Definitely read the Numerical Recipes (chapter on PDEs).  You'll
discover there is a distinct difference between Euler-style and
implicit techniques.  I recommend going for the implicit technique --
it respects the properties of the Schrod. eqn as mentioned by the
other poster.  If you use a strict Euler technique you will find that
rounding errors quickly mount and your wave function will become non
physical (ie, total probability != 1).  As I recall, the implicit
technique was also *much* faster than Euler for the same precision
level.
I believe I used the technique in NR in C with good results.  You'll
need to solve a tri-diagonal system of equations, which is also solved
in NR -- but you will also have to convert the routine to solve
complex numbers.
Complex numbers are not too hard in C.  You might find a C++ class on
the net which does the hard part for you.  I recall making a C struct
with a real and an imaginary component.  For the algebra used in
solving the tridiagonal system, etc., you will need to express complex
multiplication and division in terms of the constituent real and
imaginary parts -- I used C macros.  It's pretty nifty when you get it
all together.
If you are doing this project as a demonstration, you will also find
that you spend a lot of time setting up initial and boundary
conditions.  To get interesting situations such as partial
transmission/reflection, particle in box potential, particle in
harmonic potential, tunnelling, etc., you will need to fine-tune your
parameters.  Specifically, you need to roughly match the momentum of
your wave packet with the height of the potential barrier.
Best of luck,
Craig
-- 
---------------------------------------------------------------------
Craig Markwardt UW-Madison 608 262 7555    | "To cogitate and
internet: craigm@astrog.physics.wisc.edu   |  to solve ..." -MathNet
---------------------------------------------------------------------

In article <54kj05$92l@newsbf02.news.aol.com>, lbsys@aol.com (LBsys) writes:
>Im Artikel <54h44d$6d8@panix2.panix.com>, +@+.+ (G*rd*n) schreibt:
>
>>Now, if I were to call Jesus (or Karl Marx) a raving
>>necrophiliac, I'm sure I'd be ignored.  Or a racist
>>slaveholder, for that matter.  So it seems we have changed
>>our gods.  Isn't this a matter of interest to you?  It is
>>to me.
>>
>>I have to admit (hi, Patrick!) that the Jefferson tizzy was
>>pretty mild next to the Newton tizzy.  But I think it had
>>similar qualities.  (But the Newton tizzy's isn't even over
>>yet -- I've caught sight of yet more earnest crusaders
>>soldiering up the hillside to Moggin Keep....)
>
>Sorry to interupt, or even being late in this thread, but actually the
>Newton tizzy did show a completely different picture wrt the 'similar
>qualities, as some posters unwithspoken and unasked for referred to the
>most unpleasant personality of Mr. Newton himself - which of course
>doesn't devaluate his achievements. Thus one shouldn't confuse the
>defending of the validity of Newtons findings with defending the person
>himself, which you may not be lucky to find anyone doing.
>
Not a fat chance for this, indeed.  According to all accounts, Newton 
was quite an unpleasant character, mildly put.  Which, as you rightly 
said, is irrelevant to his work.  But, my feeling is that people from 
fields of activity where the notions of correct versus incorrect are 
based on reverence (or lack of) towards a specific guru and where "So 
and so said such and such" is considered a valid argument, find the 
notion of complete separation between a person and his/her work 
difficult to comprehend.
Mati Meron			| "When you argue with a fool,
meron@cars.uchicago.edu		|  chances are he is doing just the same"

: rayvd@shocking.com (Ray Van Dolson)
: Could anyone explain to me (in fairly good detail if possible) why
: ordinary plane mirrors are coated on the back instead of the front?
Ray has made me realize that I'm not sure of the answer, but I've long
had a preconception.  A simple matter of pragmatics: you need a very
smooth surface to form a good mirror, and the glass surface is already
smooth.  If you put the coating on the "front" side, you'll have to go
to some pains to ensure a a smooth coating-surface, but by putting it on
the back, the glass-to-coating transition is automatically a smooth one,
unlike the coating-to-air transition. 
I reached this conclusion by observing that on the back of mirrors I
examined, the coating's air-side was "matte", dull, and not really
reflective. 
But I don't really know if the conclusion I leapt to all those
years ago is the right one.
Of course, telescope mirrors are another kettle of fish...
--
Wayne Throop   throopw@sheol.org  http://sheol.org/throopw
               throopw@cisco.com

In article <326E23A1.20DD@eskimo.com>, Stephen La Joie  writes:
>If someone was to ask "is metal a solid", I would be unable
>to answer until they told me what metal or metal alloy, what 
>is their definition of solid, and under what conditions.
>
Right on!
>I am surprised at the number of learned experts who would
>venture an opinion without having a clue as to what "glass"
>they are talking about.
Surprised?  On sci.physics?  You must be kidding :-)
Mati Meron			| "When you argue with a fool,
meron@cars.uchicago.edu		|  chances are he is doing just the same"

In article <54jb68$h52@herald.concentric.net>, Hitech  wrote:
>
>...  If an infinite number of perfect random number
>generators were each to generate an infinite string of random numbers
>until a specified time in the infinite future, then upon placing a period
>followed by a zero at the end of each generated string prior to reversing
>the string, one would discover the entire set of transcendental numbers.
I see there is opportunity for confusion in my last post so let me clear
it up before it becomes a big deal.  In my reference to a complete set of
transcendental numbers I failed to mention that the numbers pi, 2*pi and
pi/10 are the same element in the set.  There, it should be clear sailing
from here.  Like picking cherries.

In article <54lc44$fe7@newsbf02.news.aol.com>, jmfbah@aol.com (JMFBAH) writes:
> meron@cars3.uchicago.edu wrote:
>
>, rafael cardenas
>< writes:
><>
><>A more serious problem than the mathematization of physics, which has
><>been going on for centuries and, while it may confuse laypeople, doesn't
><>confuse people who are already working in the discipline, is the growing
><>mathematization of many other fields (biology; geography since the
><>1950s;
><>now history; even textual criticism) which, many suspect, is an
><>obfuscation
><>that hides feeble conceptualization, dubious assumptions,
><> technical or disciplinary mistakes, or even fraud. (A person who,
><> to use an analogy with physics, is an
><>experimental incompetent, may get away with murder by using mathematical
><>techniques which the majority of workers in the discipline can't cope
><>with).
><
>
>I agree that this is a problem; it can be even more complex than what you
>describe, Mati.  Even if you did understand the techniques in the
>pre-packaged data-massaging software,  you also need to know what computer
>language generated this software and how your computer's processor  does
>its arithmetic.  I have a fairly long war-story about precisely this
>problem where a bank couldn't believe its eyes when reports showed that
>$.02 + $.02 = $.05;   the program package they paid [big money] for was
>written in FORTRAN and all the arithmetic and display expressions were
>done in single-precision floating point.
>
Cute, may do wonders for the yearly balance.  Yeah, I've seen these 
problems happening many times.  In various numerical procedures 
(numerical solving of differential equations is notorious, and same 
with matrix operations) such errors may accumulate very rapidly with 
quite spectacular results.  Then, if the person using the technique 
doesn't even know what to expect and what to beware off, these 
"results" are reported as real ones.
Mati Meron			| "When you argue with a fool,
meron@cars.uchicago.edu		|  chances are he is doing just the same"

Skipping a few levels of nested references on daytime stars...
: >> john baez (baez@math.ucr.edu) wrote:
: >> 
: >> >>Yes, and if the shaft were *that* deep its field of view would be
: >> >>so small you'd be lucky to see even one star, even at night!  
: >> 
: >> >Nonetheless, I've read in various reputable sources that one
: >> >can see the stars in the day, this way.  I haven't actually tried
: >> >it, personally.  
: >> 
: >> But not sources sufficiently reputable that you are willing to cite
: >> them, apparently.
I have managed to see magnitude 0 and brighter stars (Vega, Arcturus,
Sirius, tried Alpha Centauri once from Chile but didn't know quite
well enough where to look) some time before sunset at good sites
with clean skies. The only way the apocryphal well shaft enters into
the problem is an odd one - the interior of the eye scatters a lot
of light, so if you're standing in daylight some fraction close to
1/2 of the sky brightness is scattered (which is why you gain a little
bit in contrast at night looking through a telescope, or naked-eye
at things like Andromeda, if you block stray external light). So
in principle you gain a little bit (0.75 magnitude) in seeing stars
from a dark location in the daytime. However, this would normally
be overshadowed by the fact that your eye usually dark-adapts to
a mean brightness, and the circle of daylight would be too dazzling to
pick out a star.
Bill Keel
Astronomy, University of Alabama

pri@algonet.se wrote:
>
> /Ulf Hammarström
See my message on Tue 10/22.  I am learning how to use this news
service.
Ed

The current issue of Science, a respected journal, speculates on a FTL mechanism
on v. 274 p. 202.  Apparently some escape clause in general relativity
(accelerating reference frames) compared to special relativity (constant velocity).
I haven't reviewed the equations myself, but am mystified by this Star Trek'ish
article in Science.

In article <549ii9$da1@elaine8.Stanford.EDU>, aleistra@leland.Stanford.EDU (Andrea Lynn Leistra) writes:
> In article <548mfh$6d0@csugrad.cs.vt.edu>, Nathan Urban  wrote:
> >In article , Jan Pavek  wrote:
> 
> >> OK. And what is with the electrons not falling down to the proton?
> >
> >Try asking yourself why the moon doesn't fall onto the Earth.
> 
> Well, he *could* do that, but he wouldn't get very far - the analogy is a
> poor one, since the classical view of an electron as a point particle
> orbiting the nucleus would have the electron radiating energy away (as
> do all accelerating charges), which the moon does *not* do, and thus
Yes It Does.  Any accelerating charge (of any kind) will radiate energy.
Mass is a charge.  The moon has mass.  The moon is accelerating.  The
moon radiates energy.
Of course, the coupling constant is 40 orders of magnitude smaller than
for electromagnetism, so it doesn't radiate much.
> eventually spiraling in to the nucleus.  In fact, this was one of the 
> indicators that the classical picture of the electron was flawed.
> 
> The real answer has to do with quantum mechanics, particularly the
> uncertainty principle (which states that the position and momentum 
> of any particle cannot be defined with arbitrary precision) and the
> exclusion principle (which states that two fermions, which electrons are,
> cannot occupy the same quantum state).
That's true, but to my ear the *original* original poster was questioning
what counteracted (in the radial direction) the attraction between the
electron and the nucleus.  The very short answer to that is "conservation
of angular momentum".  Questions of energy radiation are of secondary
importance, IMHO.
-- K.
-------------------------------------------------------------------------------
Kevin L. Sterner  |  U. Penn. High Energy Physics  |  Smash the welfare state!
-------------------------------------------------------------------------------

A pan of mass .2 kg is hanging from a massless spring.  The spring is
stretched 10cm due to the pan.  A piece of putty, mass .2 kg, is dropped
from a height of 30cm onto the pan.  How far does the pan descend due to
the added putty?
The spring constant given is 19.6 N/m.
Thank you very much for your help.  Please e-mail me with your resonse at
Bammer13@aol.com.  I really appreciate your effort.

dangrdoc@sound.net wrote:
> 
> meron@cars3.uchicago.edu wrote:
> >>Depends on the situation. For systems with an upper bound to possible energy,
> >>one can define a negative temperature. See F. Reif, "Fundamentals of
> >>Statistical and Thermal Physics" for a complete discussion of the definition
> >>of temperature from a statistical view.
> >>
> >Yeah, but the funny thing is that a negative temperature is "hotter"
> >then any positive temperature.
> 
> >Mati Meron                     | "When you argue with a fool,
> >meron@cars.uchicago.edu                |  chances are he is doing just the same"
> 
> I'm a physician not a physicist, can you explain this in English?
Imagine this analogy:
There is a box with a bunch of marbles inside and a number of cups taped to the 
walls at various heights.  You start off with all the marbles at the bottom of the 
box.  Then start shaking it - this is increasing the "temperature".  If you shake 
it a little, there will be very little chance of marbles in the top cups, but at 
higher "temperatures" (more shaking), the odds will be higher.  In fact, you would 
never expect to find more filled cups at any given level than there were at a level 
beneath.  The more you drive towards "infinite temperature", the more uniformly 
filled the cups will be regardless of level.  At infinite temperature, all cups are 
equally likely to be filled regardless of their level.
There exist some physical systems where in this analogy it is possible to spend 
some time in a state where the higher cups are fuller than the lower cups.  In the 
mathematical description this corresponds to having passed infinite temperature, 
and the more the marbles tend to be found in the higher cups, the closer one gets 
to zero from the negative side. 
Hope the analogy is helpful.
|++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++|
| Doug Craigen                                                 |
|                                                              |
| Need help in physics?  Check out the pages listed here:      |
|    http://www.cyberspc.mb.ca/~dcc/phys/physhelp.html         |
|++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++|

In article <54la4t$k6q@guitar.sound.net>, dangrdoc@sound.net writes:
>meron@cars3.uchicago.edu wrote:
>
>>In article , jamesl@netcom.com (James Logajan) writes:
	... snip ...
>>>
>>>Depends on the situation. For systems with an upper bound to possible energy,
>>>one can define a negative temperature. See F. Reif, "Fundamentals of
>>>Statistical and Thermal Physics" for a complete discussion of the definition
>>>of temperature from a statistical view.
>>>
>>Yeah, but the funny thing is that a negative temperature is "hotter" 
>>then any positive temperature.
>
>>Mati Meron			| "When you argue with a fool,
>>meron@cars.uchicago.edu		|  chances are he is doing just the same"
>
>I'm a physician not a physicist, can you explain this in English?
Gladly, though you'll have to take some of what I say on faith (either 
this or read the book recommended above).
First, the relevant physical quantity is really not the temperature, 
T, but the inverse temperature, 1/T (that's what appears in the important 
equations).  Now, the issue is what does "hotter" mean.  The answer is 
simple.  Given two bodies, the first is hotter if, when the bodies are 
brough in contact there is a flow of energy from the first to the 
second.  And thermodynamics tells you that the flow will be from the 
body with lower 1/T to the one with higher 1/T.  So, the lower 1/T is, 
the hotter is the body.  Since lower 1/T means higher T (for positive 
values of T), the thermodynamic notion agrees here with what we 
understand by "hotter".
But, mind you, 1/T is positive for any positive value of T, no matter 
how high.  Now, if you assume that a system with negative T may exist, 
its 1/T is lower then zero, i.e. lower then this for any body with a 
positive T, no matter how high.  Brought in contact with any body with 
positive T, energy will flow from the one with negative T to the one 
with positve temperature, thus the one with negative T is hotter.
I know that it looks like mathematical nitpicking, so lets look at 
itfrom a different side.  The deeper meaning of temperature has to do 
with the energy levels which are accessible to a system.  Statistical 
mechanics (see the book above, again), tells you that, given a system 
of entities (say, particles) at temperature T, the probability for any 
of them to have energy E is given by an exponential function
	P(E) = C*exp(-E/kT)
where C is just for normalization and k is the so called Boltzmann constant.
What you can see from the above is as follows.  First (for a positive 
T), the higher the energy, the lower is the probability.  That makes 
sense, the distribution gives highes probability for the lowest 
possible energy state and when you go higher the probability drops.  
Now, how fast it drops?  That's governed by T.  If T is small, 1/T is 
large and the exponential function drops very rapidly when E 
increases.  Again, that makes sense, at low temperatures almost all 
the particles concentrate at the lowest energy level possible.  When T 
grows higher, the exponential drops less rapidly and there are more 
particles at higher states.  If you imagine an extremely high 
temperature, tending to infinity, the argument of the exponent becomes 
very close to zero for a huge range of energies and the distribution 
is almost flat.  You can see the general trend, the higher the 
temperature, the bigger the probability to have the higher energy 
states occupied.
Now, whet happens if T is negative.  The argument of the exponential 
function becomes positive and the probability grows instead of 
diminishing with E, meaning even more high energy states are occupied 
then for any arbitrarily high but positive temperature.  So, such body 
is indeed hotter.
You can see from the above however that in the general case (where 
energy states with arbitrarily high energy exist) such situation is 
impossible.  You would get a probability distribution peaked at 
infinite energy, and it would take infinite energy to achieve this 
situation.  But, if a system has just a limited number of energy 
states, a negative temperature situation may be achieved.  Lasers are 
a good example (but that's another story).
Mati Meron			| "When you argue with a fool,
meron@cars.uchicago.edu		|  chances are he is doing just the same"

In article <01bbc07e$ccf76c00$868caec3@tolgas.pcworld.com.tr>,
Tolga  wrote:
>
>I once thought of the following:
>
>The frequency shifting in sound waves is certain, but what if it doesn't
>apply to light? 
>If frequency shifts proportional to the distance light travels, we would
>observe that the more distant stars are the more shift in frequency, just
>like we do today?
The fact that light exhibits a "doppler" shift is very well established. Just
look at some binary star radial velocity curves. 
Phil

Matt Austern  wrote:
>dangrdoc@sound.net writes:
>> >Yeah, but the funny thing is that a negative temperature is "hotter" 
>> >then any positive temperature.
>> 
>> >Mati Meron			| "When you argue with a fool,
>> >meron@cars.uchicago.edu		|  chances are he is doing just the same"
>> 
>> I'm a physician not a physicist, can you explain this in English?
>It's easier to understand if you think about 1/T (also called beta)
>than about T.  If something is cold, beta is large; if something is
>hot, beta is small.  Beta can (in certain special circumstances) be
>negative, and beta < 0 is hotter than beta > 0.
Sorry I still don't buy it.  When is Beta zero.

"RICHARD J. LOGAN"  wrote:
[snip]
>2.  But this is beside the point.  I was startled by a previous posters response 
>that religious people daily question the founding principles of their faith (at 
>least that's the way I interpretted the posters comment) and that the practice of 
>science was in some sense a religious enterprise. 
That was me and I did not mean to startle you.  I meant that religions
study and debate their meanings and purposes.  Separate and apart from
that, many people do indeed treat science as a religion in the sense
that they believe it offers the key to the origin and structure of the
world.  
 I don't accept this view 
>primarily because (to use my example) it's possible to question and revise 
>fundamental concepts like space and time in science but I think it would be 
>impossible for a christian to question and revise the divine nature of christ.  To 
>most (if not all) classical physicists, the nature space and time were concepts as 
>hallowed as the divinity of christ to a believer (so I think this satisfies your "it 
>is good to behave in such a fashion..." requirement).
You are viewing this in much too narrow a sense.  Religion is a belief
in a divine power as the creator of the universe.  Science is a belief
that something other than a divine power created the universe.  Each
religion has its own precepts and beliefs, just as does each branch of
science.  To use your example of christianity, people who believe in
Christ as Son of God have for two thousand years engaged in studies
and debates over what this means.  This has resulted in major schisms
such as a reformation or the separation of the secular from the
religious in most christian countries, relatively minor things like
papal infallibility, and unresolved matters such as the role of women
in the church (which is very different in different christian
religions, as you may be aware) or the role of the church in poor
countries governed by dictators.  What is right and moral has changed
radically, often in dramatic fashion, over the centuries, just like
science.
>Science is not a religion.  A person holding this position doesn't understand 
>science.  Again, I'd appreciate your comments.
I did not say that science is a religion in the formal sense.  But
science has become very much like a religion in the sense that large
numbers of people "believe" in its infallibility and often cite
various of its "facts" and "theories" to support both sides of moral
issues in hopes of attracting to a position others who believe in the
"god" of science.
Ken MacIver

In article <326DC38A.2E7A@pobox.com>, Philip Gibbs 
wrote:
> What about the symmetry under permutation of identical
> particles? What is the conserved quantity associated
> with that?
A beautiful question.
I could be wrong about this, but I think it's something like
(-1)^(number of fermions)
Of course this also follows from angular momentum conservation,
but only via invocation of the spin-statistics theorem.
-- 
Matt McIrvin   

In article <326B9C47.41C6@ic.ac.uk>, Gavin Tabor  wrote:
> Nature and Nature's laws lay hid in night,
> Till God said "Let Newton Be", and all was light.
> 
> T'was not to last, the Devil crying "Ho",
> "Let Einstein Be", restored the status quo.
> 
> (Can't remember who wrote it, but its fun.)
The first two lines are from a poem by Alexander Pope. Of course,
the second two are by somebody else, but I don't know who.
-- 
Matt McIrvin   

In article <54jd0v$7pk@dfw-ixnews7.ix.netcom.com>,
odessey2@ix.netcom.com(Allen Meisner) wrote:
>     But we do know the dimensions of the nucleus, don't we? If this is
> so, it shouldn't be such a great step to apply general relativity. I am
> not sure how the equation would look, but you would probably not need
> the gravitational constant, since you are treating the mass in terms of
> its energy equivalent.
You need the gravitational constant even then. But that's not the real
problem.
> Since the Tensor in general relativity refers to
> the energy distribution, why couldn't we just substitute the appropiate
> values into the equation?
The problem is that the energy is not just spread out, its position can be
quantum-mechanically *uncertain*, which is a different sort of thing.
General relativity allows the energy to be spread out over space, but it
makes no provision for the energy to be in a *superposition* of states in
which it is at point A and states in which it is at point B.
Some people have proposed ignoring the distinction and using the
quantum-mechanical average or "expectation" value, but that creates other
problems. There's the question of whether the expectation values "collapse"
when you observe where a particle is. Experiments with large masses whose
positions are determined in a "Schrodinger's cat" way show that if you want
this expectation-value-coupling idea to work at all, there has to be some
sort of collapse. But then there are other problems. Suppose a particle's
wave function is spread out over space and you observe it. The wave
function collapses instantaneously into a little dot; in terms of
expectation values, stress-energy has disappeared in one place and
instantaneously appeared somewhere else. GR *breaks* if you try to plug
this sort of thing into it; it gives inconsistent results. So making
this work would involve not just imposing a particular QM interpretation,
but doctoring up general relativity somehow as well.
-- 
Matt McIrvin   

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There is no system better than the imperial system, inherited from
feudal England, when it comes to measuring a flat Earth.  I assume that
is why the US government has retained it.

>> Mark Gilbert wrote:
>> > No.  Photons of different energies travel at different speeds in
>> > material.  It is this difference in speed that enables a prism to spread
The postings so far have pretty much dealt with light as a "wave" phenomenon,
and explaining diffraction by refractive indices, etc.
If you want to think of the "particle" properties for a moment, you can
convince yourself (via some quantum mechanical arguments) that:
- Photons travel at c, within reasonable definitions of what "measuring"
  the speed of a photon is...
- A material has certain frequencies which permit transitions between
  states (of the material)... these are atomic, molecular, or
  "crystal-wide" transitions, depending on the material and the
  frequency.
- When photons travel through a medium, they are being continually absorbed
  and re-emitted by the medium (its atoms or molecules or larger systems).
  The amount of time each can be kept depends inversely on the energy
  difference between the photon's energy and the energy of the nearest
  transition between states in the medium.  The net effect of this is to
  slow down photons of different frequencies by different amounts; the
  photons which slow down the most are the closest to the transitions in
  the medium (energetically speaking).  This produces a higher index
  of refraction (the inverse of: the average photon MACROSCOPIC speed
  divided by c, which it still travels at between absorptions and
  emissions) for frequencies which are closer to the medium's transitions.
  Blue light is closer to the UV transitions in glass than red light, so
  it is being absorbed for longer periods of time, and travels slower and
  gets bent more.  Recognize the uncertainty principle (dE dt .le. hbar)
  in the time each is absorbed?
- If you read the above and said, "well then, photons at EXACTLY the right
  frequency can be absorbed indefinitely", then pat yourself on the back!
  This is just absorption of light by a material.
Cheers,
- Paul Arendt (parendt@aoc.nrao.edu)

Robert Coe (bob@1776.COM) wrote:
: On Sun, 13 Oct 1996 03:37:38 GMT, pcuni@cris.com (Paul Cuni) wrote:
: : whats' the bottom line on this faster than light travel yes or no?
: No.
Not true.  Travel Faster than the speed of light relative to another 
object is impossible in SR (special relativity) where all space-time is 
assumed to be flat (a simplifying but innacurate assumption).  However, 
in GR (general relativity) space time does not have to be flat (since it 
isn't really, this is good).  You can manipulate space-time (in GR) in 
such a way that you _can_ actually go faster than the speed of light.  
I'm not making this up either, you can read a description of FTL in 
Science magazine's I believe 11 Oct issue.  Anyway, anyone who says going 
faster than the speed of light is "totally 100% absolutely impossible" 
isn't thinking as scientifically as they should be.  I'm not saying that 
faster than light travel is easy or that it is even possible to construct 
a device which can make it possible.  All I'm saying is that FTL is 
_permitted_ by the laws of physics as we know them.

In article <54jd0v$7pk@dfw-ixnews7.ix.netcom.com>,
 on 22 Oct 1996 21:06:39 GMT,
 Allen Meisner  writes:
>...
>    But we do know the dimensions of the nucleus, don't we? If this is
>so, it shouldn't be such a great step to apply general relativity. I am
>not sure how the equation would look, but you would probably not need
>the gravitational constant, since you are treating the mass in terms of
>its energy equivalent. Since the Tensor in general relativity refers to
>the energy distribution, why couldn't we just substitute the appropiate
>values into the equation? Or you could use the equations that Jason
>Blood used, in the "finding the curvature for given QM field" posting.
>He used equations to find the curvature of a massless boson. Couldn't
>this equation be used? It might give interesting results.
>
>Edward Meisner
In what sense interesting?  The total angle by which space is curved
across an elementary particle of mass m, assuming its size to be of a
similar order of magnitude to its de Broglie wavelength, is around
Gm^2/(hbar c), which is around 10^-39 for a proton.
Numerologists and more serious students of Dirac's LNH (Large Numbers
Hypothesis) will also recognize this number as being of a similar order
of magnitude to the reciprocal of the age of the universe in units based
on the frequency of the proton.  That is to say, if something had been
changing direction by the above angle in each cycle with the frequency
corresponding to the proton energy (roughly 10^23 times per second) then
the time it took to rotate right round in a circle would be similar to
the age of the universe.
Jonathan Scott
jonathan_scott@vnet.ibm.com  or  jscott@winvmc.vnet.ibm.com

-*-------
In article <54ltgc$ikf@news-central.tiac.net>,
Ken MacIver  wrote:
> I did not say that science is a religion in the formal sense.  
> But science has become very much like a religion in the sense 
> that large numbers of people "believe" in its infallibility 
> and often cite various of its "facts" and "theories" to support 
> both sides of moral issues in hopes of attracting to a position 
> others who believe in the "god" of science.
What response does MacIver recommend to this?
Russell
-- 
 Newton plain doesn't work, even as an approximation, 
 except within certain limits.        -- Moggin

stephanie  wrote:
>Why does a plane mirror reverse left to right but not up to down?
>
>Stephanie
>
>
Because up and down are global concepts, whereas left and right are
local concepts.  These local concepts depend on the persons position
relative to some object.
Hope that helps.
Casey

Philip Gibbs wrote:
> 
> Stephen La Joie wrote:
> >
> > If someone was to ask "is metal a solid", I would be unable
> > to answer until they told me what metal or metal alloy, what
> > is their definition of solid, and under what conditions.
> >
> > I am surprised at the number of learned experts who would
> > venture an opinion without having a clue as to what "glass"
> > they are talking about.
> 
> We were talking about soda-lime glass and other similar glasses
> used in antique windows.
The devil is in the details...
In the glasses I studied, a slight change in composition or
contamination greatly changed the characteristics of the
"glass." And under certain conditions, I could change it's
state from "glass" (or whatever...) to crystalline. I was
mostly interested in it's thermal characteristics. This could
change a great deal by only slight changes in composition.
The only way we can really put this question to rest is to
go and get some of this rippled glass and find out what it
is made of, exactly, and what is it's state. We would also need
to know what were the characteristics of the house that it
was installed in.
If you were to ask me if metal flows I'd be a fool to say
yes or no. Some, such as iron, never deform when the forces 
applied are below a certain level at STP. Others, such as 
mercury...
See my point?

"RICHARD J. LOGAN"  wrote:
>
> Ken MacIver wrote:

> > What does it say to you about science when both
> > sides to an irreconcilable difference plead their case through
> > citations to science?
> > 
> 
> It tells me that even lay people recognize that science has provided 
> unambiguously positive solutions to problems in the past and that, by implying 
> scientific evidence supports their position (and not the position of people on 
> the other side of the issue), they hope to convince the uncommitted masses of 
> the correctness of their cause.
Exactly. 
And this is one of the reasons science is attacked from several 
directions like "New Age", pomo etc. Until they diminish the standing
of science in our society by claiming that it is just one among many
worldviews and its practices are like religious rituals, founded on
arbitrary beliefs, or that science is wrong, the public will always
ask them: But are your assertions scientifically proven. 
This is why eg. moggin constantly uses phrases like 
"newton was wrong, as wrong as ptolemy" 
or 
"If "some of the unstated assumptions used in classical mechanics
have turned out to be wrong," then quite clearly there _was_ something to
cast doubt on"
without mentioning that he uses "wrong" etc in an extremely weird way,
which would not be expected by lay people. They hear "wrong" and
think: Gee,it doesnt work, lets switch to say astrology.
> 
> Relying on science alone to resolve social and political disputes is 
> counter-productive.
Agreed, but science changes the options.
Anton Hutticher
(Anton.Hutticher@sbg.ac.at)

In article , Keith Stein
 wrote:
>  "John D. Leckie"  writes
> 
> >Would you
> >mind explaining it anyway, for MY benefit?  :)  How DOES a moving
> >atmosphere cause light to bend?
> 
> 
> OK John, but it comes directly just from  vector addition of velocities.
> Consider a light ray moving from still air into an air current at right
> angles to its direction of motion, as illustrated below. 
>  
> 
>          Still air                      Wind moving due North at v 
>         ----------                      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>     Light moving due East at c   ->   'X'
> 
> West of 'X' the light has a velocity c to the East.
> East of 'X' the light has a velocity c to the East, PLUS a velocity
>          of v to the North, (as it is carried along by the medium).
I think that THIS is where I had the problem.  I did not know light could
be "carried along" by a moving medium.
> 
> Therefore the velocity of the light East of 'X' is:-
>         (c^2 + v^2)^.5  (relative to the ground)     .....(1)               
> 
> And the angle the light makes with the ground  is:-
>         arctan (v/c)    (degrees North of East)      .....(2)
> 
> Equation (2) gives the correct value for the aberration of      
>         starlight as found by the astronomer Bradley in 1728.
> 
> Of course i know that Equation (1) violates Einstein's Special Theory of
> Relativity, but that's my point:-
> 
>                           'SR *IS* WRONG'
Thanks for your reply.  So, you think that Special Relativity is wrong? 
What a unique viewpoint.  I don't know, at THIS point, anyway, enough
about physics or Einstien's physics to argue that point, but I must say
that I've never heard that before.  :)
John

nanken@tiac.net (Ken MacIver):
| ... 
| You are viewing this in much too narrow a sense.  Religion is a belief
| in a divine power as the creator of the universe.  Science is a belief
| that something other than a divine power created the universe.  ...
I disagree with the part about science.  Science, as I see
it, is the practice of finding or composing interesting
statements which correspond to phenomena.  It requires only
the belief that such statements can be found or composed.
However, one may believe this and also take a great variety
of religious positions, including most versions of
Christianity, Buddhism, Islam, and so on.  Many scientists
have claimed to believe that a divine power created the
universe, including Newton and Einstein.  On the other hand,
one could also believe that science was possible and be
almost any sort of atheist or agnostic.  There is no
inherent conflict between religion and science, although of
course if religions produce statements about phenomena they
may come into conflict with scientific statements about
phenomena.
-- 
   }"{    G*rd*n   }"{  gcf @ panix.com  }"{

Im Artikel , kfischer@iglou.com (Ken Fischer)
schreibt:
>: On
>: the other hand it's a problem to imagine any force else than gravity
>: having been able to contract all that mass in the first place to give
rise
>: to the Big Bang. 
>
>         I have never heard that one before, do you mean
>some think we are on a second bounce?
I don't think I thought up this myself, but rather got it somewhere. (if
it'd be right I'd be too small for it, if it's wrong, I certainly don't
want to be the inventor ;-)
Yes, I do think we may possibly be on the umpteenth bounce... until
someone can show me, we are not.
Oh, yes, I know now where I got that idea: Poul Andersons "Flight into
eternity" if I recall right. A starship on the way to Alpha Centauri with
a fusion drive fuelled by free space hydrogen (which is collected by means
of a huge magnetic field derived from the engines, I think he called it
eagle drive or falcon drive) has a minor havary. Now they cannot turn
round the ship to decelarate. They are way too fast to send someone out in
a space-suit for repairs, as he would get grilled by particles. So instead
they accelarate even more to make for the intergalaxian dark space. They
reach this and repair the thing, but now are way too fast to be able to
stop while passing through any of the galaxies at their disposal, as they
(the galaxies) have 'shortened' too much in their view. So they accelarate
even further to find a huge galaxy to fit their needs. On their way they
see more and more red giants and burnt out stars and conclude, that the
universe is rapidly coming to an end. They speed up even more circling the
universe, are witness to the final contraction and following new Big Bang
- and happy ending being a must - find a young galaxy to their needs, find
a solar system with planets, one of them being suitable to set up a new
earth. Interesting fiction, quite well written. About the physics
mentioned I'm not so sure, especially the assumption, that anything can
survive the final singularity. Yep, this is where I got it from [puuuh].
Cheerio
The most dangerous untruths are truths slightly deformed.
Lichtenberg, Sudelbuecher
__________________________________
Lorenz Borsche
Per the FCA: this eMail adress is not to 
be added to any commercial mailing list.
Uncalled for eMail maybe treated as public.

Christopher McKinstry (chris@clickable.com) wrote:
> I believe probability is relativistic.
>  Here’s a simple experiment you can try at home to demonstrate
> probability changing with speed:
> 1)  Let "V" the maximum number of digits you can write per second.
> 2)  In "T" seconds, write down a random number in decimal form.
> Now, the maximum number you could have written is "9" repeated VT times.
> This is your Reality Radius "RR". The fact you even have one proves
> probability behaves relativistically.
> Consider, as V decreases, there comes a point at which the only number
> you have time to write is "1". At this point another person would be
> able to guess your "random" number in 100% of all trials at that V. As V
> increases the probability that that same person could guess your
> "random" number approaches zero. Only at infinite V,  could you truly
> pick a random number. What was thought to be random is thus
> deterministic. Probability changes with speed.
> A person traveling near the speed of light would be able to write many,
> many times more digits than a person at rest  in a given time period,
> due to relativistic time dilation. The person moving at near light speed
> would thus have a much larger RR and could generate much more random
> numbers than the person at rest. At the speed of light, a person could
> write an infinite number of numbers and thus choose an actual random
> number.
I don't think so. If i would look at a fast moving passenger, i would
see "his time" passing by very slow. Thats "his" proper time.  On the
other hand, if he looks at my clock, he would see a very fast running
clock. Thats "my" proper time. And when he returns (e.g. after a year
in ** his ** reference system) for me (in ** my ** reference system
there have passed a lot of more than one year (e.g. some millions
year, if he was travelling at near light speed).  This means ** I **
would be able to write much more digits than the moving passenger.
> Unless you’re moving at the speed of light you can’t generate a random
> number.
> -- 
> -K. Christopher McKinstry : Homepage
>  http://www.clickable.com/employees/chris/index.html
> -Join In The World's Largest AI Effort
>  http://www.clickable.com/mist_corpus.html
--
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************************************************************************

haneef@engin.swarthmore.edu (Omar Haneef '96) wrote:

> I just want to point out the important point here that these
> examples of bad speech are NOT CRITICISMS of ANY SCIENTIFIC
> KNOWLEDGE! Neither of these statements attacks ANY SCIENCE in
> any way. "Newton was wrong", according to Maggin (as far as I
> can tell from what I have read, in exactly the way scientists
> take him to be "wrong." The argument has been about the use of
> the word "wrong" - a semantic, and ironically linguistic (as
> opposed to scientific), debate. They both agree that the results
> of N's laws hold for certain domains of experience. I am fairly
> certain that your own bad speech is equally misunderstood "good
> speech." 
Then you have read moggin exactly the "wrong" way around. Moggins
claim is essentially that only at v = 0 or c = infinite Newton
is right and the slightest deviation from the "exactly true" value
makes him wrong. This is *not* how scientists take Newton to be
"wrong".
Yes, it has been mainly a debate about semantic issues. These
can be important.
Anton Hutticher
(Anton.Hutticher@sbg.ac.at)

SAggarwal  wrote:
>I am a grade 12 student and was wondering if someone could tell me, is
>space-time curved because of the presence of matter, or is matter
>created because of the curvature of space-time? Also, I understand that
>the curvature of space-time affects gravity. How does it affect it?
I would like to recommend _Relativity Visualized_ by Lewis Carrol
Epstein.  I have no training in GR (I've a B.S. in physics; no grad work),
and I found that it was a very good non-technical description of
Relativity (both Special and General).  I think you'll find that it
answers many of your questions, though you'll still need to work through
the mathematics to get "real" answers.
Regards,
Tom

Mati Meron:
> Yeah, but the funny thing is that a negative temperature is "hotter" 
> then any positive temperature.
Matt Austern  wrote:
> It's easier to understand if you think about 1/T (also called beta)
> than about T.  If something is cold, beta is large; if something is 
> hot, beta is small.  Beta can (in certain special circumstances) be
> negative, and beta < 0 is hotter than beta > 0.
dangrdoc@sound.net:
> Sorry I still don't buy it.  When is Beta zero.
Mati and Matt are of course correct, but you'll have to relax your 
intuition regarding temperature for a moment.  In thermodynamics, 
before a quantity called temperature appears in any equations, a 
natural function arises when one examines how a system approaches 
equilibrium; this quantity is
                      d(ln N)
            beta(E) = -------
                        dE
where E is the system energy, and N(E)dE is the number of "accessible 
states" in the energy range dE.  One then introduces the absolute 
temperature T=1/(k beta) where k is the Boltzmann constant.
  beta:   -inf  -10    -1       0     1      10    inf
  kT  :    -0   -0.1   -1  -inf   inf 1      0.1    +0
If N(E) can decrease (as in spin-systems), then absolute temperature 
can be negative.
Consider this: plasma discharges in the TFTR and JET tokamaks
are hotter than 100 million degrees Kelvin!
Jeff
-------------------------------------------------------------------
Jeff Candy                        The University of Texas at Austin
Institute for Fusion Studies      Austin, Texas
-------------------------------------------------------------------

In article ,
Matt McIrvin  wrote:
#In article <326B9C47.41C6@ic.ac.uk>, Gavin Tabor  wrote:
#
#> Nature and Nature's laws lay hid in night,
#> Till God said "Let Newton Be", and all was light.
#> 
#> T'was not to last, the Devil crying "Ho",
#> "Let Einstein Be", restored the status quo.
#> 
#> (Can't remember who wrote it, but its fun.)
#
#The first two lines are from a poem by Alexander Pope. Of course,
#the second two are by somebody else, but I don't know who.
I don't know either.
On a related literary topic, there's the Blegsdamsvej Faust,
which is printed in English translation in Gamow's _Thirty
Years That Shook Physics_. Written by several of Bohr's students,
and first (maybe last) performed in 1932.
Bill
-- 
Bill Jefferys/Department of Astronomy/University of Texas/Austin, TX 78712
E-mail: bill@clyde.as.utexas.edu     |    URL: http://quasar.as.utexas.edu
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